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Some acoustical principles of clarinet multiple sounds

The general acoustic principles of the clarinet have been previously discussed; our problem here is to discover how they explain the phenomenon of multiple sounds.11 It is obvious that multiple sounds are based on partials of a fundamental pitch. However, they are not always related as odd partials of one likely fundamental. Where do these unrelated partials come from, then? The answer may be related in some way to the even partials that exist in particular clarinet spectra mentioned by Backus and others.12 These findings are important when one considers the derivation of pitches in clarinet multiple sounds; pitches which are not logically explained as the odd-partials of a given

fundamental, may actually be out-of-tune, even-partials, or partials from another fundamental.

It is clear that multiple sounds are based on partials of at least one fundamental, but why are there such drastic timbre differences between multiple sounds and between

individual pitches of one multiple sound? There must be more to an explanation of the acoustics of multiphonics. Unfortunately, many terms used to describe multiple sounds are misleading and oversimplified. Early acoustical descriptions of woodwind

multiphonics often refer to them as "harmonics," pertaining to partials produced

according to the standard overtone series from a fundamental pitch. This is a dangerous usage, since it invites comparison to string harmonics, which consist of one pitch

produced from a single fundamental. In reality, the more accurate acoustical explanation of clarinet multiphonics is much more complex and not universally agreed upon.

Another misnomer is the labeling of multiphonics as "chords." Again, a comparison with string double or triple stops is not appropriate, since each multiple sound has a different texture as well as a different timbre and intensity for each of its tones.

Ronald Caravan has suggested some interesting theories in his 1974 dissertation.13 He cautions us, however, with regard to our interpretation of numerical figures to draw conclusions about the acoustical characteristics of the clarinet. "The human variable, which must be present to produce the sounds is great....it appears that it possesses a greater latitude of variation than the margin for error would impose even in

computations on as elementary a level as those made here."14 Nevertheless, results from spectrum analyses that he conducted fuel speculation that more than one fundamental and set of overtones are present in each multiple sound. When a multiple sonority is produced, it appears that there are actually two tube lengths at work simultaneously (Example #1).

Example #1

This seems to be supported by the following example, which shows a sequence of multiphonics with a lowest pitch that changes very little from one to the next (Example

#2).

Example #2

The upper pitches, however, gradually progress upwards. It is significant that the left hand fingering remains the same; it appears that the open hole (second finger, left hand) behaves as the terminating hole of the shorter tube (Caravan calls this L1). This is similar to a E3 fingering, but is slightly lower because of the additional fingers on the right hand placed over holes. The right hand fingers gradually are lifted (in a chromatic or microtonal ascending motion); these control the length of the longer tube (L2), and cause the higher pitch, and to a lesser extent the lower pitch, of the multiphonic to gradually ascend. Thus, the terminating hole of tube L1 (open hole in the left hand fingering) also functions as a register opening or vent for L2. Caravan has labeled this hole the "register-terminator hole." THE REGISTER-TERMINATOR HOLE

PERFORMS TWO SIMULTANEOUS FUNCTIONS: IT TERMINATES THE SHORTER TUBE AND ACTS AS A REGISTER OPENING OR VENT FOR THE LONGER TUBE.

Obviously, since all fingerings on the clarinet with these characteristics do not produce multiple sounds with the same ease, there must be particular limitations to the register-terminator hole. Caravan believes, through a series of informal tests, that the size of the diameter of the register-terminator hole is crucial to the ease of multiphonic production.

Decreasing the size of a successful register-terminator hole lessens the ease with which the hole can be made to act as the end of a length of pipe (L1); increasing the size of a successful register-terminator hole increases the ease with which this hole can act as the terminator of a length of tube, but decreases its ability to act as a register hole for the longer tube (L2). In other words, the smaller the opening of the register-terminator hole, the greater the tendency to act exclusively as a register hole, and the larger the opening, the greater the tendency to act exclusively as the effective termination of a tube length.

This theory can be used to explain why multiphonics that use the conventional register key, which has a small opening, as their register-terminator hole are more difficult to produce.

Caravan has also hypothesized that the ratio between the length of tube 1 and tube 2 must also be more than 50% and less than 80% for a multiple sound to work well.

However, he admits that the size of the register-terminator hole most likely effects the relative success of these ratios. The number of variables are, indeed, numerous.

