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OF NEON LIGHT: MULTIPHONIC AGGREGATES ON THE ELECTRIC GUITAR

Published online by Cambridge University Press:  19 December 2019

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Abstract

Considerable research has been made into the harmonic properties and playability of woodwind multiphonics, while the utility of string multiphonics has received far less attention. In recent years, however, there has been an increasing amount of interest in the topic, and several publications have been devoted to acoustic guitar multiphonics. Primarily written for non-guitarist composers, these studies range from the scientific to the practical. Variously, they describe the sonic qualities of the multiphonics, discuss methods of performing them, or examine their spectral content and morphology. Until now, published research into guitar multiphonics has been limited to the acoustic guitar and has examined only its three lower strings. In this study, we analyse multiphonics on all six strings of the electric guitar and present a catalogue of harmonic aggregates on strings 3–1. We test these multiphonics on five different guitars and examine their response to three commonly used analogue effect pedals (compression, overdrive and distortion). In order to precisely indicate the spectral components and harmonic nodes, we have used the Extended Helmholtz-Ellis JI Pitch Notation (HEJI).

Type
RESEARCH ARTICLE
Copyright
Copyright © Cambridge University Press 2019

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1. Introduction

Compared to the extensive efforts devoted to cataloguing woodwind multiphonics, as well as their frequent use in art music of the present day, far less has been explored in the world of string multiphonics. As with woodwind multiphonics, these sonorities are fragile and temperamental, requiring a specialised technique on the part of the performer. Though any string player may unwittingly produce them in the sweep of a harmonic glissando, it is a different matter to elicit them individually, selecting precisely which partials to emphasise in the harmonic aggregate. In order to do so a more studied approach has to be taken, and a reliable body of knowledge among string players will have to be developed. Previous research has established a reliable catalogue of multiphonics on strings 6–4 of the acoustic guitar, but has left unexamined the upper strings and the immense potential of the electric guitar in performing these sonorities.

In the present study we examine multiphonics on all six strings of the electric guitar and propose a catalogue of performable aggregates on strings 3–1. We have adopted the Helmholtz-Ellis JI Pitch Notation in order to indicate the nodal positions and spectral components with extreme precision.Footnote 1 We have also drawn upon the mathematical model known as the Farey sequence, in order to demonstrate its practicality in performing and composing with string multiphonics. Through spectral analysis we compare the acoustic behaviour of these multiphonics on all six strings, across five different electric guitars. We also use spectrograms to compare the influence of various effect pedals (compression, overdrive and distortion) and the efficacy of two corollary finger positions (one closer to the bridge and one closer to the nut). The discussion also addresses practical aspects of performing these multiphonics, as well as their possible uses in composition.

Existing Literature

Acoustic Guitar

The first mention of guitar multiphonics comes from John Schneider, in his book The Contemporary Guitar (1985).Footnote 2 Using a map of the fretboard, Schneider plotted out a select group of multiphonic stopped positions on strings 6–4 and notated their corresponding pitch aggregates on the staff. More recently Josel and Tsao extended this research in The Techniques of Guitar Playing (2014), a book also intended as a guide for composers.Footnote 3 In a lengthy section devoted to acoustic guitar multiphonics, the authors present a map of the fretboard as well as staff notation and considerably extend Schneider's catalogue of performable aggregates on strings 6–4. Another important study is the PhD dissertation of Rita Torres, devoted entirely to multiphonics on the acoustic guitar.Footnote 4 With her background in composition as well as physics and engineering, Torres has applied a wealth of scientific training in this thorough and exacting analysis. Though she explores the multiphonic potential of the low E-string (positing a total of 88 touch points), Torres does not examine any of the other strings, leaving open the question of how these multiphonics would sound in the higher register. A study from 2014 by Martin L. Vishnick explores a wide range of extended techniques for the acoustic guitar and includes a section on multiphonics for strings 6–4. Rather than attempting to expand the existing catalogue, Vishnick focuses on aggregates already established, and he proposes a number of technical exercises for learning to perform them.Footnote 5

Electric Guitar

Until now there has been no published research focusing specifically on electric guitar multiphonics. A number of studies have emerged which discuss related factors, such as the overtone response of the open strings,Footnote 6 or how various kinds of tone wood influence harmonic resonance, but the scope of these studies has been much broader.Footnote 7 Two recent contributions by Jan-Peter Herbst closely examine the effects of distortion on commonly used stopped chords in rock music (major and minor triads, as well as power chords), and use spectrograms to analyse their overtone structure.Footnote 8 However, the performance of harmonics, not to mention multiphonic aggregates, is well outside the purview of either study. Given the recent interest directed toward multiphonics on the acoustic guitar, an equally close examination of the electric guitar's capabilities is warranted. With its much greater power and resonance, the electric guitar is by far the more potent vehicle for conveying the harmonic structure of multiphonics. The results presented in this study are intended not only for the edification of theoreticians, but even more as a practical guide for composers and performers.

