Multiphonics on the Double Bass

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Multiphonics on the double bass

An investigation on the development and use of multiphonics on the double bass in contemporary music

Hkon Thelin

2011

DEFINITIONS Page Introduction to Multiphonics on the Double Bass 2 Left-Hand-Finger Positions 6 Bow 8 Pizzicato Multiphonics 18 MULTIPHONICS ILLUSTRATED Semitonic Multiphonics 18 Quartertonic Multiphonics 21 Bow-Above-Finger Multiphonics 25 Pizzicato Multiphonics 27 Colourative Effects 28 Acknowledgements, literature and list of scores 38 Eivind Buene: Blacklight for two double basses Charts of multiphonics

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DEFINITIONS

Introduction to Multiphonics on the Double Bass

Introduction Multiphonics in wind instruments has been around for a while. Nowadays you often hear saxophone players utilizing the technique in jazz and contemporary music. In brass instruments the effect probably dates back even longer, and can be found in music even from the classical period: here the musician sings along with the lip-controlled pitch, and thus creates a quite audible series of difference tones. Woodwind players mostly use special fingering in combination with very precise embouchure. In string instruments, multiphonics is mainly a filtering technique, where the potential energy of certain partials of an (in most cases) open-string fundamental is restrained by a left-hand finger pad lightly touching the string. This favours the conditions for some of the remaining partials, separately or in narrow clusters. In this survey I will keep strictly to the research of clearly defined and reproducible multiphonic sounds. The vast arrays of sounds that can be created with prepared instruments or amplification are not subject to this scrutiny. The article is presented in two main parts. In the first part called DEFINITIONS I explain the left-hand finger positions that are used to play multiphonics, present new concepts of bow placement and describe how to play pizzicato multiphonics. And I also suggest solutions on how to notate the different multiphonics. The second chapter called MULTIPHONICS ILLUSTRATED presents musical examples of multiphonics, from the basic use to complex colourative effects. What is multiphonics? By carefully positioning the bow and a lightly touching finger on the string, the string spectrum can be conditioned to provide narrow bands of pronounced energy. This leaves the impression of multiple complex tones with the normal (Helmholtz) fundamental as the lowest pitch. The phenomenon is seen to be caused by two additional signal loops, one on each side of the finger, which through the repeating slip pattern get phase locked to the full loop of the fundamental. Within the nominal period, however, the slip pulses will not be uniform like they are during the production of a normal harmonic, but may vary considerably in shape, size, and timing. For each string there are large numbers of bow/finger combinations that bear the potential of producing such tones. There are also two classes, depending on whether the bow (2.class), or the finger (1.class), is situated closest to the bridge. Touching the string with the finger closest to the bridge, as in class-one, will somewhat emphasize the (Helmholtz) fundamental, a particular audible effect of a narrow cluster that accumulates around the loudest sounding partial. In the class-two of multiphonics the partials are (usually) more spread out in the spectrum. Examples of the respective partial clusters are shown in figure 1 and 2.

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Fig. 1. A class-one multiphonics where a narrow cluster that accumulates around the loudest sounding partial. The figure is a copy of figure 7 in Guettler and Thelins article Bowed-string multiphonics analyzed by use of impulse response and the Poisson summation formula. See this article for a precise description of the figure.

Fig. 2. A class-two multiphonics where the partials are spread out in the spectrum. The figure is a copy of figure 8 in Guettler and Thelins article Bowed-string multiphonics analyzed by use of impulse response and the Poisson summation formula. See this article for a precise description of the figure.

The position of the bow on the string determines the tone that is muted in the sounding spectrum, while the left-hand finger position determines which tones will be prominent in the sound. Multiphonics is applicable to double bass and cello, while less practical on shorter-stringed instruments. Historical notes The first comprehensive description of multiphonics is dated to 1995, when French bassist Jean-Pierre Robert published his bilingual book Les modes de jeu de la contrebasse un dictionaire de son/Modes of playing the doublebass a dictionary of sound in collaboration with IRCAM (Institut de Recherche et Coordination Acoustique/Musique). This research, which started in 1985, also made a noticeable impact on composers working in Paris and at

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IRCAM at the time. A similar description on the production of multiphonic sounds was later found in the article A personal pedagogy (2000) by the American bassist Mark Dresser. Dresser has been further exploring multiphonics, without being much influenced by the European achievements, and his discoveries where presented in the article Double bass multiphonics, published in the October 2009 issue of The Strad. The composer Michael Liebman presented a detailed study on multiphonics on the cello and double bass in a compilation consisting of his piece Movement of Repose and the article New Sounds for cello and double bass, which were published in 2010. His study on new sonic possibilities of string instruments began in 1998 and manifested itself quickly in the compositions Movement of Repose (1998) for cello and Sonata for double-bass (2001), in which the second movement Legato sonore shows multiple variations of the multiphonic technique, as well as the articles Multiphonics Neue Moglichkeiten im Cellospiel (Das Orchester 4/2001) and Multiphonics: new sounds for double bass (2001, unpublished). Multiphonics played with the finger position between bow and bridge (bow-above-finger multiphonics) was performed by Italian double bassist Fernando Grillo already during the 1970s.

Fernando Grillo, apparently in action with multiphonics of the first class. Picture from

http://www.discogs.com/viewimages?artist=Fernando+Grillo Stefano Scodanibbio was for a short period the student of Grillo and in his early works e/statico (1980) and Joke from Sei Studi (1981/83) we find some of the first notated examples of double bass multiphonics. Bertram Turetzky, author of The Contemporary Contrabass (1989, rev.ed.) and one of the worlds foremost experts on 20th century double bass, surprisingly doesnt mention the bow-above-finger multiphonics in his book but points out that he knows of no music employing string multiphonics. Nevertheless, he says, they do exist and, as with most other harmonic techniques, the contrabass is especially well suited to the task (Turetzky, p.138). He continuo to shortly describe the production of some multiphonic sound by giving specific instructions of finger position, bow pressure and bow placement (p.139). It is unclear which piece was the first to directly employ multiphonic techniques other than the bow-above-finger multiphonics. Prior to 1990, multiphonic sounds have in some cases influenced composers to use the timbre and chords as generative sound material and concrete analytical musical tools. In her work Io (1986-87), for ensemble with live electronics and computer-generated tape, Kaija Saariaho draws harmonies from double bass multiphonics, whose spectrum is played on tape and then orchestrated for the ensemble. Saariaho also used cello multiphonics as generative source for harmonies in the earlier piece Lichtbogen (1986) for small ensemble and live electronics. Composed in 1999, the piece Ciel toil scored for percussion and double bass adopt several multiphonics that is obtained directly from the research of Jean-Pierre Robert. In the solo double bass piece Thrust (1989, rev. 1991), by Saariaho fellow Finnish composer Kimmo Hakola, the whole last part marked Rubato (Adagio) is dedicated to the exploration of multiphonic sounds. Hakola lived in Paris and worked at IRCAM during the 1980s, and his use of multiphonics is directly influenced from the work done by Robert and fellow musicians, composers and researchers in France at

