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Intonation in a new composition in
19-tone equal temperament
Richard Parncutt
Department of Musicology
University of Graz, Austria
Graham Hair
Department 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)
Literature
Burns, 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 Unpublished PhD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
notation
cents above C
1
2
3
4
5
6
C C# Db D D# Eb E
0
63
126
189
253
316
379
7
8
E#/Fb
F
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:
• Erik Satie:
• John Cage:
“17 Lyrics of Li-Po”
“Socrate”
"Cheap Imitation“
– itself based on "Socrate“
Cage:
 Hair:
chromatic modality
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
no. of frequencies falling in each 5-cent bin
Wine, bars 1-9, clarinet
First peak:
1= 1/19 octave
63 = 63 cents
9
568
5
316
2
126
7
442
1
63
4
253
3
189
13
821
16
1011
15
947
12
758
6
8
379 505
14
884
18
17
1074 1137
10 11
631 695
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