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1
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0013666098
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The persistence of pythagorean tuning systems
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J. M. Barbour, "The Persistence of Pythagorean Tuning Systems," Scr. Math. 1, 286 (1933).
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(1933)
Scr. Math.
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Barbour, J.M.1
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2
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0013686928
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Musical logarithms
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J. M. Barbour, "Musical Logarithms," Scr. Math. 3, 21 (1940).
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(1940)
Scr. Math.
, vol.3
, pp. 21
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Barbour, J.M.1
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3
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0004220068
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Dover, New York
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H. Helmholtz, in On Sensation of Tone (Dover, New York, 1954), Chaps. I and XVI (originally published in 1885).
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(1954)
On Sensation of Tone
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Helmholtz, H.1
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4
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33744633445
-
-
originally published in
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H. Helmholtz, in On Sensation of Tone (Dover, New York, 1954), Chaps. I and XVI (originally published in 1885).
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(1885)
Chaps. I and XVI
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-
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5
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0013685632
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Modulation
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edited by D. M. Randell Belknap, Cambridge, MA
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"Modulation," in The New Harvard Dictionary of Music, edited by D. M. Randell (Belknap, Cambridge, MA, 1986), p. 503.
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(1986)
The New Harvard Dictionary of Music
, pp. 503
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-
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7
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0028308871
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A measurement of the reasonableness of equal-tempered musical scale
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R. J. Krantz and J. Douthett, "A Measurement of the Reasonableness of Equal-Tempered Musical Scale," J. Acoust. Soc. Am. 95, 3642-3650 (1994).
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(1994)
J. Acoust. Soc. Am.
, vol.95
, pp. 3642-3650
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Krantz, R.J.1
Douthett, J.2
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8
-
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0013682716
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The objective measure of goodness-of-fit for tunings and temperaments
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D. E. Hall. "The Objective Measure of Goodness-of-Fit for Tunings and Temperaments," J. Music Theory 17, 274 (1973).
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(1973)
J. Music Theory
, vol.17
, pp. 274
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-
Hall, D.E.1
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9
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0013692597
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Quantitative evaluation of musical scale tunings
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D. E. Hall, "Quantitative Evaluation of Musical Scale Tunings," Am. J. Phys. 42(7), 543 (1974).
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(1974)
Am. J. Phys.
, vol.42
, Issue.7
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-
Hall, D.E.1
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10
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0013673367
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Acoustical numerology and lucky temperaments
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D. E. Hall, "Acoustical Numerology and Lucky Temperaments," Am. J. Phys. 56(4), 329 (1988).
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(1988)
Am. J. Phys.
, vol.56
, Issue.4
, pp. 329
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-
Hall, D.E.1
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11
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0013667229
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A systematic evaluation of equal temperaments through N=612
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D. E. Hall, "A Systematic Evaluation of Equal Temperaments Through N=612," Interface (USA) 14, 61-73 (1985).
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(1985)
Interface (USA)
, vol.14
, pp. 61-73
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Hall, D.E.1
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12
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84967851744
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A numerical exercise in musical scales
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G. C. Hartmann, "A Numerical Exercise in Musical Scales," Am. J. Phys. 55(3), 223 (1987).
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(1987)
Am. J. Phys.
, vol.55
, Issue.3
, pp. 223
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Hartmann, G.C.1
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14
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0013647214
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Theoretical possibilities for equally tempered musical systems
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edited by H. B. Lincoln Cornell University Press, Ithaca, NY
-
W. Stoney, "Theoretical Possibilities for Equally Tempered Musical Systems," in The Computer and Music, edited by H. B. Lincoln (Cornell University Press, Ithaca, NY, 1970), pp. 163-171.
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The Computer and Music
, vol.1970
, pp. 163-171
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-
Stoney, W.1
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15
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0013670653
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Equal temperament
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D. De Klerk, "Equal Temperament," Acta Musicol. 51, 140 (1979).
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(1979)
Acta Musicol.
