Octaphore: Difference between revisions

Unque (talk | contribs)
m Minor formatting changes for the temperaments section
Undo revision 188752 by Unque (talk). No duplicate data. Restore mapping generators
Tag: Undo
Line 16: Line 16:


{{Mapping|legend=1| 1 2 2 4 | 0 -8 0 -23 | 0 0 1 0 }}
{{Mapping|legend=1| 1 2 2 4 | 0 -8 0 -23 | 0 0 1 0 }}
: mapping generators: ~2, ~28/27, ~5


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~28/27 = 62.233, ~5/4 = 386.314
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~28/27 = 62.233, ~5/4 = 386.314
Line 45: Line 47:
===2.3.7 Unicorn===
===2.3.7 Unicorn===
{{See also | Unicorn }}
{{See also | Unicorn }}
If we temper the octaphore in its minimal prime subgroup of 2.3.7, we get the 2.3.7-subgroup version of [[unicorn]]:
If we temper the octaphore in its minimal prime subgroup of 2.3.7, we get the 2.3.7-subgroup version of [[unicorn]], where it finds prime 5 by interpreting five gens as a flat [[~]][[6/5]] by tempering [[126/125]].


[[Subgroup]]: 2.3.7
[[Subgroup]]: 2.3.7
Line 52: Line 54:


{{Mapping|legend=1| 1 2 4 | 0 -8 -23 }}
{{Mapping|legend=1| 1 2 4 | 0 -8 -23 }}
: mapping generators: ~2, ~28/27


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~28/27 = 62.233
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~28/27 = 62.233


{{Optimal ET sequence|legend=1| 19, 20d, 39d, 58, 77, 96d, 135 }}
{{Optimal ET sequence|legend=1| 19, 20d, 39d, 58, 77, 96d, 135 }}
==== Septimal Unicorn ====
By noticing that the interval at five generators is nearly [[6/5]], we can introduce prime 5 to the mapping by tempering out [[126/125]].
[[Subgroup]]: 2.3.5.7
[[Comma list]]: 10976/10935, 126/125
{{Mapping|legend=1| 1 2 3 4| 0 -8 -13 -23 }}
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~28/27 = 62.324
{{Optimal ET sequence|legend=1| 19, 39d, 58, 77, 135c, 212c}}


==See also==
==See also==