2. Characteristics of an Electric Guitar Multiphonic

Unlike acoustic guitar multiphonics, which have a subdued, often brittle tone, those on the electric guitar have much greater sustain, harmonic colour and clarity. In spectral analyses of acoustic guitar multiphonics we see a rapid decay of the higher partials and a generally less-saturated harmonic spectrum.Footnote 9 On the electric guitar the spectral array is much fuller and livelier, with the partials glinting and buzzing long after the attack (see Figures 2 and 3 for spectral comparisons). The distinction is as vivid as that between pastel and neon.

Composing with acoustic guitar multiphonics can yield convincing results, but, given their subtlety, they are best suited to intimate performance settings, with close amplification or a considerable amount of natural resonance. Even in these cases, however, the sound can only be amplified to a certain limit without inducing the risk of unwanted feedback. On the electric guitar this restriction does not exist, and decibels can safely be raised to whatever level is desired. Also, with the arsenal of effects that can be applied to an electric guitar, it becomes possible to morph and enhance the harmonic spectrum of a multiphonic, emphasising particular frequency ranges or adding sustain. Effects such as compression, overdrive and distortion are perennial to the sound and appeal of the electric guitar, and they are aptly applied to multiphonic sonorities. (For a thorough discussion of effect pedals, please refer to section 9, below.)

Finally, of particular importance to the present study, are the resonant steel strings of the electric guitar's upper register, which facilitate multiphonics on strings 3–1. Unlike the nylon strings of the acoustic guitar's upper range, these robust steel strings are resonant enough to allow tiny high-range multiphonics to glisten with clarity. (For a catalogue of multiphonics on strings 3–1, please refer to section 7 below.)

Spectral Comparison Between Acoustic and Electric Guitars

Figure 1 shows staff notation for multiphonics VI+17 (on string 6) and X−4 (on string 4), and Figures 2 and 3 show a spectral comparison of these aggregates, as performed on both the acoustic and electric guitar.Footnote 10 We have used Spear for all spectral analysis in this article. The frequency in Hz is shown on the Y-axis and the duration in seconds is on the X-axis. Relative darkness of the lines indicates amplitude.

Figure 1a: Multiphonic VI+17 notated on string 6.

Figure 1b: Multiphonic X−4 notated on string 4.

The images hardly require summary: it is clear that the sustain and amplitude are significantly greater on the electric guitar. Comparing the spectrograms on string 6 (see Figure 2) we can see how the intonation above the 10th harmonic (ca. 830 Hz) is comparatively erratic on the electric guitar, which contributes perhaps to the ‘fuzzier’ sound of its multiphonics. Also note the swelling of amplitude which is clearly pronounced in the 3rd partial (ca. 247 Hz) of the electric guitar (see Figure 2b).

Figure 2a: Spectrogram of multiphonic VI+17 performed on string 6 of acoustic guitar (82.41 Hz)Footnote 11

Figure 2b: Spectrogram of multiphonic VI+17 performed on string 6 of the Parker electric guitar (82.41 Hz)Footnote 12

A Notable Anomaly

Spectral analysis of string resonance reveals a slight warping of the intonation just after the string has been forcefully stimulated. This occurs both in the case of plucking the strings or bowing them. Following the attack, or after the string is no longer being stimulated, this fluctuation settles down gradually but continues throughout the duration of the resonance. In our analysis of the multiphonics in this study we found that the partials most susceptible to this effect are the fundamental and 2nd harmonic. This slight wavering behaviour does not give the impression of inharmonicity, but contributes, perhaps, to the ‘fuzzy’ or ‘dirty’ character of some multiphonics.