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the time. Thrust is the first piece I have found with semitonic multiphonics, and Hakola also presents one of the most complex usages of the technique to this date! Philippe Boivin uses quartertonic multiphonics in the fifth movement Spectral from his work Cinq algorithmes pour contrebasse seule (1991). Boivin was a long time collaborator with Jean-Pierre Robert, a working relationship that already manifested itself in the remarkable piece Zab ou la passion selon st. Nectaire (1981). In 1996, the Argentine composer Carlos Mastropietro wrote the piece En una cara for solo double bass where he uses both semitonic and quartertonic multiphonics. Mastropietro learned about multiphonics reading Fingerboards and overtones (1991) by Michael Bach, an artistically sketched book on contemporary cello technique. He then conducted his own experiments on a double bass, searching for a good technique for the left hand and the bow. The result was an innovative use of multiphonics, presented in his personal notation, chord analysis and definitions. The piece gained some attention when it won the first prize at the 2000 International Society of Bassists (ISB) Composers Competition in the USA. A big leap forward was done with the research of Michael Liebman. This Russian pianist and composer, now living in Israel, discovered in 1997 what he calls the new multiphonic technique for cello and bass, and identify it as a similar sounding technique to that described by Bruno Bartolozzi in The new sounds for woodwind (1967). Liebman conducted his research independently, without any knowledge of the European and American advances. His thorough study introduces many new concepts concerning definitions, notation and combinations with other techniques. The second movement, Legato sonore, of his Sonata for double bass (2001) is an advanced musical exploration of his discoveries. Many of my own descriptions of chord colorization and combined techniques use expressions that are established by Liebman.

The way forward In the material from Robert, Liebman and Dresser we find extensive information about the physics, technical production and timbre variations of multiphonic sounds, together with chord schemes (spectral analysis) that illustrate the most known multiphonic sounds. However, the acoustical implications in terms of string waveforms, etc. was never touched upon by these authors. And neither Robert nor Dresser has in their research any reference to multiphonics used in written music. My main aim of this presentation is therefore to illustrate multiphonics thru examples from composed works, were I will look at the practical use of the technique, from the production of single chords to effects that determine chord coloration. Initially, I compare previous research and suggest new definitions and suggestions for notation. And in the article Bowed-string multiphonics analyzed by use of impulse response and the Poisson summation formula, professor Knut Guettler presents his research into the acoustical realm surrounding the production of multiphonic sounds. This article has been accepted for publication (2011) in Journal of Acoustical Society of America. Until recently, most research and use of multiphonics was done independently, without any interaction and knowledge of the work of others. We see that experiments have been done by a handful of composers and performers in Europe, Russia/Israel and America. Still there is an insufficient knowledge of the technique, if not non-existent, among musicians. Multiphonics on the double bass is a specialized technique, yet it carries a great potential for creating new sonorities, expanding the timbre of the instrument, and forming new theoretical and practical grounds for compositions. Since 2001 my own experiments with multiphonics have inspired several composers to explore the technique as well as incorporating it into my own music. So far, I have been involved in the creation of ten works where multiphonics have been used. The rising number of works with multiphonics has given me the opportunity to get experience with both composing and performing with the technique. And for the first time, I present a review of how the technique has been used in more than a dozen works. I end my survey with presentation of a double bass duo from the composer Eivind Buene called Blacklight. This duo is originally part of the larger piece Into the Void (2008) for wind orchestra (with double bass) and a soloist group of saxophone, accordion, double bass and drums. In Blacklight he uses a combination of semitonic, quartertonic and bow-above-finger multiphonics in a contemplative and calmly breathing piece. The duo is relatively easy to play and is accessible also for intermediate students or players. It serves well as an introduction to multiphonic techniques and sounds.

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Left Hand Finger Positions Semitonic, Quartertonic and Artificial multiphonics We can organize the second-class of multiphonics, where the bow is situated closer to the bridge than the left hand, in three general groups of left-hand finger positions. Each group is clearly defined through its own characteristics of sound and playability.

1. Semitonic multiphonics. Played with fingers in a natural chromatic scale related position. Multiphonics is created by manipulating bow placement, bow pressure and bow speed. This is the most common way of producing a multiphonic sound.

2. Quartertonic multiphonics. Played with quartertone finger position. Multiphonics is either created on the corresponding harmonic, as with semitonic multiphonics, or by the interference between neighbouring harmonics. Generally, light bow pressure and fast bow speed is needed to create this type of multiphonics. Manipulations of left-hand finger pressure can greatly enhance certain partials in the cord or make the fundamental tone more present.

3. Artificial multiphonics. This type can be played both as a semitonic multiphonics and as a quartertonic multiphonics. Semitonic artificial multiphonics can be produced with the artificial harmonics of major seconds, minor and major thirds and augmented fourths. Artificial multiphonics of major seconds, minor and major thirds are best performed in the lower positions and they get gradually more difficult to control in the higher positions (above the first thumb position). Artificial multiphonics of augmented fourths is best performed from the 4th or 5th position and upwards (because of the stretching of the fingers). Quartertonic artificial multiphonics is produced with the finger lightly touching the string at a distance of a fourth diminished of a quartertone from the depressed thumb. The sound is then coloured by the interference of the neighbouring harmonics/partials. Glissando is possible with artificial multiphonics.

