Informing Microtonal Performance through Listening
Introduction
In this paper we present a qualitative evaluation of a novel solution to the problem of performing in the 19-tone equal-tempered (19-ET) scale on the clarinet: a WX7 Yamaha wind MIDI controller is employed together with the 19-ET synthesizer developed at the Centre for Music Technology in Glasgow University. We discuss and demonstrate some performance issues raised by the use of the acoustic clarinet, and diverse methods of employing the WX7. The eventual goal of this project is the realization of an instrument suitable for performing music written in 19-ET, with accurate intonation and the full expressive capabilities of the acoustic clarinet, furthermore one which makes use of the skill set and technique of a player of the existing acoustic instrument.
This work builds on the AHRC-funded pilot study carried out in 2005-2007 by Graham Hair, Ingrid Pearson, Amanda Morrison, Nicholas Bailey, Douglas McGilvray and Richard Parncutt, and reported in [Hair et al].
Some 19-ET Terminology
The 19-ET scale can be seen as a logical development of the 12-ET scale, and may be referred to as the hyper-chromatic scale. The octave is divided into 19 equal hyper-chromatic tones of 63 cents, compared to the 100 cents of the semitone in the 12-ET scale. A convenient way to think of this scale is as an extension of the seven-note diatonic scale (7+12), in which the 'white notes' are separated by either one or two 'black notes'. The scale can then be straightforwardly notated as C-C#-Db-D-D#-Eb-E-E#-F- etc, where it should be emphasized that C# and Db (and so on) refer to different pitches. The 19-ET scale is particularly interesting from an intervallic perspective - when compared with the 12-ET scale the major and minor thirds are much closer to just intonation (although the perfect fifth is a little further from the just 3:2 ratio).
A Test Piece
The 'test piece' used in this research is Graham Hair's set of Three Microtonal Songs (/ProgrammeNotes). An audio recording of the work was made in July 2008 in Glasgow University Chapel by Lisa Swayne (soprano), Alex South (clarinet) and Graham Hair (keyboard), for presentation at the International Computer Music Conference held in Belfast in August 2008.
Performance Issues for the Clarinettist in Hair's 19-ET Microtonal Songs
Hair's Three Microtonal Songs place unusual technical and interpretative demands upon the performers who are unlikely, when approaching them for the first time, to have significant experience in the performance of 19-ET music. From the technical viewpoint, it was initially thought that the largest barrier to an accurate performance would be for the singer; since the clarinettist is mechanically aided in the production of pitch, and the harmonium part may be reasonably easily realized using a MIDI keyboard connected to a 19-ET synthesizer and playing from scordatura notation. However, it has proven to be a specious notion that a simple adaptation of existing fingerings and embouchure would quickly satisfy the demands of this alternative tuning for the clarinet player.
Performing 19-ET Music on the Acoustic Clarinet
In the first instance, South took a similar approach to that of Pearson in the pilot study, working out a set of fingerings and embouchure corrections to enable the 19-ET pitches to be produced. Pearson's set of fingerings together with quartertone fingering charts in Rehfeldt's New Directions for Clarinet were modified to make them suitable for South's half-Boehm clarinet. This procedure may be regarded as a simple extension of the existing model for pitch correction in 12-ET: every clarinettist is accustomed to altering the pitch produced by her instrument for a variety of reasons, whether to compensate for temperature changes in the performance venue or to match intonation with other performers. Such alterations are usually fairly small, typically involving the addition of a finger or two to the standard fingering, for just a small subset of the pitch range. By comparison, the fingering and/or embouchure corrections required to produce the 19-ET scale are substantial and global. Aside from the 'reference pitch' (concert pitch A), every note has to be bent, by an amount from 5 to 47 cents from the closest 12-ET pitch.
Thus in every octave, 18 out of 19 pitches require a combination of embouchure and fingering correction, resulting in over 60 new fingerings to learn across a typical playing range of three and a half octaves. This might be compared with the situation in 24-ET, where exact quartertones are placed between the regular pitches of 12-ET. In this scale, 'only' 12 new fingerings are required per octave, and the standard notes are played with their regular fingerings, resulting in significantly less of the 'cognitive overload' experienced in the performance of 19-ET music. It should be noted that several factors interact in producing this cognitive overload: principally the mastering of the theoretical knowledge of the new fingerings and finger patterns, and practical incorporation of them into kinaesthetic memory. This learning of 19-ET fingerings must also be accompanied by the 'unlearning', at least on a temporary basis, of those 12-ET associations between notated pitches on the score and finger positions, usually acquired over thousands of hours of practice and performance. Furthermore, as the composer now has an expanded tonal palette, the performer is likely to encounter passages which are daunting simply through unfamiliarity with keys such as B# or Fb major. Finally, at least some ear-training is required: it is vital to become accustomed to the sound of the 19-ET scale with its new intervals, and to practise lipping up and down pitches to be able to play in tune with other performers. In other words, listening is as important as always, but it is a new mode of listening.
