Sensipent family: Difference between revisions
Move a large chunk of sporadic-subgroup temps to the bottom so that we see sensi earlier |
Tag: Undo |
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The aforementioned extension with prime 17 through tempering out 1089/1088 implies tempering out [[256/255]] ({{s|16}}), as {{nowrap| 256/255 {{=}} (22/17)/(165/128) }}. | The aforementioned extension with prime 17 through tempering out 1089/1088 implies tempering out [[256/255]] ({{s|16}}), as {{nowrap| 256/255 {{=}} (22/17)/(165/128) }}. | ||
Sensible uses the accurate mapping of prime 31 in sensipent, so that the sensible generator serves many roles in subgroup harmony, but it is not ~[[9/7]] or ~[[13/10]] which would incur more damage. Its [[S-expression]]-based comma list is {([[ | Sensible uses the accurate mapping of prime 31 in sensipent, so that the sensible generator serves many roles in subgroup harmony, but it is not ~[[9/7]] or ~[[13/10]] which would incur more damage. Its [[S-expression]]-based comma list {{nowrap| is {([[8019/8000|S9/S10]], [[256/255|S16]],) [[529/528|S23]], [[576/575|S24]], [[961/960|S31]], [[1024/1023|S32]], [[1089/1088|S33]]} }} implying also tempering out [[496/495]] (S31⋅S32) and [[528/527]] (S32⋅S33) as well as [[16337/16335]] (S31/S33) = ([[17/15]])/([[33/31]])<sup>2</sup>. A notable [[patent val]] tuning not appearing in the optimal ET sequence is [[157edo]]. | ||
Subgroup: 2.3.5.11 | Subgroup: 2.3.5.11 | ||
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Comma list: 55/54, 66/65, 77/75, 143/140 | Comma list: 55/54, 66/65, 77/75, 143/140 | ||
Mapping: {{mapping| 1 -1 -1 -2 -1 0 | 0 7 9 13 12 | Mapping: {{mapping| 1 -1 -1 -2 -1 0 | 0 7 9 13 12 10}} | ||
Optimal tunings: | Optimal tunings: | ||