Intonation in a new composition in 19-tone equal temperament

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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

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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.

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Data of Burns
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Microtonal scales

• gt12 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

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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.

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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!

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19ET

• Smallest interval 121/19
• 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.

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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
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Aims

• Develop microtonal
• composition tradition and skills
• performance tradition and skills
• Document how musicians adapt
• thinking
• perception
• performance

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Method

• Participants
• Materials
• music
• equipment
• Procedure

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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

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The music

• Three short 19ET songs _at_ 1 minute
• Voice, clarinet, keyboard
• Composer Graham Hair

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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

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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

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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

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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

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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

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Wine, bars 1-9, clarinet
First peak 1 1/19 octave 63 63 cents
9 568
16 1011
13 821
5 316
15 947
2 126
7 442
12 758
1 63
no. of frequencies falling in each 5-cent bin
6 379
8 505
14 884
4 253
18 1137
17 1074
3 189
10 631
11 695
Log of center frequency of bin (0 cents 440 Hz)
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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

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Implications

• Scalar bilingualism
• enormously broadens compositional possibilities
• Microtonal music can become mainstream
• if one system is used consistently
• with large repertoire and sustained tradition