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912:, one aspect of the psychoacoustic concept of dissonance....high tonalness corresponds to low entropy and low tonalness corresponds to high entropy."
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evoked by a set of two or more pitches. This measures how easy or difficult it is to fit the pitches into a single
17:
908:. "Harmonic entropy is a measure of the uncertainty in pitch perception, and it provides a physical correlate of
38:
Harmonic entropy for triads with lower interval and upper interval each ranging from 200 to 500 cents. Compare
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645:(a) compute the areas defined by the normal (Gaussian) bell curve on top, and the mediants on the sides
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647:(b) normalize the sum of the areas to add to 1, such that each represents a probability
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263:). In the harmonic series, the integers are much lower for the harmonic seventh chord,
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See external links for a detailed description of the model of harmonic entropy.
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is subtracted by the mediant between the element and the next lowest element:
101:, Massachusetts. He is known for his seminal role in developing the theory of
961:
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chord. Both have exactly the same set of intervals between the notes, under
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The space around intervals is shown above for the Farey sequence, order 50.
34:
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948:
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From here, the process to compute harmonic entropy is as follows:
255:, but the first one is easy to fit into a single harmonic series (
938:
A Middle Path: Between Just
Intonation and the Equal Temperaments
926:
118:
791:
98:
343:. Components of dissonance not modeled by this theory include
74:. See full resolution for locations of the triads on the plot
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649:(c) calculate the entropy of that set of probabilities
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633:{\displaystyle {\frac {a_{j-1}+a_{j}}{b_{j-1}+b_{j}}}}
544:{\displaystyle {\frac {a_{j}+a_{j+1}}{b_{j}+b_{j+1}}}}
355:
even though both can be tuned to the same size, as in
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has received attention from music theorists such as
851:"Tuning, Tonality, and Twenty-Two-Tone Temperament"
140:. It is intended to model one of the components of
132:, a refinement of a model by van Eck influenced by
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833:: CS1 maint: bot: original URL status unknown (
815:. Archived from the original on 5 November 2013
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347:roughness as well as tonal context (e.g. an
27:For other people with similar names, see
949:Harmonic Entropy on the Xenharmonic Wiki
874:
842:
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144:as a measure of the uncertainty of the
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105:, including being the first to define
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244:{\displaystyle {\tfrac {1}{4:5:6:7}}}
152:. For example, most listeners rank a
146:virtual pitch ("missing fundamental")
993:21st-century American male musicians
809:""Alternate Tunings Mailing List",
763:{\displaystyle {\tfrac {a+c}{b+d}}}
24:
927:Some music theory from Paul Erlich
25:
1004:
919:
458:{\displaystyle f_{j}=a_{j}/b_{j}}
336:{\displaystyle {105:120:140:168}}
465:, and the next highest element:
897:Tuning, Timbre, Spectrum, Scale
878:Tuning, Timbre, Spectrum, Scale
718:{\displaystyle {\tfrac {c}{d}}}
689:{\displaystyle {\tfrac {a}{b}}}
888:
661:
13:
1:
875:Sethares, William A. (2004).
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29:Paul Ehrlich (disambiguation)
109:and its decatonic scales in
7:
667:The mediant of two ratios,
10:
1009:
894:Sethares, William (2005).
26:
351:is more dissonant than a
296:{\displaystyle {4:5:6:7}}
185:{\displaystyle {4:5:6:7}}
983:American male guitarists
978:American music theorists
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988:21st-century guitarists
798:. Accessed 2013-10-29.
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849:Erlich, Paul (1998).
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382:th iteration of the
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103:regular temperaments
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128:His definition of
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403:{\displaystyle j}
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18:Harmonic entropy
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134:Ernst Terhardt
113:. He holds a
95:music theorist
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817:. Retrieved
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410:th element,
390:between the
361:
259:rather than
198:as far more
129:
127:
106:
97:living near
86:
85:
973:1972 births
953:en.xen.wiki
942:DKeenan.com
353:minor third
87:Paul Erlich
962:Categories
778:References
261:undertones
142:dissonance
117:degree in
931:Lumma.org
910:tonalness
607:−
576:−
257:overtones
253:inversion
200:consonant
91:guitarist
829:cite web
362:For the
68:10:12:15
388:mediant
202:than a
119:physics
904:
794:", on
792:Pajara
386:, the
99:Boston
62:, and
882:(PDF)
854:(PDF)
819:3 May
725:, is
655:Notes
357:12-ET
196:chord
121:from
111:22-ET
56:6:7:9
44:4:5:6
902:ISBN
835:link
821:2019
696:and
93:and
951:",
940:",
929:",
359:).
330:168
324:140
318:120
312:105
964::
862:17
860:.
856:.
831:}}
827:{{
125:.
50:,
947:"
944:.
936:"
933:.
925:"
864:.
839:.
837:)
823:.
813:"
790:"
770:.
754:d
751:+
748:b
743:c
740:+
737:a
710:d
707:c
681:b
678:a
623:j
619:b
615:+
610:1
604:j
600:b
592:j
588:a
584:+
579:1
573:j
569:a
534:1
531:+
528:j
524:b
520:+
515:j
511:b
503:1
500:+
497:j
493:a
489:+
484:j
480:a
451:j
447:b
442:/
436:j
432:a
428:=
423:j
419:f
398:j
370:n
327::
321::
315::
290:7
287::
284:6
281::
278:5
275::
272:4
235:7
232::
229:6
226::
223:5
220::
217:4
213:1
179:7
176::
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170::
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164::
161:4
31:.
20:)
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