Perfect fifth: Difference between revisions

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== In just intonation ==

The only "perfect" fifth in JI is the ~~'''~~Pythagorean perfect fifth~~'''~~ of [[3/2]], about 702{{c}} in size, which corresponds to the mos-based interval category of the diatonic perfect fifth, and is the generator for Pythagorean tuning and the diatonic scale. However, various "out of tune" fifths exist, such as the ~~'''~~Pythagorean wolf fifth [[262144/177147]]~~'''~~, which is flat of 3/2 by one [[Pythagorean comma]], and is about 678{{c}} in size.

The only "perfect" fifth in JI is the Pythagorean perfect fifth of [[3/2]], about 702{{c}} in size, which corresponds to the mos-based interval category of the diatonic perfect fifth, and is the generator for Pythagorean tuning and the diatonic scale. However, various "out of tune" fifths exist, such as the Pythagorean wolf fifth [[262144/177147]], which is flat of 3/2 by one [[Pythagorean comma]], and is about 678{{c}} in size.

Other "out of tune" fifths in higher [[prime limit|limits]] include:

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== In edos ==

The following table lists the best tuning of 3/2, as well as other fifths if present, in various significant [[~~edos~~]].

The following table lists the best tuning of 3/2, as well as other fifths if present, in various significant [[edo]]s.

{| class="wikitable"

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* Various historical [[well temperament]]s generated by tempered 4/3s or 3/2s, equivalent to 12edo as compton and meantone

== In ~~moment-of-symmetry~~ scales ==

== In mos scales ==

Intervals between 654 and 750{{c}} generate the following [[~~MOS~~]] scales:

Intervals between 654 and 750{{c}} generate the following [[mos]] scales:

These tables start from the last monolarge ~~[[MOS]]~~ generated by the interval range.

These tables start from the last monolarge mos generated by the interval range.

~~MOSes~~ with more than 12 notes are not included.

Scales with more than 12 notes are not included.

{| class="wikitable"

|-

! Range

! colspan="6" | ~~MOS~~

! colspan="6" | Mos

|-

| 720–750{{c}}

@@ Line 10: / Line 10: @@
 == In just intonation ==
-The only "perfect" fifth in JI is the '''Pythagorean perfect fifth''' of [[3/2]], about 702{{c}} in size, which corresponds to the mos-based interval category of the diatonic perfect fifth, and is the generator for Pythagorean tuning and the diatonic scale. However, various "out of tune" fifths exist, such as the '''Pythagorean wolf fifth [[262144/177147]]''', which is flat of 3/2 by one [[Pythagorean comma]], and is about 678{{c}} in size.
+The only "perfect" fifth in JI is the Pythagorean perfect fifth of [[3/2]], about 702{{c}} in size, which corresponds to the mos-based interval category of the diatonic perfect fifth, and is the generator for Pythagorean tuning and the diatonic scale. However, various "out of tune" fifths exist, such as the Pythagorean wolf fifth [[262144/177147]], which is flat of 3/2 by one [[Pythagorean comma]], and is about 678{{c}} in size.
 Other "out of tune" fifths in higher [[prime limit|limits]] include:
@@ Line 20: / Line 20: @@
 == In edos ==
-The following table lists the best tuning of 3/2, as well as other fifths if present, in various significant [[edos]].
+The following table lists the best tuning of 3/2, as well as other fifths if present, in various significant [[edo]]s.
 {| class="wikitable"
@@ Line 108: / Line 108: @@
 * Various historical [[well temperament]]s generated by tempered 4/3s or 3/2s, equivalent to 12edo as compton and meantone
-== In moment-of-symmetry scales ==
+== In mos scales ==
-Intervals between 654 and 750{{c}} generate the following [[MOS]] scales:
+Intervals between 654 and 750{{c}} generate the following [[mos]] scales:
-These tables start from the last monolarge [[MOS]] generated by the interval range.
+These tables start from the last monolarge mos generated by the interval range.
-MOSes with more than 12 notes are not included.
+Scales with more than 12 notes are not included.
 {| class="wikitable"
 |-
 ! Range
-! colspan="6" | MOS
+! colspan="6" | Mos
 |-
 | 720–750{{c}}