Notation of finger positions for 2.class multiphonics (Semitonic, quartertonic and artificial multiphonics) Multiphonics is always notated with the harmonic diamond sign, in tablature notation indicating finger positions rather than musical pitches. I suggest using the symbol M. above or below the note to indicate that it is a multiphonic sound, together with the indication on which string to play the note (in Roman numerals). Fig. 1. Examples of semitonic multiphonics

Fig. 2. Examples of quartertonic multiphonics

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Fig. 3. Examples of artificial multiphonics

Finger pressure The realisation of certain multiphonics demands a specific left hand finger pressure technique. Variation of finger pressure can in most cases create small changes in the colourisation of the sound due to a suppression or reinforcement of certain overtones. Light finger pressure gives a stronger presence of the fundamental sound, but at the same time it becomes more difficult to keep a totally stable sustained chord. I suggest using the abbreviation l.f.p. (light finger pressure) for specifically indicating a light finger pressure. Fig.4. Notation of finger pressure

Bow-above-finger multiphonics For the first-class of multiphonics, the finger is positioned close to the end of the fingerboard or beyond the fingerboard, between bow and bridge. Bow-above-finger multiphonics has generally greater dynamic potential than other multiphonics, but comes with more limited possibilities of being combined with other playing techniques. Notation of finger positions for first-class multiphonics (Bow-above-finger multiphonics) I recommend using a symbol created by Stefano Scodanibbio for notating bow-above-finger multiphonics (see fig. 5). Fig.5. Symbol for notating bow-above-finger multiphonics

This symbol can either indicate a random finger position as shown in fig. 6, or a precise finger position as shown in fig. 7 and 8. Fig. 6. Stefano Scodanibbio: e/statico

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Fig. 7. Hkon Thelin: oibbinadocS Fig.8. Eivind Buene: Blacklight

Bow The placement of the bow is essential to create and control a multiphonic sound. Michael Liebman defines the bow position into seven areas of 3.15 cm, with the distance measured from the bridge. He creates this table: Fig.1. Table of bow positions created by Michael Liebman. Movement of Repose, New sounds for cello and double bass, 2010, page 30. Molto ponticello 0 cm Ponticello 3.15 cm Ordinare/Ponticello 6.3 cm Ordinare 9.45 cm Ordinare/Tasto 12.6 cm Tasto 15.75 cm Molto tasto 18.9 cm A general area can for example be marked with Molto tasto while the specific point of contact can be marked as 19 cm. In cases where a chord can be performed in adjacent areas, e.g. pont. and ord./pont., bow position is marked as pont. o/p. The double bass has no standard size. And string length and length of fingerboard vary greatly between different instruments although string manufacturers consider a length of 106 cm to be standard. The areas and positions indicated in Liebmans table doesnt exactly match all instruments, and he asks for the player to be aware that minor position corrections may be required for each individual instrument. Central harmonic nodes In my attempt to make more precise definitions of bow placement I followed Liebmans chart of multiphonics, writing down the exact harmonic node where the bow is placed within the given areas. I ended up defining the 9th, 11th (22nd in the fifth octave) and 13th partial as central harmonic nodes on where to place the bow. The bow position for the creation of semitonic and quartertonic multiphonics will now be given according to a central harmonic node, which is similar on all instruments. The resulting new chart shows precisely where the bow should be theoretically placed on the string. Once tried and practised, it also gives a more precise visual image of where to place the bow. It is seldom necessary to place the bow at any exact given harmonic node, but usually it is enough to be within the area of the node. For reasons unclear, some multiphonics require a more precise placement of the bow than others. Further, the areas (1-2 cm) around the 13th and 11th harmonic nodes on both sides of the fourth octave, can be found to be the most flexible and available bow positions for producing multiphonics.

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Fig.2. Chart by Hkon Thelin and Knut Guettler. Natural harmonics to be used for bow positions in multiphonics. Notice that all harmonics can be found at several places along the string. Vertical arrows indicate which node to use, starting with no arrow at the uppermost node. At the bottom of the plot, Liebmans bow positions are included for comparison. Even though the harmonics positions in this figure are marked on single strings onlyfor reasons of claritythey can of course be used on every string. The figure is based on 106 cm string length and can be scaled up to fit over the strings.

Fig. 3. Chart by Hkon Thelin that show the harmonic nodes bow position for semitonic and quartertonic multiphonics on all the strings. Notice that the vertical arrows indicate which node to use, starting with no arrow at the uppermost node.

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Bow Resistance In his article on Double bass multiphonics (The Strad, October 2009) Mark Dresser defines bow resistance as a combination of pressure (bow force) and bow speed. It is difficult to define any general behaviour of bow resistance, each multiphonics require a specific combination of pressure and speed which can only be learned by experience. Michael Liebman (Movement of Repose, New sounds for cello and double bass, 2010, page 30) uses four general designations for bow pressure, from light pressure to drilling pressure (very strong bow pressure). In multiphonics the pressure is not always in direct correlation to the dynamics, and the notion is more accurate for portraying the character of playing chords. In some cases, Liebman also make use of the designations slow bow and quick bow to describe the bowing speed. With multiphonics, as with normal (Helmholtz) tones, the volume of sound is, in most cases, proportional to bow speed. In my new chart of multiphonics I mark bow resistance only in special cases, where it is absolutely decisive for the production of the multiphonics. I suggest using Liebmans designations for pressure and speed, with a reduced category of pressure and with capital letters for easier reading: Fig.4: Chart by Hkon Thelin on bow resistance Pressure: Light pressure - L.pr Normal pressure - N.pr. Heavy pressure - H.pr.

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In an email conversation on bow angle which I had with the American double bass player Mark Dresser, Dresser describes another multiphonic effect which is obtained by drawing the bow at a diagonal angle: with the tip downwards and the bow placed at the lower third of the string so the angle is transversing several nodes consistently. With some pressure, and speed, one can get a warbling phasing multiphonic effect, creating a loop of several partials phasing. Sounds like a turkey 'gobbling' or a kind of yodeling effect. Notation systems for the bow The notation of the left-hand position causes no problem, as a normal note with a diamond or rectangular head will do nicely, and is readily understood by the musician. The position of the bow is somewhat harder to indicate in a concise manner, as the sign should be small and placed either below or above the fingered note. Liebman suggests two ways of indicating the bows position: (1) a series of Italian expressions ranging from molto tasto to molto ponticello. These ranges are predefined with approximate distances from the bridge. (2) By describing the distance from the bridge in centimetres.

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Ex. 5a. Example of notation by Liebman (from Legato Sonore). By playing the lower stave with the bow placed in proper distance from the bridge; the harmonics (multiphonics) shown in the upper two staves will be dominant.

However, in this area of the string, the (accomplished) player will be more familiar with the positions of the highest harmonics (flageolet tones), and should without too much of a problem be able to place the bow there, regardless of non-standardised string lengths and other trivialities. In example 5b, I suggest a notation for bow position, where the upper-case letters determine the choice of string, the number gives the harmonic, and the arrow indicates which harmonic node to use, starting with no arrow at the highest node. (See Figure 3.) Ex. 5b. Alternative notation of bow position and string choice based on natural harmonics: E13! and A11! mean bow positions of the 13th and 11th harmonics, second node, on the E and A string, respectively. See Figure 1 for explanation.

More examples of this notation are seen in the following figures. In example 5c there are several different bow positions to choose from, and the player is free to select from these. In example 5d, the bow moves from the position 13! to the slightly lower position 11!, to enable multiphonics on adjacent strings to be played together.

