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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 Liebman’s table doesn’t 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 Liebman’s 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.

Fig.2. Chart by Håkon 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, Liebman’s bow positions are included for comparison. Even though the harmonics’ positions in this figure are marked on single strings only―for reasons of clarity―they 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 Håkon 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.

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 Liebman’s designations for pressure and speed, with a reduced category of pressure and with capital letters for easier reading:

Fig.4: Chart by Håkon Thelin on bow resistance

Pressure: Speed:
Light pressure - L.pr Slow bow
Normal pressure - N.pr. Quick bow
Heavy pressure - H.pr.

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 bow’s 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.

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.

Ex. 5c. Glasperlenspiel, Håkon Thelin

Fig. 5d. Glasperlenspiel, Håkon Thelin

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 didn’t 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).

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.

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, Håkon Thelin