64/63: Difference between revisions

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{{~~interwiki~~

{{Interwiki

| en = 64/63

| de = 64/63

~~| en = 64/63~~

}}

: ''"Septimal comma" redirects here. For non-idiomatic usages, see [[Septimal]] and [[Comma]].''

{{Infobox Interval

| Name = septimal comma, Archytas' comma

| Color name = r1, ru unison, <br/>~~Ru comma~~

| Color name = r1, ru unison,<br/>rM, ruma

| Sound = Ji-64-63-csound-foscil-220hz.mp3

| Comma = yes

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== Temperaments ==

[[Tempering out]] this comma 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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== See also ==

* [[Septimal comma]] (disambiguation page)

* [[Gallery of just intervals]]

* [[List of superparticular intervals]]

@@ Line 1: / Line 1: @@
-{{interwiki
+{{Interwiki
+| en = 64/63
 | de = 64/63
-| en = 64/63
 }}
+: ''"Septimal comma" redirects here. For non-idiomatic usages, see [[Septimal]] and [[Comma]].''
 {{Infobox Interval
 | Name = septimal comma, Archytas' comma
-| Color name = r1, ru unison, <br/>Ru comma
+| Color name = r1, ru unison,<br/>rM, ruma
 | Sound = Ji-64-63-csound-foscil-220hz.mp3
 | Comma = yes
@@ Line 13: / Line 14: @@
 == Temperaments ==
-[[Tempering out]] this comma 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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 == See also ==
-* [[Septimal comma]] (disambiguation page)
 * [[Gallery of just intervals]]
 * [[List of superparticular intervals]]