, vol.51
, pp. 140
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-
De Klerk, D.1
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16
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0013647215
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Tempered music scales for sound synthesis
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M. Yunik and G. Swift, "Tempered Music Scales for Sound Synthesis," Comput. Music J. 4(4), 60 (1980).
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(1980)
Comput. Music J.
, vol.4
, Issue.4
, pp. 60
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Yunik, M.1
Swift, G.2
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19
-
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33744678111
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note
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In July of 1993 Clough (SUNY at Buffalo) assembled a group - known as the "SUNY Buffalo Working Group" - of music theorists, music psychologists, and mathematicians to investigate and expand on the ideas put forth by Richard Cohn (University of Chicago) on late 19th century voice leading. The term P-cycles was introduced by Cohn and was among the topics explored at the meeting. This group met again in July of 1997 to explore a related topic, neo-Riemannian Transformations. For more information on the above, including a bibliography of related topics, see the special topics edition of the Journal of Music Theory 42(2) (1998).
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-
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21
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0013665083
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Cycle scales
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J. Chalmers, "Cycle Scales," Xenharmonikon 4, 69-78 (1975).
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(1975)
Xenharmonikon
, vol.4
, pp. 69-78
-
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Chalmers, J.1
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22
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0013645562
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Polychordal matrices and MOS scales
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J. Chalmers, "Polychordal Matrices and MOS Scales," Xenharmonikon 7-8, 156-167 (1979).
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(1979)
Xenharmonikon
, vol.7-8
, pp. 156-167
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Chalmers, J.1
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23
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0013685097
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Construction and harmonization of microtonal scales in non-twelve-tone equal temperaments
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Venice, Italy (unpublished)
-
J. Chalmers, "Construction and Harmonization of Microtonal Scales in Non-Twelve-Tone Equal Temperaments," Proceedings of the 8th International Computer Music Conference, Venice, Italy, pp. 534-555, 1982 (unpublished).
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(1982)
Proceedings of the 8th International Computer Music Conference
, pp. 534-555
-
-
Chalmers, J.1
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24
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33744608444
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Private communication to J. Douthett
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E. Wilson, Private communication to J. Douthett (1996).
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(1996)
-
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Wilson, E.1
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25
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0013666043
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Some combinatorial resources of equal-tempered systems
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C. Gamer, "Some Combinatorial Resources of Equal-Tempered Systems," J. Music Theory 11(1), 32-59 (1967).
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(1967)
J. Music Theory
, vol.11
, Issue.1
, pp. 32-59
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Gamer, C.1
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26
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0001872697
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The group-theoretic description of 12-fold pitch systems
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G. Balzano, "The Group-Theoretic Description of 12-Fold Pitch Systems," Comput. Music J. 4, 66-84 (1980).
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(1980)
Comput. Music J.
, vol.4
, pp. 66-84
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Balzano, G.1
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27
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0013644905
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Musical scales and the generalized circle of fifths
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J. Clough and G. Myerson, "Musical Scales and the Generalized Circle of Fifths," Am. Math. Monthly 93(9), 695-701 (1986).
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(1986)
Am. Math. Monthly
, vol.93
, Issue.9
, pp. 695-701
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Clough, J.1
Myerson, G.2
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28
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0013665084
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Variety and multiplicity in diatonic systems
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J. Clough and G. Myerson, "Variety and Multiplicity in Diatonic Systems," J. Music Theory 29, 249-270 (1985).
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(1985)
J. Music Theory
, vol.29
, pp. 249-270
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Clough, J.1
Myerson, G.2
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29
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0013669356
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Theoretical and experimental explorations of the bohlen-pierce scale
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M. V. Mathews, J. R. Pierce, A. Reeves, and L. A. Roberts, "Theoretical and Experimental Explorations of the Bohlen-Pierce Scale," J. Acoust. Soc. Am. 84, 1214-1222 (1988).
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(1988)
J. Acoust. Soc. Am.
, vol.84
, pp. 1214-1222
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Mathews, M.V.1
Pierce, J.R.2
Reeves, A.3
Roberts, L.A.4
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30
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0013673368
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A mathematical model of the diatonic system
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E. Agmon, "A Mathematical Model of the Diatonic System," J. Music Theory 33, 1-25 (1989).
