Old Instruments, New Sounds, Same Language The Notation, Orchestration, and Compositional Use of Contemporary Techniques for Orchestral Stringed Instruments By Chase Jordan University of Wyoming Bachelors of Music, Viola Performance, 2020 Minor in the Honors College Honor’s Thesis Table of Contents PREFACE ii Abstract, ; Acknowledgements, INTRODUCTION 1 Background, 1; Scope & Purpose, 3; 
 Conceptual Framework & Methodology, 4; PART I: Techniques Affecting Pitch CHAPTER 1: Microtonality 8 Quarter-Tones, 9; 72-EDOs & It’s Subsets, 12; 31-EDO, 16; Thoughts on Developing the Notations of Other EDOs, 18; Non-Octave EDOs, 20; Just Intonation, 22; CHAPTER 2: Harmonics and Related Effects 25 Natural Harmonics, 27; Dual-Node Harmonics, 36; Artificial Harmonics, 37 Harmonic Trills, 37 Multiphonics, 41; Subharmonics and ALFs, 45; CHAPTER 3: Vibrato 46 Changes in Speed, 47; Changes in Width, 48; Changes in Regularity, 49; Changes in Shape, 49; CHAPTER 4: Other Extensions of Pitch 50 Indiscriminate Pitch, 50 Scordatura, 52; Peg Glissando, 54; Bowing Under the Strings / Bowing with Two Bows; 55 PART II: Techniques Affecting Timbre CHAPTER 5: Pizzicato Techniques 57 Variations along the Length of the String, 57; Bartok Pizz., 59; Buzz Pizz., 60; Fingernail Pizz., 60; ii CHAPTER 5: Pizzicato Techniques (cont.) Pizzicati with an Implement, 61 Slurred Pizz., 62; Strumming, 63; Left Hand Techniques, 63; Pizzicato with Multiple Fingers, 65; Sweeping the Strings, 66; CHAPTER 6: Unpitched and Percussive Sounds 67 Muffling Strings, 67; Bowing on Other Parts of the Instrument, 68; Percussion on the Body of the Instrument, 72 CHAPTER 7: Using Different Parts of the Bow 72 Col Legno Battuto, 73; Col Legno Tratto, 75; Using the Screw of the Bow, 75 Extensions of these effects, 76; CHAPTER 8: Changes in Bow Placement 76 The Sul Tasto — Sul Ponticello Spectrum, 76; Sub Ponticello, 78; Bi-Tones, 80 CHAPTER 9: Changes in Bowing Patterns 81 Spazzolare, 82; Circular Bowing, 83; Helicopter Effect, 84; Vector Bowing, 84; Vertical Bowing, 86; Jeté and Balzando, 87; Split-Tones, 88; Bow Whip, 89; CHAPTER 10: Changes in Bow Pressure 89 Flautando, 89; Overpressure, 90; Ponticello pressato, 91 CONCLUSION 92 WORKS CITED 94 iii Abstract This research project utilizes semiotic principals in order to outline a comprehensive notational system for orchestral stringed instruments and the contemporary practices and extended techniques composers ask for in 20th- and 21st-century repertoire. This work acts as both a survey of the repertoire of orchestral string music, selected based upon the use of these techniques, and as a notational guide targeted towards composers. Techniques are chosen based upon their accessibility, historical importance, and my own personal experience composing with and performing works containing them. Additionally, the techniques discussed within this thesis can be viewed as building blocks to more extensive techniques that combine multiples of these techniques within a single mass effect. 
 iv Acknowledgements This project was made possible and generously funded through the University of Wyoming Honors College. Thanks to those who aided and guided in the research for this project, and provided firsthand training on the instrument with these contemporary methods of performance and extended techniques; including James Przygocki, John Fadial, Beth Vanderborgh, & Sherry Sinift. Special thanks must be given to Ann Roggen for leading two private week-long personal workshops in New York City that both ignited my interest in the topic and continued professional education in it and to the University of Wyoming Symphony Association who helped fund the original workshop that ignited the interest. In addition, thanks should be given to Aaron Kirschner (Professor, Utah Valley University) for his aid in research due to his immense knowledge in the field of contemporary music. Thanks also to James Przygocki for mentoring this project. Additionally, thanks to my numerous friends at the University of Wyoming and throughout the country for working with me as I used my compositional and performance abilities to experience these techniques firsthand, especially Ross McIntosh (University of Indiana, B.M. ‘22), Hannah Rice (Louisiana State University, B.M. ‘22), and Stephen Weigel (Ball State University, M.M. ’19). Finally, thank you to all of the composers who allowed excerpts of their work to be decimated through this thesis. v Introduction Instrumental musicians and music performance education covers a narrow range of playing an instrument that has come to define technique of the common practice period. The technique and pedagogy of the common practice period are sufficient for performing most of the traditional solo, orchestral, and chamber music repertoire. Hence, instrumentation, arranging, and orchestration courses at universities and their standard texts, including Samuel Adler’s The Study of Orchestration and Kent Kennan’s The Technique of Orchestration, provide a limited and insufficient analysis of important musical techniques known as extended techniques and other contemporary performance practices of the twentieth and twenty-first centuries,1,2 Background The composer Matthew Burtner in his article, “Making Noise: Extended Techniques after Experimentalism,” provides a concise definition of an extended technique as something that “requires the performer to use an instrument in a manner outside of traditionally established norms.”3 Extended techniques are often considered an advent of the twentieth-century with influences from the musical avant-garde movement, including the composers of John Cage, Henry Cowell, & George Crumb, and from the musical futurist movement, including the composers George Anthiel, Alexander Mosolov, & Edgar Varèse. This twentieth-century search for new sounds came as a result of futurist composers and artist pushing for the incorporation of noise sounds into, 1 Samuel Adler, The Study of Orchestration, 4th ed (New York: W.W. Norton). 2 Kent Kennan and Donald Grantham, The Technique of Orchestration, 6th ed (Upper Saddle River, NJ: Prentice Hall). 3 Matthew Burtner, “Making Noise: Extended Techniques after Experimentalism,” NewMusicBox, New Music USA, March 1, 2005. 1 or even replacing, the traditional musical sounds and ensembles, as Filippo Tommaso Marinetti and Luigi Russolo accomplished through their Intonorumori noise orchestra.4 Luigi Russolo, in his 1913 letter to the futurist composer Balilla Partella, writes that: At first the art of music sought purity, limpidity and sweetness of sound. Then different sounds were amalgamated, care being taken, however, to caress the ear with gentle harmonies. Today music, as it becomes continually more complicated, strives to amalgamate the most dissonant, strange and harsh sounds. In this way we come ever closer to noise- sound. He further argues that this next step is noise sounds supplanting the traditional sounds of 
 music.5 While this prediction that noise sounds and the noise orchestra would replace the traditional orchestra and traditional sounds was incorrect, its influence on future composers to imitate noise- sounds and innovate new ways of playing instruments continued a trend of technical and timbral development that had begun long before. In 1605, the Scottish composer and viol player Tobias Hume, wrote his First Part of Ayres. In one of the pieces in this collection, “Harke, Harke”, Hume request the viol player to “play nine letters with your finger” and to “drum this with the backe of the bow”.6 This constitutes the earliest documented use of pizzicato and col legno, and is one of the earliest technical, timbral advances in string playing that was an extended technique for its time.7 Col legno was not the only technique developed in the common practice period to make it into musical compositions. Circa 1738, the French violinist and composer Jean-Joseph de Mondonville wrote the first composition that made 4 Ibid. 5 Luigi Russolo, The Art of Noise (futurist manifesto, 1913), trans. Robert Filliou (Chelsea, NY: Something Else Press, 1967). 7-9. 6 Tobias Hume, “Harke, Harke”, in The First Part of Ayres, (London: John Windet, 1605; facsimile reprint, Atelier Philidor, 2014). Spelling is left as it is written in the original; while capitalization has been adjusted to fit contemporary standards. 7 Peter Walls, “Bow”, The New Grove Dictionary of Music & Musicians, eds. Stanley Sadie & John Tyrrell (London: MacMillan Publishers, 2001), i: 894. 2 extensive use of natural harmonics, Le Sons Harmoniques (Opus 4).8,9 These techniques would continue to be used and innovation in playing would continue, but it was not until the twentieth- century that the proliferation of extended techniques became a ubiquitous part of a musical style. Furthermore, as Matthew Burtner explains in his article, some technical advancements that were once considered extended techniques, or at least considered at the edge of what a standard technique was, have widely been adopted as part of the standard orchestral lexicon. These include pizzicato, harmonics, col legno, and playing with a mute in the world of stringed instrument technique.10 This boundary of what is considered an extended technique today is blurred as the norms of solo, chamber, and orchestral playing have evolved; and these norms will continue to evolve in the future. Scope and Purpose Within this thesis, I will lay out a guide for composers on how to notate extended techniques in a manner most useful to composers. This means that the techniques chosen are chosen due to their use in historically important works, accessibility to performers, and my own personal experiences as a performer of these techniques and a composer who utilizes these techniques — the techniques I am familiar with from these two musical perspectives are the ones I will better be able to explain and evaluate notations for. In recognizing that the boundaries between the norms of technique and innovative extended techniques have been blurred, standard techniques have been included when they would help clarify the notational scope and how the symbology builds upon 8 David D Boyden, “The Violin and Its Technique in the 18th-Century,” The Musical Quarterly 36, no. 1 ( Jan. 1950): 27. 9 Jean-Joseph Cassanea de Mondonville, 6 Violin Sonatas, ‘Les sons Harmoniques’, Op. 4, (Paris: Madame Boivin, 1738; facsimile reprint, Indianapolis: Performer’s Edition, 2008). 10 Burtner, “Making Noise”. 3 itself when developing contexts for new notations or when these conventions are often misunderstood and misused among composers. Techniques that lie in this blurred zone, such as microtonal pitches, have been included to accurately display the ways string instruments can be pushed into new sound worlds, even if it isn’t strictly an extended technique.11 This thesis is organized based upon the resultant effects on sound by techniques. Section I of this thesis focuses on extended techniques that affect primarily pitch, recognizing that some of these techniques may also change the timbre of pitches. Section II focuses on techniques that affect timbre of sound, while also recognizing that some of these techniques may be used to access pitches outside of the normal range. Conceptual Framework & Methodology The conceptual framework for the notational philosophy within this guide will follow the following criteria: 1. Notation should build upon the music engraving and music composition community’s professional standards and should, as little as possible, supplant commonly understood standard notation. Elaine Gould’s Behind Bars is the principal book in defining music notation practices in the twenty-first-century and will be used as the primary resource for defining these professional standards of notation12. 2. Notations advocated for in this text should seek to expand upon notation growing in popularity rather than replacing them. It is important to provide as little disruption as possible to music notation practices and to musicians reading scores from early experimentalism and futurism through to contemporary scores in order for a cohesive 11 Sarah Wei-Yan Kwok, “Breaking the Sound Barriers: Extended Techniques and New Timbres for the Developing Violist” (DMA diss., University of British Columbia, 2018), 2. 12 Elaine Gould, Behind Bars: the Definitive Guide to Music Notation, (London: Faber Music, 2011). 4 semiotic code to be developed for maximum clarity to be evident across the range of the repertoire. When making notational decisions using this criterion, sources such as Kurt Stone’s Music Notation in the Twentieth Century, and Gardner Reeds Music Notation: A Manual of Modern Practice. Additionally, credence will be given to important established and emerging composers who make use of the technique effectively in their music. 3. When no consensus can be found, the semiotic principals of Charles Morris and René Thom should govern the adoption and development of notation. Morris’ semiotic beliefs is built primarily on textual signs and Thom’s primarily on image and symbology. While both theories of semiotics can be cross-applied, they are succeedingly discussed individually for sake of clarity. Charles Morris assigns three properties to signs (extended to this field, the symbology and textual elements of music notation): the designative, the consummatory, and the prescriptive.13 The designative property of the notation requires that it be different than other aspects of notation derived in criteria 1 and 2. The consummatory property dictates that it is clear when this process should be completed, and will often build off of consummatory notations derived from criteria 1 and 2. The prescriptive property of notation indicates that the textual elements and symbology should be representative of the sound and (or) the process of execution, without reducing its clarity to be designative and consummatory. René Thom assigns a signifying icon, image, or symbol an expressed meaning through an isomorphic spatially related model.14 In terms of music notation this means that notational symbology should 13 Charles Morris, “Signs and the Act” in Semiotics: An Introductory Anthology, ed. Robert E Innis (Bloomington: Indiana University Press, 1985), 178-89. 14 René Thom, “From the Icon to the Symbol,” in Semiotics: An Introductory Anthology, ed. Robert E Innis (Bloomington: Indiana University Press, 1985), 275-91. 5 represent the execution of the technique spatially on the page, or should represent the aural changes in sound spatially on the page. 4. The author recognizes that different kinds of notation, including graphic notation and standard notation on the staff have different needs and that the considered notations should be as similar as possible. That said, greater importance will be given to notations making use of the five-line staff as that has greater practicality among musicians and is in greater use among composers today. Additionally, continued use of the 5-line staff is imperative where possible, as it is a system all classically trained musicians are familiar and comfortable in. 5. Music notation should be clear, concise, and in keeping with traditional standards as much as possible. This is the ultimate litmus test for notation that has been used in the creation of this text. Symbols with duplicate meanings are unclear and should be used as little as possible. In recommending a notation, I have included a brief discussion of the history of notating the technique, where appropriate, including various musical examples or references where it would aid the discussion — both of the musical usage and notational decision-making; and any reasoning as to why an alternative to the previously proposed and used notations has been selected or as to why one proposal has been accepted in this document at the expense of another. When discussing the use of extended techniques in orchestration and composition, excerpts from solo, chamber, and orchestral music will be analyzed using the score analysis, aural analysis, and analysis derived from physically playing the composition. In the limited cases where analysis of these extended techniques are given in principal texts of orchestration, a brief summary and commentary on these analyses will be included. 
