16ed5/3: Difference between revisions

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== Commas ==

Depending on your mapping, 16ed5/3 can be said to temper a number of commas, including the diaschisma, the marvel comma, Archytas' comma, and the jubilisma, all discussed in the temperaments section. In addition, being an even division of the 5/3, it tempers the sensamagic comma ([[245/243]]), as the half mosoctave is midway between [[9/7]] and [[35/27]]. This is analogous to the tritone in 2n edo systems. The keema ([[875/864]]) is tempered due to the septimal interpretation of the diatonic sevenths, and the Motwellsma ([[99/98]]) is tempered by two major mos3rds ([[7/6]]) resulting in an augmented mos5th ([[11/8]]).

== Temperaments ==

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The tempered marvel comma also means that the two large [[Tritone|tritones]] ([[64/45|pental]] and [[10/7|septimal]]) are addressed by the same scale step. The tempered diaschisma, on the other hand, means that both pental tritones are also addressed by the same scale step.

As 3 semitones make a period-reduced octave, and it alludes to ~~the~~ tritone tempering, [[User:Ayceman|I]] propose the name '''tristone''' for the basic [[Diaschismic family|diaschismic temperament]], based on the 16/15 to 6/5 relationship, as well as the following variants and extensions:

Both of the 7-limit approaches also temper Archytas' comma ([[64/63]]) as a result of equating the [[14/9]] with [[7/4]], and the jubilisma ([[50/49]]) due to tritone equivalence. These are relatively large commas, given the step size (about half, and 7/11ths respectively).

This shows the close relationships with [[Srutal]] and [[Pajara]] octave temperaments. In 16ed5/3's case, there is a close equivalence to [[22edo]]'s pajara tuning.

As 3 semitones make a period-reduced octave, and it alludes to tritone tempering, [[User:Ayceman|I]] propose the name '''tristone''' for the basic [[Diaschismic family|diaschismic temperament]], based on the 16/15 to 6/5 relationship, as well as the following variants and extensions:

=== Tristone ===

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[[Subgroup]]: 5/3.20/9.10/3.1000/189

[[Comma]] list: 2048/2025, 225/224

[[Comma]] list: 2048/2025, 225/224, 64/63, 50/49

[[POL2]] generator: ~5/4 = 389.6140

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[[Subgroup]]: 5/3.20/9.5/2.250/63

[[Comma]] list: 2048/2025, 225/224

[[Comma]] list: 2048/2025, 225/224, 64/63, 50/49

[[POL2]] generator: ~5/4 = 390.5430

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+== Commas ==
+Depending on your mapping, 16ed5/3 can be said to temper a number of commas, including the diaschisma, the marvel comma, Archytas' comma, and the jubilisma, all discussed in the temperaments section. In addition, being an even division of the 5/3, it tempers the sensamagic comma ([[245/243]]), as the half mosoctave is midway between [[9/7]] and [[35/27]]. This is analogous to the tritone in 2n edo systems. The keema ([[875/864]]) is tempered due to the septimal interpretation of the diatonic sevenths, and the Motwellsma ([[99/98]]) is tempered by two major mos3rds ([[7/6]]) resulting in an augmented mos5th ([[11/8]]).
 == Temperaments ==
@@ Line 428: / Line 431: @@
 The tempered marvel comma also means that the two large [[Tritone|tritones]] ([[64/45|pental]] and [[10/7|septimal]]) are addressed by the same scale step. The tempered diaschisma, on the other hand, means that both pental tritones are also addressed by the same scale step.
-As 3 semitones make a period-reduced octave, and it alludes to the tritone tempering, [[User:Ayceman|I]] propose the name '''tristone''' for the basic [[Diaschismic family|diaschismic temperament]], based on the 16/15 to 6/5 relationship, as well as the following variants and extensions:
+Both of the 7-limit approaches also temper Archytas' comma ([[64/63]]) as a result of equating the [[14/9]] with [[7/4]], and the jubilisma ([[50/49]]) due to tritone equivalence. These are relatively large commas, given the step size (about half, and 7/11ths respectively).
+This shows the close relationships with [[Srutal]] and [[Pajara]] octave temperaments. In 16ed5/3's case, there is a close equivalence to [[22edo]]'s pajara tuning.
+As 3 semitones make a period-reduced octave, and it alludes to tritone tempering, [[User:Ayceman|I]] propose the name '''tristone''' for the basic [[Diaschismic family|diaschismic temperament]], based on the 16/15 to 6/5 relationship, as well as the following variants and extensions:
 === Tristone ===
@@ Line 448: / Line 455: @@
 [[Subgroup]]: 5/3.20/9.10/3.1000/189
-[[Comma]] list: 2048/2025, 225/224
+[[Comma]] list: 2048/2025, 225/224, 64/63, 50/49
 [[POL2]] generator: ~5/4 = 389.6140
@@ Line 478: / Line 485: @@
 [[Subgroup]]: 5/3.20/9.5/2.250/63
-[[Comma]] list: 2048/2025, 225/224
+[[Comma]] list: 2048/2025, 225/224, 64/63, 50/49
 [[POL2]] generator: ~5/4 = 390.5430