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.
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).
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.)
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.
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.
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) Parker Fly Deluxe
−20 dB pad (DI)
2) Gibson Les Paul
−20 dB pad
3) G&L Legacy
no pad
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) 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.
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.
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 13–15.)
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
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
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
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.