3. The Farey Sequence

For composers and performers interested in working with string multiphonics it is useful to understand some of the underlying physics. Unlike the case of single harmonics, where a discrete pitch is sounded by lightly touching a specific node, multiphonics are produced when the finger activates several neighbouring nodes, sounding an array of harmonic partials. Because the entire string length traverses harmonic nodes of varying sensitivity, producing specific multiphonics is a very delicate matter, and minute changes in finger position may have a great effect on the resulting pitch aggregate.

The pattern in which harmonic nodes are distributed along the string length is described by a mathematical model known as the Farey sequence.Footnote 13 For any two harmonic nodes (known as a ‘Farey pair’) the touch point at the so-called ‘mediant’ of their respective string lengths will produce the sum tone of the pair's respective partial numbers. For example, a touchpoint which activates the 11th partial will be located between nodes for the 5th and 6th partials. Likewise, the 17th partial can be activated by touching between the 6th and 11th nodes, and so on. (Figure 4 demonstrates this using staff notation.)

Figure 3a: Spectrogram of multiphonic X−4 performed on string 4 of acoustic guitar (146.83 Hz)

Figure 3b: Spectrogram of multiphonic X−4 performed on string 4 of the Les Paul electric guitar (146.83 Hz)

Figure 4: Farey sequence chart for low E-string

Understanding the Farey sequence is useful for performers because it provides them with a simple method for mapping harmonic touch points. When playing multiphonics it is of even greater practical value, as the performer must negotiate a balance between multiple partials at once. The Farey sequence is also useful for composers working with multiphonics, as it suggests complementary pitches for harmonisation. For example, a composer can ‘colour in’ or extend a multiphonic aggregate by having other instruments strengthen or sustain complementary pitches. (For more information about the factors involved in performing multiphonics, please refer to section 6 below.)

A Map of Playable Nodes

Figure 4 shows a sequence of 41 harmonic nodes between 1/3 and 2/3, symmetric around 1/2. These touch points are notated on the low E-string of the guitar, with distances from the bridge measured in millimetres (as performed on a string of scale length 635 mm, or 25 in). Harmonics up to the 19th are indicated using Helmholtz-Ellis JI Pitch Notation. Melodic ratios in italics denote the microtonal intervals between successive nodes, and the fractions in boxes represent the distance along the string length. Cent deviations from equal temperament are shown next to the finger placements.

4. Instruments and Gear

The five guitars used in this study were selected from Josel's personal collection for their variety in tone quality, build and playability. Given their wide variety of features, these instruments provide a fairly representative sample of today's electric guitar craftsmanship (see Table 1). However, despite this range of attributes, the group is not entirely comprehensive in its coverage of popular designs. Notable absences include a hollow-body arch-top guitar, typical in jazz performance,Footnote 14 a semi-hollow guitar, typical in blues and jazz rock, and a guitar with extended tail piece (i.e. with strings attached to the body several inches below the bridge), such as the Fender Jazzmaster.

Table 1: Complete list of specifications for the five guitars.

Strings

  • D'Addario XL 110–3D were used for the Legacy, ASAT and Parker

  • Pyramid 010–046 for the Les Paul

  • Zachary Optimum Gauge 10+ RWs for the Zachary

Plectrum

In our search for the ideal plectrum we experimented with dozens of different models ranging, in shape, size and material. After testing some made of plastic, celluloid, nylon, metal, tortex and bone, we finally selected a wooden one, made of Padauk and African Ebony.Footnote 15 With its relatively heavy gauge, this plectrum induces a crisp and clear response.

Spectral Comparisons

In order to show the response of a single touch point on all five guitars, we present spectrograms for multiphonic III+47, as performed on the 4th string. Figure 5 shows staff notation for this aggregate and Figure 6 displays the spectrograms for each of the five guitars.

Figure 5: Multiphonic III+47 notated on string 4.

Figure 6: Spectrogram of Multiphonic III+47 performed on string 4 of all guitars (146.83 Hz)

As we can see, harmonics 5 (ca. 734 Hz), 6 (ca. 881 Hz) and 11 (ca. 1619 Hz) sound prominently on all five instruments, varying somewhat in sustain and amplitude.