 6 Part I: Techniques affecting Pitch Chapter 1: Microtonality While microtonality is not strictly an extended technique, nor strictly for strings, it is becoming a vital part of contemporary performance practice and, allows for greater clarity towards the notation of high partial harmonics. Microtonal compositions are not an everyday occurrence for string players. Therefore, composers should be cognizant of the aural limitations of the individual or ensemble, physical limitations of the instrument, and the experience of the individual player or ensemble in the genre when composing the new works involving microtonality. While there will be variations in the aural skills of different musicians, research suggests that the just noticeable difference in pitch, or the smallest musical interval the human ear can respond to, is anywhere between 5 cents15 and 8 cents16. The just difference in pitch will vary around that 5 to 8 cent range depending on the tessitura of pitch, volume, duration of sound, suddenness of pitch change, and wether it is in a melodic or harmonic context.17 For composers, the last three variables are the most important in consider when composing microtonal passages for the orchestra stringed instrument family. Microtonal passages where notes are of short duration in quick succession will be more difficult to execute accurately if the intervallic content is approaching the just difference in pitch. Additionally, these passages will be less likely to be understood by an audience member than passages where the musical gestures are in longer durations and the pitches in slower succession. When using microtones in melodic and harmonic contexts, research shows that, “intervals of less 15 Beatus Dominik Loeffler, “Instrument Timbres and Pitch Estimation in Polyphonic Music,” MS thesis, Georgia Institute of Technology, 2006. 16 Thomas D Rossing, F Richard Moore, and Paul A Wheeler, The Science of Sound, 3rd ed (New York: Addison Wesley, 2002). 17 Ibid. 7 than a few cents are imperceptible to the human ear in a melodic context,” but “in harmony very small changes can cause large changes in beats or roughness of chords.”18 The practical application of this reality is that compositions requiring successive small intervals in a melodic context may better be served by slow glissandi between the outer edges of the pitch range. Because the distance between intervals in orchestral stringed instruments gets smaller as the tessitura becomes higher, composers will find that music written in the upper registers of string instruments is not easily navigated in microtonal contexts. It is therefore recommended to limit microtonality to the bottom 3.5 octaves of the instrument for best results in execution. Microtonal scales are discussed below using this nomenclature: the number of equal divisions of an interval. The number indicates the number of steps in the scale - the twelve-tone equal tempered (semi-tone chromatic) scale can be written this way as 12EDO, and scales such as third-tones may be written as (18-EDO). “ED” means: "equal divisions of”, the last letter indicates the interval divided. O is the most common, as it represents the octave. Other intervals can be easily notated using their just intonation ratios, as 8 equal divisions of the perfect fifth can be written as 8ED(3/2). While most players of an orchestral stringed instruments will have limited or no experience in performing microtonal compositions, there are a few principles to keep in mind when choosing the microtonal scale to work with. Notational and compositional strategies will be included for each of these within this chapter. First, intervallic content that can be easily related to the twelve-tone equal tempered scale through divisions of the semitone and whole tone, such as third-tones, quarter- tones, sixth-tones, and eighth-tones, will be be the most easily executed. Second, intervallic content that is easily relatable to the tuning of the instrument are effective and idiomatic ways to write microtonal music (equal divisions of the fourth and fifth). Finally, microtonal compositions whose 18 Dave Benson, Music: A Mathematical Offering (Cambridge, UK: Cambridge University Press, 2007), 368. 8 tunings are based on commonly understood or learned temperaments and tunings systems such as mean-tone temperaments and just-intonation will be able to be aurally parsed more easily, and therefore performed more effectively. Quarter-Tones (24-EDO) Perhaps the mostly commonly used tuning system outside of twelve-tone equal- temperament in Western-art music, is the quarter-tone scale, which divides the octave into twenty- four equal steps.19 Various symbologies for quarter-tones have been proposed over the last several centuries, dating back to Giusseppi Tartini’s proposed notation for quarter-flats in 1754.20 During the twentieth-century, many important and lesser-known composers wrote music in 24-EDO (including Aaron Copland, Gunther Schuller, Alberto Ginastera, Charles Ives, and Toru Takemitsu), although many did not devise a comprehensive system and only devised the symbols that piece required, nor did they have their symbology used widely among other composers. Two major music conventions in the latter half of the twentieth century proposed competing methods of notating quarter-tones. In 1967 in Ljubljana, Yugoslavia, the International Musicological Society’s working committee for notation proposed an expansion of the symbology for accidentals to include quarter- shapes and three-quarter-sharps that were modified sharp symbols, while for quarter-flats and three-quarter-flats Tartini’s original symbols were adopted. In 1974, the International Conference on New Musical Notation in Ghent, Belgium proposed the addition of upwards and downwards arrows to the standard accidentals (arrow notation).21 Neither of these have gained much steam 19 Gardner Read, 20th-Century Microtonal Notation (Westport, CT: Greenwood Press, 1990), 13. 20 Ibid, 20. 21 Ibid, chapter 1. 9 among contemporary composers of microtonal music, although Elaine Gould, in Behind Bars,22 and Kurt Stone, in Music Notation in the Twentieth Century (which was a result of the Ghent Convention and the Index of New Musical Notation), have recommended arrow notation, while including other options in their texts.23 Neither of these solutions are workable due to the increasingly complex microtonal pitch material in compositional use since these conventions. The ideal notation for 24-EDO will modify the current accidentals for the twelve-tone equal temperament scale in order to maintain visual similarity and will be able to be easily expanded to other tuning systems that are closely related to twelve-tone equal temperament including eighth-tones and twelfth-tones. The flats in Tartini notation are unlike the commonly used flats symbols and are difficult to read on the stave. Arrow notation has limited expansion ability, and the multiple symbols that are enharmonic. This creates Figure 1.1: Stein-Zimmerman Quarter-Tone Notation from double-flat to double-sharp ultrachromatically. ambiguity on the page. Instead, the most apt notation is the one catalogued as Stein-Zimmerman accidentals. It is easily expandable using a combination of these symbols with Ivan Wyschnegradsky’s 72-EDO symbols (See Chapter 1: Microtonality; 72-EDO and its Subsets), and the way that they are expansions of the standard accidentals make clear their musical prescription without symbols being too similar, obfuscating their meaning. These symbols can be used in conjunction with trills and tremolos in standard notation, without new symbols or workarounds being invented, creating a seamless transition between the new musical needs and traditional 22 Gould, Behind Bars, 94-96. 23 Kurt Stone, Music Notation in the Twentieth Century (New York: W. W. Norton & Company, 1980), 67-8. 10 notation. Additionally, it is highly recommended to include a description and key to the microtonal accidentals used in the preface pages of both the score and parts to a microtonal composition. Important quarter-tone compositions for stringed instruments the composer should be familiar with include Alois Hába’s String Quartet No. 2, Bela Bartok’s String Quartet No. 6, and Garth Knox’s “In Between” from Viola Spaces. Alois Hába’s String Quartet No. 2 can best be described as ultrachromatic, as it utilizes quarter-tones to create tighter leading-tones, quarter-tone enclosures and quarter-tone chromaticism, but Hába Figure 1.2: The opening (m. 1-3) of Alois Hába’s String Quartet No. 2. Notice how his chosen accidentals are hard to read on the staff. In addition notice the presence of neutral intervals and ultrachromatic lines in the music, demonstrative of the new harmonies and contours available in microtonal music. Excerpt is in the public domain. also makes use of new harmonic intervals made possible by the quarter-tone system including the opening neutral-sixth in the counterpoint between the first and second violin.24 Meanwhile, Bela Bartok’s 6th string quartet utilizes quarter-tones25 as a parodistic effect to emulate out-of-tune gypsy playing.26 Finally, violist and composer Garth Knox devotes an entire study of his collection, Viola Spaces to the technique. This composition, “In Between” is an excellent study for the composer 24 Alois Hába, String Quartet No. 2 in Vierteltonsystem, Op. 7 (Vienna: Universal Editions, 1921). 25 Bela Bartok, String Quartet No. 6 (London: Boosey & Hawkes, 1941). 26 Peter Laki, “The Complete Bartok String Quartets,” program notes for the 6 Bartok String Quartets, The Takacs Quartet, Princeton: Richard Auditorium, Oct. 12, 2013. 11 to see what variety is possible in terms of technique when performing in quarter-tones as a basic level. It includes virtuosic arpeggiated passages, quarter-tone trills, and limited double stops with an open string to investigate the shifting harmonies provided by the pitches.27 While this work does not represent the limits of virtuosity in quarter-tone music, it provides a benchmark for reasonable expectations for a first-time performer of quarter-tone music at the undergraduate level. Players more experienced in microtonality and music in the quarter-tone system can reach much higher levels of virtuosity. 72-EDO and Its Subsets Microtonal composers, including Alois Hába28, Ivan Wyschnegradsky29, Ezra Sims30,31, Joe Maneri32 and Iannis Xenakis (Antikhthon33), have also frequently divided the whole tone into third- tones, sixth-tones, and twelth-tones, often in the scope of a single work. These are all collected under the category of 72-EDO. This tuning system was first theorized in western music by Alois Hába and Ivan Wysnegradsky (outside of Europe, dividing the octave into 72 parts can be traced 27 Garth Knox, “In Between” from Viola Spaces, Mainz: Schott Editions, 2007. 28Alois Hába, “Harmonielehre des diatonischen, chromatischen, Viertel-, Dreittel-, Sechstel-, und Zwölftel- Tonsystems [Theory of Harmony for Diatonic, Chromatic, Quarter-, Third-, Sixth-, and Twelth-Tone Tuning Systems], annotated and translated by Suzette Mary Battan in “Alois Haba’s Harmonielehre des diatonischen, chromatischen, Viertel-, Dreittel-, Sechstel-, und Zwölftel-Tonsystems,” DMA diss., Eastman School of Music, 1980. 29 “Catalogue,” Ivan Wyschnegradsky Association, Ivan Wyschnegradsky Association, 2019. 30 Ian Wiese, “Ezra’s Path: Two Years in the Making,” The Boston Musical Intelligencer, April 25, 2017. 31 Kyle Gann, “American Composer Ezra Sims,” Kyle Gann Music, 2019. 32 New Music Box Staff, “What is your Favorite Tuning System? Why?: Joe Maneri, Composer and Saxophonist,” NewMusicBox, New Music USA, September 1, 2000. 33Iannis Xenakis, Antikhthon, Paris: Éditions Salabert: 1986. 12 back to the music theorists of the Byzantine empire34), but composers such as Ezra Sims, Joe Maneri, and Iannis Xenakis have popularized its use and it is frequently used by musicians of the Boston Microtonal Society. There are three primary notations that have gained popularity when engraving music in 
 72-EDO - Saggital notation, (both mixed and and pure saggital), Ivan Wyschnegradsky’s notation, and the Maneri-Sims notation. As will be discussed later - Saggital is useful for notating microtonal scales that have limited or no relation to the twelve-tone equal tempered scale and its predecessors, and because of that should be limited to these scales in order to reduce the number of musical symbols to which multiple meanings must be assigned (For a discussion of notating these tunings, see Chapter 1: Microtonality; Thoughts on Developing the Notations of Other EDOs). Wyschnegradsky’s notation for 72-EDO utilizes different accidentals for quarter tone-flats than the Figure 1.3: Stein-Zimmerman-Wyschnegradsky Notation for 72-EDO. Each flag raises or lowers the primary accidental by 1/6 of a tone, making for a logical 1/12-tone notation. Stein-Zimmerman notation, but by combining the quarter-tone symbols of the Stein-Zimmerman 24-EDO notation with the 1/12-tone flags from Wyschnegradsky’s notation for 72-EDO, a beautiful and logical notation can be created that is clear to the music reader and easily expandable. It is also important for composers and performers working in 72-EDO to be familiar with the Maneri-Sims notation, as this is likely the most widespread notation for the tuning system - 34 G. Chryssochoidis, D. Delviniotis and G. Kouroupetroglou, "A Semi-Automated Tagging Methodology for Orthodox Ecclesiastic Chant Acoustic Corpora", Proceedings SMC'07, 4th Sound and Music Computing Conference, Lefkada, Greece (11–13 July 2007), 216. 13 Figure 1.4: Maneri-Sims Notation for 72-EDO having been endorsed by the International Ekmelic Music Society and the Boston Microtonal Society.35 If this is the conventional notation for the scale, one may wonder why I do not recommend using it for this tuning system. In short — the quarter-tone tuning system is in far greater use among performers and composers, and therefore it makes sense to use the Wyschnegradsky extension of the Stein-Zimmerman quarter-tone notation as opposed to using a more complex notation such as Maneri-Sims and creating redundancies in the symbols. That said, this notation is popular among both the International Ekmelic Music Society and the Boston Microtonal Society, and should be used when working with musicians from these organizations. Additionally, creating editions using multiple notational dialect may help to increase the number of players able and willing to perform a work in 72-EDO. Regardless of which notation system is used, these symbols can be used in trills and tremolos and other aspects of standard notation but should always be included in the front matter of both the score and instrumental parts within compositions they are used. Figure 1.5: Maneri-Sims notation utilized in Ian Weise’s Dancing for Myself. Score excerpt used with permission of the composer. 35 “Notation of Ekmelic Music,” Ekmelic Music, International Ekmelic Music Society, 2019. 14 Figure 1.6: Robert Lopez-Hanshaw’s vokas animo for orchestra and chorus utilizes a combination of the Helmholtz Ellis symbology with additional symbols from other systems to notate 72-EDO. Score excerpt used with permission by the composer. 15 There are several important pieces of repertoire that fall under the category of 72-EDO and its subsets, including Iannis Xenakis’ Antikhthon for full orchestra (which utilizes quarter-tones and third-tones organized using sieve-theory)36 and Georg Friedrich Haas’ composition for six piano and orchestra, limited approximations, which makes use of twelfth-tone intervals to create clusters of different timbres and to approximate various overtone chords.37 Boston-based composer Ian Weise utilizes the sixth-tone subset of 72-EDO (36-EDO) in a manner that is consistent with the composers of the Boston Microtonal School in his composition for solo viola, Dancing By Myself.38 Additionally, Robert Lopez-Hanshaw utilizes 72-EDO to imitate 11-limit just-intonation harmonies in his composition for chorus and symphonic orchestra, vokas animo. While his notation is not standard (see Figure 1.7), it represents an efficient and effective combination of notating 72-equal divisions of the octave with the appropriate accidentals from the Helmholz-Ellis Just Intonation accidental set.39 31-EDO 31-EDO is the most important tuning system that is derived from extending quarter-comma meantone temperament. Its development arose during the Rennaissance Era, when Nicola Vicento in 1555 proposed a 31 pitch-class extended meantone scale. A century later in 1666, Lemme Rossi proposed a 31 pitch-class equal temperament based upon Vicento’s scale.40 Independently, the Dutch 36 Xenakis, Antikhthon 37 Georg Friedrich Haas, limited approximations (Vienna: Universal Editions, 2010.) 38 Ian Weise, Dancing By Myself (2020), unpublished composer computer manscript. 39 Robert Lopez-Hanshaw, vokas animo, unpublished full score from world premiere. 40 H.F. Cohen, Quantifying Music: The Science of Music at the First Stage of Scientific Revolution 1580-1650 (Dordrecht, Netherlands: Springer Science and Business Media), 217-19. 16 physicist Christiaan Huygens also innovated a 31-tone equal tempered scale.41 While composers lost interest in this tuning system during much of the common practice era, the Dutch physicist, music theorist, and composer Adriaan Fokker revived interest in this scale during the 1950s, particularly among dutch composers such as himself and Henk Baldings. Fokker’s and Balding’s innovations in notation and instrument creation should provide the basis for utilizing this tuning system. 31-EDO is best notated using Adriaan Fokker’s notation, which uses a circle of thirty-one quarter-comma meantone fifths to generate the pitch-classes, while replacing double-flats and double-sharps with quarter-flats and quarter-sharps respectively.42 A clarification should be included in the preface material to the score explaining the pitch of each note (see figure 1.6). While quarter tones require only an explanation of the individual accidentals, because 31-EDO is notated Figure 1.7: Preface material from Chase Jordan’s Atlantic Opalescence V: Timeless Sea Breeze for Cello and Hammered Dulcimer shows a table of pitch-classes useful for showing how each notated pitch differs from the standard intonation. Also notice the different stylization of the notation to differ from Wyschnegradsky Quarter- Tone symbols. Score excerpt use by permission of the composer. 41 Dirk de Klerk, “Equal Temperament,” Acta Musicologica 51, No. 1 ( Jan.-June 1979): 140-150. 42 Adriaan Daniël Fokker, “Equal Temperament and the 31-Keyed Organ,” Huygens-Fokker Foundation, Huygens-Fokker Centre for Microtonal Music, 1955. 17 Figure 1.8: 31-EDO notation in Chase Jordan’s Atlantic Opalescence V: Timeless Sea Breeze for cello and 
