FKH Extended-diatonic Interval Names: Difference between revisions

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*22edo, 27edo and 34edo (through 17edo) are superpythagorean tunings from the use of 'K' and 'k'.

*29edo, 41edo, 46edo, 53edo and 72edo are Pythagorean tunings through the use of both 'S' and 's'; and 'K' and 'k'.

*34edo, 43edo, 53edo and 72edo (through 24edo) are barbados tunings through the use of intermediates. We can find the scale Barbados[9] 4|4, P1 ~~1-2~~ M2 2-3 3-4 P4 P5 5-6 6-7 m7 ~~7-8~~ P8 in all of those edos, but not necessarily in the primary interval names.

*34edo, 43edo, 53edo and 72edo (through 24edo) are barbados tunings through the use of intermediates. We can find the scale Barbados[9] 4|4, P1 M2 2-3 3-4 P4 P5 5-6 6-7 m7 P8 in all of those edos, but not necessarily in the primary interval names.

Every edo in which we see SM2/sm3 also supports barbados, where this interval is the generator, at half a fourth, however rather than 15/13 the generator is more simple represented as 8/7~7/6. The temperament generated by the semi-fourth wherein it represent both SM2 and sm3 (tempering out [[49/48]]) is called Semaphore.

Semaphore[9] 4|4 has primary interval names P1 ~~S1/sm2~~ M2 SM2/sm3 SM3/s4 P4 P5 S5/sm6 m7 ~~SM7/s8~~ P8, which can be seen in 19edo, 24edo and 29edo, so we know they are Semaphore tunings.

Semaphore[9] 4|4 has primary interval names P1 M2 SM2/sm3 SM3/s4 P4 P5 S5/sm6 SM6/sm7 m7 P8, which can be seen in 19edo, 24edo and 29edo, so we know they are Semaphore tunings.

Well-ordered primary and their secondary interval names for 22edo, 41edo and 53edo are shown below in more detail.

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 *22edo, 27edo and 34edo (through 17edo) are superpythagorean tunings from the use of 'K' and 'k'.
 *29edo, 41edo, 46edo, 53edo and 72edo are Pythagorean tunings through the use of both 'S' and 's'; and 'K' and 'k'.
-*34edo, 43edo, 53edo and 72edo (through 24edo) are barbados tunings through the use of intermediates. We can find the scale Barbados[9] 4|4, P1 1-2 M2 2-3 3-4 P4 P5 5-6 6-7 m7 7-8 P8 in all of those edos, but not necessarily in the primary interval names.
+*34edo, 43edo, 53edo and 72edo (through 24edo) are barbados tunings through the use of intermediates. We can find the scale Barbados[9] 4|4, P1 M2 2-3 3-4 P4 P5 5-6 6-7 m7 P8 in all of those edos, but not necessarily in the primary interval names.
 Every edo in which we see SM2/sm3 also supports barbados, where this interval is the generator, at half a fourth, however rather than 15/13 the generator is more simple represented as 8/7~7/6. The temperament generated by the semi-fourth wherein it represent both SM2 and sm3 (tempering out [[49/48]]) is called Semaphore.
-Semaphore[9] 4|4 has primary interval names P1 S1/sm2 M2 SM2/sm3 SM3/s4 P4 P5 S5/sm6 m7 SM7/s8 P8, which can be seen in 19edo, 24edo and 29edo, so we know they are Semaphore tunings.
+Semaphore[9] 4|4 has primary interval names P1 M2 SM2/sm3 SM3/s4 P4 P5 S5/sm6 SM6/sm7 m7 P8, which can be seen in 19edo, 24edo and 29edo, so we know they are Semaphore tunings.
 Well-ordered primary and their secondary interval names for 22edo, 41edo and 53edo are shown below in more detail.