5. Recording conditions

For the warmth of its tone production, a fine tube amplifier would have been our aesthetic preference in making these recordings. However, as our primary concern was to produce a clean, unmediated signal for the purpose of analysis, we recorded the guitars ‘direct-in’ to a preamp. In section 9, we discuss how analogue effect pedals can be used to enhance and modify the harmonic make-up of a multiphonic structure. Apart from a few minor exceptions (see below), bridge pickups were used for all recordings, as they are punchier and allow the higher harmonics to sound at a greater amplitude than the fundamental. The volume potentiometers were set to maximum, and the tone controls were at the brightest setting.

All recordings were made at the Universität der Künste Berlin, Altbaustudio, on 23, 24 and 31 March 2019, with engineer Ole Jana, using the set-ups shown below:

DI Box: Behringer Ultra-DI DI100

Preamp: Merging Technologies Horus

Recording Software: Sequoia 14

Guitars:

  1. 1) Parker Fly Deluxe

    −20 dB pad (DI)

  2. 2) Gibson Les Paul

    −20 dB pad

  3. 3) G&L Legacy

    no pad

  4. 4) G&L ASAT

    Bass strings: −20 dB pad

    Treble strings: no pad

    Bridge pickup for strings 3 and 2, middle pickup for string 1.

  5. 5) Zachary

    Multiphonics on all single strings (I – VI): no pad

    Dyads: −20 dB pad

    Humbucker pickup for strings 6–2, single coil for string 1

The guitars were tuned to 440 Hz. Audio samples were normalized for volume.

6. Performance Techniques

Some previous guitar studies have been conducted in highly controlled settings with the instruments mounted on a frame and the plucking actions executed mechanically.Footnote 16 As these experiments only examined properties of the open strings and did not involve a specialised performance technique, a uniform method was justified.Footnote 17 However, given the complex nature of performing multiphonics, with the variability in touch required for each position and the delicate synchronicity which must be achieved between the hands, our task could not be relegated to a mechanical device. As it is our intention to present results that will be of practical use to musicians, all of the multiphonics in this study have been performed by a single human player.

Plucking

For all recordings the strings were plucked molto sul ponticello, in order to allow the higher harmonics to speak with greater clarity. Josel adopted a plucking technique similar to an apoyando stroke, where the plectrum comes to rest on the adjacent string. In order to create a richer response, the plectrum was angled slightly toward the bridge.Footnote 18

Left Hand

Josel adopted an unorthodox position of the left hand for this study. Instead of supporting the guitar from behind the neck, in the usual manner, he brought his thumb around the neck and held it adjacent to his index finger in a relaxed position. Josel's left wrist was bent a few degrees inward to his body, enabling him to angle his little finger at the stopped position very slightly. Thus he was able to reduce the amount of skin making contact with the string, allowing him a greater degree of precision.

7. Multiphonic Aggregates on Strings 3–1

Extending the efforts made by Josel and Tsao, we have endeavoured to make a catalogue of well-sounding aggregates on strings 3–1. These sonorities, which hardly speak in the nylon upper register of the acoustic instrument, become more audible when amplified on resonant steel strings.Footnote 19 With a very careful little finger, tiny but glistening multiphonic sounds may be drawn from these upper strata. The task is more difficult, however, than on the lower strings, as the performer will have to substantially minimise the amount of skin contacting the string and more fleetingly remove the finger from the touch point.

Despite the greater difficulty of finding reliable multiphonics in this register, we have given special attention to the following aggregates for their relative ease of execution and particular clarity. Figure 10 shows spectrograms for multiphonic IX+33, as recorded on strings 3–1 of the G&L ASAT.

Figure 7: Multiphonics notated on string 3

Figure 8: Multiphonics notated on string 2

Figure 9: Multiphonics notated on string 1

Figure 10a: Spectrogram of multiphonic IX+33 performed on string 3 of G&L ASAT (196.00 Hz)

Figure 10b: Spectrogram of multiphonic IX+33 performed on string 2 of G&L ASAT (246.94 Hz)

Figure 10c: Spectrogram of multiphonic IX+33 performed on string 1 of G&L ASAT (329.63 Hz)

Progressing from string 3 to 1 we see how the spectral array becomes more delicate. The concentration of partials around the attack denotes the relative prominence of the pluck sound, which is especially percussive in this register. In these data a shift in balance occurs between the amplitudes of the most audible harmonics: on string 3 the 12th partial (ca. 2373 Hz) is approximately equal in amplitude, if not slightly weaker, than the 5th and 6th, whereas on strings 2 and 1 it has the greatest amplitude in the spectrum.

