Perfect fourth: Difference between revisions
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== In just intonation == | == In just intonation == | ||
=== By prime limit === | === By prime limit === | ||
The only "perfect" fourth in JI is the | The only "perfect" fourth in JI is the Pythagorean perfect fourth of [[4/3]], about 498{{c}} in size, which corresponds to the mos-based interval category of the diatonic perfect fourth and is the octave complement of the perfect fifth of [[3/2]]. However, various "out of tune" fourths exist, such as the Pythagorean wolf fourth [[177147/131072]], which is sharp of 4/3 by one [[Pythagorean comma]], and is about 522{{c}} in size. | ||
Other "out of tune" fourths in higher [[ | Other "out of tune" fourths in higher [[prime limit|limits]] include: | ||
* The 5-limit '''acute fourth''' is a ratio of 27/20, and is about 520{{c}} | * The 5-limit '''acute fourth''' is a ratio of 27/20, and is about 520{{c}} | ||
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* The 11-limit '''augmented fourth''' is a ratio of 15/11, and is about 537{{c}}. | * The 11-limit '''augmented fourth''' is a ratio of 15/11, and is about 537{{c}}. | ||
** There is also an 11-limit '''grave fourth,''' which is a ratio of 33/25, and is about 480{{c}}. | ** There is also an 11-limit '''grave fourth,''' which is a ratio of 33/25, and is about 480{{c}}. | ||
* The 13-limit '''infrafourth''' is a ratio of 13/10, and is about 454{{c}}, but it might be better analyzed as an [[ | * The 13-limit '''infrafourth''' is a ratio of 13/10, and is about 454{{c}}, but it might be better analyzed as an [[major third|ultramajor third]]. Despite that, it is also here for completeness. | ||
=== By delta === | === By delta === | ||
See [[Delta-N ratio]]. | See [[Delta-N ratio]]. | ||
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== In edos == | == In edos == | ||
The following table lists the best tuning of 4/3, as well as other fourths if present, in various significant [[ | The following table lists the best tuning of 4/3, as well as other fourths if present, in various significant [[edo]]s. | ||
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=== Temperaments that use 4/3 as a generator === | === Temperaments that use 4/3 as a generator === | ||
* [[Compton]], the temperament of the Pythagorean comma, equivalent to 12edo | * [[Compton]], the temperament of the Pythagorean comma, equivalent to 12edo | ||
** The 3-limit [[ | ** The 3-limit [[circular temperament]]s in general | ||
* [[Archy]], the temperament flattening 4/3 such that three 4/ | * [[Archy]], the temperament flattening 4/3 such that three 4/3's stack to [[7/6]] | ||
* [[Meantone]], the temperament sharpening 4/3 such that three 4/ | * [[Meantone]], the temperament sharpening 4/3 such that three 4/3's stack to [[6/5]] | ||
* [[Mavila]], the temperament sharpening 4/3 such that three 4/ | * [[Mavila]], the temperament sharpening 4/3 such that three 4/3's stack to [[5/4]] | ||
* Various historical [[ | * Various historical [[well temperament]]s generated by tempered 4/3's or 3/2's, equivalent to 12edo as compton and meantone | ||
== In moment-of-symmetry scales == | |||
Intervals between 450 and 545 cents generate the following [[mos]] scales: | |||
These tables start from the last monolarge mos generated by the interval range. | |||
Scales with more than 12 notes are not included. | |||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! Range | ! Range | ||
! colspan="6" | | ! colspan="6" | Mos | ||
|- | |- | ||
| 450–480{{c}} | | 450–480{{c}} | ||