Harmonic entropy: Difference between revisions

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__FORCETOC__

'''Harmonic Entropy''', sometimes abbreviated as "HE", is a simple model to quantify the extent to which musical chords exhibit various psychoacoustic effects, lumped together in a single construct called psychoacoustic '''concordance'''. It was invented by Paul Erlich and developed extensively on the Yahoo! tuning and harmonic_entropy lists. Various later contributions to the model have been made by Steve Martin, Mike Battaglia, Keenan Pepper, and others.

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<math>\displaystyle \left[S \ast K\right]^a(-c)</math>

represents the convolution of <math>S</math> and </math>K, taken to the <math>a</math>'th power, and flipped backwards. Note that if <math>S(x)</math> is a symmetrical (even) spreading function, and if for each ratio <math>n/d</math> in <math>J</math>, if the inverse <math>d/n</math> is also in <math>J</math>, then the above convolution will also be symmetrical, and we also have

represents the convolution of <math>S</math> and <nowiki></math></nowiki>K, taken to the <math>a</math>'th power, and flipped backwards. Note that if <math>S(x)</math> is a symmetrical (even) spreading function, and if for each ratio <math>n/d</math> in <math>J</math>, if the inverse <math>d/n</math> is also in <math>J</math>, then the above convolution will also be symmetrical, and we also have

<math>\displaystyle \left[S \ast K\right]^a(-c) = \left[S \ast K\right]^a(c)</math>

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[http://www.tonalsoft.com/enc/h/harmonic-entropy.aspx Harmonic entropy (TonalSoft encyclopedia)]

[~~http~~://~~launch~~.~~groups~~.~~yahoo.com/group~~/harmonic_entropy/ Harmonic entropy group on Yahoo]

[https://yahootuninggroupsultimatebackup.github.io/harmonic_entropy Harmonic entropy group on Yahoo] (archive)

[http://www.mikebattagliamusic.com/HE-JS/HE.html Harmonic entropy graph calculator (JavaScript)]

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 __FORCETOC__
 '''Harmonic Entropy''', sometimes abbreviated as "HE", is a simple model to quantify the extent to which musical chords exhibit various psychoacoustic effects, lumped together in a single construct called psychoacoustic '''concordance'''. It was invented by Paul Erlich and developed extensively on the Yahoo! tuning and harmonic_entropy lists. Various later contributions to the model have been made by Steve Martin, Mike Battaglia, Keenan Pepper, and others.
@@ Line 342: / Line 343: @@
 <math>\displaystyle \left[S \ast K\right]^a(-c)</math>
-represents the convolution of <math>S</math> and </math>K, taken to the <math>a</math>'th power, and flipped backwards. Note that if <math>S(x)</math> is a symmetrical (even) spreading function, and if for each ratio <math>n/d</math> in <math>J</math>, if the inverse <math>d/n</math> is also in <math>J</math>, then the above convolution will also be symmetrical, and we also have
+represents the convolution of <math>S</math> and <nowiki></math></nowiki>K, taken to the <math>a</math>'th power, and flipped backwards. Note that if <math>S(x)</math> is a symmetrical (even) spreading function, and if for each ratio <math>n/d</math> in <math>J</math>, if the inverse <math>d/n</math> is also in <math>J</math>, then the above convolution will also be symmetrical, and we also have
 <math>\displaystyle \left[S \ast K\right]^a(-c) = \left[S \ast K\right]^a(c)</math>
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 [http://www.tonalsoft.com/enc/h/harmonic-entropy.aspx Harmonic entropy (TonalSoft encyclopedia)]
-[http://launch.groups.yahoo.com/group/harmonic_entropy/ Harmonic entropy group on Yahoo]
+[https://yahootuninggroupsultimatebackup.github.io/harmonic_entropy Harmonic entropy group on Yahoo] (archive)
 [http://www.mikebattagliamusic.com/HE-JS/HE.html Harmonic entropy graph calculator (JavaScript)]