8. Corollaries

All of the multiphonics presented thus far have been produced in positions below the 12th fret. Performing them here is a natural choice as the lower stopped positions allow a greater portion of the string to resonate freely. However, we decided to also record multiphonics in their corollary positions close to the bridge to see how the results would compare sonically. Being able to play a particular multiphonic in two different positions could be advantageous to a performer, so it is useful to know if and how the sounds may differ.

From our own aural evaluation of multiphonic VIII+41, along with its corollary, XVI+54, we found that there is a very subtly audible difference between the two positions, with the lower one yielding a slightly richer sound. However, as we can see from the spectrograms in Figure 12, this difference is so minute as to be nearly indistinguishable. Therefore, the two positions can be used interchangeably.

Figure 11: Multiphonic VIII+41 and corollary XVI+54, notated on string 5

Figure 12a: Spectrogram for multiphonic VIII+41, performed on string 5 of the Zachary (110.00 Hz)

Figure 12b: Spectrogram for multiphonic XVI+54, performed on string 5 of the Zachary (110.00 Hz)

9. Effect Pedals

With the variety of specialised equipment needed to set up an electric guitar rig, performers have a great many parameters in which to define their personal sound. Aside from the crucial choice of instrument, there are also the amplifiers, pickups, cables, strings and pedals, all of which combine in the Gestalt of a musical performance. Given the popularity of compression, overdrive and distortion among electric guitarists, we decided to see how these effects would influence the sonic profile of a multiphonic. We selected a single aggregate (VI+17) and subjected it to three different sets of variables.

Procedure

In Set (1) multiphonic VI+17 was performed on the low E-string of three different guitars: Legacy, ASAT and Les Paul.Footnote 20 Here the comparison was between (a) clean signal, and (b) distortion.Footnote 21 In Set (2) multiphonic VI+17 was again examined, now only on the low E-string of the Les Paul. This time we compared (a) clean signal with two new conditions: (c) compression and (d) compression + overdrive. In Set (3) multiphonic VI+17 was performed on the G-string of the Zachary. Here, (a) clean signal was compared with (c) compression, and (d) compression + overdrive. (Spectrograms for each set of comparisons are shown in Figures 1315.)

Description of Effects

Compression

Typically, compression is used to provide clean sustain, with the note attenuated at the outset and the gain gradually increased as the note decays. Originally, compressors were designed to reproduce the characteristic ‘sag’ of a tube amplifier, but later implementations focused on improving and customizing particular qualities of tone. We thought that adding a moderate amount of compression to the multiphonic would generally produce a longer and fuller sound envelope.

Overdrive and Distortion

Overdrive and distortion are intended to approximate the sound of an overdriven amplifier, coaxed into its clipping region. The difference between the two effects is mainly one of extent: overdrive induces a subtle soft clipping, while distortion more radically clips the signal, nearly transforming it into the hard-edged contour of a square wave. We expected that both effects would enrich the harmonic spectrum, add sustain, and contribute a searing quality to the sound. Effects not used include:

  • Amplitude-altering effects, which would intensify the distortion

  • Pre-distortion EQ, which could cause certain frequencies to become more susceptible to distortion

  • Post-distortion EQ, which could be used to modify the amplitude of specific frequencies

  • Time delays, phasers and chorus

Pedal Specs and Settings

Listed below are the three analogue effect models used and their respective settings (scale is from 0–24).

  • Compression (Walrus Audio – ‘Deep Six’)

  • Level: 12

  • Sustain: 14

  • Blend: 12

  • Attack: 12

  • Overdrive (Friedman – ‘Dirty Shirley’)

  • Bass: 12

  • Treble: 12

  • Presence: 12

  • Mid: 12

  • Gain: 12.15

  • Volume: 11

  • Distortion (ProCon – ‘RAT’)

  • Distortion: 14

  • Filter: 10

  • Volume: 14

Spectrograms

Variable set 1: Multiphonic VI+17 performed on string 6 of three guitars

Figure 13.1a: Spectrogram of multiphonic VI+17 performed on string 6 (82.41 Hz) of G&L Legacy: Variable (a) clean

Figure 13.1b: Spectrogram of multiphonic VI+17 performed on string 6 (82.41 Hz) of G&L Legacy: Variable (b) distortion