 hammered dulcimer. Score excerpt used with permission of the composer. as an extension of quarter-comma meantone temperament, of which the intricacies of are not common knowledge to the average musicians, this additional aid is nessecary to encourage a properly in-tune performance. Compositions demonstrating effective uses of 31-EDO that composers and performers should be familiar with include the Sonata No. 3 for Two Violins of Dutch composer Henk Badings and my own Atlantic Opalescence V: Timeless Sea Breeze for cello and hammered dulcimer. Badings has been described as having made the “largest and most important contribution” to Dutch music in 31-EDO of any of his contemporaries. His compositions, including the Sonata No. 3 for Two Violins, has been described as neoclassical in the aspects of form, rhythmic treatment, and harmony.43 This lush composition highlights the beauty that can be pulled from this tuning within the context of a string instrument work. This can be compared to my own composition for cello and hammered dulcimer, Atlantic Opalescence V: Timeless Sea Breeze. This work utilizes repeating pitch- class sets made up of 31-EDO pitches. The limited and repeating sets reduces the number of cells that the performer is required to learn, making the serialized thirty-one pitch-classes more manageable to the performer. This composition also combines the different tuning system with 43 “Henk Badings,” Huygens-Fokker Foundation, Huygens-Fokker Centre for Microtonal Music, 2019. 18 indiscriminate pitches, glissandi, extended pizzicato techniques, overpressure, and aleatoric devices, showing its applications in a setting with more contemporary techniques.44 Thoughts for Developing the Notation of Other EDOs Other EDOs outside of the common 12n-EDOs such as 72-EDO and its subsets, and the mean-tone derived systems, such as 31-EDO, require careful thought when notating for orchestral stringed instruments. While it is not the purpose of this book to provide notation for every possible tuning system that can theoretically be applied to stringed instruments, it is important to note what makes notation effective for composers exploring these tunings. Tunings are effectively grouped into four categories: 1. Other 12n-EDOs (tunings that further divide the semi-tone into equal parts) 2. Tunings that can described as a subset of a 12n-EDO. For example, 15-EDO can be described as a subset of the 12n-EDO 60-EDO) 3. Meantone Generated Tunings (tunings that are generated by a cycle of approximately 696-cent meantone fifths) 4. Other EDOs When utilizing these categories of tuning systems, effort should be made to assign duplicate meanings to other symbols with already clear meanings. George Secor’s and Dave Keenan’s Sagittal Microtonal Notation System provides a wealth of accidental symbols for utilization by composers.45 12n-EDOs (and EDOs that can be described as their subsets) should make use of a set of symbols that repeat through every half-step. When using sagittal notation in this context, it is advisable to used the mixed-saggital symbol set in order to allow pitches to be easily related to the 44 Chase Jordan, Atlantic Opalescence V: Timeless Sea Breeze (Laramie, WY: Chase Jordan Music, 2019). 45 George Secor & Dave Keenan, “Sagittal: A Microtonal Notation System.,” Xenharmonikôn, An Informal Journal of Experimental Music, 18 (2006), revised Nov. 2016. 19 Figure 1.9: 15-EDO music notated as a subset of 60-EDO in Stephen Weigel’s work for viola and synthesizer, Songs of the Ill and Jaded. Used with permission of the composer. twelve-note chromatic scale. One example of this can be found in Stephen Weigel’s Songs of the Ill and Jaded for viola and synthesizer, where, in the first movement, he notates 15-EDO in mixed sagittal notation using every fourth pitch from the 60-EDO (one-fifth-tone) superset. Meantone generated tunings (19-EDO, 31-EDO, & 55-EDO) should be notated using the standard accidentals and how they related to the circle of meantone fifths. Double-flats and double- sharps can be enharmonically spelled as quarter-flats and quarter-sharps in Adriaan Fokker's 31- EDO notation, which can provide a greater clarity to voice-leading and ultrachromaticism in most contexts.. Finally, scales with a number of divisions that do not easily fit into the other categories should be notated with extreme care. While the general notational considerations may vary between tuning systems, a system that provides the string player with the cent-deviation from a 12- or 24- EDO pitch will be highly valuable. While certain scales may be generated by chains of small and 20 large fifths, the theory behind each individual scale is often difficult to parse for the non-microtonal specialist. Providing cent-deviations in the score in addition to associated symbology allows for easily understood notations of microtonal scales with diminishing relation to the twelve-note chromatic scale. This symbology can be sourced through the pure sagittal accidental set. Non-Octave Scales While scales that do not repeat at the octave are not idiomatic to notation, they do have the potential to be idiomatic to stringed instruments. By dividing the interval between the strings into equal parts, non-octave repeating scales can be created. On violins, violas, and cellos these scales can be described as equal divisions of the fifth (ED3/2); on basses, these scales can be described as equal divisions of the fourth (ED4/3). Other intervals can be subject to equal divisions divisions through the use of scordatura. Particularly idiomatic non-octave tunings lie in the range of four to twelve equal divisions of the interval-of-repetition. When notating these intervals, it is best to “translate” the tuning into the closest scale that makes use of an octave as its interval-of-repition. For example, in the tuning system of 8ED3/2 (eight equal divisions of the fifth), the individual step sizes are between 87.5- and 88-cents. In order to notate this tuning, the smallest accidental will need to change the note by 12.5-cents, or a 1/16- tone. For notating this, the sagittal notation for 96-EDO would be effective, replacing the sagittal sharp symbol with a regular sharp symbol.46 These microtonal inflections can then be used to adjust Figure 1.10: Pure sagittal notation for 96-EDO using the trojan symbol set. Symbols from left-to-right are: natural 1/16-sharp, 1/8-sharp, 3/16-sharp, 1/4-sharp, 5/16-sharp. 3/8-sharp, 7/16-sharp, regular sharp (can be replaced with a standard symbol in mixed-sagittal. The author advocates for using the first 5 symbols and their reflections (for flats) in the mixed-sagittal format. 46 Ibid, 19. 21 the standard pitches of the twelve-tone scale into a 8ED3/2 scale using 96-EDO symbols. It is far more important for the notation to be applicable to the performer than inventing another notation that is more applicable to the theoretical needs of the scale. When working with significantly more complex scales, such as the 30-note subset of 59- equal divisions of the 7th-subharmonic scale, which is used in my in-progress composition for 20 solo strings, Lunar Harmonies47, it is important to make absolutely clear what the tuning of each pitch-class is. In notating the score, I use the Herculean level just-intonation symbols of the Sagittal accidental set in addition to cent-deviations in the score. While these accidentals are commonly used for just intonation, because these are intervals not based upon the harmonic series, it is advisable to use this lesser known system in order to prevent confusion between the non-octave equal division work’s and a just intonation work’s on a performer’s programs. The accidentals visually clarify the duration of the pitch-class on repeated notes from its neighboring pitch-classes, while the cent- deviations allow for the performers to know the intonation adjustment from the twelve-tone chromatic scale without having to memorize a multitude of accidentals. This essentially balances the Figure 1.11: A portion of the preface material to my composition Lunar Harmonies showcases the combination of sagittal accidentals with cent deviation markings to notate a highly complex scale in an easy way for performers to understand. 47 Chase Jordan, Lunar Harmonies, Chase Jordan Music, unpublished composers manuscript. 22 Figure 1.12: Accidentals for intervals of the third- through thirteenth-limits of just intonation in Extended Helmholtz-Ellis Notation. While most composers only need use of the 3-limit through 13-limit intervals, Extended Helmholtz Ellis Notation includes notations through the 61-limit. minimizing the clutter of the score and the understanding of the performer, providing the benefits of reading accidentals without the hassle of learning twenty or more new symbols. Just Intonation Moving away from scales made up of equal-divisions, just-intonation scales and pitch-sets are important in works for instruments in the orchestral string family. Not only is just intonation something that is easily executed on string instruments without more than a movement of a single finger, it also allows greater clarity in notating high partial harmonics (see chapter 2). Just intonation has been utilized extensively in the compositions (including string quartets 2 through 10) of the American composer, Ben Johnston48, as well as in the music of Ukrainian-Canadian composer and 48 John Fonville, “Ben Johston’s Extended Just Intonation: A Guide for Interpreters,” Perspectives of New Music 29, No. 2 (Summer 1991), 106-137. 23 violinist Marc Sabat49. Sabat has become an influential figure in the field of extended just intonation music theory and composition. Together, he and Wolfgang von Schweinitz have designed a notation derived from traditional staff symbols based upon the tuning theory work of Hermann von Helmholtz (microtonal co mma alteration) and Alexander Ellis (cent-intervals). This notation, called The Extended Helmholtz-Ellis Pitch Notation is the clearest way to notate any just intonation interval. As Sabat writes: “the Extended Helmholtz-Ellis JI Pitch Notation enables exact notation of all intervals that may be tuned directly by ear (natural intervals). It provides a method of writing any pitch-height in the glissando-contiuum as a note on the five-line staff, and of specifying, in the case of any natural interval, the harmonic relationships by which this note may be precisely tuned.”50 Just intonation allows for this acute control over consonances and dissonances, allowing the composer to dictate the pure intervals of the harmonic series.51 These are represented fractionally, as ratios between different harmonics. Extended Helmholtz-Ellis Just Intonation notation allows for the combination of symbols to allowing the proper ratio to be deduced by the musicians, allowing each type of symbol to describe intervals of a certain prime interval (known as the limit).52 Despite the fact that the interval can be deduced by musicians through intimate knowledge of this tuning Figure 1.13: Marc Sabat’s Partite Requiem for solo cello utilizes Helmholtz-Ellis extended Just Intonation to show the pitch content, and includes harmonic rations where they may be of assistance to the performer. 49 Nick Storring, “The Idiosyncratic Musicality of Marc Sabat,” MusicWorks Magazine, 125 (Summer 2016). 50 Marc Sabat, The Extended Helmholtz-Ellis JI Pitch Notation. Plainsound Music Editions, 2005. 51 Fonville, “Ben Johnston’s Extended Just Intonation,” 106. 52 Sabat, The Extended Helmholtz-Ellis JI Pitch Notation. 24 systems theory, it is advisable to include ratios in the music to help the musicians tune, as Marc does in his work for Solo Cello, Partite Requiem.53 The passage included below also includes high partial harmonics notated using Extended Helmhotz-Ellis Just Intonation symbols; for for information on this, see chapter 2. Chapter 2: Harmonics and Related Effects Through the use of light finger-weight on the string, players of orchestral stringed instruments are able to extend their range and create pitches with a different timbre. These techniques are not uncommon during music of the common practice era, but composers of the 20th- and 21st-centuries have expanded this technique to allow for a larger range of natural and artificial harmonics to be accessed by players, new trill effects to be performed, as well as multiple sounds through use of the finger and bow. Through changing bow-weight and bow placement, the subharmonic series and other anamalous low frequency tones can be accessed by players. Composers and performers wishing to investigate music composed using only harmonics of different kinds should explore Salvatorre Sciarino’s Tre Notturni Brilliante for solo Figure 2.1: The first six partials of the overtone series shown as graphically as sine waves in relation to an open string with their nodal points. From CelloMap.Com. 53 Marc Sabat, Partite Requiem, for Solo Cello, Plainsound Music Editions, 2019. 25 viola, especially the recording by Garth Knox. This collection of three solo compositions shows the immense timbral capabilities of natural harmonics, artificial harmonics, harmonic trills, and harmonic glissandos in three brilliant compositions. These works also explore the performance of harmonics in tremolo, getatto, sul ponticello, sul tasto, flautando, col legno, and spazzolare.54 To explore the use of harmonics within overpressure, investigate Andrew Norman’s Sabina for solo violin or solo viola.55 To explore the the use of harmonics with circular bowing and spazzolare, investigate my composition for viola and piano, Downtown Dichotomy. Finally, to explore the use of harmonics in Figure 2.2: Arpeggios of natural harmonics properly notated in Maurice Ravel’s Trois Poémes de Stéphan Mallarmé. Score is public domain. 54 Salvatorre Sciarrino, Tre Notturni Brilliante (Milano, It: Riccordi, 1975). 55 Chase Jordan, Downtown Dichotomy (Laramie, WY: Chase Jordan Music, 2019). 26 combination with other effects, it is highly recommended for composers to work with a string player to explore the combinations of techniques. Natural Harmonics Natural harmonics are produced through lightly touching the strings at points which divide the string into proportions of equal amounts. For example, touching the string lightly at the 1/3- point creates a clear pitch that is the 3rd-partial in the harmonic series. A common misconception among string players is that the harmonic at the halfway point of the string is the first partial of the harmonic series. This is not true. The open string itself is actually the first partial of the harmonic series series, and the harmonic at the halfway point of the string is the second partial of the harmonic series.56 This misconception appears to be widespread - Gerald Warfield, a composer, former lecturer on music notation at Princeton University, and a committee member on notation at the 1974 International Conference on New Music Notation also calls this harmonic the first harmonic.57 Natural harmonics, generally, should be notated with diamond noteheads as opposed to the old notation where a circle is used about a notehead. The exception to this rule is that when the fingered pitch is the same as the resultant pitch, the a regular notehead and a circle should be used. Traditionally diamond noteheads are white in the middle regardless of rhythmic duration in order to clarify that a note is a harmonic. Due to the increasing complexity of music utilizing harmonics, one of two solutions should be employed so that the rhythm is immediately clear to the 56 Garth Knox, Stretching the String: Embedding Pedagogical Strategies in Extended Techniques Compositional Strategies for Strings, DMA diss., Middlesex University, 2018, 24-25. 57 Gerald Warfield, “The Notation of Harmonics for Bowed String Instruments,” Perspectives of New Music 12, No. 1/2 (Autumn 1973-Summer 1974), 336. 