The experience of preparing and recording Hair's Three Microtonal Songs demonstrated that although the new fingering/embouchure set could be made to work in relatively simple or slow passages, fast music was especially challenging to the performer. Furthermore, although the pitches were attainable with reasonable accuracy across most of the scale, this was occasionally achieved only at the expense of other dimensions of musical performance, such as legato and timbre.
A New Acoustic Clarinet?
Thus far our approach to performance in the 19-ET scale is essentially that of moving a long way in the direction of what might be termed an existing model for correcting pitch in 12-ET, involving the redesigning of the neural and muscular architecture of the player. But we’ve seen that it can be a very tricky procedure. An alternative approach is to redesign the instrument, for which there are precedents: shown below is Fritz Schüller's rather magnificent double-barrelled instrument built to produce a 24-ET scale [Wikipedia:quarter_tone_clarinet]. A more recent redesign of the acoustic instrument is Stephen Fox's clarinet constructed to play the pitches of the Bohlen-Pierce scale, made by dividing a just twelth into thirteen equal intervals [Fox]. However, the design of an acceptable replacement instrument is a long undertaking, requiring at least a year's dedicated work of a master instrument-maker, and unfortunately exceeding the resources available to the current study.
The WX7
An alternative to designing and building a new acoustic instrument is to investigate ways that existing electronic instruments can be repurposed to sound 19 equal divisions of the octave. The Yamaha WX7 wind MIDI controller is an example of such an electronic musical instrument, featuring keywork enabling the use of saxophone or flute fingerings, a mouthpiece and reed offering a degree of pitch-bending, a pitch bend wheel (operated by the right thumb) allowing further pitch-bending, a seven octave range accessed by depressing one or octave keys located under the left thumb, and the potential for simple chordal playing (a pitch may be sounded and held as a drone against other pitches). The player's breath pressure, tightness of embouchure and key presses are converted into MIDI data, and output through a cable to a suitable audio device.
We have investigated diverse methods of configuring it for 19-ET performance, and here we evaluate the benefits accruing from a dedicated electronic 19-ET instrument against the inevitably dire electronically synthesized sound it produces without the use of its dedicated (12-ET) Yamaha woodwind synthesizer. In this project we also seek significantly to improve the sound of the instrument through the use of advanced synthesis techniques.
Developing the WX7
The following candidate methods have been tested by South in the performance of Hair's microtonal songs:
- Hardware modification.
- Use the pitch bend wheel to mess with the MIDI codes.
- Use an external foot pedal to shift pitches up or down by one hyper-chromatic tone.
- Add thumb switches to do the same.
- Scordatura: change the musical score and remap the MIDI codes appropriately.
As the WX7 is hardwired to output a particular MIDI note number for a given fingering, and only twelve note numbers per octave are produced (whichever fingerings are used), the problem of making the instrument produce a 19-ET scale cannot be solved by reprogramming the wind controller and the additional seven note numbers must be obtained in another fashion. From the clarinettist’s perspective, two basic approaches were adopted: in the first, standard fingerings were employed to produce the following 19-ET pitches: C-C#-D-D#-E-F-G-G#-A-A#-B (together with their octave transpositions), and existing or additional hardware was used in combination with these standard fingerings to allow the production of flatted notes and the notes between E and F, and B and C. In this approach, seven new fingerings must be learnt per octave, compared to the eighteen for performance on the acoustic clarinet; furthermore, as the WX7 'overblows' at the octave (rather than the twelth of the acoustic clarinet), the fingering pattern in each octave is the same, offering a still larger reduction in the overall number of new fingerings required (seven compared to sixty-three across a three and a half octave range). In the second approach, the musical score was altered and standard fingerings only were used, i.e. no new fingerings had to be learnt.
As an aside, we point out here that the saxophone fingering system used on the WX7 is practically identical to that of the clarinet's upper register, so that with respect to learning fingering patterns the clarinettist typically has very little difficulty moving from clarinet to saxophone, or by extension, to the WX7 (in the case where standard fingerings only are used).