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Bow position for bow-above-finger multiphonics I find the best bow position for bow-above-finger multiphonics to be around a fourth or a fifth above the fingered note. Finger glissando is possible with the bow-above-finger multiphonics and the bow must be moved in proportion to the left hand. I didnt find it necessary to introduce any specific notational systems for the bow-above-finger multiphonics. Bow position for multiphonics on the 4th-7th natural harmonics on each string The bow position for bow-above-finger multiphonics applies also for ordinary semitonic multiphonics played at the major 3rd, 5th and minor 7th partial of the third octave, as well as the fourth octave; these special cases are best played with the bow about a fourth or a fifth below the fingered note. Bow position for artificial multiphonics Defining bow placement for artificial multiphonics proved to be a major challenge. The experiments told me that each finger position demanded a bow position in equal proportion to the left-hand. For each half step (semitone) the position of the artificial multiphonics moves upwards the string, the bow should similarly rise to the next harmonic node. The bow position is measured in semitones from the fingered harmonic tone, and two different distances, of 22 and 29 semitones, can be used. With these distances as a starting point, the bow can also in theory be moved to other octave positions, but the practical use limits the positions to 34 and 41 semitones, an octave higher, when playing certain artificial multiphonics. Two different combinations of speed and pressure are also used, either normal pressure and normal speed (N.pr.) or high pressure (H.pr.) and slow speed (Slow bow).

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Fig. 6. Bow positions for semitonic artificial multiphonics on the E-string. Harmonic partial indicate the sounding harmonic partial, bow node position indicate on which harmonic node to place the bow on the string, notation indicate the score notation for the bow, and fingering indicate the score notation for the left-hand. A general mark on the playability is included below the staffs. The finger positions for artificial multiphonics are major second, minor and major third, and augmented fourth.

17

Example of score notation of artificial multiphonics An example of notation, taken from the piece Glasperlenspiel, is shown in example 7. The bow is placed on the 10th harmonic partial and moved in parallel glissando with the left hand when the artificial multiphonics slides up two semitones. Ex. 7. Glasperlenspiel, Hkon Thelin

18

Pizzicato multiphonics Pizzicato multiphonics are easy to produce, and are most effective and clear from the 3rd-8th partial. Place the left hand finger over the harmonic with very light pressure and pluck energetically close to the bridge. As the string is plucked release the left hand finger from the string. This is also possible with right hand finger pizzicato technique. Place the right hand thumb lightly over, or on the side of, the harmonic and pluck energetically with index finger. Release the thumb from the string as the string is plucked. This technique was first shown to me by the Finnish bassist and composer Teppo Hauta-aho, and the first written description is by Mark Dresser in the article Double bass multiphonics (The Strad, October 2009). Notation of pizzicato multiphonics I suggest using the symbol M. above or below the harmonic to indicate that it is a multiphonic sound, together with the indication on which string to play the note (in Roman numerals). In example 1, the multiphonics is played with the right hand finger pizzicato technique. Example 1. Hkon Thelin: Glasperlenspiel

MULTIPHONICS ILLUSTRATED

Semitonic Multiphonics Multiphonic sounds are most commonly produced with the semitonic finger positions, which also provide the basis for the most comprehensive timbral variation and combinatory use with other techniques. In Kimmo Hakolas Thrust from 1989 (rev. 1991) we find some of the first examples of semitonic multiphonics: Example 1: Thrust Ex. 1. Kimmo Hakola: Thrust, page 6, Rubato (Adagio)

19

The finger positions of the multiphonics are notated on the bottom stave while the resulting sounds are notated in parenthesis on the top stave. In example, 1 all multiphonics are played in the first octave on the G-string (marked with number I). Hakola uses an M on the note stem for marking the multiphonics, which works well within the frame of the piece. There are no markings for bow placement and bow resistance in the beginning of the line, but it is to be assumed that the bow should be in an ordinary position from the beginning. From the middle of the line the bow moves gradually to sul ponticello (SP) and the three last multiphonic sounds are played with the bow poco sul ponticello. This suggests that Hakola either indicates a bowing position that works well for these multiphonic sounds, or that he will enhance certain overtones by moving the bow closer to the bridge. Example 2: Foxfire Zwei In my own transcription of Foxfire Zwei (1993/2007) by Helmut Oehring (originally written for bass clarinet), I mark the multiphonics with the M above or below the note head or stem, and the designated string with numbers (I-IV). Example 2 shows multiphonics on the third string. This particular multiphonics is very easy to produce, and I have not indicated bow placement, bow resistance and sounding tones. My suggestion for bow placement is above the fourth octave, around the 9th, 11th or 13th central harmonic node. Ex. 2. Helmut Oehring: Foxfire Zwei (arr. Hkon Thelin)

Example 3: oibbinadocS Generally, I use a simple notation similar the one used in example 2. As seen in examples 3a and 3b, from oibbinadocS the first piece in which I used multiphonics, I didnt find it necessary to notate the placement of the bow, as the multiphonics is easy to play. Ex. 3a. Hkon Thelin: oibbinadocS

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20

Example 4: Thrust Going back to Thrust, the next two examples show semitonic multiphonics on strings I-III and in the first and second octave. Ex. 4a. Kimmo Hakola: Thrust, page 6, Rubato (Adagio)

Ex. 4b. Kimmo Hakola: Thrust, page 7, Rubato (Adagio)

Examples 5-7: Glasperlenspiel Semitonic multiphonics with markings for bow placement is shown in example 5 through 7. In example 5 there are multiple possible bow positions to choose from, and the markings can be viewed as guide to the area in which to place to bow. I found it convenient to only suggest the bow positions, since the context of the sound allows for slight transformations of timbre and dynamics. Ex. 5. Hkon Thelin: Glasperlenspiel

Examples 6 and 7 display situations where a specific bow position is preferred for the production of multiphonics. The transformation from an open string to multiphonics signifies the first situation. The finger gradually touches the string above the E-flat harmonic, which helps defining the multiphonic sound more easily. A precise bow position is marked, and the bow can be moved towards this position during the transformation of the sound. A precisely

21

positioned bow will help the final establishment of a stable sound, which gradually fades through a slow decrescendo. Ex. 6. Hkon Thelin: Glasperlenspiel

In example 7 the bow moves from the position B13! on the E-string to the slightly lower position B11!, to enable multiphonics on both the A and E-string to be played together. The cluster sound of the two chords is particularly difficult to control, as the distribution of bow pressure between the two strings, as well as the bow speed, must be practised to find the optimal combination for a balanced sound. Ex. 7. Hkon Thelin: Glasperlenspiel

Quartertonic Multiphonics Example 1-3: Spectral The French composer Philippe Boivin uses quartertonic multiphonics in the fifth movement Spectral of his piece Cinq algorithmes pour contrebasse seule (1991). A bowing technique described as spectral phase difference by Jean-Pierre Robert (Modes of playing the doublebass, 1995, 42) is employed throughout the movement. This technique gives the impression of hearing two consecutive attacks for each bow shift in a rapid flautando movement, thus reinforcing the harmonic spectrum of the open strings. The multiphonics is meant to expand the harmonic spectrum, creating even richer overtone sounds.

