Cassaschismic: Difference between revisions
fix (note that gariwizmic was originally also correct, but subtracting the half-octave feels more natural than half a Pythagorean comma) |
Reversal on rank-2 aberschisma location: I use gariwizmic regularly, trust me on this one... besides, all these temperaments are connected by the chain of fiths, so it's logical that chain-of-fifthy numbers of gens would appear |
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Other rank-2 temperaments of cassaschismic include [[cotoneum]], [[gariwizmic]], [[newt]], [[satin]], and [[vulture]]; these temperaments, instead of tempering out the aberschisma, find it deep in the generator chain. | Other rank-2 temperaments of cassaschismic include [[cotoneum]], [[gariwizmic]], [[newt]], [[satin]], and [[vulture]]; these temperaments, instead of tempering out the aberschisma, find it deep in the generator chain. | ||
{{Databox|Generators needed to reach the aberschisma|Newt (41 & 270) finds it at -41 hemififths.<br>Cotoneum (41 & 217) finds it at -41 fifths.<br>Gariwizmic (94 & 270) finds it at + | {{Databox|Generators needed to reach the aberschisma|Newt (41 & 270) finds it at -41 hemififths.<br>Cotoneum (41 & 217) finds it at -41 fifths, equating it with the 41-comma.<br>Gariwizmic (94 & 270) finds it at +53 fifths (mercator comma) minus a half pythagorean comma.<br>Vulture (53 & 217) finds it at -41 1/4-fifths.<br>Satin (94 & 217) finds it at -94 1/3-fourths.}} | ||
Cassaschismic is [[support]]ed by notable [[equal temperament]]s such as {{EDOs| 217, 270, 311, and 364 }}, where the aberschisma step is well represented by one edostep. It is also trivially supported by edos of cassandra, these being [[41edo|41]], [[53edo|53]], [[94edo|94]], and of course, [[12edo]] through the 12e [[val]], where both the comma step and the aberschisma step are tempered out, so it can be used in any of those forms as well. | Cassaschismic is [[support]]ed by notable [[equal temperament]]s such as {{EDOs| 217, 270, 311, and 364 }}, where the aberschisma step is well represented by one edostep. It is also trivially supported by edos of cassandra, these being [[41edo|41]], [[53edo|53]], [[94edo|94]], and of course, [[12edo]] through the 12e [[val]], where both the comma step and the aberschisma step are tempered out, so it can be used in any of those forms as well. | ||