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ratio
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1
Journal Article
Journal of Music Theory (2013) 57 (2): 245–286.
Published: 01 October 2013
...). Furthermore, coincidence theories conclude
that the fourth (with its simple ratio of frequencies 3:4) is more consonant or
agreeable than the major sixth and the major third (with more complicated
ratios 3:5 and 4:5, respectively) (Cohen 1984, 95–96, 103–9). Euler looked
upon these discrepancies...
Journal Article
Journal of Music Theory (2021) 65 (2): 325–374.
Published: 01 October 2021
..., which explains both the ME(12, 7) diatonic scale and the ME(19, 12) chromatic scale, and a similar approximation of a desired periodicity ratio in the rhythmic case. Exactly what this desired frequency ratio is requires further investigation. That is the task of the next section. Reich constructed...
FIGURES
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Journal Article
Journal of Music Theory (2022) 66 (1): 1–42.
Published: 01 April 2022
... as follows: Consonance . . . is a mixture of low and high sound that reaches our ears smoothly and uniformly; and it has the power to alter the sense [of hearing]. Or it is (as Aristotle defines it) a ratio of numbers in high and low [pitch]. From which definitions we can understand that consonance arises...
FIGURES
Journal Article
Journal of Music Theory (2009) 53 (2): 163–190.
Published: 01 October 2009
...
Ellis was referring to Euler’s diatonic-chromatic genus, composed of the
twelve pitches in the just intonation ratios given in Figure 7a (Ellis 1864a, 93;
Euler 1739, 136). Euler derived the pitches of the genus from a very simple
tuning method (1739, 147...
Journal Article
Journal of Music Theory (2022) 66 (2): 255–261.
Published: 01 October 2022
... explication of how to calculate harmonic ratios from the octave, proceeding to a handful of mathematical issues in Boethius and Aristoxenus that present problems for the modern reader, followed by an overview of the three mathematical means in selected writings, and closing with a commentary on Guido's...
Journal Article
Journal of Music Theory (2022) 66 (2): 280–290.
Published: 01 October 2022
... the overall narrative. So why 50/50? Auerbach does not provide a compelling reason, and consequently, the supposedly objective system rests on an arbitrary ratio. Just as dubious as the choice of ratio itself is the decision to use the same ratio across all repertoires. Auerbach's concept of style in chapter...
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Journal Article
Journal of Music Theory (2009) 53 (1): 1–56.
Published: 01 April 2009
... distance relation pro- example, in converting 1, 2, 4, 12, 36 and 1, 3, 9, 18, 36,
viding “finer distinctions” (2001, 301) than those offered by four 3:2 ratios are required: one each for 2 to 3 and 12 to 18
dissimilar-pulse distance relations (2001, 300: ex. 4c). While and two for 4 to 9...
Journal Article
Journal of Music Theory (2002) 46 (1-2): 127–151.
Published: 01 October 2002
... believed that melody,
harmony and rhythm were all ruled by ratio and proportion. Perhaps ever
since, western musicians and music theorists have sought universal prin-
ciples of musical structure. At bottom of such claims is the belief that
pitch and time are somehow isomorphic. Faith in the isomorphism...
Journal Article
Journal of Music Theory (2008) 52 (1): 159–180.
Published: 01 April 2008
... concerns actual
sounding music created by instruments or the human voice. Described in
Neoplatonic terms as a manifestation of Pythagorean numerical ratios, musica
instrumentalis is similar in conception to the other two species of musica and
cannot...
Journal Article
Journal of Music Theory (2020) 64 (1): 105–121.
Published: 01 April 2020
... definition of consonance, and only once (obliquely and in passing) does she associate dissonance with complex ratios (155). This creates the lingering impression that consonance and dissonance can be reduced to matters of mathematical ratios, without much regard for the role of the culturally situated...
Journal Article
Journal of Music Theory (2013) 57 (2): 419–431.
Published: 01 October 2013
... as such concepts as “simple proportions” and “sufficiently elementary
ratios.”
The authors’ idea of grouping structure depends on temporal segmen-
tation and, like “paradigmatic” analyses by Nicolas Ruwet (1972) and Jean-
Jacques Nattiez (1975), involves...
Journal Article
Journal of Music Theory (2015) 59 (2): 321–332.
Published: 01 October 2015
... and Gesture , ed. Gritten Anthony King Elaine , 203 – 20 . Farnham : Ashgate . Friberg Anders Sundström Andreas . 2002 . “Swing Ratios and Ensemble Timing in Jazz Performance: Evidence for a Common Rhythmic Pattern.” Music Perception 19 / 3 : 333 – 49 . Frigyesi Judit...
Journal Article
Journal of Music Theory (2002) 46 (1-2): 1–56.
Published: 01 October 2002
... to the “height” aspect of a
musical tone. Pitch may be represented by a note name with register
(A4), or by a frequency (440 cps), or by the logarithm of the frequency.
An ordered interval is comprised of an ordered pair of pitches. The size
of an interval is given either by the ratio between the respective...
Journal Article
Journal of Music Theory (2022) 66 (2): 147–187.
Published: 01 October 2022
... being spun across History of Music Theory 2 (and its predecessor, History of Theory 1), that narrative is a familiar and a conventional one: Music theory begins with the Greeks, who noted things like the relationship between consonances and simple number ratios and who developed sophisticated...
Journal Article
Journal of Music Theory (2009) 53 (1): 57–94.
Published: 01 April 2009
... a figure (our sense of ratio) and occur at subtactus
levels.9 Time-span stretches always apply to the entire texture, but note-value
transformations may (and usually do) apply only to the melody. Both proce-
dures involve the perception of musical time, and hence...
Includes: Supplementary data
Journal Article
Journal of Music Theory (2002) 46 (1-2): 207–283.
Published: 01 October 2002
... effects for complex tones tend to be
minimized by simple frequency ratios (Plomp–Levelt 1965). This impact of fre-
quency ratios is left outside the present discussion.
24. The perceptual factors discussed here—virtual-pitch perception, critical-band
effects, and streaming—are also included...
Journal Article
Journal of Music Theory (2007) 51 (2): 211–243.
Published: 01 October 2007
... from Cohn 2001, 304)
pulse levels are isochronous (consisting of evenly spaced pulses) and in which
each pulse level relates to the next by a ratio of 2 or 3,1 ensuring that each
metric state is “fully consonant” as defined by Cohn (1992b, 8...
Journal Article
Journal of Music Theory (2004) 48 (2): 295–324.
Published: 01 October 2004
... in a stratified score. Cone approaches this topic in his discussion
305
of tempi within the Symphonies of Wind Instruments. Cone notes that if
Π= 72 is taken as the common measure, the various tempi of this work
relate to one another as simple ratios...
Journal Article
Journal of Music Theory (2000) 44 (1): 171–229.
Published: 01 April 2000
... notes or pairs of notes with preceding or following
notes to form larger groups.16
The ratio of discontinuities within a particular Domain to the total
number of events represents an approximation of the likelihood that a par-
ticular Domain will yield segmentational groups of three to five notes...
Journal Article
Journal of Music Theory (2020) 64 (1): 37–61.
Published: 01 April 2020
... silence, registral silence, and many different piano sounds in a 2005 composition. Simultaneous changes in registral and notational silences, the use of held pitches to foster continuity across fluctuating registral fields, and consistent treatments of the ratio between sound and notated silence...
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