Intonation in a new composition in 19-tone equal temperament

Richard ParncuttDepartment of MusicologyUniversity of Graz, Austria

Graham HairDepartment of Music & Centre for Music Technology

Umiversity of Glasgow, Scotland

Presented at CIM08, Thessaloniki

Musical pitch categories

• apply to both relative and absolute pitch• typical tolerance: + half category width

Chromatic scale, equal temperament (12ET):• tolerance = + quarter tone• learned from experience (e.g. piano)

LiteratureBurns, E. M., & Ward, W. D. (1978). Categorical perception - phenomenon or epiphenomenon:

evidence from experiments in the perception of melodic musical intervals. Journal of the Acoustical Society of

America, 63, 456-468. Siegel, J. A., & Siegel, W. (1977). Absolute identification of notes and intervals by musicians.

Perception & Psychophysics, 21 (2), 143-152.

Data of Burns

Microtonal scales

• >12 pitch categories per octave• perceptually analogous to 12ET

Hypotheses:• category centers, widths can be learned• typical tolerance: + half category width• scalar bilingualism is possible

– retune internal representation– juxtapose two internal representations

Inspiration: Kopiez (2003)

• accompaniment: either ET or pure/just• solo: ~ET in both cases

Intonation (deviation from ET) depends on– specific interval– musical structure – instrumental limitations

Kopiez, R. (2003). Intonation of harmonic intervals: Adaptability of expert musicians to equal temperament and just intonation. Music Perception, 20, 383-410.

Microtonal composition

• Substantial minority tradition

• Wide range of systems

• Favored instruments: keyboard, fretted strings, mallet percussion, mechanically tuned electronic, computer

No tradition develops perceptual performance skills of musicians!

19ET

• Smallest interval: 1:21/19

• Closely approximates small-integer ratios• Assumption:

– easiest microtonal system to perceive and perform

Mandelbaum, J. (1961). Multiple division of the octave and the tonal resources of 19-tone temperament. Unpublished PhD Dissertation, University of Indiana.

19ET

19ths above C 0 1 2 3 4 5 6 7 8

notation C C# Db D D# Eb E E#/Fb F

cents above C 0 63 126 189 253 316 379 442 505

Our notational rule: sharp (#) = +1/19 flat (b) = -1/19

Aims

• Develop microtonal…– composition tradition and skills– performance tradition and skills

• Document how musicians adapt…– thinking– perception– performance

Method

• Participants

• Materials– music– equipment

• Procedure

Participants

Clarinettist: Dr. Ingrid Pearson• Regular performances at UK national level in/with

early music ensembles– Hanover Band, Gabrieli Consort and Players, Orchestra of the Age of

Enlightenment, English Baroque Soloists, English Concert, Symphony of Harmony and Invention.

• Deputy director, graduate school, RCM London

Soprano: Amanda Morrison• Regular performances at UK national level in/with

vocal ensembles• Synergyvocals, BBC Singers, Steve Reich and Musicians, Scottish

Voices, Tallis Scholars, The Sixteen, Monteverdi Choir, Crafty Musick, Gesualdo Consort of London, Exaudi

The music

• Three short 19ET songs @ 1 minute

• Voice, clarinet, keyboard

• Composer: Graham Hair

Graham Hair: 3 microtonal songs

Radical Simplicity• reaction against modernist complexity• helps singers, instrumentalists achieve 19ET

Inspiration: • Harry Partch: “17 Lyrics of Li-Po”• Erik Satie: “Socrate”• John Cage: "Cheap Imitation“

– itself based on "Socrate“

Cage: chromatic modality Hair: hyperchromatic modality

Equipment

• 19-ET keyboard – scordatura (re-tuned)– keyboard is 12ET, sound is 19ET

• 19ET keyboard tablature– conventional notation– helps pianist put fingers on right keys

• Pitch-tracking software (Rosegarden)– Listens to performers– Feedback on microtonal accuracy

Procedure– Practice and rehearsal

• soloists alone– with recording of accompaniment – with pitch tracker software

• with composer as co-repetiteur – at 19ET keyboard final revisions of score

– Recording• with keyboard accompaniment• separate tracks for each instrument/voice

– Frequency measurement • of separate tracks for soprano and clarinet

Practice time

• about 4 hours at home• about 4 hours rehearsal with composer recordings of "Wine" and "Dance"

– sop and clar separately– about 40 takes in 4 hours– criterion for choice of takes to analyse:

• best overall performance• most in tune according to composer• most in tune according to real-time pitch tracker

Frequency measurement

1. Divide time axis into frames• frame length: 1024 samples = 1/43 s

2. Each frame one frequency• autocorrelation?• FFT?• harmonic spectral product?

3. Assign frequencies to 5-cent bins • 240 bins in 1 octave, 440-880 Hz

161011

2126

Wine, bars 1-9, clarinet

3189

4253

6379

5316 7

442

8505

12758

11695

10631

9568

15947

14884

13821

163

171074

181137

First peak:1= 1/19 octave63 = 63 cents

no.

of f

requ

enc

ies

falli

ng

in e

ach

5-c

ent

bin

Log of center frequency of bin (0 cents = 440 Hz)

Tentative results

• Singers and instrumentalists can learn 19ET– emulating 12ET-categorical perception/performance

• Practice time is reasonable– with appropriate computer and personal support

• Further improvement is expected– with practice time (cf. expertise research)

• Scalar bilingualism – a realistic goal

Implications

Scalar bilingualism • enormously broadens compositional possibilities

Microtonal music can become mainstream• if one system is used consistently• with large repertoire and sustained tradition