2L 3s (3/2-equivalent): Difference between revisions

Line 33:

|}

== Theory ==

2L 3s&lang;3/2&rang; can be interpreted as the [[nonoctave]] [[regular temperament]] named [[subgroup temperaments#pythium|pythium]] by [[User:CompactStar]], tempering out [[81/80]] in the 3/2.4.5 subgroup. This is the simplest 3/2-equivalent temperament not containing octaves. Because the 3/2-reduced 5th harmonic of [[40/27]] is conflated with the just perfect fifth, the CTE generator of this temperament is exactly the [[32/27]] Pythagorean minor third~~. Although the most accurate tunings use near-32/27 generators, pythium can be tuned with minor thirds as sharp as that of [[11edf]]'s (319 cents)~~. The best extension of pythium to the 3/2.4.5.7 subgroup adds [[64/63]] to the comma list, making the CTE generator slightly flatter than 32/27, near [[~~22edf~~]]'s ~~minor third of 287~~ cents.

2L 3s&lang;3/2&rang; can be interpreted as the [[nonoctave]] [[regular temperament]] named [[subgroup temperaments#pythium|pythium]] by [[User:CompactStar]], tempering out [[81/80]] in the 3/2.4.5 subgroup. This is the simplest 3/2-equivalent temperament not containing octaves. Because the 3/2-reduced 5th harmonic of [[40/27]] is conflated with the just perfect fifth, the CTE generator of this temperament is exactly the [[32/27]] Pythagorean minor third. The best extension of pythium to the 3/2.4.5.7 subgroup adds [[64/63]] to the comma list, making the CTE generator slightly flatter than 32/27, about 286 cents. Although the most accurate tunings use near-32/27 generators, pythium can be tuned with minor thirds as sharp as that of [[11edf]]'s (319 cents).

== Modes ==

The mode names are based on the 5 largest satellites of Saturn.

@@ Line 33: / Line 33: @@
 |}
 == Theory ==
-L 3s&lang;3/2&rang; can be interpreted as the [[nonoctave]] [[regular temperament]] named [[subgroup temperaments#pythium|pythium]] by [[User:CompactStar]], tempering out [[81/80]] in the 3/2.4.5 subgroup. This is the simplest 3/2-equivalent temperament not containing octaves. Because the 3/2-reduced 5th harmonic of [[40/27]] is conflated with the just perfect fifth, the CTE generator of this temperament is exactly the [[32/27]] Pythagorean minor third. Although the most accurate tunings use near-32/27 generators, pythium can be tuned with minor thirds as sharp as that of [[11edf]]'s (319 cents). The best extension of pythium to the 3/2.4.5.7 subgroup adds [[64/63]] to the comma list, making the CTE generator slightly flatter than 32/27, near [[22edf]]'s minor third of 287 cents.
+L 3s&lang;3/2&rang; can be interpreted as the [[nonoctave]] [[regular temperament]] named [[subgroup temperaments#pythium|pythium]] by [[User:CompactStar]], tempering out [[81/80]] in the 3/2.4.5 subgroup. This is the simplest 3/2-equivalent temperament not containing octaves. Because the 3/2-reduced 5th harmonic of [[40/27]] is conflated with the just perfect fifth, the CTE generator of this temperament is exactly the [[32/27]] Pythagorean minor third. The best extension of pythium to the 3/2.4.5.7 subgroup adds [[64/63]] to the comma list, making the CTE generator slightly flatter than 32/27, about 286 cents. Although the most accurate tunings use near-32/27 generators, pythium can be tuned with minor thirds as sharp as that of [[11edf]]'s (319 cents).
 == Modes ==
 The mode names are based on the 5 largest satellites of Saturn.