27 performer: (1) utilizing black diamond noteheads for all note-values that are a quarter-note or less, or (2) providing a rhythmic cue above unclear passages. When notating harmonics from the first through fifth partial, the standard sharps and flats can be used as accidentals. Beginning with the 6th partial, multiple nodes are found where equal- tempered pitches are notated and lie on the fingerboard. To solve this issue, composers should utilize the Extended Helmholtz-Ellis Just Intonation to identify the harmonic nodes and resultant pitches. These harmonics are practical for the violinist / violist to sound up to the 12th partial58,59 (but are increasingly difficult to consistently sound on higher strings, especially the violin E-string), while the cellist and bassist can execute harmonics of even higher partials, although these high partials may be inconsistent and unstable. When using these harmonics, the following notational principals should be considered for maximal clarity to the performer: 1. In addition to the appropriate accidental, the string number (in roman numerals), and, for harmonics of the 7th partial or higher, the partial number (in arabic or superscript numerals) should be included for maximal clarity as to the resultant pitch (i.e. 7º/III; see figure 2.360). Figure 2.3: Notice how a rhythmic cue allows for natural harmonics to be notated with rhythmic percussion in the violin part of Chase Jordan’s Crimson for Pierrot Ensemble and Percussion. Used by permission of the composer. 58 Garth Knox, “Harmonic Horizons” from Viola Spaces (Mainz: Edition Schott, 2007). 59 Marc Sabat, Natural Harmonics Above a Violin A String (Plainsound Music, 2005.) 60 Chase Jordan, Crimson (Laramie, WY: Chase Jordan Music, 2018). 28 Figure 2.4: In Marc Sabat’s Partite Requiem for Solo Cello, extended Helmholtz-Ellis notation is used to indicate precise high-partial harmonics in combination with string numbers, partial numbers, and resultant pitches depicted in cue- sized accidentals. Additionally, notice the use of white and filled-in diamond notepads to clarify rhythm. 2. Complex passages of harmonics using the 7th partial and above should include a staff with parenthesized cue notes for resultant pitches (see figure 2.3). 3. Harmonics in double-stops with stopped notes or other harmonics should be notated in different voices (see figure 2.2)61, in order to clarify between their notation, the notation of artificial harmonics, and the notations of double node harmonics. This also provides greater clarity to what string the harmonic should be played on in music with multiple voices (see figure 2.462). 4. Use of harmonics of the 7th partial or higher requires a performance note for explanation. Figure 2.5: Double-stops containing harmonics are notated with separate voices in order to clarify their use as natural harmonics in Thomas Nicholson’s Bercer for solo cello. 61 Maurice Ravel, Trois Poémes de Stéphan Mallarmé (Paris: Durand Editions, 1914). 62 Sabat, Partite Requiem. 29 Figures 2.6-2.10 = show the first 12 partials in the harmonic series on each string and demonstrate their notation, location upon which the nodes may be played, and their resultant pitch. While these are shown in convenient clefs, they may be transposed into their appropriate octave for violin, viola, cello, and bass. Figure 2.6: Natural Harmonics on the violin A-string notated using extended Helmoltz-Ellis Just Intonation symbols. 30 A Figure 2.7: Natural Harmonics on the D-string. glissando can be performed on natural harmonics on the open string. This produces a popcorn like effect as the different partials are brought out. During the common practice era, it was common for glissandos on natural harmonics to be notated showing each harmonic’s sounding pitch (see figure 2.2, violin II part). In the modern era, this is only necessary when the composer wants a specific rhythm of the harmonics popping out. If the general effect is all that is required without, the player 31 Figure 2.8: Natural Harmonics on the G-string. only needs the fundamental, the rhythmic locations of the top and bottom of the gesture, and (if necessary), the top and bottom note of the glissando (see figure 2.11) Natural harmonics can also be manipulated through pulled harmonics. Pulled harmonics are natural harmonics that have had their pitch “pulled” upwards by up to a semitone. This is executed by the performer placing their finger, at harmonic weight, on the inside of the string and pulling it 32 Figure 2.9: Natural Harmonics on the C-string sideways.63 While this technique is not technically a harmonic, due to the tension placed on the string, it is often grouped as such by Italian string players because the string is not stopped against the fingerboard, but is stopped in the manner of a harmonic.64 Aurally, this technique has the timbre 63 Allen Strange & Patricia Strange, The Contemporary Violin: Extended Performance Techniques (Lanham, MD: Scarecrow Press, 2003), 138. 64 Knut Guettler, A Guide to Advanced Modern Double Bass Technique (London: Yorke Edition, 1992), 112. 33 Figure 2.10: Natural Harmonics on the Contrabass E-string. Due to the size and length, and fundamental pitch of the string, natural harmonics of higher partials are more usable on Contrabass than on violin, and hence are shown appropriately here. of a harmonic, and so it has been classified as such within this text. According to Allen Strange, in The Contemporary Violin, pulled harmonic techniques work best on the second, third, and fourth partials65, but in my experience, I have had success pulling harmonics up to the 6th partial when utilizing the nodes closer to the bridge of the instrument. Practically, pulled harmonics require time for preparation if the first note to be sounded is not in the harmonic series of the fundamental 65 Strange, The Contemporary Violin, 138. 34 Figure 2.11: Harmonic glissando ending Salvatore Sciarrino’s Tre Notturni Brilliante, No. 1: “Di volo”. Copyright © 1975 by Casa Ricordi S.r.l. – Milan, Italy. All Rights Reserved. International Copyright Secured. Reproduced by kind permission of Hal Leonard Europe S.r.l. – Italy Figure 2.12: Example of pulled harmonic notation. Measure 1 shows pulling from a normally available harmonic, while measure 2 shows beginning from a pulled harmonic and moving to the typical pitch at the pulled node. string. When the pulled harmonic starts on the fundamental and then is pulled away, no preparation of the effect is required. For investigating the sound of pulled harmonics, Allen Strange’s Shaman: Sisters of Dreamtime for solo violin should be explored.66 Pulled harmonics should be notated like a glissando, with accompanying text to clarify the meaning. Due to the lack of repertoire using this technique, it is highly recommended to include description of the technique and a notation key in the preface material to the score. 66 Ibid, 139. 35 Dual-Node Harmonics Figure 2.13: Dual-node harmonic for the thirteenth partial in Marc Sabat’s Partite Requiem for Solo Cello. High partial harmonics can be very unstable when sounded, due to the exactitude required of the left hand finger placement and execution of the bow speed and placement. These left-hand problems can be mitigated through use of dual-node harmonics. With dual-node harmonics, performers can mitigate the left-hand problems associated with the highest partial harmonics, and expand the upper range of accessible partials. These are most practical in providing easier access to harmonics around the twelfth harmonic as opposed to extending range, but with proper bow speed and bow placement, the higher partials are possible. On the string bass up to the 21st partial, which is impossible to isolate by itself, can be accessed through the use of dual-node harmonics.67 In practice, two nodes can be isolated simultaneously, and the partial of their least common multiple will sound. These should be notated as done by Marc Sabat: as two diamond noteheads, showing the two nodes that are isolated with a resultant pitch notated on an auxillary stave with a parenthesized 67 Eric Daino, The Double Bass: A Technical Study of Timbre, Honors Bachelor of Music Thesis: University of Delaware, 41-42. 36 cue-sized notehead. In addition the desired harmonic partial should be given as it would be if it was Figure 2.15: Harmonic trill notated using fingered tremolo notation. a normal natural harmonic (i.e.: 21º/IV).68 Artificial Harmonics While artificial harmonics were standardized into the string music literature by Niccolo Paganini69, and are no longer considered an extended technique, they are covered here to aid the composer in the possibilities of what can be played. The third through sixth partials of the harmonic series are easily used as artificial harmonics on all members of the orchestral string family, but use of artificial harmonics on string basses is limited to thumb position due to the physical size of the instrument. The notation is standard - a regular notehead for the fundamental stopped note, and a diamond notehead for the node that is isolated through the harmonic weight of another finger. For a notational example, see figure 2.3, which also shows artificial harmonics in double stops . Harmonic Trills This will discuss three types of harmonic trills: (1) the trill between two harmonics (natural or artificial), (2) the trill between a natural harmonic and an open string, and (3) the trill between a natural or artificial harmonic’s node and a fully depressed finger in a single location on the fingerboard. 68 Marc Sabat, Partite Requiem. 69 Knox, Stretching the String, 17. 37 Figure 2.19: A trill between tow artificial harmonics sharing a node. Figure 2.14: Harmonic trills notated with trill line and auxillary notes in Salvatore Sciarrino’s Tre Notturni Brilliante, No. 1, “Di Volo.” Copyright © 1975 by Casa Ricordi S.r.l. – Milan, Italy. All Rights Reserved. International Copyright Trilling between two natural harmonics is a relatively accessible technique for string players, and is simple to notate. Both pitches should be notated with diamond noteheads, and can be notated using either a trill line with auxillary note (figure 2.14) or as a tremolo between two pitches (figure 2.15). A trill between an artificial harmonic and a natural harmonic can be accomplished through either the changing of the fundamental with a shared node (figure 2.16) or through changing both the node and the fundamental (figure 2.17). Trills between two artificial harmonics are the most idiomatic when they share either the node (figure 2.18) or the fundamental (figure 2.19). If these trills are used as part of a double stop, the notes should be condensed into one voice and a dotted tie Figure 2.16: A trill between an artificial harmonic and a natural harmonic through a change in fundamental. Notice the use of a dotted tie to show the sustain of the nodal finger. Figure 2.17: A trill between an artificial harmonic and a natural harmonic changing both the fundamental and the node. 38 Figure 2.18: A trill between two artificial harmonics sharing a fundamental. Figure 2.20: A trill between a natural harmonic and open string. should be used to show the sustained use of the appropriate finger, as in figure 2.16. Trills between two artificial harmonics that require the change in both fundamental and node are not idiomatic, as the action of having to raise the 1st and 3rd fingers and lower the 2nd and 4th fingers is in opposition to mechanics of the left hand and have a speed limit on how fast they can be executed. Therefore these trills should be used with extreme care. When used, these should be notated using a fingered tremolo notation. Trills between a natural harmonic and an open string should be notated as a fingered tremolo (2.20). Use of a trill line in these instances reduces clarity on if the node should be sustained through or not. These trills are imply for the performer to separate the harmonic and fundamental pitches into as clean of a trill as string mechanics allow. But, this technique can also be executed to sound a “trilled multiphonic” that includes the fundamental and the the pitches of the node(s) that lie under the trilling finger. This technique is most effective towards the nut of the instrument and towards the bridge of the instrument (where clearer dyads are created). For a greater discussion of multiphonics, including the notation of their resultant pitches of trilled multiphonics, see Chapter 2: Harmonics and Related Techniques: Multiphonics. It should be noted that these trilled multiphonics 39 are not effective in combination with dual-node harmonics, artificial harmonics, and other similar techniques. The finally category of trilled harmonic is the harmonics that are trills between a natural or artificial harmonic’s node and a fully depressed finger in a single location on the fingerboard. These harmonics are utilized in works such as Kaija Sarriaho’s Vent Noctures70 and Garth Knox’s Violin Spaces71 and Satellites72, where he calls them “trembling harmonics”. Trembling harmonics should be notated after Saariaho using a trill line and a regular or diamond auxillary notehead to show whether they start from harmonic weight (figure 2.21) or normal finger weight (figure 2.22). It is Figure 2.21: Trembling harmonics beginning from harmonic finger weight. Figure 2.22: Trembling harmonics beginning from normal finger weight. more effective to start trembling harmonics from the harmonic finger weight, unless they come from a sustained note or tone in the same finger position as the harmonic node. Additionally, I recommend using the textual description “trembling harmonic” in the score, as the description of the sound can be immensely helpful to the performer realizing the technique. The trembling harmonic can be combined with downward glissando of the trilling fingers to creates a “shower of 70 Kaija Sarriaho, Vent Nocturnes (London: Chester Music, 2007). 71 Garth Knox, Violin Spaces (Mainz: Schott Editions, 2018). 72 ———, Satellites (San Fransisco: Kronos Perfomring Arts Association, 2016). 40 Figure 2.23: Shooting Star Tremolo notation. ascending harmonics.” Garth Knox calls this technique a “shooting star tremolo”.73 To notate this effect, add a downward glissando from both the primary notehead as it is assumed that trilled distance (in this case a fingered unison of a timbral effect) remains the same (see figure 2.23). If performed on artificial harmonics, it is important to clarify if only the nodal point moves (requiring glissandi only on the diamond notehead, or if the fundamental moves as well, requiring glissandi on both noteheads. The notations proposed here are more similar to the notations proposed by Saariaho than those proposed by Garth Knox. I have opted for this kind of notation in order to more clearly differentiate between and give the composers more control over the various ways each effect can be produced. While these are not the simplest notations, they prevent multiple meanings being given to multiple notations, and show the performer how to perform the technique with minimal additional text in footnotes or notes to the performers in the preface material. A clear notation that clearly shows the mechanics and their operation for the effect that minimizes redundancies will provide for a clearer directives to the musician not just among a single composition, but among the growing body of compositional work. Multiphonics Multiphonics are a phenomenon where a single vibrating string creates multiple sounding pitches. This technique is perhaps best known for its place in the repertoire of flute, saxophone, clarinet, and brass players. While string multiphonics do not share the abrasive qualities with 73 Knox, Stretching the String, 26. 41 Figure 2.24: Notation for the trilled Multiphonic utilizing the 8th harmonic on the violin and viola G String. woodwind and brass multiphonics74, and are significantly less codified, they no less add usable and interesting sounds to the pallet of the composer and performers. Multiphonics can be produced in three primary ways on all stringed instruments: (1) the trilled multiphonic (discussed earlier in this chapter), (2) through using bow speed and bow-weight to sustain a harmonic after switching to the open string, and (3) through placing the finger at harmonic weight in a location that activates multiple harmonic nodes. Trilled multiphonics should be written like a fingered tremolo, but include an M notation, signifying multiphonic, with an optional extra stave for sounding pitches (see figure 2.24). Trilled multiphonics are the easiest to predict the sounding pitches of, as they include the trilled nodal point Figure 2.25: Drawing out a multiphonic with the bow in Marc Sabat’s Partite Requiem. 74 Daino, The Double Bass, 50. 42 Figure 2.26: A multiphonic (as part of a double stop with a harmonic), produced by utilizing a harmonic near several others in Marc Sabat’s Partite Requiem. Marc, in addition provides the primary pitch produced to the multiphonic symbol. Used with permission of the composer. and the fundamental as their primary two notes. When played towards the bridge of the instrument, a dyadic interval is the easiest to create. When played towards the nut of the instrument, a harmonic cluster above the fundamental is most apt to be created. For this reason, trilled multiphonics can be used as an aid to allow harmonics at the edges of the usable range speak. It is recommended when using trills between a natural harmonic and an open string for the purpose of multiphonics to include a performance note similar to what Knox writes is the performance notes to “Harmonic Horizons”: Figure 2.27: Transition between a multiphonic and an ordinary harmonic in Marc Sabat’s Partite Requiem. Used with permission of the composer. 