Microtonalism

Stage one of the microtonal project ("Rehearsing Microtonal Music: Grappling with Performance and Intonational Problems") is supported by an AHRC Small Grant (1/1/2006 – 31/12/2006). Ingrid Pearson is the Principal Investigator. Collaborating researchers are Graham Hair, Dougie McGilvray, Nick Bailey, Amanda Morrison and Richard Parncutt.

Microtonal music, where the scale is broken into more than twelve divisions, or those divisions are different from the normally accepted ones, is usually performed on fretted or keyboard instruments. On other instruments which do not inherently quantize the pitch of the sound produced, the players require sophisticated tools to help retrain the ear to the new tunigs. The more experienced the players, the more demands are placed on the training tools.

The Microtonalism project brings together singers and players of the highest professional standards and thus places huge demands on the signal processing accuracy and presentation of the software which was delivered.

Melismata: A 19-ET Study

The above piece, "Melismata" by Graham Hair, is at first sight a traditionally notated short study for Clarinet and Keyboard Continuo. Closer examination reveals some enharmonic peculiarity: bar 8's E-flat, B-sharp, A-sharp in the clarinet part, for example. The reason for this is that it is intended for performance in 19-TET, with the octave divided into nineteen equal divisions instead of the usual twelve.

Dividing the octave into nineteen is not an unusual idea. In the sixteenth century, the concept of using the same pitch for C-sharp and D-flat would have been considered completely alien. The problem arises from the attempt to shoe-horn the twelve chromatic notes of the scale into a system where they are equally spaced. The concept of an octave as a ratio of 2:1 seems to be the musical equivalent of conservation of energy in physics: to change the rule would render invalid so many virtually axiomatic principles as to make the act unthinkable. However, the desire to make each "semitone" (as we have called them only since the nineteenth century) equal so that music "works" equally well in all keys has caused us to ignore the lesser pure intervals: the perfect fifth (3:2), perfect fourth (4:3), major third  (5:4) and minor third (6:5) have been "degraded" because of the requirement that they be composed of an integer number of semitones, but of course such rational fractions cannot be made available in 12-tone equal temperament where the semitone corresponds to the irrational ratio of adjacent note frequencies of 21/12.

The choice of dividing the octave into nineteen is sometimes justified by the greater accuracy with which the just intervals are represented, but as Wikipedia's article "19 equal temperament" points out, there are superior temperaments if this is the only goal. The particular reason for addressing 19-TET here arise from Graham Hair's desire to investigate a scale which while clearly diatonic (in that major and minor scales are instantly recognisable) has an extended capacity for chromatic expression. Thus one might view the scale as having seven notes with not five extra chromatic ones as in 12-TET, but 12 extra. The altered division of the scale with a major one having a pattern of 3-3-2-3-3-3-2 smallest intervals (no longer may they be called semitones!) instead of the 2-2-1-2-2-2-1 associated with conventional tuning makes possible what was previously impossible: the perfect fourth, now an interval of eight rather than five smallest-intervals permits its division into four equal intervals.

An Historical Demonstration

Keyboard layout for 19 keys to the octave Historically, 19-tone keyboards have been constructed to look like the keyboard on the right, with the rear of the divided black keys often raised. Christopher Stembridge's on-line article about the chromatic harpsichord ("cembalo cromatico") describes the motivation for performing on these instruments, as constructed in modern times by Denzil Wraight whose web page also contains a link to an extract from a recording made on a 19-key-per-octave instrument. As far as we know, these instruments were not tuned to an equal temperament, but to an extended mean-tone system, attempting to preserve the rational nature of the intervals as far as possible. To demonstrate the difference between 19-TET and 19-XMT, we have used FluidSynth to produce a synthesised rendition of a piece by the English composer John Bull who wrote a piece entitled "Ut, re, me, fa, sol, la" which uses eighteen of the nineteen enharmonic sellings available in the nineteen-note systems. The synthesiser used in rendering this piece, FluidSynth, is also capable of real-time rendition, so a version of Bull's score for a specially re-tuned conventional MIDI keyboard, with sounding and "scordatura" parts has been produced. Although just about playable by expert organists (John Butt very kindly gave a partial rendition in front of a live audience at a research seminar held in Glasgow University in 2006), the increased stretch demanded of the performer makes some of the piece all but impossible to play on such an instrument. The first part of the score is shown below.

John Bull Ut Re Me Fa Sol La (Scordatura version)

The score is also available for download as a PDF file.