With these theories in mind, the pitches of a multiple sound in Example #2 can be explained as follows:

The lowest pitch of a) is derived from tube length L1 (c). This pitch (a sharp D3) is lower than E3 because of the added fingers of the left and right hand below the register-terminator tone hole (2nd finger of the left hand). The G4 and C-sharp5 found in multiphonic a) are produced from tube length L2 (b). This tube length would normally produce the 3rd (E4) and 5th (C-sharp5) partials above its fundamental (A3). The middle pitch of multiphonic a) is a minor third higher than the normal third partial (G4 instead of E4) because of the excessive size of the terminator hole.

It has often been noted that the same multiphonic fingering will not produce the same pitches for different players, or even for the same player from one day to the next. It is true that on equipment of the same system (Boehm, for example), the precise pitch content may not be consistent; however, these are very minor variations, at least in the multiple sounds presented in this study. These inconsistencies can result from any of a

variety of reasons; an unbalanced reed, an insufficiently warmed-up instrument, specific mouthpiece characteristics, or customized clarinets, are four frequent causes. More likely, however, are deficiencies found in the construction of all clarinets and/or properties of the acoustical phenomena involved. As Paul Drushler points out, the clarinet is very much out of tune in its upper register (based on upper partials).15 As a result, fingerings must be altered to play single pitches. However, fingerings can not be changed for each pitch of a multiple sound; they, therefore tend to be out of equal-tempered tuning, very often creating acoustical beats (amplitude modulation or

interference tones) which can change markedly according to the adjustment of the reed and mechanics of the instrument. In addition, the combination of sonorities in a multiple sound may often produce difference or summation tones.16 Difference tones may only be audible if the pitches of the multiple sound are in tune and at an adequate volume.

All of these acoustical phenomena may alter principle pitches, add new pitches, or appear to the ear to do either (often they change or fade in and out during the period of sustain of the multiple sound).17 Spectrum analyses by Caravan indicate that the strengths and tunings of partials which comprise multiple sounds do not remain in a very stable relationship among one another while the sound is produced, even though the composite sound may appear to remain constant to the listener.18 One more variable that comes into play is the fact that pitches in a multiple sound may alter because of the adjustments required of the player to produce the split sonority; this will generally lower pitches (Example #2 is a good illustration).

Caravan presents some other valuable, although more general, insights as to why certain multiphonic fingerings seem to work better than others. "Important to note is that the smaller the degree of departure from normal playing practices a multiphonic fingering requires, the more manageable it is."19 This is logical, since the instrument has been built to deal with problems of standard performance practice. Multiphonics built from new, but technically feasible, fingerings are closer to standard performance practice than multiphonics produced from conventional fingerings through varying the oral cavity, breath pressure, and/or embouchure. Extreme flexibility of embouchure and breath, as well as flexible mouthpiece and reed set-ups, have long been characteristics of jazz players. Thus, it is not surprising that many of William O. Smith's multiphonics are produced by this manner. The author supports Caravan's statement about the unpredictability of this type of multiple sound. "The problem with multiphonics produced in this way is that in most cases they require such significant adjustments on the part of the performer that they tend to be very difficult to play, tend to be quite unstable and limited in dynamic range, and may not be attainable by every

performer."20 Composers should be cautious when writing such sonorities.

Chart of Multiple Sounds for Clarinet

The following chart has been compiled from hundreds of musical compositions, and experiments; it has been checked by numerous players for accuracy. I have striven to organize the material according to acoustic principles of the clarinet and basic principles of clarinet technique. All of the multiple sounds presented are playable on any

traditional professional mouthpiece/reed set-up. They demand only slight deviations from normal finger expectations and embouchure.

Many previous studies have organized multiple sounds according to verbal descriptions of categories of production and/or sound, regardless of acoustical relationships. This

study employs acoustical relationships as the first order of organization, and briefly describes characteristics of each multiple sound (see explanation of notation, below). Of course, it is impossible to discuss every conceivable context for a particular multiple sound. BE SURE TO CONSULT A CLARINETIST ABOUT FEASIBLE CONTEXTS FOR PARTICULAR MULTIPLE SOUNDS.

Multiple sounds have been placed in groups (labeled by letter, beginning with those with the lowest fundamental); a common denominator within each group is an identical register/terminator hole. In other words, the left hand fingering remains constant within a group. The multiple sounds are ordered according to the right hand fingerings which ascend in chromatic or microtonal intervals. Care has been taken to insure that these groups are playable as sequences; this means limited (minimum) finger movement, and a lack of contrary motion, wherever possible. The fastest possible tempo of legato connections of multiphonics within a group has been notated between the staves:

very fast fast

moderately fast moderate not possible

A broken vertical line ( ) between multiple sounds in a group indicates that a legato connection is not possible, even though the adjacent sounds utilize the same series of partials. A double bracket ( [ ] ) between sounds in a group indicates that a legato connection is not possible, because the series of partials changes.