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(1989)
J. Music Theory
, vol.33
, pp. 1-25
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Agmon, E.1
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31
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0013669116
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Hyperscales and the generalized tetrachord
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J. Clough, J. Cuciurean, and Douthett, "Hyperscales and the Generalized Tetrachord," J. Music Theory 41(2), 67-100 (1997).
-
(1997)
J. Music Theory
, vol.41
, Issue.2
, pp. 67-100
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Clough, J.1
Cuciurean, J.2
Douthett3
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32
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0013667230
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Generalized diatonic and pentatonic scales: A group theoretic approach
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P. Zweifel, "Generalized Diatonic and Pentatonic Scales: A Group Theoretic Approach," Perspect. New Music 34(1), 140-161 (1996).
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(1996)
Perspect. New Music
, vol.34
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, pp. 140-161
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Zweifel, P.1
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33
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0013645193
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To get a sense of why these sets are called maximally even
-
constructed a measure of the eveness of subsets in the same cardinal family (e.g., same chromatic cardinality or same diatonic cardinality). This measure is consistent with the ME algorithm
-
To get a sense of why these sets are called maximally even, S. Block and J. Douthett, J. Music Theory 38, 21 (1994) constructed a measure of the eveness of subsets in the same cardinal family (e.g., same chromatic cardinality or same diatonic cardinality). This measure is consistent with the ME algorithm.
-
(1994)
J. Music Theory
, vol.38
, pp. 21
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Block, S.1
Douthett, J.2
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34
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0013682717
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Ph.D. dissertation University of New Mexico, Albuquerque, NM, May
-
J. Douthett, "The Theory of Maximally and Minimally Even Sets, the One-Dimensional Antiferromagnetic Ising Model, and the Continued Fraction Compromise of Musical Scales," Ph.D. dissertation (University of New Mexico, Albuquerque, NM, May 1999).
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(1999)
The Theory of Maximally and Minimally Even Sets, the One-dimensional Antiferromagnetic Ising Model, and the Continued Fraction Compromise of Musical Scales
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-
Douthett, J.1
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35
-
-
33744716674
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-
note
-
3(9/7)≈3/13. This coincidence explains why this small chromatic cardinality has such an extraordinarily good desirability.
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-
-
-
36
-
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0013686656
-
13 tonstufen in der doudezeme
-
H. Bohlen, "13 Tonstufen in der Doudezeme," Acustica 39, 76-86 (1978).
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(1978)
Acustica
, vol.39
, pp. 76-86
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-
Bohlen, H.1
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37
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0021396035
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Intonation sensitivity for traditional and nontraditional chords
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L. Roberts and M. Mathews, "Intonation Sensitivity for Traditional and Nontraditional Chords," J. Acoust. Soc. Am. 75, 954-959 (1984).
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(1984)
J. Acoust. Soc. Am.
, vol.75
, pp. 954-959
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Roberts, L.1
Mathews, M.2
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38
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0013647268
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Tempered scales and continued fractions
-
M. Schechter, "Tempered Scales and Continued Fractions," Am. Math. Monthly 87, 40-42 (1980).
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(1980)
Am. Math. Monthly
, vol.87
, pp. 40-42
-
-
Schechter, M.1
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39
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0013685298
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Musical scale construction: The continued fraction compromise
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J. Douthett, R. Entringer, and A. Mullhaupt, "Musical Scale Construction: The Continued Fraction Compromise," Util. Mathemat. 42, 97-113 (1992).
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(1992)
Util. Mathemat.
, vol.42
, pp. 97-113
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-
Douthett, J.1
Entringer, R.2
Mullhaupt, A.3
-
40
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0003918560
-
-
The University of Chicago Press, Chicago
-
A. Ya Khinchin, Continued Fractions (The University of Chicago Press, Chicago, 1992).
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(1992)
Continued Fractions
-
-
Khinchin, A.Ya.1
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