22

Ex. 1. Philippe Boivin: Spectral, bar 10-17

Ex. 2. Philippe Boivin: From the performance instructions to Cinq algorithmes pour contrebasse seule

Generally, a fast bow and light finger pressure will help to produce the wanted effects. The strings are all tuned to D during a short and improvised prelude, and Boivin stresses the importance of the players voice in bringing out clear harmonics in the colouring of the vocals which blend in with the instruments sounds.

23

Ex. 3. Philippe Boivin: Spectral, bar 35-36

The multiphonic sounds are often played in combination with ordinary harmonics or multiphonics on adjacent strings. The second and third string is tuned in octaves, thus reinforcing the tonal harmonic spectrum. The sound is very open and free, assisted by the resonance of the open strings. Example 4: oibbinadocS Playing simultaneously on adjacent strings can dramatically transform the multiphonic sounds. In my own composition oibbinadocS (2004), a quartertonic multiphonics on the A-string is played in combination with a natural harmonic trill on the D-string. The effect is very much the same as in the similar examples from semitonic multiphonics; a stable chord coloured by the interweaving roll of overtones. Ex. 4. Hkon Thelin: oibbinadocS

The technical challenge in this particular example is to keep the first finger steady on the precise point of the multiphonics on the string while the second and fourth finger do a fast trill on the higher string (this involves a rather big stretch for the fingers). At the same time, the bow must be positioned in a way that both the multiphonics and the harmonics in the trill speak out clearly. This demands a bow position close to the bridge, and the position that works best, in my experience, is around the 18th harmonic partial. Example 5: Foxfire Zwei In the transcription of Foxfire Zwei (1993/2007), I used a multiphonics that has similar sound qualities as the quartertonic multiphonics, which is, however, not included in the chart. The finger is positioned close to the nut and the indicated bow position is poco sul tasto, a lower position than for most quartertonic multiphonics. An airy oscillation between adjacent harmonics and the fundamental is the wanted effect, aided by the gradual change of left hand pressure. The bow position (poco sul tasto) brings out a deep, rumbling fundamental sound on top of which the high harmonics can mingle.

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Example 6: Thrust A similar multiphonics to the one displayed in example 5 appears in Kimmo Hakolas Thrust (1989), where the finger position is very close to the nut (slightly above the open string). Here again the effect is an oscillation between adjacent harmonics and the fundamental. Contrary to the previous example, the expression here is strong, almost wild, with an intense mingle of high and low frequencies. I would suggest the bow position(s) to remain between ordinario and molto sul ponticello. Ex. 6. Kimmo Hakola: Thrust, page 8, rubato [andante]

Example 7: Sonata for double bass Only a few instances of quartertonic multiphonics appear in Michael Liebmans Sonata for double bass (2001). Liebman uses the technique of gradual transformation as an input to the multiphonic sound; coming from a single flageolet in a quartertone finger position, with a very light bow pressure (L.pr.), the gradually intensified pressure (N.pr.) carefully transform the flageolet sound into a chord effect. These occurrences are shown in examples 7a and 7b. In example 7b, the transformation from a flageolet into a chord effect happens towards the middle of the system (the accidentals applying to the whole system). Ex. 7a. Michael Liebman: Legato Sonore, page 1, third system

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25

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Bow-above-finger multiphonics Bow-above-finger multiphonics generally more easy to play than class-two type multiphonics, but doesnt offer as many variations in sonority. Since most of the multiphonics are produced with the finger is positioned close to the end of the fingerboard or beyond the fingerboard, between bow and bridge, they require some preparation time unless being used in phrases where the left-hand is already playing high up on the strings. It is possible to play relatively loud and violent with bow-above-finger multiphonics, but also extremely soft with a smooth, even sound. Example 1: e/statico Stefano Scodanibbio composed e/statico in 1980 as one of his first pieces for the double bass. The piece investigates isolated sonorities, in which various sound shapes, usually separated by pauses, seem to be juxtaposed without any meditation. In example 1, the finger is places somewhere beyond the end of the fingerboard on the D-string, between bow and bridge, and the multiphonic sound lives its own short life during the two bow strokes that are indicated. Ex. 1. Stefano Scodanibbio: e/statico

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26

Example 2: Joke A loud, noise-like gesture surprise us in Scodanibbios Joke, the first movement from his Sei Studi (1981-83). The double bass really screams through this rather swift glissando of bow-above-finger multiphonics, performed on strings one and two. Ex. 2. Stefano Scodanibbio: Joke, from Sei Studi

Examples 3-4: oibbinadocS In oibbinadocS (2004) I use a technique where I combine bow-above-finger multiphonics with a natural harmonics. The sounds are played on each side of the bow: The harmonics is fingered with the thumb above the bow (closer to the nut), while the multiphonics is fingered below the bow (closer to the bridge). The position of the left-hand is being anticipated though double-stops of harmonics, and only a slight movement is needed to bring the bow into the new position between the fingers. Examples 3 and 4 are from the very beginning and end of the piece. Ex. 3. Hkon Thelin: oibbinadocS Ex. 4. Hkon Thelin: oibbinadocS

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Pizzicato multiphonics

Pizzicato multiphonics is used extensively in all of the two-hand flageolet pizzicato passages in my piece Glasperlenspiel (2010). I wanted the effect of loud, ringing tones to equal the tones that are being hammered by the left hand on the fingerboard. A passage is shown in example 1, where pizzicato multiphonics can be studied in bar 90 and bar 92-95. The left-hand flageolet pizzicato and hammer-on is notated with upward stems, while the right-hand pizzicato is notated with downward stems. Ex. 1. Hkon Thelin: Glasperlenspiel