43 The opening section features harmonics with left hand tremolo [fingered tremolo]. Here, a light, fast left hand tremolo allows us to hear the harmonic clearly, and at the same time hear the presence of the open string underneath. This technique makes the harmonic more stable.75 A variation of this technique is to draw out the multiphonic through use of bow speed and bow weight by changing the lifting the finger from the harmonic it is playing (see notation in figure 2.25).76 Depending on the harmonic, variations in bow speed and bow weight may be required, but most times, a flautando bowstroke will make this work. Multiphonics may also be created through the use of playing a single note with the finger positioned at harmonic weight. Typically, these sound multiple, close harmonic partials together, and so their content can be inferred by checking which harmonics are close to the given point.77 For notation, it is suggest to notate as if it was a harmonic, while attaching a stylized M to the stave (see figure 2.26). Through slight changes in finger movement, transitions between multiphonics and ordinary natural harmonics may be accomplished (see figure 2.27). These multiphonics on string instruments are not codified, and little research has been done into where all possible location are located. A research study at the Norwegian Academy of Music mapped many possible multiphonics on string bass, and found that more multiphonics were available when the bow was place precisely on certain harmonic nodes in addition to the placing of certain fingers.78 This kind of research does not exist for other instruments, and attempts to draw precise tones out of a multiphonic are often inconsistent.79 75 Knox, “Performance Notes” from Viola Spaces, 5. 76 Sabat, Partite Requiem. 77 Daino, The Double Bass, 51. 78 Håkon Thelin, Multiphonics on the Double Bass: An Investigation on the Development and Use of Multiphonics on the Double Bass in Contemporary Music (Oslo: Norwegian Academy of Music, 2011). 79 Strange, The Contemporary Violin, 133. 44 Subharmonics and ALFs Subharmonics are pitches below the sounding note of the string that are drawn out through a change in bow weight. While the execution for the performer is not related to that of harmonics, subharmonics make use of similar acoustics phenomena to harmonics and are grouped here for the Figure 2.28: Descending G Major Scale on subharmonics. understanding of the composer. Perhaps the most famous use of subharmonics is in George Crumb’s string quartet, Black Angles, where he asks the performers to draw out pitches one octave below the fingered note on their lowest strings.80 Subharmonics are played by fingering the note normally, and utilizing an increased bow weight, similar to overpressure (see chapter 10), and precise placement of the bow on the string, notes one octave below the fingered pitch can be created. Additionally, it is only feasible to play these on the lowest string of an instrument, unless played as a subharmonic double stop on the lowest two strings. Double stops subharmonics produce the clearest sound when used in octaves or fifths.81 In addition, the characteristic sound of subharmonics is somewhat distorted in comparison to normal playing, making it timbrally similar to the overpressure technique. It is not recommended to write these for double bass beyond a basic manner, as the thickness and inflexibility of double bass strings get in the way.82 80 George Crumb, Black Angles (Glendale, NY: Edition Peters, 1970). 81 Daino, The Double Bass, 56. 82 Ibid, 47. 45 To notate these, square noteheads should be used for the fingered pitch (similar to overpressure notation for single notes proposed in chapter 10), and the resultant pitches should be notated on the stave below (see figure 2.28). This is the same notation as Crumb uses in Black Angels; as this is the most famous use of the technique, this notation has been borrowed. Notations for bow placement and pressure should not be included, as the inconsistencies from player-to-player and instrument-to-instrument prevent a standardized execution of the technique.83 Other pitches have been documented in improvisation and practice outside of this below the fingered pitch that do not follow the subharmonic series, lying between the fundamental and the second subharmonic in pitch. These pitches are described by Allen and Patricia Strange in The Contemporary Violin as “Anamalous Low Frequencies” or ALFs.84 The accoustical phenomenon that allows these pitches remains unknown, but violinist Mari Kumari has advanced this technique to a virtuosic level.85 These are notated just as subharmonics, but with the appropriate resultant pitch on the lower staff. Chapter 3: Vibrato String players typically add vibrato to all notes in a passage using their own musical instincts to vary the width, speed, regularity, and shape of the vibrato. It is sometimes desirable to have greater control of this as the composer. It is common in contemporary literature to see markings such as senza vib. (no vibrato), poco vib. (little vibrato), molto vib. (much vibrato), and vib. ord. (ordinary vibrato). In some cases, even more control is necessary. This chapter will discuss notational methods 83 Kimura, Mari, “How to Produce Subharmonics on the Violin,” Journal of New Music Research 28 ( June 1999): 178-184. 84 Strange, The Contemporary Violin, 25. 85 James Reel, “Mari Kimura on Subharmonics,” Strings 170 ( June 2009). 46 for controlling each aspect of the vibrato. Each section will break the different aspects of vibrato down individually, but the modular aspect of the notation as proposed will allow easy combinations of each effect. It is not recommend to reduce the instructions in this section to abbreviations except for in music that requires quick changes between various styles, such as the new complexity works of Brian Ferneyhough. The graphical elements in notation within this chapter have been devised in order to create clarity between themselves, trill, and other lines. They symbology utilized lacks similarities in style to the trill line, allowing for easy recognizability on the page of the musical score. Speed of the Vibrato Vibrato speed can be controlled on a spectrum between senza vibrato and a very fast vibrato. This can be controlled using textual instructions (very slow vib., slow vib., fast vib., very fast vib.). Gradual changes between different speeds of vibrato can be notated using an arrow between two Figure 3.1: Using text and an arrow to notate changes in the speed of vibrato. Figure 3.2: A line used to notate a gradual change in speed. Notice that the text “vib.” is still included for clarity. 47 textual instructions (figure 3.1) or using graphics above the stave, such as a line depicting the changing speed (see figure 3.2). Width of the Vibrato Additionally, it is not uncommon for composers to ask for varying widths of vibrato. Again, this can be controlled using textual instructions (very small vib., small vib., wide vib., and very wide vib.). Gradual changes in width can be notated through arrows between textual instructions, as in figure 3.1, or a graphical illustration above the musical stave. When the composer would like to specify the width of vibrato by an interval, a textual description instruction can be given (i.e.: quarter-tone wide vibrato) or attach an interval to the graphic (figure 3.3). When the graphic is used, additional clarification in the front matter of the score will be required. Figure 3.3: A line with attached symbols to show the notation of semi-tone wide vibrato and quarter-tone wide vibrato. It is important to note for composers that vibrato is typically performed “towards the flattened side of the pitch.”86 When using instructions affecting vibrato width, the play will adjust this flattening of the pitch as opposed to adding an upward oscillation. Hence why, in the symbology attached to the lines, flattening symbols are used. If the composer wants the oscillation in another 86 Ivan Galamian, Principles of Violin Playing and Teaching, 3rd ed., edited by Elizabeth A.H. Green (Ann Arbor, MI: Shar Products Company), 42 48 method (only above the pitch, both below and above the pitch) it is best to notate this with a textual description. Regularity of Vibrato Typically, vibrato is performed consistently throughout the phrase in regular cycles. Sometimes it is desirable to have irregular cycles. This can be given via a textual instruction: “senza vib., with random vibrato oscillations ad lib.” or “senza vib., insert 4 vibrato oscillations ad lib.” Or another similar marking that fits the need of the composition. This can also be notated graphically, with line segments, notated in approximate positions (figure 3.4). When the graphic is used, Figure 3.4: Use of single segments of a vibrato line to graphically notate approximate positions of single vibrato cycles, additional clarification in the front matter of the score will be required of the symbology and that the space between the vibrato cycles should be senza vibrato. Shape of Vibrato A typical vibrato is rounded in character. Sometimes, it is desirable for the composer to utilize a more sharp angular vibrato. This description of the vibrato will be the most effective notational devise for the composer to communicate their wishes. 49 Chapter 4: Other Effects of Pitch So far, changes to the pitch through microtonality, harmonics and their related techniques, and vibrato have been explored. The techniques in this chapter do not fit into those other categories and are provided a description and notation, as well as reference to repertoire that makes use of these techniques to aid composers studying how these techniques are used. Indiscriminate Pitch When the composer does not wish to dictate specific pitches, instead desiring to ask for the player to choose pitches in a certain shape. There are two primary ways indiscriminate pitch is used: (1) a collection of headless stems to show approximate pitch and shape, and (2) asking the player to execute the highest indiscriminate pitch on a certain string. To notate approximate pitches in a certain shape, it is recommended to use headless stems (omitting ledger lines when leaving the range of the staff, as Elaine Gould suggests in Behind Bars87; figure 4.1). When the approximate pitches are to be performed in specific double stops — that is the horizontal movement of the pitches indiscriminate, but the interval between the two notes is held constant — it is recommended to use square noteheads, as Andrew Norman uses in the Companion Figure 4.1: Headless stems used to notated approximate range of indiscriminate pitches. 87 Gould, Behind Bars, pg. 640. 50 Figure 4.2: Square noteheads and a textual description on the first occurrence notating indiscriminate pitch material with a specific sounding double stop.range of indiscriminate pitches. Guide to Rome,88 and I use in Atlantic Opalescence V: Timeless Sea Breeze.89 This requires a performance note, and a note can be included as to what the the interval(s) should be if desired within the score (figure 4.2). In addition, roman numerals dictating the strings to be played on can be used for greater control over the timbre. Figure 4.4: Glissando in the first violin and viola part downwards from highest indiscriminate pitch with harmonic finger weight in the second movement of Chase Jordan’s String Quartet No. 1: A Propos of the Wet Snow. 88 Andrew Norman, The Companion Guide to Rome (Mainz: Edition Schott, 2010). 89 Jordan, Atlantic Opalescence V: Timeless Sea Breeze. 51 Figure 4.5: The performer reads two staves in Chase Jordan’s Atlantic Opalescence I. The top stave represents to sounding pitch, and the bottom the fingered pitch. Additionally, it is common to ask the performer to execute the highest possible pitch on a string. This can be performed both with normal finger pressure and with a harmonic finger pressure, which gives a cloudy sound. Use an upward pointing triangular notehead for this as suggested by Gould, in addition to a notation for which string to play on as a roman numeral. (figure 4.3).90 Include the circle used for natural harmonics above the triangular notehead if harmonic pressure is desired (see figure 4.4).91 Scordatura Scordatura is a technique where a stringed instruments are retuned differently from their standard tuning92, either by slight microtonal deviations as Ben Johnston notates in his String Quartet No. 4: Amazing Grace93 or as more complex retuning of multiple strings by various intervals 90 Gould, Behind Bars, 12-13. 91 Chase Jordan, String Quartet No. 1: A Propos of the Wet Snow (Laramie, WY: 2018). 92 Nathan Cook, Scordatura Literature for Unaccompanied Violoncello in the 20th Century: Historical Background, Analysis of Works, and Practical Considerations for Composers and Performers, DMA Thesis, Rice University, 2005. 93 Ben Johnston, String Quartet No. 4: Amazing Grace (Sharon, VT: Smith Publications, 1990). 52 as Henri Dutilleux uses in Trois Strophes sur le nom de SACHER94. While scordatura tunings by default change the range of the instrument, it is not recommended to use this technique as primarily a tool to extend the range of the instrument, as it is more effectively used to change the instrument’s timbre and resonance. In microtonal contexts, it can be used to keep the open strings within the scale being used, allowing for greater technical mobility. When writing in scordatura tunings, it is important to keep in mind over- and under- tensioning the strings. With modern day metal strings, tunings that raise the pitches of strings by more than a whole-step put the strings at risk of snapping. While most orchestration texts say the limit in retuning the string below the normal pitch is also a whole-step, this is overly stringent.95 In Iannis Xenakis’ composition for solo cello, Nomos Alpha, the C-string is retuned to a low C, 1 octave below the typical tuning.96 In practice, the commissioner of a particular composition should be consulted and the maximum amount of retuning collaborated upon; although it appears that there is a far greater limit to how far strings may be retuned lower rather than higher. A brief note in the preface material to a score and on the first page suffices for most retunings. Complex retuning of the strings, as in Henri Dutilleux’s Trois Strophes sur le nom de SACHER and in my own composition, Atlantic Opalescence I, should be notated using both notations for fingered pitch and for sounding pitch to aid the performer (figure 4.5). On the sounding pitch stave, it is important to make it absolutely clear what the string the finger is placed on to produce the note, hence the roman numerals dictating the strings for notes played outside of first position. 94 Henri Dutilleux, Trois Strophes sur le nome de SACHER (Paris: Heugel & Cie, 1976). 95 Cook, Scordatura Literature for Unaccompanied Violoncello, 26. 96 Iannis Xenakis, Nomos Alpha (London: Boosey & Hawkes, 1965). 53 Peg Glissando / “Glissando Scordatura” In addition to playing a composition where the strings of the instrument are tuned scordatura, string players are sometimes asked to detune a string using their tuning pegs. Perhaps the most characteristic use of this is in Alfred Schnittke’s Stille Nacht for violin and piano, where the violinist is asked to glissando between the open G-string and a D, a perfect fourth below, by using the tuning peg. At the end of the composition, Schinttke asks the violinist to wobble around the low, scordatura D using the tuning peg.97 Peg glissandos function best when the performer has the opportunity to tune immediately after their occurrence, making them best suited for the ends of movements. If time is not given to Figure 4.6: A Peg glissando between an open string and a pitch below, notated with a pictogram. retune, there is a high likelihood, even among advanced players, to have the string not in tune. Additionally, it is unwise to ask the player to perform a peg glissando more than a whole tone upwards. The increase of tension on modern, metal strings beyond this interval places extreme tension of the instrument and risks breaking the string. Peg glissandos should be noted both with the glissando text (optionally reading glissando scordatura) and with a pictogram in the score to alert the player to the technique. This is all that is necessary for glissandi between two pitches (figure 4.6). Peg glissandi can descend to an indiscriminate pitch below the open string. This should be notated 97 Alfred Schnittke, “Stille Nacht” from Stille Musik and Stille Nacht (Hamburg: Edition Sikorski, 1987). 54 with a downward pointing triangle, without ledger lines below the staff in addition to the text and pictogram (see figure 4.7). Figure 4.6: A Peg glissando between an open string and an indiscriminate pitch below, notated with a pictogram. Bowing Under the Strings / Bowing with Two Bows In cello literature of the last century, a growing number of composers and performers have been developing a two bow technique where one bow is under the strings, playing the C and A strings, while the other is in normal playing position, bowing the G and D strings. The French cellist Frances-Marie Uitti can be credited with much of this development in technique.98 This technique can be performed in two methods, with both bows in the right hand, allowing for complex chordal playing, or with the bows in separate hands, allowing for complex rhythmic and textural treatment of sound, but only on the four pitches of the open strings. When the two bows are held in the right hand, no change in notation is necessary except for with a textual description of the technique. In music that asks the two bows to be held in separate hands with complex textural changes, two staves should be used, as in Lewis Inghams, A Storm, A City for solo cello and electronics (see figure 4.8).99 98 Robin Stowell, The Cambridge Companion to the Cello (Cambridge University Press, 1999), 26. 