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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 ... The Sixteen, Monteverdi Choir, Crafty Musick, Gesualdo Consort of London, Exaudi ... – PowerPoint PPT presentation

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Title: Intonation in a new composition in 19-tone equal temperament


1
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

2
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.

3
Data of Burns
4
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

5
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.

6
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!

7
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.

8
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
9
Aims
  • Develop microtonal
  • composition tradition and skills
  • performance tradition and skills
  • Document how musicians adapt
  • thinking
  • perception
  • performance

10
Method
  • Participants
  • Materials
  • music
  • equipment
  • Procedure

11
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

12
The music
  • Three short 19ET songs _at_ 1 minute
  • Voice, clarinet, keyboard
  • Composer Graham Hair

13
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

14
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

15
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

16
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

17
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18
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

19
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)
20
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

21
Implications
  • Scalar bilingualism
  • enormously broadens compositional possibilities
  • Microtonal music can become mainstream
  • if one system is used consistently
  • with large repertoire and sustained tradition
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