Figure 13.2a: Spectrogram of multiphonic VI+17 performed on string 6 (82.41 Hz) of G&L ASAT: Variable (a) clean

Figure 13.2b: Spectrogram of multiphonic VI+17 performed on string 6 (82.41 Hz) of G&L ASAT: Variable (b) distortion

Figure 13.3a: Spectrogram of multiphonic VI+17 performed on string 6 (82.41 Hz) of Les Paul: Variable (a) clean

Figure 13.3b: Spectrogram of multiphonic VI+17 performed on string 6 (82.41 Hz) of Les Paul: Variable (b) distortion

Here (Figure 13) we see the dramatic effect that distortion (even at this moderate setting) has on the multiphonic. The spectrum is densely filled out and the duration greatly extended. Where the clean recordings show a generally steady decay of partials after the attack, the distortion causes the spectrum to swell in amplitude. A rippling effect also takes place, with the partials undulating slightly in frequency.

Variable set 2: Multiphonic VI+17 performed on string 6 of Les Paul

Figure 14a: Spectrogram of multiphonic VI+17 performed on string 6 (82.41 Hz) of Les Paul: Variable (c) compression

Figure 14b: Spectrogram of multiphonic VI+17 performed on string 6 (82.41 Hz) of Les Paul: Variable (d) compression + overdrive

In this comparison (Figure 14), the Les Paul shows a subtle response to the compression pedal. With the addition of overdrive, the spectrum is transformed into a saturated harmonic field. The same swelling and undulation occur, but now even more pronounced. The strengthening of the 7th partial (ca. 576 Hz) is particularly distinct.

Variable set 3: Multiphonic VI+17 performed on string 3 (196.00 Hz) of the Zachary

Figure 15a: Spectrogram of multiphonic VI+17 performed on string 3 (196.00 Hz) of the Zachary: Variable (a) clean

Figure 15b: Spectrogram of multiphonic VI+17 performed on string 3 (196.00 Hz) of the Zachary: Variable (c) compression

Figure 15c: Spectrogram of multiphonic VI+17 performed on string 3 (196.00 Hz) of the Zachary: Variable (d) compression + overdrive

In this higher register (Figure 15) multiphonic VI+17 is considerably more fragile. The compression pedal compensates for this by extending the resonance without compromising clarity. Once overdrive is added to the mix, the sound is again radically transformed, with a starkly drawn-out 7th partial (ca. 1374 Hz).

10. Double Stops

With the abundance of single multiphonic stopped positions throughout the fretboard, the potential to combine them in double stops will be very appealing to composers. Those interested in working with sound masses can generate dense harmonic fields by stacking multiphonics from adjacent strings. Composers with a particular interest in achieving intonational purity may use a Pythagorean tuning to minimize beating between partials. Alternatively, a scordatura based on more complex intervals from the harmonic series could be used to create even headier combinations of partials.

Given the challenge of performing these multiphonics accurately in combination, composers will have to be particularly mindful of left-hand technical logistics. It is recommended that composers not exceed the limit of a minor 3rd (i.e. a span of four frets, with one finger per fret), as any further is likely to compromise accuracy. In The Techniques of Guitar Playing, Josel and Tsao discuss the efficacy of different left-hand finger positions, and they recommend Henri Pousseur's composition L'ibericare as a paradigm for mapping finger placement.Footnote 22 The ‘Rubik's Cube’ format presented in this piece provides a compelling way of exploring the fingerboard, and it could also be extended to performing multiphonic dyads.

11. Conclusion

In publishing these findings, we endeavour to stimulate further interest in electric guitar multiphonics. It is our hope that future researchers will feel emboldened to continue these efforts and will follow down the various rabbit holes we have pointed out. With a growing understanding of string multiphonics, composers may be more inclined to use them, and performers will be encouraged to develop the techniques necessary for their performance.

Previous research into guitar multiphonics has been limited to the lower three strings of the acoustic guitar. We have hereby extended this focus to the electric guitar, and we have closely examined multiphonics on all six of its strings. In light of our findings we have no doubt that the electric guitar, with its greater power and resonance, is by far the superior instrument for conveying the harmonic structure of these aggregates.

The multiphonic catalogue we propose for strings 3–1 is by no means exhaustive. Though it includes some of the more resonant finger positions, there are still other aggregates to be drawn from these strings. As with many performance techniques, the methods of producing multiphonics will vary depending on a player's style and anatomy. In addition, the choice of instrument, as well as a host of other technical appurtenances, will crucially determine the results. With this in mind, we encourage composers and performers to build on what we have established, and to conduct further research in consultation with one another.