99 Lewis Ingham, A Storm, A City (Lewis Ingham Music, 2017). 55 Figure 4.8: Two bow technique in Lewis Ingham’s A Storm, A City for solo cello. For a note on notating thrown, metered bow strokes, see chapter 10. When using this technique, provide the cellist with about five seconds to switch between single and double bowing.100 Additionally, the text “bow under strings” can be used by itself in single bowing technique to ask for double stops on the lowest and highest string of the instrument. This technique is best suited to the cello literature. On the violin and viola, it is difficult to insert the bow under the strings without excess noise from the bow hitting the wood of the instrument, while on the bass it is impractical due to left hands role in keeping the bass balanced. 100 Stowell, Cambridge Companion to the Cello, 26. 56 Part II: Techniques affecting Timbre Chapter 5: Pizzicato Techniques In addition to the bow, it is common for string players to use their fingers or an implement to pluck the strings. This is known as pizzicato. The conventional pizzicato is done with the flesh of the finger plucking the string similarly to a classical guitar. In addition the conventional pizzicato, there are a multitude of timbres and techniques that can be explored on stringed instruments, both to create new percussive sounds and to allow greater facility in technical passages. This chapter can be divided into three sections. The first section will discuss types of pizzicato that result in significant timbral changes to the sound. These include the Bartok pizzicato, the buzz pizzicato, the fingernail pizzicato, plucking with an implement, location of pizzicato between the bridge and nut of the instrument, and slurred pizzicati. Second, techniques that increase technical facility in pizzicato, such as the left hand pizzicato and pizzicato with multiple fingers will be discussed. Finally, the section labeled “other similar techniques” will discuss special effects made by the fingers on the string that include wiping and scraping the string with an implement. Variations along the Length of the String Pizzicato techniques can be performed in multiple places along the string, similar to bowed techniques (see chapter 8). The conventional pizzicato, is performed on the edge of the fingerboard. Pizzicato performed out over the middle of the string has a softer, less vibrant sound. This is notated as “pizz., sul tasto”. Pizzicato performed near the bridge, known as “pizz., sul pont.” creates a deadened sound with significantly less sustain. 57 In addition, pizzicato behind the bridge is known as “pizz., sub pont.” and creates an indiscriminate pitch. To notate this, utilize Penderecki’s behind the bridge symbols and the textual instruction, along with x-shaped noteheads to indicate the string that should be plucked (see figure 5.1). The use of Penerecki’s bridge clef symbols allow for clarity and consistency between the arco and pizzicato variations of this technique. The pitches produced correspond relative to the pitch of the string, meaning that lower strings produce lower pitches while higher strings produce higher Figure 5.1: Pizzicato sub ponticello on the four strings of a viola. pitches, but are not distinctly pitched themselves, varying between instruments based on relative string length and tension. Pizzicato can also be performed in the peg-box of the instrument. This is most practical on the middle two strings, while playing with the fingernail, as the sides of the peg box get in the way, giving more room for a louder sound to ring, but the other two strings are usable as well. In terms of volume, this technique does not project and creates only subtle sounds, making it only feasible in solo, unision, or amplified contexts.101 The pitch content of these relates not the the pitch of the string, but to both the size of the string and the vibrating distance between the peg and the nut. This means that the order to the pitches from highest to lowest using string numbers is III, II, IV, I on most instruments. To notate this, utilize a x-shaped noteheads and a textual instruction: “pizz., in the peg-box”. An additional instruction for the fingernail can be added via text, “with nail”, or with a pictogram (see “Fingernail Pizzicato”). 101 Strange, The Contemporary Violin, 66. 58 Bartok Pizzicato / Snap Pizzicato The Bartok pizzicato, also known as the snap pizzicato, is commonly associated with the music of Bela Bartok. It is often thought that Bartok invented the technique, but in fact, its first Figure 5.2: Bartok pizzicato on the downbeat of a bar in the second movement of my String Quartet No. 1, A Propos of the Wet Snow. documented use on modern instruments is by Gustav Mahler in his Seventh Symphony102, and on the contrabass violone in the music of Heinrich Ignaz Franz von Biber.103 This techniques adds an unpitched snap while maintaining the sounding ringing from the note. The notation for the Bartok pizzicato is standardized and well-understood by musicians (see figure 5.2), and it does not require a preface note for clarity in the score. In single Bartok pizzicatos among normally bowed notes, it is wise to include a textual instruction — “pizz.” — in order to alert the performer to the change in technique and allow for greater clarity. The Bartok pizzicato cannot be performed sub ponticello or sul ponticello, as it requires the fingerboard to snap against. Sul tasto Bartok pizzicato is also ineffective as a timbral effect. 102 Norman Del Mar, The Anatomy of the Orchestra, 98. 103 Alfred Planyavsky, The Baroque Double Bass Violone, trans. By James Barket (Lanham, MD: Scarecrow Press, 1998), 61. 59 Buzz Pizzicato Another pizzicato technique is the buzz pizzicato. The pizzicato is performed in the conventional manner, but once the string begins to vibrate, the finger pad or nail can lightly touches the vibrating string, making a buzzing sound. This is most effective on open strings, as a wider vibrating area is accessible allowing it to last longer.104 To notate this effect, it is suggested to use a Figure 5.3: Repeated buzz pizzicati in my composition Whitéd Sepulchre for Viola and Percussion. sideways snap pizzicato symbol105, and a note in the perface material in the score will be required for clarity (figure 5.3). In single snap pizzicatos among normally bowed notes, it is wise to include a textual instruction — “pizz.” — in order to alert the performer to the change in technique and allow for greater clarity. Buzz pizzicato can be performed both sul ponticello and sul tasto. Fingernail Pizzicato Another variation in the execution in pizzicato is the fingernail pizzicato, where the performer uses the fingernail to pluck the string as opposed to the flesh of the finger, creating a sharper, piercing sound compared to the warmer sound of a conventional pizzicato. One of the earliest and most effect examples of this technique is in Music for Strings, Percussion, and Celeste by Bela Bartok, where the sharp piercing sound is used to complement percussion and piano lines 104 Strange, The Contemporary Violin, 63. 105 Sevsay Ertugrul, The Cambridge Guide to Orchestration (Cambridge, MA: Cambridge University Press, 2013). 60 Figure 5.4: The sideways crescent pictogram in the cello (bottom) line of my composition, Atlantic Opalescence V: Timeless Sea Breeze represents fingernail pizzicato. within the composition.106 This technique can be notated with a pictogram of a fingernail above the note (figure 5.4). Like the buzz pizzicato and Bartok pizzicato among normally bowed notes, single fingernail pizzicati should include a textual instruction — “pizz.” — in order to alert the performer to the change in technique and allow for greater clarity. Fingernail pizzicato, can be performed anywhere on the string, and is sometimes considered more effective for pizzicato sub ponticello, pizzicato sul ponticello, and pizzicato in the peg-box107. Pizzicati with an Implement Sometimes, it is asked for the performer to use an implement to pluck the strings. Most commonly, these include a guitar pick (plectrum), a thimble, and a paper-clip (as is used in Crumb’s Black Angles108). For plectrums, a pictogram (with a definition in the preface material; see figure 5.5) Figure 5.5: A pictogram of a plectrum with an extension line showing a passage utilizing plectrum pizzicato. 106 Strange, The Contemporary Violin, 63-64. 107 Ibid, 66. 108 Crumb, Black Angles. 61 can be used; all other implements require a textual description. Like the other pizzicati mentioned, when this among normally bowed notes, single fingernail pizzicati should include a textual instruction — “pizz.” — in order to alert the performer to the change in technique and allow for greater clarity. Experimentation with the implement will be required to determine if it affects the sound substantially when used on various parts of the string. Slurred Pizzicato Slurred pizzicato is an effect where the first note of the slur is plucked and then a second pitch (or third) is produced by placing the finger and not re-striking the string. This is similar to the guitar techniques known as a hammer-on and pull-off.109 They can be notated using a slur (see figure 5.6)110, and a performance note should be included in the preface material. Slurred pizzicati can follow any of the techniques mentioned above. Figure 5.6: Slurred pizzicato within an extended pizzicato passage in the second movement of my String Quartet No. 1, A Propos of the Wet Snow. Note the asterisk to draw the performer’s attention to a footnote clarifying the intention of the notation. 109 Strange, The Contemporary Violin, 70. 110 Chase Jordan, String Quartet No. 1: A Propos of the Wet Snow (Laramie, WY: Chase Jordan Music, 2018) 62 Figure 5.7: Arpeggiated pizzicato in “Nine Fingers” from Garth Knox’s Viola Spaces. Used with permission of the composer. Figure 5.8: Notation for strummed pizzicato. Notice the arrows above the notes dictating the direction of the strumming. Strumming When writing pizzicato passages, it is possible to strum the stringed instrument like a guitar or banjo. When the instrument is held in the normal position, the bow can still be held in the right hand, and an upward strum with the flesh of the finger and a downward strum with the fingernail is created. When held quasi chitara, both the downward and upward strums can be played with the flesh of the finger. It is important to notate this in a way that makes clear the difference between arpeggiated pizzicato chord (figure 5.7), and strummed chords (figure 5.8), as the player will performed the arpeggiated pizzicato chord with more break between the notes than a strummed chord, where the finger will quickly articulate all four strings. Left Hand Techniques The left hand can activate the string through tapping it or slapping it. Left handed finger taps are very quiet and subtle. Therefore they are best utilized in solo, unision, or amplified contexts. 63 Figure 5.9: Slapping the strings with the left hand in “Nine Fingers” from Garth Knox’s Viola Spaces. Because this slap should dampen the sound, it should be performed at the upper bout of the instrument. Used with permission of the composer. These can be notated with a textual cue: “L.H. tapping”. This is also used extensively to great effect in Jani Christou’s Praxis for 12 in an aleatoric context111. The left hand can also slap the strings. This is most effective at two different locations on the instrument, at the nut, and at the upper bout of the instrument. Slapping the strings at the nut creates a percussive sound with the longer strings sympathetically vibrating a collection of indiscriminate pitches, while slapping at the upper bout creates a sound that is mostly percussive and deadens the whole string. To notate each of these techniques, it is recommended to use x-shaped noteheads on the four open-strings of the instrument with a textual description indicating the action, timbre, and location (see figure 5.9). In addition, pizzicato can be performed with the left hand. This has become standard, especially among violinists, and should be notated with a plus sign (+). A variation of the left-hand pizzicato is the pizzicato fluido that is utilized in the work of Helmut Lachenmann, including his Toccatina for solo violin.112 In this technique the screw of the bow is used to stop the string on the bridge side of the string and the left hand is responsible for plucking the string. The screw of the bow can then be used to create vibrato through vertical 111 Jani Christou, Praxis For 12 (London: Chester Music, 1966). 112 Helmut Lachenmann, Toccatina: Studie für Violine allein (Weisbaden, DE: Breitkopf & Härtel, 1986). 64 Figure 5.10: Garth Knox’s notation of left and right hand pizzicati utilizing numbers enclosed in circles for the right hand and triangles for the left hand, and no enclosure for the fingerings. movement of the string. This should be notated textually — “pizz. fluido” — with an optional depiction of the vibrato graphically. Pizzicato with Multiple Fingers Pizzicato passages in music of the common practice period is decidedly less virtuosic than the complex and virtuosic passagework of passages played with the bow. In order to allow complex passagework in pizzicati, it is possible to have the musician put their bow down, and utilize all fingers of the right hand. Garth Knox has music with this technique, including “Nine Fingers” from Viola Spaces and “Ten Fingers” from Violin Spaces, that utilizes the fingers of the right hand to allow for pizzicato chords to be played non arpeggiato and using multiple fingers to create pizzicato tremolo. In these circumstances, textual directives and the standard notations for arpeggiato, non- arpeggiato, and tremolo will suffice for notation. In most circumstances, dictating which fingers should play each note is unnecessary, but in certain cases it may be useful to provide for editorial purposes or to aid in execution. While Knox uses numbers enclosed a shaped box to differentiate between fingers of the left and right hands113 (see figure 5.10), I recommend repurposing the letters for guitar finger-picking, as these techniques are comparable between instruments and it provides cleaner engraving and clarity of meaning between left hand fingers, right hand fingers, and rehearsal 113 Knox, “Ten Fingers” from. Violin Spaces. 65 numbers, which are often notated as numbers enclosed in a circle or square.114 In addition, utilizing Figure 5.10: Notation for sweeping across the strings. different systems for the two hands provides greater distinction for the brain to parse the information on little practice and rehearsals. Sweeping the String with the Fingers or an Implement Finally, the fingers, fingernails, palm of the hand, or an implement may be used to sweep along the length of the string, similar to the action performed piano in Henry Cowell’s The Banshee. This technique is used in Lachenmann’s Pression for solo cello. Direction should be notated using arrows above the stave for each note, x-shaped noteheads should be utilized to classify the technique as indiscriminately pitched, and a textual description of the implement or part of the hand to be used (see figure 5.11). The arrows should be notated so that they match the relative pitch of the fingerboard the being sweeped towards. Sweeps toward the bridge, should be notated upwards, as the higher notes are towards the bridge Sweeps towards the scroll and nut of the instrument should be notated as downward sweeps, as they move towards the lower tessitura of the instrument. This technique creates very little pitch, but can be effectively used in amplified music or in sections 114 Gould, Behind Bars, 484-86. 66 requiring semi-pitched white noise. Additionally, this effect is more noticeable on larger instruments such as the cello and bass. CHAPTER 6: Un-pitched and Percussive Sounds While stringed instruments are primarily used to create melodic lines and harmonies, there are unpitched and percussive effects can be used both to enhance the sound palette of orchestral compositions and provide new sound groups for expressive and effectual moments in solo and chamber compositions. These techniques as discussed in this chapter will include percussive sounds on the body of the instrument and white noise effects created by bowing on the various non-string parts of the instrument and Krysztof Penderecki uses a multitude of the techniques in this chapter for his composition, Threnody for the Victims of Hiroshima, but these techniques can also be found in the works of Kaija Saariaho and Garth Knox, among others. Muffling Strings An easy way to create unpitched white noise and sound is to muffle the strings with the left hand and then proceed to play with the bow or pizzicato as desired. Each string has its own timbre that is related to the thickness of the string. When playing with the bow, white noise in various timbres is created; with pizzicato, a semi-pitched thudding sound can be created. Additionally, this technique is also useful for drawing out pitches using col legno and the screw of the bow while using vector bowing (see chapter 7). 