5-7-13-15 by 22/13 bihexany: Difference between revisions
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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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Latest revision as of 12:01, 20 November 2025
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 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.
! 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