28

Colourative Effects In the following, I will present effects that determine the colouration of multiphonic sounds. There are multiple combined techniques that are used in a great number of works, and my aim has been to provide a thorough presentation of existing techniques and their practical utilisation in a selection of composed works. The multiphonic technique is still in its early stages of development, and there are many more sounds to be discovered. This general presentation can be seen as a first excursion in to the field of multiphonic sound effects and will hopefully serve as an impulse or inspiration for further explorations into this technique, by both performers and composers. Transformation Semitonic multiphonics can be transformed into harmonics, ordinary tones or other sounds. In Foxfire Zwei, I use the gradual change between multiphonics, harmonics, fundamental and air sounds, to create living sounds, constantly changing the colour of the multiphonics. In example 1, the sounds change gradually between multiphonic, harmonic and air sounds (created by damping the string with the left hand and playing with a light bow). The changes between multiphonic and harmonic sounds are caused by small changes in bow position, pressure and speed. Ex. 1. Transformation between multiphonic, harmonic and air sounds. Helmut Oehring: Foxfire Zwei (arr. Hkon Thelin)

Transformations from harmonic to multiphonics are possible through changing the spot at which the bow touches the string and by applying additional pressure to the string (Liebman, Movement of Repose, New sounds for cello and double bass, page 31). The bow must be moved to a central harmonic node, which facilitates the creation of the multiphonic sound. A smooth transition can be controlled by manipulation of bow pressure and bow speed. Usually this means applying more pressure to the string and bowing with a slightly reduced speed. Illustrations of this effect are shown in example 2 and 3. In example 2, the bow should move to the central harmonic node position 13 when modulating into the multiphonic sound. Ex. 2. Transformation from harmonic to multiphonics. Hkon Thelin: Light

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Ex. 3. Transformation from harmonic to multiphonics. Michael Liebman: illustration from Movement of Repose, New sounds for cello and double bass

In Thrust, Kimmo Hakola makes use of sound transformations by alternating multiphonics and ordinary tones. The effect is a rather quick in-and-out transformation of the sound. The bow pressure must be precisely synchronised with the left hand movement in order to get the full effect of the changing sounds. Ex. 4. Transformation between multiphonics and ordinary tones. Kimmo Hakola: Thrust, page 7, Rubato (Adagio)

The transformative process seen in example 5 shows an artificial multiphonics on the E-string, to be played together with the open A-string. This artificial multiphonics dissolves into an open string, which again is gradually converted into a multiphonic sound as the finger slowly dampens the string over the E-flat harmonic. The bow position indicated above the stem (B E22! and B13) is notated in accordance to figure 3 and example 5b in the chapter on Bow placement.

30

Ex. 5. Transformation from artificial multiphonics, via open string, to semitonic multiphonics. Hkon Thelin: Glasperlenspiel

Tremolo Tremolo is possible on most multiphonics. The effect is usually a noisy, complex, and often, unstable sound. The types of multiphonics that are easy to play, give the most stable noise-like sounds when playing tremolo. Example 6 includes this effect with tremolo multiphonics on the second and third strings, the sounds being initiated by slightly accentuated grace notes. All the multiphonic sounds in this example are rather easy to play. Ex. 6. Tremolo. Hkon Thelin: Shared moments

Example 7 illustrates ordinary multiphonics going into tremolo multiphonics and vice versa. Ex. 7. Going in and out of tremolo. Helmut Oehring: Foxfire Zwei (arr. Hkon Thelin)

When applying tremolo on multiphonics that are more difficult to play, careful attention must be given to finger pressure, bow position and bow pressure, for the sound generally fluctuates more randomly between the overtones. Multiple variations of the tremolo effect are possible, e.g., changing bow speed (slow or fast tremolo), changing bow pressure (greater pressure creates a harder, more noisy sound while less pressure gives a brighter, airy sound), and changing bow position (this can enhance certain overtones of the cord as well as the overall timbre of the cord). Vertical vibrato, hammer-on multiphonics and legato tremolo Michael Liebman employs what he calls a vertical vibrato to multiphonics: By rapidly varying the amplitude of finger pressure on a string from slight to deep (almost, but not actually touching the fingerboard), we achieve the vertical vibrato[...] (Movement of Repose, New sounds for cello and double bass, 2010, page 35). Hitting the string against the fingerboard creates a variant of this technique. Liebman writes [] in such cases, in addition to the multiphonic chord, a "flickering" tone is produced corresponding to the point where the finger

31

touches the fingerboard (Ibid., page 35). The presence of the stopped note in the sound can also be controlled by how hard the finger hits the fingerboard. I will refer to this technique as hammer-on multiphonics. Liebman further describes an open string tremolo where the player rapidly alternates between touching the string and raising the finger. An effect I would describe as a legato tremolo between the multiphonics and the open string. It is possible to control the presence of the fundamental tone through the force of the finger that pulls the string; contrary to the faint fundamental sound that is perceived when the finger is only lifted (and not pulled) from the string. In example 8, the first action is a vertical vibrato (where the finger does not touch the fingerboard), followed by a legato tremolo between the multiphonics and the open string. I would interpret this particular legato tremolo as to be performed only with a slightly lifted finger, so that the change of timbre is only scarcely audible, and led naturally on from the vertical vibrato. The third action in example 8 is a rhythmical vibrato, the effect being created when the finger softly hits the harmonic a half note above the multiphonics. Make sure that the multiphonic sound is kept constant throughout the action. Ex. 8. Vertical vibrato, legato tremolo and rhythmical vibrato. Michael Liebman: Sonata for double bass, 2.movement Legato sonore

The different types of vibrato, legato tremolo and hammer-on multiphonics are relatively idiomatic techniques. They open up a wide area of rhythmical possibilities as well as means of colouring multiphonic sounds. In Shared moments (2009), I use hammer-on multiphonics, which, during the course of interpretation was played as a sound that rapidly alternates between and blends the multiphonics, stopped note and open string. The notation in example 9a and 9b, however, is still the same as with hammer-on multiphonics. The techniques can be seen in the context of the longer musical line in example 9c. Ex. 9a. Hammer-on multiphonics. Hkon Thelin: Shared moments

Ex. 9b. Hammer-on multiphonics. Hkon Thelin: Shared moments

32

Ex. 9c. Hammer-on multiphonics. Hkon Thelin: Shared moments

Example 10 shows a legato tremolo on the A-string with a flageolet trill on the F on the D-string, while a variation is shown in example 11 where a legato tremolo on the A-string is combined with an artificial harmonic on the D-string. The two multiphonics used in these examples are easy to play and most bow positions work well. The occurrence of artificial harmonics, however, calls for a placement of the bow somewhere towards the bridge, although not necessarily sul ponticello. Ex. 10. Legato tremolo combined with artificial harmonic trill on the adjacent string. Hkon Thelin: Light

Ex. 11. Legato tremolo combined with artificial harmonic on the adjacent string. Hkon Thelin: Light

In a passage from Glasperlenspiel, shown in example 12, I use legato tremolo and hammer-on multiphonics in a play with timbre and harmonies. The first action is a legato tremolo on the D-string, where the multiphonic sound blends with the opens string. A crescendo brings