67 Figure 6.1: Notation for muffling the strings in the indicated locations along with rhythmic and bowing information for the performer.. To muffle the strings, place the fingers at specified locations along the string, using a fast, flautando bow, and using somewhere between normal and harmonic finger weight to stop the string. To notate this effect, utilize x-shaped noteheads to indicate where the fingers should be placed (figure 6.1). If notating the exact fingering is unnecessary, one may use the open strings for the x- shaped noteheads and utilize a textual instruction. Bowing Other Parts of the Instrument Figure 6.2: Bowing different parts of the instrument in “No pitch, no problem,” from Garth Knox’s Violin Spaces. Due to the fact the whole movement is in unhitched and percussive techniques, a percussion clef has been utilized. A variety of white noise effects can be created through bowing various parts of the instrument, namely the scroll, pegs, ribs, tailpiece, bridge, and winding of the string. Bowing the scroll, pegs, and ribs of the instrument are not commonly done and lack a standardized symbology. In most cases a textual instruction is recommended, but in rhythmic passages combining these white 68 noise sounds with other pitched and unpitched sounds, it may be useful to use alternative noteheads for each symbol. Extended passages may be written with a change to percussion clef (figure 6.2). For bowing the ribs of the instrument, I recommend using a half-moon shaped notepad (figure 6.3), as Figure 6.3: Half-moon noteheads are notated on the appropriate side of the staff to represent wether they are played on the rib on the high string or low string side of the instrument. This notation allows for greater clarity in reading music. the similarity in shape between the notepad and the shape of the instruments ribs create an obvious visual link (Garth Knox utilizes this technique in Violin Spaces115; figure 6.2) Additionally, it may be useful to notate wether it is on the high-string or low-string side of the instrument, as Garth Knox does in “Ghosts” from Viola Spaces by placing them on the high string side (above the stave), and low string side (below the stave).116 I recommend removing the ledger lines as well to reduce association with pitch. While the pegs and scroll lack this effective of a visual cue, my notation stretches the obvious but still creates a semiotic link between the notation and the instrument; a sideways triangle notepad can be used for the scroll (one could say that this represents the scroll; figure 6.4) and a circle with a dot notehead can notate the pegs (the circle is the peg box and the dot the peg; 6.5). It will be useful to create a notational cue if these are used in the front matter of the score. With each Figure 6.4: Notation for bowing on the scroll of the instrument, 115 Knox, “No pitch, no problem” from Violin Spaces. 116 ———, “Ghosts” from Viola Spaces. 69 Figure 6.5: Notation for bowing on the peg of the instrument. of these techniques (although due to the shape of the peg it is less effect than that other parts of the instrument), it is possible to create an upwards or downwards “scale” of relative indiscriminate pitches through shortening and lengthening the bow hair willing bouncing the bow, as Garth Knox uses in “No pitch, no problem” from Violin Spaces117. This should be notated with he appropriate symbol for the part of the instrument organized in ascending or descending pitch as appropriate, and staccato dots (to represent spiccato). It may also be useful to specify “middle to tip” for ascending scales and “tip to middle” for descending scales (figure 6.6). Figure 6.6: Notation for bouncing the bow on the rib of the instrument, shortening the bow hair length in order to create a rising scale. Bowing the tailpiece and on the bridge should utilize the symbols common in the music of Krysztof Penderecki (figure 6.7 and 6.8) in his scores such as Threnody for the Victims of Hiroshima118 as attachments to the stems. In addition, when bowing on the bridge, the string to be bowed should 117 ———, “No pitch, no problem” from Violin Spaces. 118 Krysztof Penderecki, Threnody for the Victims of Hiroshima (Boca Raton, FL: Edwin F. Kalmus Editions, 1960). 70 Figure 6.7: Notation for bowing on the bridge of the instrument, utilizing Penderecki’s symbol on the stem. Figure 6.8: Notation for bowing on the bridge, utilizing Penderecki’s symbol on the stem. be indicated. While these symbols are not yet considered standard, the growing number of his works becoming standard repertoire should behoove the composer to utilize his notation where applicable. For bowing the winding of the string, which creates a croaking sound through use of a heavy bow, a modified behind the string notation should be used. Utilize the same behind the bridge stem attachment but the modify the notehead to differentiate - I suggest a square notehead to immitate the overpressure notation due to the heavy bow weight required to produce the effect (figure 6.9). When writing music utilizing these techniques, the composer should be cognizant of providing time to move around the instrument. Bowing the pegs and scroll require approximately two seconds to prepare for normal playing position but can be switched between easily, while bowing the tailpiece requires approximately one second to prepare. Additionally, bowing the ribs, on the bridge, on the winding and normal playing can be easily switched between in a passage. Figure 6.9: Notation for bowing on the winding, combing Penderecki’s symbol for behind the bridge on the stem and the rectangular box for overpressure as the notehead. 71 Percussion on the Body of the Instrument It may be desirable to ask for percussive effects on the body fo the instrument. The notational requirements for this depend upon the complexity of what is being asked. When only a singular percussive sound is required, it is recommend to use ornate x-shaped noteheads on the middle line of the stave to indicate the percussive effect — of which hitting the bout of the instrument is most idiomatic (figure 6.10). When more complex passages of body percussion on the Figure 6.10: Notating slapping the bout of the instrument in the midst of normal playing using ornate x-shaped noteheads. instrument is requested, it is recommended by to utilize a switch to the percussion clef (figure 6.11). This is useful to alerting the player that an extensive section of the music requires percussion on the body of the music, helping them prepare appropriately. A key in the preface material should be Figure 6.11: Notating a passage of percussion utilzing 5 locations on the body of the instrument in percussion clef with ornate, x-shaped noteheads. included. This kind of body percussion is best used on larger instruments such as the cello and bass. due to their larger resonating chambers and larger difference in size of the wooden pieces that make up the instrument. 72 CHAPTER 7: Using Different Parts of the Bow In addition to playing with the hair of the bow (arco) it is sometimes desirable to use other parts of the bow to draw out sounds from the strings to create timbral variation. The use of col legno battuto in Symphonie Fantasique by Hector Berlioz119, and “Jupiter” from Gustav Holst’s The Planets120 are iconic uses of this technique for programmatic and emotive effect in the orchestral repertoire. While this is the most common way the bow is often used in addition to the typical arco playing, composers have several options available to them: col legno battuto, col legno tratto, and “dabbing” with the screw of the bow. Col Legno Battuto A bouncing, off of the string stroke with the wood of the bow is called col legno battuto. This bowstroke is utilized to create a pitched percussive effect like a soft drum. This technique has limited dynamic range, and in symphonic contexts may have trouble competing with other sections of the orchestra. In “Jupiter” from The Planets, Gustav Holst has the strings performing the col legno battuto in rhythmic and octave unison, double by two harps and sometimes timpani in order to allow the sound to balance against brass swells. This careful orchestration can help this technique be heard in these settings. More pitch can be included in the texture through instructing the performer to play with both the stick of the bow and the hair of the bow. This technique is notated 1/2 col lengno battuto. 119 Hector Berlioz, Symphonie Fantastique (Kassel, DE: Barenreiter Urtext, 1971), 120 Gustav Holst, The Planets (Mineola, NY: Dover Publications, 1996). 73 Figure 7.1: Frequently changing timbral effects in my composition for solo cello, Atlantic Opalescence IV: Squall shows the use of abbreviations (in order of appearance) for col legno battuto, 1/2 col legno battuto, molto sul ponticello, and 1/2 col legno tratto. In complex passages with frequent changing of timbral effects (figure 7.1121), both of these effects are often abbreviated. Col legno battuto is abbreviated “c.l.b.” and 1/2 col lengno battuto is abbreviated “1/2 c.l.b.” Each of these effects can be played along the sul tasto — sul ponticello spectrum. Col Legno battuto, sul tasto creates a sound with more pitch compared to less wood noise, while col legno battuto, sul ponticello creates a woodier timbre that includes higher overtones of the string. 121 Chase Jordan, Atlantic Opalescence IV: Squall (Laramie, WY: Chase Jordan Music, 2019). 74 Figure 7.2: Notating dabbing with the screw of the bow. Col Legno Tratto The wood of the bow can also be drawn along the string in a legato fashion similar to the typical arco bowstroke. This technique is utilized frequently in solo and chamber music of the Second Viennese School composers, including Arnold Schoenberg’s String Trio, Op. 45.122 This technique is called col legno tratto and can be utilized in the same methods as col legno tratto. It can be abbreviated “c.l.t.” and “1/2 c.l.t”. Using the Screw of the Bow In Helmut Lachenmann’s Toccatina for solo violin, the performer is instructed to “dab with the screw of the bow.”123 This means that the performer is tapping the strings with the screw of the bow. Lachenmann’s description of the technique is a suitable notation composers to utilize. 122 Arnold Schonberg, String Trio, Op. 45 (Vienna: Universal Editions, 1946). 123 Lachenmann, Toccatina. 75 Extending Col Legno and Dabbing to New Pitched Effects In Toccatina for solo violin, Lachenmann utilizes dabbing on muffled strings to draw out pitches in an extremely high register with a light, percussive timbre. This can technique can be utilized with both dabbing and col legno battuto. For composers utilzing the technique, Lachenmann;s notation can be employed, showing three things — a textual description, a notation of the muted strings, and a notation of the pitches drawn out through the chosen technique (see figure 7.2).124 Chapter 8: Changes in Bow Placement The bow is most often used between the bridge and the fingerboard in the playing of orchestral stringed instruments, but in order to vary the timbral quality composers can ask the player to play in various locations along the string. The most common is the gradients along the sul tasto - sul ponticello spectrum (the spectrum of various contact points between the bridge and along the fingerboard of the instrument, but composers also have access to behind the bridge techniques and the bitone. The Sul Tasto — Sul Ponticello Spectrum The most common changes in bow placement are along the sul tasto — sul ponticello spectrum. This is the range of the string anywhere from the location of the left hand (or nut if it is an open string) and the bridge. In the following section, the various gradients of this spectrum will be discussed, beginning from the hand and moving towards the bridge. 124 Ibid. 76 Technique Name Abbreviation molto sul tasto mST sul tasto ST sul ponticello SP molto sul ponticello mSP Figure 8.1: Abbreviations for the different contact points of the string. The most extreme degree of sul tasto is to play directly next to the fingers. This creates a very airy, somewhat inconsistent sound, similar to that of a bass flute. This can be notated: “at the fingers”, or, on an open string, “at the nut.” This technique works best on the outer strings of the instrument (strings I and IV) due to the lack of curvature in the middle forcing double, triple, and quadruple stops to sound when playing the middle strings. Just past the middle of the string, is where molto sul tasto is played. Molto sul tasto gives the instrument a sound that is limited to lower overtones and is generally gives a softer texture. This technique is limited to strings II, III, & IV of an orchestral stringed instrument as the bout of the instrument is in the way. Sul tasto is playing just over the fingerboard of the instrument. This is a now standard technique that softens the texture and limits the instrument to lower overtones, although being less evident, but still effective compared to molto sul tasto. Sul ponticello is a notation for the player to play near the bridge of the instrument. This technique is also standard, and is used to bring out the higher overtones of a pitch for an cold icy sound. Finally, molto sul ponticello is a more extreme version of sul ponticello, bringing out more high overtones to distort the sound. 77 These techniques are most easily notated using the textual instructions provided or with abbreviations. Composers such as Andrew Norman have notated these gradients numerically using notations such as “s.p.1”, and “s.p.2”.125 Instead, it is clearer to use abbreviations for the text in notation with limited horizontal space according to table 8.1. These abbreviations are closer to the original textual instruction making their meaning immediately clearer. When gradually changing between these gradients, it is useful to utilize arrows between the two limits of the transition (figure 8.2). Figure 8.2: Changing between various contact points in quick succession in my composition, Atlantic Opalescence IV: Squall for solo cello. Changes are shown using abbreviations and arrows. Possibly the most interesting piece in terms of utilizing this spectrum of techniques is Eric Funk’s Concerto for the Violin Alone, where Funk asks the soloist to also be the orchestra, utilizing different contact points to great exactitude to emulate the various instruments of the orchestra: horns, flutes, clarinets, oboes, trumpets, and timpani.126 While this piece does not scream extended techniques to the listener, the subtle changes in texture show a beauty that can be achieved through deft control of this technique. Sub Ponticello Sub ponticello is the technique of bowing behind the bridge. This technique allows the creation of an indiscriminately pitched sounds that are of a high pitch with a bright piercing quality. 125 Andrew Norman, Sabina (New York: Edition Schott, 2008). 126 Eric Funk, “The Violin Alone: One Man Becomes an Orchestra,’ filmed March 22nd, 2013 in Bozeman, MT, TEDx Talks. 78 Figure 8.3: Arco sub ponticello sustained strokes in the first violin and viola parts of my composition for string orchestra, percussion, and piano, White Rim. Different pitches are available through the use of different strings. This should be notated using the symbol from Krysztof Penderecki’s Threnody for the Victims of Hiroshima attached to the stem of the note.127 The note-head should be x-shaped and indicate which string (using the open string pitch) should be played (figure 8.3). The symbol attached to the stem works exceptionally well, as the curve mimics the curve of the bridge, alerting the player to the fact that this is the region of the instrument upon which the technical change is occurring.128 This technique is effective using both arco and pizzicato techniques. It is considered by some musicians more effective to do a fingernail pizzicato as opposed to plucking with the flesh of the 127 Penderecki, Threnody. 128 Gould, Behind Bars, 408. 79 finger.129 Additionally, a vertical stroke (see chapter 10) can be used to create a low, percussive thud, similar to a bass drum, as Garth Knox does in “Up, Down, Sideways, Round” from Viola Spaces.130 Bi-Tones Another technique for timbral changes of notes is the bitone, where the performer plays the string in whichever manner the composer indicates on the other side of the hand. This is more effective on the cello and bass, due to their longer strings making a larger vibrating space between Figure 8.4: Bi-tone notation in the viola III part of my composition, Lunar Harmonies. The top stave represents both the fingered and sounding pitch (as they are the same in this case), while the bottom stave, in bridge clef notates the left hand position (diamond notehead) and relative bow position (triangular notehead in this instance) the fingerboard and the string in the upper half of the string. This can be notated two ways. First, it can be notated using a textual instruction along with the resultant pitch. Second, a more complex notation can be used in music that uses vector bowing or requires extensive use of the bridge clef for consistency (see chapter 10). This notation requires two pieces of information: (1) the resultant pitch (in the appropriate clef for the instrument and tessitura), and (2) location of the left hand in comparison to the bow and instrument’s body, notated using the bridge clef (see figure 8.4). 