References

1 In order to precisely notate the spectral components of these multiphonics, we have used the Extended Helmholtz-Ellis JI Pitch Notation (HEJI), devised by Marc Sabat and Wolfgang von Schweinitz. First released in 2004, this extensive collection of precisely defined accidentals has become a standard for writing music in just intonation. Building upon the methods of pitch classification pioneered by Hermann von Helmholtz and Alexander J. Ellis, this notation system is able to indicate any pitch in the glissando spectrum within a few cents’ accuracy in many harmonically derived enharmonic shadings. For more information about Helmholtz-Ellis Notation, see Marc Sabat and Natalie Pfeiffer, ‘The Extended Helmholtz-Ellis JI Pitch Notation’ (2005), www.marcsabat.com/pdfs/notation.pdf (accessed 22 September 2019).

2 Schneider, John, The Contemporary Guitar (Los Angeles: University of California Press, 1985), pp. 135–8Google Scholar.

3 Josel, Seth F. and Tsao, Ming, The Techniques of Guitar Playing (Kassel: Bärenreiter, 2014), pp. 118–25Google Scholar.

4 Rita Torres, A New Chemistry of Sound: The Technique of Multiphonics as a Compositional Element for Guitar and Amplified Guitar (PhD Thesis, Universidade Católica Portuguesa, 2015).

5 Martin L. Vishnick, A Survey of Extended Techniques on the Classical Six-String Guitar with Appended Studies in New Morphological Notation (PhD thesis, City University of London, 2014), pp. 239–44.

6 Fleischer, Helmut, Schwingungsuntersuchungen an Elektrische Gitarren, Beiträge zur Vibro- und Psychoakustik, 2/01 (Neubiberg: Institut für Mechanik, 2001)Google Scholar; or, more recently, Manfred Zollner, Physik der Elektrogitarre (Regensburg: Self-published, 2014).

7 Ulrich May, Elektrische Saiteninstrumente in der populären Musik: Entstehung, Konstruktion und Akustik der elektrischen Gitarre und verwandter Instrumente (PhD thesis, Universität Münster, 1984).

8 Herbst, Jan-Peter, Die Gitarrenverzerrung in der Rockmusik (Berlin: Lit Verlag, 2016)Google Scholar; Herbst, Jan-Peter, ‘Heaviness and the Electric Guitar: Considering the Interaction Between Distortion and Harmonic Structures’, Metal Music Studies 4/1 (2018), pp. 95113CrossRefGoogle Scholar.

9 Josel and Tsao, Techniques of Guitar Playing, p. 212.

10 For audio samples of these aggregates and all others included in this study, please visit https://soundcloud.com/musikforschungbasel/sets/audio-examples-tempo-string-multiphonics-thomas-ciszak-and-seth-josel.

11 Acoustic guitar crafted by Gary Southwell, A-Series.

12 For a complete list of instrument specifications and equipment, see below.

13 For more information, please see Thomas Nicholson and Marc Sabat, ‘Farey Sequences Map Playable Nodes On A String’ in this issue.

14 Because hollow-body guitars do not usually provide the same level of power, sustain and harmonic brilliance as solid-body instruments, we wouldn't expect them to be as viable for performing multiphonics.

15 ‘Tri-Tones’, designed by Timber Tones (UK) www.timber-tones.com/tri-tones-padauk-1-guitar-pick-1082-p.asp (accessed 18 August 2019).

16 See May, Elektrische Saiteninstrumente in der populären Musik and Diego Leguizamón, Florent Masson and Shin-ichi Sato, ‘Subjective Preference of Electric Guitar Sounds in Relation to Psychoacoustical and Autocorrelation Function Parameters’, Paper presented at the International Congress on Acoustics conference paper, Beunos Aires, 2016.

17 Leguizamón, Masson and Sato, ‘Subjective Preference of Electric Guitar Sounds’, p. 4.

18 Readers interested in the physics of the plectrum motion and its effect on the string's vibration may refer to Zollner, Physik der Elektrogitarre, pp. 1–31.

19 Though not as powerful as the electric guitar, the steel-string acoustic could also produce fairly convincing results on strings 3 and 2.