Re-tuning the Ear

Musicians whose instruments can continuously vary their pitch (which is to say practically all of them except for keyboard players) rarely if ever play in 12-TET. Changing the basis from 12 to 19 is however very demanding because those with the necessary pitch discrimination are, ipso facto those most loath to leave the familiarity of the 12-pitches-per-octave system.

Rehearsal Session at the Royal College of Music, London

Rehearsing 19-TET music in the photograph above, the effort and concentration is evident on the faces of (from left to right): Richard Parncutt (Systematic Musicologist, University of Gratz); Dougie McGilvray (CMT Glasgow, author of The Rosegarden Codicil); Ingrid Pearson (Clarinetist, Royal College of Music); Amanda Morrison (Soprano, Scottish Voices, BBC Singers etc.) and Graham Hair (Composer, CMT Glasgow).

RCM Rehearsal

A Light-hearted Moment during a 19-TET Rehearsal at the Royal College of Music, London

For rehearsal purposes, accompaniment is provided by a synthesiser tuned to 19TET and the performer equipped with a microphone connected with software which provides pitch metering functionality.

Notationally, the rehearsal system uses 19-TET scores which are apparently very conventional, except that the greater division of the scale means that instead of the seven enharmonic equivalences per octave, there are only two. D sharp and E flat now represent different pitch values for example and although E sharp and F flat are equivalent, neither are eqivalent to E or F. This places demands on the rehearsal system which cannot be satisfied or even approached by systems which rely on MIDI note representation internally. This is because MIDI, the industry standard, represents pitch as "note number", essentially numbering the chromatic scale for a keyboard counting upwards from the lowest note. Even in 12-TET, this essentially loses all information about enharmonic spelling, and really is oriented towards the control of electronic synthesizers rather than attempting to represent musical data more richly.

To avoid overloading the performer with information, the rehearsal system supports the concept of "hot" and "cold" notes. The former are pivotal are required to be absolutely in tune. The latter form part of the melodic elaboration of the piece. This feature is also beyond the capacity of MIDI to represent because the musical significance of a note event is clearly inconsequential to a synthesiser which is there only to emit the defined pitch at an appropriate amplitude without regard to higher-level musical information.


The Rosegarden Codicil

Ingrid Pearson at Microfest 2005

Dr Ingrid Pearson performing microtonally at Microfest 2005, Surrey, UK

Rosegarden Screen Shot

The "Rosegarden-Codicil" Pitch Tracker
(Click to enlarge)

Rosegarden is an advanced music sequencer for the Linux platform. It's web page describes it as follows:

Rosegarden is a professional audio and MIDI sequencer, score editor, and general-purpose music composition and editing environment.

Rosegarden is an easy-to-learn, attractive application that runs on Linux, ideal for composers, musicians, music students, and small studio or home recording environments

For the Microtonalism project, it is simply infeasible to write an entire environment as sophisticated as this from scratch (the Rosegarden source code runs to almost 300000 lines of C++), so an obvious solution is to choose a current package to extend.

The overwhelming advantages of using Rosegarden as opposed to proprietary software are:

The Pitch Tracker offers several different methods of measuring pitch, among them HSP ("Harmonic Spectral Product") which repeatedly scales and multiplies the spectrum of the performance signal resulting in emphasis of the fundamental. There is also the facility to ignore the octave of the performance in drawing the tuning graph: the most usual failure mode of any pitch-tracker is incorrectly identifying the octave by falsely identifying a harmonic as the fundamental frequency, so this further increases reliability.

Performance Review Screenshot

The Pitch Tracker in Performance Review Mode
(Click to Enlarge)

The graph on the screen shows "pitch error" in real time, and does so reliably when the best operational parameters have been selected. The audio track can be saved after the rehearsal session and reloaded for subsequent analysis. In this screenshot, the score has been editted after the audio recording was made. The singer's approximately constant pitch appears to have jumped in the third beat of the second bar and the second beet of the third bar. The graph is dynamically updated as the score is changed or as notes are deleted from it when in performance review mode. Because the pitch trajectory is recalculated for each display, it is possible to save several different sessions in different audio tracks, then choose which is used to generate the "pitch error" graph.


Publications and Resources

Also available, a "live CD" (700MB!) image enabling trial use of the software, without installation, on a "wintel" machine (standard desktop PC or laptop which would normally be expected to run Microsoft(R) Windows(TM)). This is a bootable CD which you can download and burn. The software will run directly from it on the majority of PC hardware without any installation or changes to your machine being necessary.