Bill Sethares: Difference between revisions

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He then uses this to derive scales for timbres with non-harmonic spectra, such as the [http://en.wikipedia.org/wiki/Bonang bonang] used in gamelans, which, combined with harmonic spectra, [http://www.musicandmeaning.net/issues/showArticle.php?artID=1.3 maps to the slendro scale used to tune them] . "In the same way that Western harmonic instruments are related to Western scales, so the nonharmonic spectrum of gamelan instruments are related to the gamelan scales."

However, when applied to more than 2 tones, it measures major chords (4:5:6) and minor chords (10:12:15) as equally dissonant, which is not the usual interpretation. [[~~Joe~~ Monzo]] explains the discrepancy by [http://www.tonalsoft.com/sonic-arts/td/erlich/entropy.htm calling this measurement] "[[roughness|roughness]]", not dissonance, and stating that it must be combined with "[[tonalness]]" ([[Paul Erlich]]'s similarity to a [[harmonic series]]) to find the overall [[sonance]].

However, when applied to more than 2 tones, it measures major chords (4:5:6) and minor chords (10:12:15) as equally dissonant, which is not the usual interpretation. [[Joseph Monzo]] explains the discrepancy by [http://www.tonalsoft.com/sonic-arts/td/erlich/entropy.htm calling this measurement] "[[roughness|roughness]]", not dissonance, and stating that it must be combined with "[[tonalness]]" ([[Paul Erlich]]'s similarity to a [[harmonic series]]) to find the overall [[sonance]].

== See also ==

@@ Line 8: / Line 8: @@
 He then uses this to derive scales for timbres with non-harmonic spectra, such as the [http://en.wikipedia.org/wiki/Bonang bonang]  used in gamelans, which, combined with harmonic spectra, [http://www.musicandmeaning.net/issues/showArticle.php?artID=1.3 maps to the slendro scale used to tune them] .  "In the same way that Western harmonic instruments are related to Western scales, so the nonharmonic spectrum of gamelan instruments are related to the gamelan scales."
-However, when applied to more than 2 tones, it measures major chords (4:5:6) and minor chords (10:12:15) as equally dissonant, which is not the usual interpretation.  [[Joe Monzo]] explains the discrepancy by [http://www.tonalsoft.com/sonic-arts/td/erlich/entropy.htm calling this measurement] "[[roughness|roughness]]", not dissonance, and stating that it must be combined with "[[tonalness]]" ([[Paul Erlich]]'s similarity to a [[harmonic series]]) to find the overall [[sonance]].
+However, when applied to more than 2 tones, it measures major chords (4:5:6) and minor chords (10:12:15) as equally dissonant, which is not the usual interpretation.  [[Joseph Monzo]] explains the discrepancy by [http://www.tonalsoft.com/sonic-arts/td/erlich/entropy.htm calling this measurement] "[[roughness|roughness]]", not dissonance, and stating that it must be combined with "[[tonalness]]" ([[Paul Erlich]]'s similarity to a [[harmonic series]]) to find the overall [[sonance]].
 == See also ==