20 These three models represent a classic family of electric guitar design, and they have had iconic status since the early 1950s. The ‘Legacy’ is a Leo Fender design, in the mould of his earlier Stratocaster; similarly, the ‘ASAT’ is modelled after the Telecaster.

21 For each of the post-effect signals we also mixed in the clean recording in order to clarify the attack and strengthen the general profile. This is a common production technique used both on stage and in the recording studio.

22 Josel and Tsao, Techniques of Guitar Playing, pp. 37–9.

Figure 0

Figure 1a: Multiphonic VI+17 notated on string 6.

Figure 1

Figure 1b: Multiphonic X−4 notated on string 4.

Figure 2

Figure 2a: Spectrogram of multiphonic VI+17 performed on string 6 of acoustic guitar (82.41 Hz)11

Figure 3

Figure 2b: Spectrogram of multiphonic VI+17 performed on string 6 of the Parker electric guitar (82.41 Hz)12

Figure 4

Figure 3a: Spectrogram of multiphonic X−4 performed on string 4 of acoustic guitar (146.83 Hz)

Figure 5

Figure 3b: Spectrogram of multiphonic X−4 performed on string 4 of the Les Paul electric guitar (146.83 Hz)

Figure 6

Figure 4: Farey sequence chart for low E-string

Figure 7

Table 1: Complete list of specifications for the five guitars.

Figure 8

Figure 5: Multiphonic III+47 notated on string 4.

Figure 9

Figure 6: Spectrogram of Multiphonic III+47 performed on string 4 of all guitars (146.83 Hz)

Figure 10

Figure 7: Multiphonics notated on string 3

Figure 11

Figure 8: Multiphonics notated on string 2

Figure 12

Figure 9: Multiphonics notated on string 1

Figure 13

Figure 10a: Spectrogram of multiphonic IX+33 performed on string 3 of G&L ASAT (196.00 Hz)

Figure 14

Figure 10b: Spectrogram of multiphonic IX+33 performed on string 2 of G&L ASAT (246.94 Hz)

Figure 15

Figure 10c: Spectrogram of multiphonic IX+33 performed on string 1 of G&L ASAT (329.63 Hz)

Figure 16

Figure 11: Multiphonic VIII+41 and corollary XVI+54, notated on string 5

Figure 17

Figure 12a: Spectrogram for multiphonic VIII+41, performed on string 5 of the Zachary (110.00 Hz)

Figure 18

Figure 12b: Spectrogram for multiphonic XVI+54, performed on string 5 of the Zachary (110.00 Hz)

Figure 19

Figure 13.1a: Spectrogram of multiphonic VI+17 performed on string 6 (82.41 Hz) of G&L Legacy: Variable (a) clean

Figure 20

Figure 13.1b: Spectrogram of multiphonic VI+17 performed on string 6 (82.41 Hz) of G&L Legacy: Variable (b) distortion

Figure 21

Figure 13.2a: Spectrogram of multiphonic VI+17 performed on string 6 (82.41 Hz) of G&L ASAT: Variable (a) clean

Figure 22

Figure 13.2b: Spectrogram of multiphonic VI+17 performed on string 6 (82.41 Hz) of G&L ASAT: Variable (b) distortion

Figure 23

Figure 13.3a: Spectrogram of multiphonic VI+17 performed on string 6 (82.41 Hz) of Les Paul: Variable (a) clean

Figure 24

Figure 13.3b: Spectrogram of multiphonic VI+17 performed on string 6 (82.41 Hz) of Les Paul: Variable (b) distortion

Figure 25

Figure 14a: Spectrogram of multiphonic VI+17 performed on string 6 (82.41 Hz) of Les Paul: Variable (c) compression

Figure 26

Figure 14b: Spectrogram of multiphonic VI+17 performed on string 6 (82.41 Hz) of Les Paul: Variable (d) compression + overdrive

Figure 27

Figure 15a: Spectrogram of multiphonic VI+17 performed on string 3 (196.00 Hz) of the Zachary: Variable (a) clean

Figure 28

Figure 15b: Spectrogram of multiphonic VI+17 performed on string 3 (196.00 Hz) of the Zachary: Variable (c) compression

Figure 29

Figure 15c: Spectrogram of multiphonic VI+17 performed on string 3 (196.00 Hz) of the Zachary: Variable (d) compression + overdrive