Perfect fourth: Difference between revisions
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''This page is about the interval region. For the just perfect fourth, see [[4/3]].'' | |||
A perfect fourth is an interval that is near 500 [[Cent|cents]] in size, distinct from augmented fourths (a type of [[tritone]], about 600 cents). A rough tuning range for the perfect fourth is about 450 to 550 [[cents]], though this is extremely wide; some might prefer to restrict it to around 470-530 cents. | |||
"Perfect fourth" may also refer to the [[diatonic perfect fourth]], which is a tempered fourth used to generate the diatonic scale, and is not the subject of this article. | |||
== In just intonation == | |||
The only "perfect" fourth in JI is the '''Pythagorean perfect fourth''' of [[4/3]], about 498 cents in size, which corresponds to the MOS 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 cents in size. | |||
Other "out of tune" fourths in higher limits include: | |||
* The 5-limit '''acute fourth''' is a ratio of 27/20, and is about 520 cents | |||
* The 7-limit '''subfourth''' is a ratio of 21/16, and is about 471 cents. | |||
* The 11-limit '''augmented fourth''' is a ratio of 15/11, and is about 537 cents. | |||
** There is also an 11-limit '''grave fourth,''' which is a ratio of 33/25, and is about 480 cents. | |||
* The 13-limit '''infrafourth''' is a ratio of 13/10, and is about 454 cents, but it might be better analyzed as an [[Major third|ultramajor third]]. Despite that, it is also here for completeness. | |||
== In tempered scales == | |||
The following table lists the best tuning of 4/3, as well as other fourths if present, in several significant EDOs. | |||
{| class="wikitable" | |||
|+ | |||
!EDO | |||
!4/3 | |||
!Other fourths | |||
|- | |||
|5 | |||
|480c | |||
| | |||
|- | |||
|7 | |||
|514c | |||
| | |||
|- | |||
|12 | |||
|500c | |||
| | |||
|- | |||
|15 | |||
|480c | |||
| | |||
|- | |||
|16 | |||
|525c | |||
|450c ≈ 13/10 | |||
|- | |||
|17 | |||
|494c | |||
| | |||
|- | |||
|19 | |||
|506c | |||
| | |||
|- | |||
|20 | |||
|480c | |||
|540c ≈ 15/11 | |||
|- | |||
|22 | |||
|491c | |||
|545c ≈ 15/11 | |||
|- | |||
|24 | |||
|500c | |||
|450c ≈ 13/10, 550c ≈ 15/11 | |||
|- | |||
|25 | |||
|480c | |||
|528c ≈ 27/20 | |||
|- | |||
|26 | |||
|508c | |||
|462c ≈ 21/16, 13/10 | |||
|- | |||
|27 | |||
|489c | |||
|533c ≈ 15/11 | |||
|- | |||
|28 | |||
|514c | |||
|471c ≈ 21/16 | |||
|- | |||
|29 | |||
|496c | |||
|455c ≈ 13/10, 537c ≈ 15/11 | |||
|- | |||
|31 | |||
|503c | |||
|464c ≈ 21/16, 541c ≈ 15/11 | |||
|- | |||
|32 | |||
|488c | |||
|525c ≈ 27/20, 450c ≈ 13/10 | |||
|- | |||
|34 | |||
|494c | |||
|458c ≈ 13/10, 529c ≈ 27/20, 15/11 | |||
|- | |||
|41 | |||
|498c | |||
|468c ≈ 21/16, 526c ≈ 27/20 | |||
|- | |||
|53 | |||
|498c | |||
|452c ≈ 13/10, 476c ≈ 21/16, 521c ≈ 27/20, 543c ≈ 15/11 | |||
|} | |||
== In temperaments == | |||
The following list goes over the use of 4/3 in temperaments. | |||
=== Temperaments with 4/3 as a generator === | |||
* [[Compton]], the temperament of the Pythagorean comma, equivalent to 12edo | |||
** The 3-limit [[Circular temperament|circular temperaments]] in general | |||
* [[Archy]], the temperament flattening 4/3 such that three 4/3s stack to [[6/5|7/6]] | |||
* [[Meantone]], the temperament sharpening 4/3 such that three 4/3s stack to [[6/5]] | |||
* [[Mavila]], the temperament sharpening 4/3 such that three 4/3s stack to [[6/5|5/4]] | |||
* Various historical [[Well temperament|well temperaments]] generated by tempered 4/3s or 3/2s, equivalent to 12edo as compton and meantone | |||