64/63: Difference between revisions

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== Temperaments ==

[[Tempering out]] this comma leads to [[superpyth]] temperament (sometimes called ''archy'' in the 2.3.7-subgroup), which equates 9/8 and 8/7, and also equates [[7/4]] with [[16/9]]~~, so~~ that the just dominant seventh chord, [[36:45:54:64|1–5/4–3/2–16/9]], and the harmonic seventh chord, [[4:5:6:7|1–5/4–3/2–7/4]], are equated to the same chord. Equal temperaments tempering out 64/63 include {{EDOs| 12, 15, 17, 22, 27, 37, 49 and 59 }}.

[[Tempering out]] this comma leads to [[superpyth]] temperament (sometimes called ''archy'' in the 2.3.7-subgroup), which equates 9/8 and 8/7, and also equates [[7/4]] with [[16/9]]. This means that the just dominant seventh chord, [[36:45:54:64|1–5/4–3/2–16/9]], and the harmonic seventh chord, [[4:5:6:7|1–5/4–3/2–7/4]], are equated to the same chord. Equal temperaments tempering out 64/63 include {{EDOs| 12, 15, 17, 22, 27, 37, 49 and 59 }}.

Archytas' comma is similar to Didymus' or the syntonic comma, 81/80, in that when it is tempered out it makes a stack of four fifths [[octave reduction|octave reduced]] equal a relatively consonant major third. In the case of 81/80, the major third is [[5/4]], while with Archytas' comma, the major third is [[9/7]].

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 == Temperaments ==
-[[Tempering out]] this comma leads to [[superpyth]] temperament (sometimes called ''archy'' in the 2.3.7-subgroup), which equates 9/8 and 8/7, and also equates [[7/4]] with [[16/9]], so that the just dominant seventh chord, [[36:45:54:64|1–5/4–3/2–16/9]], and the harmonic seventh chord, [[4:5:6:7|1–5/4–3/2–7/4]], are equated to the same chord. Equal temperaments tempering out 64/63 include {{EDOs| 12, 15, 17, 22, 27, 37, 49 and 59 }}.
+[[Tempering out]] this comma leads to [[superpyth]] temperament (sometimes called ''archy'' in the 2.3.7-subgroup), which equates 9/8 and 8/7, and also equates [[7/4]] with [[16/9]]. This means that the just dominant seventh chord, [[36:45:54:64|1–5/4–3/2–16/9]], and the harmonic seventh chord, [[4:5:6:7|1–5/4–3/2–7/4]], are equated to the same chord. Equal temperaments tempering out 64/63 include {{EDOs| 12, 15, 17, 22, 27, 37, 49 and 59 }}.
 Archytas' comma is similar to Didymus' or the syntonic comma, 81/80, in that when it is tempered out it makes a stack of four fifths [[octave reduction|octave reduced]] equal a relatively consonant major third. In the case of 81/80, the major third is [[5/4]], while with Archytas' comma, the major third is [[9/7]].