Bird's eye view of temperaments by accuracy: Difference between revisions
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Echidna is notable as achieving no-13's [[17-limit]] harmony with accuracy in a surprisingly small number of notes. [[13/8]] can be found too but is the most complex, being found at (11/10)<sup>16</sup> plus a half-octave period, octave-reduced. However, as primes 5 and 11 are also found in the same direction, intervals of 13 are common even in the 22-note MOS, so the 36-note MOS is more useful than might be suspected, despite not finding every odd from the same position. | Echidna is notable as achieving no-13's [[17-limit]] harmony with accuracy in a surprisingly small number of notes. [[13/8]] can be found too but is the most complex, being found at (11/10)<sup>16</sup> plus a half-octave period, octave-reduced. However, as primes 5 and 11 are also found in the same direction, intervals of 13 are common even in the 22-note MOS, so the 36-note MOS is more useful than might be suspected, despite not finding every odd from the same position. | ||
=== [[Catakleismic]] === | |||
Note counts: | |||
* 23 for {3, 5, 7, 9, 15, 25, 27, 39, 45, 65, 75(, 125)} ([[15L 4s]] or 19L 15s) | |||
* 29 for adding {21, 35, 63} (19L 15s) | |||
As catakleismic is largely just a certain extension of cata to prime 7, see [[#Cata]]. It admits a number of possible extensions to prime 11 depending on user preference and the tuning used, hence its listing here as a ~13-limit temperament. | |||
=== [[Diaschismic]] === | === [[Diaschismic]] === | ||