Phoenix: Difference between revisions

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By stretching the octave, though, it's possible to have a tuning that extends 12edo while maintaining most of the same equivalencies found in it.

In addition to meantone temperament, phoenix also ~~supports~~ the ''fenghuang temperament.'' A scale supports this temperament if it contains a tempered subminor ''third'' (which must be closer to 7:6 than to 8:7) that is the octave inversion of a tempered subminor ''seventh'' (which must be closer to 7:4 than 12:7). Only stretched-octave temperaments can accomplish this.

In addition to meantone temperament, phoenix also [[support]]s the ''fenghuang temperament.'' A scale supports this temperament if it contains a tempered subminor ''third'' (which must be closer to 7:6 than to 8:7) that is the octave inversion of a tempered subminor ''seventh'' (which must be closer to 7:4 than 12:7). Only stretched-octave temperaments can accomplish this.

Phoenix's approximations to undecimal and tridecimal intervals are dominated by the fact that the 12th harmonic is also split, meaning that 11:12 and 12:13 can ''each'' be approximated in two different ways (one corresponding to a whole tone and one to a diatonic semitone).

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 By stretching the octave, though, it's possible to have a tuning that extends 12edo while maintaining most of the same equivalencies found in it.
-In addition to meantone temperament, phoenix also supports the ''fenghuang temperament.'' A scale supports this temperament if it contains a tempered subminor ''third'' (which must be closer to 7:6 than to 8:7) that is the octave inversion of a tempered subminor ''seventh'' (which must be closer to 7:4 than 12:7). Only stretched-octave temperaments can accomplish this.
+In addition to meantone temperament, phoenix also [[support]]s the ''fenghuang temperament.'' A scale supports this temperament if it contains a tempered subminor ''third'' (which must be closer to 7:6 than to 8:7) that is the octave inversion of a tempered subminor ''seventh'' (which must be closer to 7:4 than 12:7). Only stretched-octave temperaments can accomplish this.
 Phoenix's approximations to undecimal and tridecimal intervals are dominated by the fact that the 12th harmonic is also split, meaning that 11:12 and 12:13 can ''each'' be approximated in two different ways (one corresponding to a whole tone and one to a diatonic semitone).