3-5-11-13 by 24/17 bihexany: Difference between revisions

Line 1:

[[File:3-5-11-13_by_24-17_bihexany.png|thumb|Circle diagram.]] A [[13-odd-limit]] [[~~Hexany~~]] ~~comprised entirely of prime numbers~~. This creates a scale of 1 13/12 11/10 143/120 22/17 13/10 24/17 26/17 132/85 143/85 11/6 156/85 2/1, with steps of 13/12 66/65 13/12 240/221 221/220 240/221 13/12 66/65 13/12 85/78 936/935 85/78. While this does have many clusters of close notes, the purpose of this particular bihexany is not to maximise melodic utility, but to illustrate just how well [[8edo]] approximates this small subgroup of just intonation because it tempers out [[17303/17280]] and [[289/288]], with no note deviating from 8edo by more than 15 cents. This makes it the octatonic counterpart of the [[1-7-13-15 by 140/99 bihexany]] and the [[1-3-9-17 by 19/16 bihexany]].

[[File:3-5-11-13_by_24-17_bihexany.png|thumb|Circle diagram.]] A [[17-odd-limit]] [[Bihexany]]. This creates a scale of 1 13/12 11/10 143/120 22/17 13/10 24/17 26/17 132/85 143/85 11/6 156/85 2/1, with steps of 13/12 66/65 13/12 240/221 221/220 240/221 13/12 66/65 13/12 85/78 936/935 85/78. While this does have many clusters of close notes, the purpose of this particular bihexany is not to maximise melodic utility, but to illustrate just how well [[8edo]] approximates this small subgroup of just intonation because it tempers out [[17303/17280]] and [[289/288]], with no note deviating from 8edo by more than 15 cents. This makes it the octatonic counterpart of the [[1-7-13-15 by 140/99 bihexany]] and the [[1-3-9-17 by 19/16 bihexany]].

<pre>

! 3-5-11-13_by_24/17_Bihexany.scl

@@ Line 1: / Line 1: @@
-[[File:3-5-11-13_by_24-17_bihexany.png|thumb|Circle diagram.]] A [[13-odd-limit]] [[Hexany]] comprised entirely of prime numbers. This creates a scale of 1 13/12 11/10 143/120 22/17 13/10 24/17 26/17 132/85 143/85 11/6 156/85 2/1, with steps of 13/12 66/65 13/12 240/221 221/220 240/221 13/12 66/65 13/12 85/78 936/935 85/78. While this does have many clusters of close notes, the purpose of this particular bihexany is not to maximise melodic utility, but to illustrate just how well [[8edo]] approximates this small subgroup of just intonation because it tempers out [[17303/17280]] and [[289/288]], with no note deviating from 8edo by more than 15 cents. This makes it the octatonic counterpart of the [[1-7-13-15 by 140/99 bihexany]] and the [[1-3-9-17 by 19/16 bihexany]].
+[[File:3-5-11-13_by_24-17_bihexany.png|thumb|Circle diagram.]] A [[17-odd-limit]] [[Bihexany]]. This creates a scale of 1 13/12 11/10 143/120 22/17 13/10 24/17 26/17 132/85 143/85 11/6 156/85 2/1, with steps of 13/12 66/65 13/12 240/221 221/220 240/221 13/12 66/65 13/12 85/78 936/935 85/78. While this does have many clusters of close notes, the purpose of this particular bihexany is not to maximise melodic utility, but to illustrate just how well [[8edo]] approximates this small subgroup of just intonation because it tempers out [[17303/17280]] and [[289/288]], with no note deviating from 8edo by more than 15 cents. This makes it the octatonic counterpart of the [[1-7-13-15 by 140/99 bihexany]] and the [[1-3-9-17 by 19/16 bihexany]].
 <pre>
 ! 3-5-11-13_by_24/17_Bihexany.scl