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2025-11-20T12:01:40Z

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	[[File:5-7-13-15_by_22-13_Bihexany.png\|thumb\|Circle diagram.]] A [[15-odd-limit]] [[Hexany]]. This creates a scale of 1 15/14 11/10 33/28 33/26 13/10 39/28 3/2 11/7 22/13 165/91 13/7 2/1, with steps of 15/14 75/77 15/14 14/13 169/165 15/14 14/13 22/21 14/13 15/14 169/165 14/13. As half the notes in the [[5-7-13-15_hexany\|base hexany]] have a 13 in the numerator, this cancels them out for simpler undecimal ones, while also being the right size to ensure that there are never multiple small intervals in quick succession, although a few fifth-tones are still inevitable due to the semiquartal nature of the scale.		[[File:5-7-13-15_by_22-13_Bihexany.png\|thumb\|Circle diagram.]] A [[15-odd-limit]] [[Hexany]]. This creates a scale of 1 15/14 11/10 33/28 33/26 13/10 39/28 3/2 11/7 22/13 165/91 13/7 2/1, with steps of 15/14 75/77 15/14 14/13 169/165 15/14 14/13 22/21 14/13 15/14 169/165 14/13. As half the notes in the [[5-7-13-15_hexany\|base hexany]] have a 13 in the numerator, this cancels them out for simpler undecimal ones, while also being the right size to ensure that there are never multiple small intervals in quick succession, although a few fifth-tones are still inevitable due to the semiquartal nature of the scale. It maps unambiguously and highly accurately to 3 1 3 3 1 3 3 2 3 3 1 3 steps of [[29edo]], due to the fact that it cancels out the errors in its 5th-15th harmonics to approximate most of these composite ratios within a few cents.

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[[File:5-7-13-15_by_22-13_Bihexany.png|thumb|Circle diagram.]] A [[15-odd-limit]] [[Hexany]]. This creates a scale of 1 15/14 11/10 33/28 33/26 13/10 39/28 3/2 11/7 22/13 165/91 13/7 2/1, with steps of 15/14 75/77 15/14 14/13 169/165 15/14 14/13 22/21 14/13 15/14 169/165 14/13. As half the notes in the [[5-7-13-15_hexany|base hexany]] have a 13 in the numerator, this cancels them out for simpler undecimal ones, while also being the right size to ensure that there are never multiple small intervals in quick succession, although a few fifth-tones are still inevitable due to the semiquartal nature of the scale.

<pre>
! 5-7-13-15_by_22/13_Bihexany.scl
!
5 7 13 15 by 22/13 2-combination Bihexany
12
!
119.442
165.004
284.447
412.745
454.213
573.656
701.955
782.492
910.790
1030.233
1071.701
1200
</pre>

[[Category:Hexanies]]
[[Category:12-tone scales]]
[[Category:Pages with Scala files]]

5-7-13-15 by 22/13 bihexany - Revision history

Yourmusic Productions: Edo it detempers.

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