Groups of multiple sounds with the same letter label (ie. A, A1, A2 etc.) utilize slightly different, but related left hand fingerings (different vents). For example, left-hand fingerings in Group A1 differ from Group A only through the addition of the register key. Left-hand fingerings in Group A2 differ from Group A only through the addition of the A-key, etc. The close technical relation of these groups makes numerous trills and tremolos possible between them (discussed later). Left-hand fingerings for A represent the lowest bottom pitches - left-hand fingerings for Z, the highest bottom pitches.

It is important to note that each multiple sound listed is available in isolation; it need not be connected to another. Various characteristics of each multiple sound have been described beneath each example in the chart. The format of this chart, top line to bottom line, is:

I - a number (1-462) - this number represents the position of this multiple sound in relation to the others in the chart, according to its lowest (and highest) pitch. The multiphonic with the lowest low pitch is #1; the multiphonic with the highest low pitch is #462.

II - dynamic range possible - pp to FF

III - stability: how stable?

a = very stable is the sustain b = moderately stable c = unstable

IV - response: the time required to begin all sounds of the multiple sound?

1 = all sounds begin simultaneously, easily 2 = all sounds appear within 1 second, easily 3 = all sounds appear within 2 seconds, resistant 4 = all sounds appear within 3 seconds, more resistant 5 = all sounds appear within 4-5 seconds, very resistant

V - timbre and texture - some general characteristics deserve mention here:

1) All diads will contain a significant amount of air when played softly.

• All multiple sounds that use keys 3 and/or 4 as register vents will have thin timbres.

• Most of the multiple sounds that do not contain undertones are capable of generating higher partials than

indicated in the chart when played very loudly. However, the production and content of these partials are not controllable or reliable.

timbre descriptions are divided into 2 categories:

a) those which describe individual pitches of a multiple sound b) those which describe the overall texture of a multiple sound dull - lack of partials

dark - few higher partials dlbt. or dl.b - dull lowest pitch wide - predominant lower partials thin - pitch is weak, lack of partials

_______________________

ft - (fat) many partials (low & high) brt or edge - (bright) many higher partials brtp - bright highest pitch

eltp - electronic "edgy" highest pitch thtp, t.h., or th.t - thin highest pitch wktp - weak highest pitch

s.tp - strong highest pitch _______________________

sbtn - subtone

=========================

elc - (electronic) 3 or more pitches, thin timbres, acoustical beats

elc! - (raucous electronic) - changing amplitudes of pitches (similar to electronic,otherwise)

bts - (acoustical beats) - acoustical beats caused by out of tune intervals slbt or sbt - (slow acoustical beats)

thk - (thick) many pitches thk! - very thick

mud - (muddy) unclear pitches _______________________

ns - noise in the sound

s.ns - some noise in the sound air - air sounds apparent in sonority _______________________

bal - (balance) all pitches of equal intensity

3vc - three voices mvc - many voices

holl - (hollow) - high and low pitch (no middle frequencies) tran - (transparent)

lite - (light) thin timbres gent - (gentle) dull timbres soft - dull timbres

rest - resistant

_______________________

diad - two pitches (an undertone - lowest pitch is weaker than the highest) Mtr! - predominant major 3rd (10th) or triad

M3! - major 3rd

VI - technique - (hints for easier production) ls! - looser embouchure, less air pressure tite - tighter embouchure, more air pressure d.lw - difficult to produce lowest pitch

!tp - aim for highest pitch

VII - arpeggiation - capability to begin multiple sound with top or bottom pitch alone, gradually adding other pitches:

top - easy to begin with top pitch bot - easy to begin with bottom pitch m.d. - moderately difficult

d. - difficult

Chart of Multiphonics

The notation system used in this chart for multiple sounds on the staff is one which the author hopes will become standardized. All pitches (or as many as possible) in the multiple sound should be written on the staff. The filled-in note heads indicate

secondary pitches, which may or may not be present according to the dynamic level of the multiple sound. It is important that the fingering for a multiple sound be indicated at

every occurrence in the music, directly under the sonority. These procedures will greatly assist the clarinetist in learning the music.