33

the sound into a hammer-on multiphonics on the E-string. The hammered C perceives as a fundamental, with intermingling partials of the E-string multiphonics. The open strings, plucked as appoggiaturas with the left hand, resonate with the legato tremolo multiphonics, which is now stripped from the C fundamental. The sound again rises through a crescendo into hammer-on multiphonics on the A-string, where the E-flat fundamental intermingles with the A-string partials, sounding together with the appoggiaturas of the E and G-strings. Ex. 12. Legato tremolo and hammer-on multiphonics. Hkon Thelin: Glasperlenspiel

A technique that is not shown here, but waiting to be explored later on, is the legato tremolo between multiphonics and either an open string, harmonic or stopped note on an adjacent string. Richochet Example 13 illustrates the opening of Shared moments. The musical gesture of this opening is repeated several times during the entire piece and can be seen as a play with timbre and resonance between the four strings. Each note is coupled with a unique attack: the short notes are played with left hand pizzicato and with the tip of the bow, while the long notes are played with a bouncing bow. A ricochet on a multiphonics then establishes the first extended tone with an accentuated and quick bouncing bow in order to release the multiphonic sound. This sound leads to the second attack where a (quick) ricochet transforms into a vertical bouncing bow, called rimbalzo verticale by Stefano Scodanibbio, which is characterised by a soft, flickering sound. Ex. 13. Richochet. Hkon Thelin: Shared moments

Playing simultaneously on two adjacent strings By adding the additional tone of an adjacent string new colours may be added to a "tonal" sounding multiphonic chord. This change may vary from a slight coloration, to dissonance, and even to a complete transformation of the colouring. 1. Multiphonics with an open string In example 14 we see an artificial multiphonics played together with an open A-string. The bow position for the artificial multiphonics is assigned to the 10th harmonic partial on the E-

34

string. The added open A-string darkens the sound and gives a slight perceptible harmonic feel in the minor third interval between the fundamental tones (G-A). Ex. 14. Artificial multiphonics played together with an open A-string. Hkon Thelin: Glasperlenspiel

The static sound that we meet in the previous example comes to life through trills and glissando movements of the multiphonics in example 15. A rumbling, full sound is heard when the glissando slowly moves towards the sound of the open string. The fundamental and the overtones in the multiphonics create a complex, constantly changing, set of interference tones with the open string drone. As in the previous example, the bow can be placed on the 10th harmonic partial on the E-string, but must be moved proportionally with the left-hand glissando up the string. Ex. 15. Artificial multiphonics trill played together with an open A-string. Hkon Thelin: Glasperlenspiel

2. Multiphonics with a natural harmonic Ex. 16. Multiphonics with a natural harmonic. Maja S. K. Ratkje: On Wombs and Vowels

In her piece On Wombs and Vowels, Maja S. K. Ratkje uses a combination of multiphonics and natural harmonics. This does not change the bright sounding colour of the overtones but

35

adds a dimension to the harmonic spectrum. The notation is practical and easy to read: In the first bar, the harmonics (top notes) are played on the first string while the multiphonics (bottom notes) are played on the second string. In the second bar, the multiphonics are the same as in the previous bar but with the harmonics played on the third string. In bar three, we have a new set of multiphonics on the third string that is played together with harmonics on the fourth string. The gradual descent from high to low strings creates a change of colour from bright to dark. On the low strings the cords have a full sound with much resonance, while the brighter sounding chords on the higher strings sound more restrained and are also more difficult to play. Bow placement is left to the decision of the performer. There are multiple options, in order to bring out the sound of the harmonic, however, a placement relatively close to the bridge is preferable. Examples 17 and 18 are taken from the double bass solo that opens Giants of jazz (1999-2001), a piece by the Norwegian composer yvind Torvund. The top stave indicates the rhythm of the bowing as well as the sounding note of the harmonics, which is notated on the lower stave and played together with normal tones or other harmonics. Towards the end of the system, the phrases are closed with combined sounds of chords consisting of multiphonics and natural harmonics. The multiphonic chords are not notated, but are marked as a cluster sound. Ex. 17. Multiphonics with a natural harmonic. yvind Torvund: Giants of Jazz

Ex. 18. Multiphonics with a natural harmonic. yvind Torvund: Giants of Jazz

3. Multiphonics with a natural harmonic trill As illustrated in example 19, this combination lets us play multiphonics together with a trill of natural harmonics on an adjacent string.

36

Ex. 19. Multiphonics with a natural harmonic trill. Hkon Thelin: oibbnadocS

Here we move from a flageolet trill on the second string, coloured by the gradual movement of the bow, into a multiphonics together with a natural harmonics trill. The effects of both sounds are similar, the multiphonics functions as a stable summary of the floating overtones of the previous action while the additional trill continues the established action and enrichens the harmonic spectrum. Michael Liebman includes the same technique in his Sonata (example 20), but uses a different notation. He classifies this technique as chord and harmonic with tremolo, and describes: []such a tremolo effect produces a variety of additional overtones. In ponticello, even a slightest shift of the bow gives a new overtone, thus varying slightly the effect on each repetition. (Movement of Repose, New sounds for cello and double bass, 2010, page 38). The variety of additional overtones creates a strongly fluctuating sound, which can be differentiated even more by moving the bow towards the bridge. Ex. 20. Multiphonics with a natural harmonic trill. Michael Liebman: Sonata for double bass, 2.movement Legato sonore

In example 21, I have used a sustained multiphonic sound together with a trill between a flageolet and the open string on the adjacent string. The combination shown here is easy to play because I use one of the most stable semitonic multiphonics on the fourth string the augmented 4th in the first octave. In this case, it is, therefore, not necessary to notate a specific bow position. Ex. 21. Multiphonics together with a trill between a flageolet and the open string on the adjacent string. Hkon Thelin: Shared moments

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Example 22 shows the same technique as used in the previous example, yet shifted to the higher strings (second and third strings). Ex. 22. Multiphonics together with a trill between a flageolet and the open string on the adjacent string. Hkon Thelin: Light

4. Two multiphonics together It is generally very difficult to play sustained chords of two multiphonics together. Even though the same bow placement applies for both multiphonics, the bow resistance (speed and, most often, pressure) differs from string to string, making it difficult to avoid slips that break the sound. In Glasperlenspiel I made an attempt of combining two multiphonics, with a defined bow position moving from B13! on the first single multiphonics, to the slightly lower position of B11! for the combined multiphonics. The bow position one octave higher (B13 to B11) also works well with these multiphonics, although the bow speed and pressure react differently when changing octaves with the bow. Ex. 23. Two multiphonics together. Hkon Thelin: Glasperlenspiel