Pitch bend wheel
Method. The pitch bend wheel on the WX7 is positioned in order that it can be reached with the right thumb; normal operation resulting in the variable bending of the pitch above or below the fingered note. Software written by Bailey and described below intercepted and interpreted the MIDI data to produce a three-state system: either no pitch change, or a pitch shift up or down by one hyper-chromatic tone, rather than the quasi-continuously variable pitch bend. Thus the pitch produced by any given standard fingering (one of the twelve pitches listed above) could be raised or lowered by a hyper-chromatic tone, making the flatted pitches accessible and also offering alternative fingerings for various pitches (e.g. F# playable either with the standard F# fingering or as an F plus pitch wheel up). Adjustable hysteresis was incorporated into the software in order to ensure that the system state did not change with minor movements of the thumb (such as could occur with a change of fingering from one note to the next).
Evaluation. Although the standard acoustic clarinet has no keys to be pressed with the right thumb, the instruments of the clarinet family with extensions to notes lower than the standard written E (e.g. bass clarinet or basset horn) usually have two keys in this position. Thus many clarinettists are familiar with incorporating right thumb movement into their fingering patterns, and it was envisaged that it would not be too hard for a player of the 19-ET WX7 to do the same. South found that the cognitive puzzle of using the right thumb (mainly to play flatted notes, although it could also be used advantageously to play sharp notes in certain passages) was an easy one to surmount, and the software performed as designed. However, there were other difficulties: the instrument, being rather lighter than an ordinary wooden clarinet (0.3kg compared to 0.8kg), tended to move away from the right thumb when the pitch wheel was operated, typically resulting in poor legato when moving to or from a flatted note, particularly when fingers had to be moved in co-ordination with the right thumb. This problem, although undoubtedly present in playing of the bass clarinet or basset horn, is minimized by the fact that these instruments are generally played with a spike anchoring them to the ground, or with a neck strap for standing performers. Although a neck strap was of assistance in performing on the WX7, it didn’t fully solve the problem (perhaps because the right thumb was rather more frequently employed than in usual performance of the bass clarinet). An alternative playing position – with the lower end of the WX7 resting on the knee, stabilized the instrument but was uncomfortable for South, and very much restricts the usual freedom of the player.
Foot switch
Method. A USB foot switch was configured to send keyboard commands to the laptop computer used to run the WX7 sound synthesis software. These commands were detected as pitch shift up and pitch shift down, allowing the player of the instrument to use her foot in confunction with standard fingerings to access the flatted notes of the 19-ET scale as described above.
Evaluation. The physical separation of pitch shifting device and instrument meant that there were none of the problems described above resulting from the instrument moving as the flatted notes were played. However, South found that the coordination of fingers and feet, particularly in fast passages, still led to problems of legato. He also encountered an unexpected difficulty resulting from a slight tendency towards foot movement in passages exhibiting rhythmic complexity. Even when the desire to tap the foot to mark the beat was not outwardly expressed, there was confusing mental ‘interference’ experienced, perhaps as different parts of the brain attempted to send conflicting commands to the foot. Although the desire to tap the foot is perhaps not universal amongst clarinettists (and presumably is well-inhibited in clarinettists who also happen to play the organ!), it is sufficiently common and manifest in musicians of all stripes to warrant caution in prescribing the use of a foot switch as a solution to our problem.
Thumb switches
Scordatura
Comparing the WX7 with the Acoustic Instrument
Methods for modifying the MIDI code
Yamaha's WX7 is a proprietary instrument which is designed to produce MIDI sequences based on the measurement of rate of air flow and fingering. The device can be set to accept a variety of different fingerings (including saxophone and flute, but not the clarinet) but of course these are set-up to produce the standard MIDI codes associated with the notes of the 12-ET scale. The alternative fingerings developed by South, based on those suggested by Pearson, themselves derived from [Rehfeldt] simply do not produce meaningful note mappings. The origins of the MIDI standard are rooted firmly in the keyboard tradition; a MIDI "note number" essentially measures the distance from the left end-cheek of the keyboard and ignores even enharmonic equivalence, let alone tuning standard.
Information as to how to "re-tune" the controller so as to associate note numbers with fingerings other than the standard ones supported could not be found, nor was it forthcoming from the manufacturers. It therefore falls to us to provide software which attempts to use the additional control features of the instrument such as they are to provide the fine control necessary to access the notes of the 19-ET scale.