The website for The Clarinet of the Twenty-First Century has an interactive, searchable database of multiphonic fingerings (http:// ) for clarinetists and composers. One may choose multiphonics based on any or all of the variables below:

lowest pitch highest pitch

number of pitches (2, 3, more than 3)

softest dynamic possible (pp, p, mp, mf, f, ff) loudest dynamic possible (pp, p, mp, mf, f, ff) stability (very stable, moderately stable, unstable)

resistance (easy, somewhat resistant, resistant, more resistant, very resistant) possible to begin from lowest pitch alone?

possible to begin from highest pitch alone?

noise in sound? (no noise, some noise, much noise)

strong acoustic beats in sonority? (not apparent, some, many) color extremes (none, dull, bright)

The website also has a database for sequences of multiphonics. The searchable variables include:

sequence with stationary lowest pitch? Which pitch?

sequence with stationary highest pitch Which pitch?

easy technical sequences - fastest possible tempo (moderate, moderately fast, fast, very fast)

Diads

Another category of multiple sounds that has received innovative treatment in several works is diads. These sonorities are generally only possible at very soft dynamic levels, and tend to have very dull, pale timbres. The interval between top and bottom pitches is

generally either a major or minor tenth. Many of them are undertones, with top pitches commonly between G-sharp4 and C5.

Isolated diads are adopted in Matsuo's Hirai III (1987), a concerto for clarinet and strings. They are blended in a marvelous texture of string harmonics (Example #13).

Example #13

Other conventional fingerings in the clarion and altissimo registers of the clarinet are available for producing marvelous dynamic and timbre contrasts with the throat register, by simply releasing the register key.

Example #23

Drake Mabry, in his work Street Cries for Solo Clarinet (1983), employs diads that gradually and softly fade in from their lowest pitch.

Example #24

Multiphonic Sequences

A number of multiphonic sequences are quite easy to produce in legato articulation. In most cases, the multiphonics in the sequence may be played in any order (indicated here). Thirteen examples are given below (with indications of fastest possible tempo) – 48 more are available on The Clarinet of the Twenty-First Century website (

http://www.research. umbc.edu/~emrich/multiphonic sequences.html ).

• Moderate tempo; any order (click on music for mp3)

2) any order [A3] (click on music for mp3)

Richard Boulanger, an American composer from Boston, also writes an effective sequence of multiple sounds in Construction #1 for Clarinet and Electronics. The top pitches relate to the melodic cell from which the work is generated (Example #41).

Example #41 (click on music for mp3)

Richard Boulanger CONSTRUCTION #1

All Rights Reserved

Used by permission from the composer

Yuasa creates appropriate musical moods through the use of sound characteristics of the following multiphonics within a phrase: the gentle qualities of #50a serve as a relaxed phrase ending; the variety of dynamic capabilities of #50b permit its use as part of the fpp thematic germ throughout the work (Example #50).

Example #50 (click on music for mp3)

Yuasa also makes very effective use of thick, distorted multiphonics at the climax of the work.

Example #51 (click on music for mp3)

Joji Yuasa CLARINET SOLITUDE

Copyright 1983 by Schott Japan

All Rights Reserved

Used by permission of European American Music

Distributors Corporation, sole U.S. and Canadian agent

for Schott Japan

In Distraction for clarinet and piano, by Masataka Matsuo, balanced soft multiphonics are interrupted by loud repeated notes in the piano.

Example #53 (click on music for mp3)

Bill Kleinsasser utilizes balanced multiphonics in numerous contexts in Smooth Wood, Flash Metal (2003) for clarinet, flute, and interactive computer (written for E. Michael Richards and Lisa Cella).

The composer writes:

The noticeable differences between interesting objects offer engagement with the particularities of the objects themselves and also the less obvious offerings provided by the implied relationships between the objects. This work offers a three-fold expression of this idea playing out on many levels with the interplay and juxtaposition of musical differences forming the compositional basis of the work. The piece is in three large sections: an extended flute solo which evolves into a duet with the computer, a duet with flute and clarinet that is augmented by computer transformation, and a clarinet solo which forms its own context through computer transformation of the live performance. The clarinet solo is based on alternation of spectral focus and diffusion. The duet combines the flute and clarinet alternations with its own

The noticeable differences between interesting objects offer engagement with the particularities of the objects themselves and also the less obvious offerings provided by the implied relationships between the objects. This work offers a three-fold expression of this idea playing out on many levels with the interplay and juxtaposition of musical differences forming the compositional basis of the work. The piece is in three large sections: an extended flute solo which evolves into a duet with the computer, a duet with flute and clarinet that is augmented by computer transformation, and a clarinet solo which forms its own context through computer transformation of the live performance. The clarinet solo is based on alternation of spectral focus and diffusion. The duet combines the flute and clarinet alternations with its own

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