5. Noise-like multiphonic sounds Glissando between semitonic and quartertonic multiphonics, combined with the open E-string in a noisy passage are found in Kimmo Hakolas Thrust (1989). The objective here is not to bring out clearly defined multiphonics, but to create as much noise and sound as possible! Ex. 24: Noise-like multiphonic sounds. Kimmo Hakola: Thrust, page 2, Allegro

38

Acknowledgements I wish to thank Knut Guettler for his significant contribution to this work. The whole section of Definitions is written in close collaboration with Guettler, and he kindly shares his own research on the physics of multiphonics through the article Bowed-string multiphonics analyzed by use of impulse response and the Poisson summation formula. The work of Michael Liebman, Mark Dresser and Stefano Scodanibbio has been an invaluable source and inspiration. In addition they have given me feedback and answered my many questions. I have been in contact with almost all composers represented here. Their works are all very important in incorporating double bass multiphonics into the repertoire of contemporary music. Litterature Anderson, Julian: Seductive solitary, article (p.616-619), The Musical Times, December 1992 Bach, Michael: Fingerboards and overtones, Edition Spangenberg, Mnchen, 1991 Bartolozzi, Bruno: The new sounds for woodwind, Oxford University Press, 1967 Dresser, Mark: A personal pedagogy, Arcana: musicians on music, John Zorn (ed.), Hips Road and Grananry Books, 2000 Dresser, Mark: Double bass multiphonics, article (Masterclass, p.72-75), The Strad, Vol. 120 No. 1434, October 2009 Guettler, Knut and Thelin, Hkon: Bowed-string multiphonics analyzed by use of impulse response and the Poisson summation formula, article accepted for publication (2011) in Journal of Acoustical Society of America Liebman, Michael: Multiphonics: new sounds for double bass, unpublished article, 2001 Liebman, Michael: Movement of repose, New sounds for cello and double bass, Kompozitor Publishing, 2010 Robert, Jean-Pierre: Modes of playing the doublebass, Editions Musica Guild, 1995 Turetzky, Bertram: The Contemporary Contrabass, rev. version, University of California Press, Berkely and Los Angeles, California, 1989 List of scores Philippe Boivin: Cinque Algorithmes pour contrebasse seule, 1990, Editions Salabert Eivind Buene: Bass duo from Into the Void, 2008, Norwegian Music Information Centre Lars-Petter Hagen: Hymn, 2008, Norwegian Music Information Centre Kimmo Hakola: Thrust, 1989, Fazer Music Inc., Finland Michael Liebman: Sonata for double-bass, 2001, manuscript from composer Carlos Mastropietro: En una cara, 1996, manuscript from composer Helmut Oehring: Foxfire Zwei, version for solo double bass by Hkon Thelin, 1993/2007, manuscript from composer Maja Solveig Kjelstrup Ratkje: On Wombs and Vowels, 2003, Norwegian Music Information Centre Maja Solveig Kjelstrup Ratkje: Rondo-Bastard-Overture-Explosion, 2004, Norwegian Music Information Centre Kaija Saariaho: Ciel toil, 1999, Chester Music Stefano Scodanibbio: e/statico, 1980, manuscript from composer Stefano Scodanibbio: Sei studi, 1981/1983, manuscript from composer Hkon Thelin: Glasperlenspiel, 2010, manuscript from composer Hkon Thelin: Light, 2008, manuscript from composer Hkon Thelin: oibbinadocS, 2004, manuscript from composer Hkon Thelin: Shared moments, 2009, manuscript from composer Hkon Thelin: Krma, 2010, manuscript from composer yvind Torvund: Giants of Jazz, 1999-2001, Norwegian Music Information Centre

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4

Charts of Semitonic and Quartertonic Multiphonics The charts show the finger positions of the most usable semitonic multiphonics, on each string up to the 4th octave. The central harmonic nodes (9, 11, 13 and 22) indicate possible placements of the bow, and the general numbers shown in the charts include all positions explained in figures 1 and 2 in the chapter on the bow. Bow positions that are practically unusable, and even impossible, are listed in the parentheses after the indication of the general central harmonic node. These exceptions may vary from player to player and between instruments, but my listings provide anyway a well-tested and general foundation for the use of multiphonics. The consideration of the playability of multiphonics quickly becomes an intimately personal matter. The instrument set-up, choice of strings, and the performers own style of playing, are all decisive qualities. Yet, I try to implement a general comparison between the different multiphonics and make an overall division in difficulty. Most multiphonics has one or several contact points for the bow on the string where it is easier to play the multiphonics than on other contact points. Consequently, a multiphonics that is classified as difficult may also have a contact point for the bow where it is easier to produce the chord. The maj3, 5th and min7 of the third octave, as well as the fourth octave semitonic multiphonics are played in a similar way, and with a similar type of bow resistance, as bow-above-finger (first-class) multiphonics. They also sound similar, but are slightly more difficult in controlling the stability of the cords. Quartertonic multiphonics is more difficult to play than semitonic multiphonics. It is at this time not appropriate to include more quartertonic multiphonics in the table due to the difficulties of placing the finger at the exact point on the string, and thus bring out the defined overtone in the given position. In the prescription of the bow positions for quartertonic multiphonics, I add also the levels above the main central harmonic nodes to the chart. For example, the levels above the 11th central harmonic node are notated as 22 and 33 (indicating the 22. and 33. harmonic node). This comes in addition to the level below the central harmonic node, notated as 11!, which is also used for the semitonic multiphonics. The bow node positions for quartertonic multiphonics are illustrated in figure 1. Descriptions of the bow node positions are given the chapter on the Bow. Only the central harmonic nodes are indicated in the chart of quartertonic multiphonics, but all bow positions in figure 1 apply. Within the first position (for quartertonic multiphonics) on each string it is possible, by very small changes in the finger position, to bring out the 7th, 8th or 9th harmonic partial. Different bow placements must be used to create multiphonics on each of these harmonic partials, which is indicated in the chart. The 8th and 9th harmonic partials are situated very close to the precise placement of for example a quartertone above A on the G-string. By moving the finger slightly closer to the perfect A, the 7th harmonic partial can be established as the sounding harmonic partial. It is relatively easy to play all quartertonic multiphonics, provided that the finger and bow positions are exact. It becomes more easy to play the multiphonics as the bow moves closer to the bridge, as it is usually more difficult to hit the exact node for the bow in the lower positions. Fig. 1. Bow node positions for quartertonic multiphonics

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Documents

Multiphonics on the Double Bass