The methods of control described above have been implemented on a Linux laptop using the Advanced Linux Sound Architecture (ALSA) and its associated user-space API, alsa-lib. As well as being entirely open-source, ALSA offers one of the lowest-latency methods of handling audio and MIDI streams. Although it is difficult to locate performance information or scientific studies on proprietary systems, MacMillan, Droettboom and Fujinaga have shown that ALSA is at least comparable (and often vastly superior) to the performance of audio and MIDI frameworks associated with proprietary operating systems.
The synthesizer demonstrated here is due to Evans (described in the next section), and offers improved control over simpler wave-table-based synthesizers. However, it is possible to use such a synthesizer if only for rehearsal purposes, and instead of routing the processed MIDI messages externally, they may be sent to FluidSynth permitting a fully redistributable, open source solution. Because FluidSynth supports retuning, it can accommodate an alternative scale in which the note numbers are separated by 1/19th of an octave. In the alternative system, the MIDI note corresponding to A440 remains unchanged in pitch.
In order to use the WX7's pitch wheel effectively, it needs to be endowed with hysteresis. This is achieved through the use of a three-state machine as shown below. The parameters determining the point at which the changes of state occur can be set from the command line, or interactively while the program is executing, thus determining the position and sensitivity of a pitch bend change. The state-change function detects whether or not an existing MIDI note is playing; in this case it issues an appropriate note-off event after the note-on event for the new pitch has been sent.
Because of the interaction between the pitch bend data from the WX7's pitch wheel and from the embouchure detector on the mouthpiece, the WXTranslator program can also be instructed to read state information from a pipe to establish whether or not any pitch bend should be applied. When this is the desired method of control, a named pipe is opened for synchronous reading and added to the program's central polling set. If the pipe becomes readable, characters are read and the pitch bend adjusted according to whether a '+' (bend up), '-' (bend down) or '0' (no bend) is received. If the MIDI pitch-bend functionality is also disabled, causing the pitch wheel control data to be passed straight through to the synthesizer, the foot switch can effectively replace the pitch wheel as the method of control.
The foot switch used in this project contains three pedals, though only the outer pair are used. The pedals emulate keyboard switches, being connected to the computer through a USB socket and adopting the HID (Human Interface Device) profile. Determining the exact time a keyboard is depressed and released is difficult in a Unix environment, so a program was written which uses the lowest level X-windows libraries to access key events before they can be intercepted and "cooked". This avoids problems associated with auto-repeat and other keyboard roll-over processing which is normally taken for granted. The program simply opens the named pipe described above for synchronous write, and sends the appropriate characters when the key events are detected. A small window is maintained which is filled with red for a downward bend, green for an upward one, and black for none, in order to provide the user with feedback and as a confidence test that the program is operating.
Conclusion and Future Work
The relative merits of the acoustic clarinet and an electronic alternative, the Yamaha WX7, have been evaluated qualitatively with regard to their suitability for the performance of music composed using the 19-ET scale. The acoustic clarinet, whilst offering far superior expressive control of sound, suffers from pitch inaccuracies and possible 'cognitive overload' for the performer. The WX7 offers perfect 19-ET intonation, but lacks tonal sophistication; however it is potentially a useful tool for enabling the performance of microtonal music in a variety of temperaments. Further development of the method of sound synthesis is desirable; also further evaluation of the different methods of controlling the pitches. If the sound produced and ergonomics of the WX7 prove inadequate, a longterm goal would be the design of a new acoustic instrument. Finally, we seek to encourage and commission the composition of further repertoire for the 19-ET clarinettist.
Bibliography
[Fox]: Fox, Stephen, “The Bohlen-Pierce clarinet project”, http://www.sfoxclarinets.com/bpclar.html
[Hair et al]: Graham Hair, Ingrid Pearson, Amanda Morrison, Nichoas Bailey, Douglas McGilvray, Richard Parncutt, “The Rosegarden Codicil: Rehearsing Music in Nineteen-Tone Equal Temperament”, Scottish Music Review, v1; also http://www.n-ism.org/Papers/Microtonalism/codicil.pdf, 2007
[Rehfeldt]: Rehfeldt, Phillip, “New Directions for Clarinet”, revised ed., Berkeley and Los Angeles: University of California Press, 1994
[Wikipedia:quarter_tone_clarinet] http://en.wikipedia.org/wiki/Quarter_tone_clarinet