129 Strange, The Contemporary Violin, 66. 130 Knox, “Up, Down, Sideways, Round” from Viola Spaces. 80 Figure 9.1: Notation of spazzolare utilizing arrows notating the direction of the brushing motion along the strings. Used with permission of the composer. CHAPTER 9: Changes in Bowing Patterns In the music of Garth Knox, Salvatore Sciarrino, Hannah Rice, Helmut Lachenmann, myself, and other composers, there is a selection of repertoire that is growing in complexity of bow use - specifically in the directional field of how the bow is used. Garth Knox, in his Viola Spaces, names the movement exploring these variations in bowing techniques “Up, Down, Sideways, Round.”131 In this chapter, these techniques and their notations will be explored. Figure 9.2: Notation of spazzolare utilizing a dynamic and the “in energy” marking in “Up, Down, Sideways, Round” from Viola Spaces by Garth Knox. Used with permission of the composer 131 Ibid. 81 Figure 9.3: Vector bowing notation for spazzolare using bridge clef. This notation is utilized in the music of Helmut Lachenmann. Spazzolare Spazzolare is an Italian word meaning, “to brush.”132 It is used to create semi-pitched white noise that is derived from the overtones isolated by wiping horizontally along the length of the string.133 The third movement of Salvatore Sciarrino’s Tre Notturni Brilliante for solo viola134 and Sei Capricci135 for solo violin, Garth Knox’s Satellites for string quartet136 (where he calls it spazzolato), and my composition Downtown Dichotomy for viola and piano137 make use of this technique. This can be notated using a textual instruction, and arrows showing the direction of the wiping are beneficial (figure 9.1). Additionally, tremolo notation and a dynamic indication can be used to notate free spazzolare, where the speed is decided on by the player to match the intention of the notated dynamic. Dynamic markings of this technique can optionally be marked, “in the energy of [dynamic]”, as this tech (figure 9.2). In music requiring significant amounts of vector bowing, it 132 Ibid. 133 Benjamin Sung, The Sei Capricci of Salvatore Sciarrino: Technique and Style, Florida State University. 134 Sciarrino, Tre Notturni Brilliante. 135 Salvatore Sciarrino, Sei Capricci (Milano, It: Riccordi, 1976). 136 Knox, Satellites. 137 Jordan, Downtown Dichotomy. 82 may be notate with an additional bridge clef, as Helmut Lachenmann does in his Tocattina for solo violin (figure 9.3). Spazzolare can be isolated into singular motions away or towards the bridge. These are notated using the same directional arrows as in figure 9.1. In his Violin Spaces, Garth Knox utilizes this technique, in combination with overpressure, to create frog-like sounds.138 These are notated with the descriptive text, the directional notation, and an overpressure wedge (see chapter 10). Circular Bowing Circular bowing is a similar technique to spazzolare that describes the combination of lateral bow movement between the tip and the frog and horizontal movement of the point of contact between the bridge and fingerboard. This technique shows up in the music of Garth Knox, Chase Jordan, and Paul Chiharra. This technique creates a similar, but richer effect to spazzolare with brief moments where the fingered pitches are exposed through the texture. This technique can be notated Figure 9.4: Notation of circular bowing in Garth Knox’s Sattelites, for String Quartet. Used with permission of the composer. 138 Knox, “No pitch, no problem” from Violin Spaces. 83 Figure 9.5: Notation utilizing bridge clef to show irregular spazzolare. using a textual instruction, or a line showing a circular motion (figure 9.4). Additionally, tremolo notation and a dynamic indication can be used to notate free circular bowing, where the speed is decided on by the player to match the intention of the notated dynamic. This dynamic marking can be marked, “in the energy of [dynamic],” just as the similar effect of spazzolare is notated. Circular bowing can also be notated in bridge clef to show irregular length of various parts of the circle (see vector bowing). Helicopter Effect The helicopter effect is a variation on spazzolare and circular bowing done at the frog of the bow. It requires additional overpressure of the string to create a noisy sound. It should be notated as “helicopter” to provide an aural description as well as name of the technique. Vector Bowing Vectors are lines that have both direction and duration. This can be applied to the playing of orchestral stringed instruments through the multitude of angles and direction the bow can be drawn across the string over a period of time. This is a sort of catch all category for bow strokes that 84 require detailed notations showing the angle and change of the bow’s point of contact on the string. In general, lateral bow movement is notated as rhythmic duration and horizontal bow movement is shown in bridge clef. A few primary examples will be provided below. The first use of this notational technique is for irregular spazzolare where the horizontal motions are not equal in horizontal length, durational length, or are in different parts of the string. This creates more variation in timbre, with more overtones being brought out on longer, faster horizontal motions closer to the bridge. Notice in figure 9.5 how the notation utilizes the bridge clef to illustrate the various locations on the string. The second primary use of this technique is for irregular circular bowing, where the speed of the lateral and horizontal motions are not in sync, creating ovular, figure eight, and other shapes in the bow changing the way overtones pop out. Notice in figure 9.6 how the rhythmic and horizontal motions are not of the same duration (2 horizontal cycles for each lateral cycle) to create a figure-8 shape in the bow. Figure 9.6: Notation using bridge clef to show a figure-8 shaped vector bowing. The final primary use of this technique is to create changing high pitches indiscriminately when using col legno battuto or dabbing with the screw of the bow techniques. Michael Seltenreich uses this in his compositions Pardés, for chamber orchestra (figure 9.7)139 and I utilize this in my 139 Michael Seltenreich, Pardés (New York: Emblem Scores, 2019). 85 Figure 9.7: Use of bridge clef to show indiscriminately pitched high notes brought out through changing the contact point of col legno battuto hits on the string in the contrabass part of Pardés, by Michael Seltenreich, Used with permission of the composer. Figure 9.8 - Bridge clef utilized in my composition, Lunar Harmonies to notate col legno battuto jete combined with vector bowing in the viola I, II, and III parts. work for string orchestra, Lunar Harmonies (figure 9.8). In Lunar Harmonies140, a downward pointing triangular notehead is used to signify as close to the end of the fingerboard (nut) as possible. This marking is accompanied by text for clarity. Vertical Bowing Vertical bowing is a type of thrown bow stroke where the bow bounces up and down at the tip. This is a softer technique in volume and does not project well, but can create a “short,bright 140 Chase Jordan, Lunar Harmonies, unpublished composer computer manuscript. 86 sound”, as Garth Knox describes in his performance notes for Viola Spaces.141 This can be notated using a textual instruction. A variation of this technique is the pan-pipe effect that Garth Knox also utilizes in “Up, Down, Sideways, Round” from Viola Spaces. This is similar to the vertical stroke, but is performed sul ponticello with a slight lateral motion, to imitate the sound of the panpipes.142 This can be notated using Garth Knox’s name for the technique. Jeté and Balzando Jeté and Balzando are two variations of thrown bow strokes, both literally meaning to leap. Jeté makes use of a lateral movement of the bow during the bounce, while balzando makes use of only a vertical bounce. The primary difference is in sound volume and the duration the effect can be sustained. Balzando is significantly shorter and quieter than jeté and there is significantly less control in the rhythmic shape of the gesture. While jeté can be controlled to the point that some rhythmic Figure 9.9 - A passage showing the similarities in notation between unmetered jeté and balzando. shape can be notated, balzando has a singular shape where the successive strikes of the bow accelerate. Because of this limited control, it is redundant to notate the shape of balzando, and for notation similar that to an unmetered jeté and balzando should share a notational symbol, with the appropriate technique text provided (figure 9.9). Metered jeté on the other hand requires only a textual instruction, with the notes to be included in the stroke under a slur with staccato dots. 141 Knox, “Up, Down, Sideways, Round” from Viola Spaces. 142 Ibid. 87 Figure 9.10: Notation of the bow whip technique at the end of Garth Knox’s Satellites for String Quartet. Used with permission of the composer. Jete is used in the second movement of my string quartet and in “Up, Down, Sideways, Round,” from Garth Knox’s Viola Spaces with good effect (although Knox calls it a synonymous gettato). Musical examples of balzando are best found in Helmut Lachenmann’s Gran Torso143 and Ryan Carter’s impaired contact with reality144. Split-Tone The split-tone is produced by a thrown a thrown bow stroke near the bridge of instrument that isolates higer overtones. It is not possible to isolate specific overtones consistently using this technique but it can be used on different open strings to create a variety of timbres. This technique is notated using a textual instruction, as Garth Knox uses in Violin Spaces.145 143 Helmut Lachenmann, Gran Torso for String Quartet (Weisbaden, DE: Breitkopf & Härtel, 1980). 144 Ryan Carter, impaired visual contact with reality (Ryan Carter Music, 2010). 145 Knox, “Up Above Our Heads,” from Violin Spaces. 88 Bow Whip The bow whip is a non-pitched technique that is created through forcibly whipping the bow through the air, creating sound as the air is forces between the hairs of the bow. This technique is used in Garth Knox’s Violin Spaces146 and his Satellites for String Quartet.147 Because this technique occurs away from the instrument a new notehead should be devised. I suggest Garth Knox’s notation in his string quartet, Satellites: using a pictogram of a bow along with an notehead that looks similar to the accent (figure 9.10). Chapter 10: Changes in Bow Pressure This final variable covered in this text that can be controlled by composers is the change of bow pressure. In additional to utilizing the normal bow weight, orchestral string instruments have different timbres depending on if too little (flautando) or too much (overpressure, ponitcello pressato, two-handed bow technique) pressure is exerted through the bow into the string. Flautando Flautando is a flute-like timbral hollering of the sound created through using a fast bow with not enough pressure. This can be notated using text. The technique is most idiomatic at softer dynamics. 146 Knox, “Rick O’Shea,” from Violin Spaces. 147 Knox, Satellites. 89 Overpressure Figure 10.1: Gradual increase in bow pressure notated through an overpressure wedge in the cello part of my composition Atlantic Opalescence V, for cello and hammered dulcimer. Overpressure is a technique where too much pressure is exerted through the bow on the string distorting the sound and creating a scratchy block of semi-pitched noise. This is most often used in two ways: first, by gradually increasing or decreasing the pressure over the course of a bow or a series of bows; and second, by immediately applying (or continuing) and sustaining pressure. Notate gradual changes with thick wedges above the stave (figure 10.1), as Andrew Norman does in Sabina148 and I do in Atlantic Opalescence V: Timeless Sea Breeze.149 This notation is also common in the music of Kaija Saariaho and Gérard Grisey, two notable spectralist composers.150 To notate the Figure 10.2: Utilization of overpressure boxes to notate sudden overpressure in Hannah Rice’s Fusion for solo viola. Used with permission of the composer. 148 Norman, Sabina. 149 Jordan, Atlantic Opalescence V: Timeless Sea Breeze. 150 Knox, Stretching the String, 33. 90 sudden application of overpressure, utilize thick, black, rectangular boxes (figure 10.2) as Hannah Rice notates the effect in Fusion.151 These notations are effective due to the intuitive link between the thick boxes and wedges and exerting more pressure on the string in relation to the thickness of the box. On the cello, overpressure can also be performed through the use of two hands on the bow. This two-handed bow technique is utilized in Helmut Lachenmann’s Pression and can only be used on the four open strings.152 This can be notated through a textual instruction. The advantage to this over normal overpressure technique is that more pressure can be exerted, and more consistent pressure can be exerted when being combined with vector bowing (see chapter 9). Ponticello pressato A variation of the overpressure technique is to utilize the overpressure while play molto sul ponitcello. This creates a thick distortion of sound including a cluster of higher overtones when compared to a typical overpressure technique. This can be notated in the exact same way as overpressure, but with a textual instruction clarifying the meaning (figure 10.3), as Garth Knox does in Violin Spaces.153 Figure 10.3: Wedge notation with a textual instruction, “pont. pressato” in Garth Knox’s “Skating” from Violin Spaces to signify the technique in a similar but distinguishable way from overpressure. 151 Hannah Rice, Fusion (Hannah Rice Music, 2019). 152 Helmut Lachenmann, Pression (Weisbaden: Breitkopf & Härtel, 2010). 153 Knox, “Skating” from Violin Spaeces. 91 Conclusion Through the course of this text, I have selected a large portion of contemporary techniques to document through their usefulness in musical composition, historical importance, and my personal experience performing the techniques and composing with the techniques. Through these experiences of performance and working with professional and student performers, I have developed an idea of what works, and what does less so. The research of this project began with an extensive review of the string solo, chamber, and orchestral genres. This revealed two underlying struggles for performers wishing to tackle contemporary scores, namely: 1. Multiple notations for the same effect. This was most prolific in the realm of microtonality, where it is easily possible to program a concert of quarter-tone music and be subject to four notations on a four composition program. 2. Standard notations being given multiple, non-standard meanings across the spectrum of repertoire. This creates the possibility that a notation is used for three different techniques across the repertoire of a musicians folder. Ultimately this led me to begin development of a comprehensive notational system for extended techniques and contemporary practices on orchestral stringed instruments. I have prioritized leaving standard notations as maintaining their standard, singular meaning. When at all possible, new notations are developed, instead music of the standard repertoire and music of immense historical importance. In order to maximize clarity, maintaining parallels between staff notation and the physical exercise that create sound with the instrument have been considered so that the notations are not only idiomatic to music notation as we know it, but also to the physical 92 efforts required to play an orchestral stringed instrument.Text, in order to reduce clutter on the page, has been kept to a minimum instead proposing a series of noteheads, stem attachments, multi- and single-segment lines, and graphics above the stave to clearly denote the selection of contemporary techniques and practices of the orchestral string family. Text is often used supplementally. The techniques covered in this text can be viewed as building blocks. Most of the techniques are not mutually exclusive to each other, and are noted where combinations are ineffective. This allows techniques to be combined for further expansions of sound, timbre, and pitch exploration on the instruments while still following the notational principals laid out above. This text will ultimately be given its meaning through the use of its principals. My catalogue of string compositions makes use of a large quantity of these techniques, and has been performed and scheduled across the United States and Denmark as of May 2020, including on performances at the New York Viola Society, and Charlotte New Music Festival. Ultimately, I hope it at least adds to the discussion to move towards addressing the need for a consistent and streamlined notation for contemporary string techniques. By streamlining the notation, a wall of understanding can be broken down between performer and composer, allowing for more performers and audience members to access new compositions that utilize these techniques. 
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