Perfect fourth: Difference between revisions
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== In just intonation == | == In just intonation == | ||
=== By prime limit === | |||
The only "perfect" fourth in JI is the '''Pythagorean perfect fourth''' of [[4/3]], about 498 cents 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 cents in size. | The only "perfect" fourth in JI is the '''Pythagorean perfect fourth''' of [[4/3]], about 498 cents 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 cents in size. | ||
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** There is also an 11-limit '''grave fourth,''' which is a ratio of 33/25, and is about 480 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. | * 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. | ||
=== By delta === | |||
{| class="wikitable" | |||
|+ | |||
!Delta 1 | |||
!Cents | |||
!Delta 3 | |||
!Cents | |||
!Delta 4 | |||
!Cents | |||
!Delta 5 | |||
!Cents | |||
!Delta 6 | |||
!Cents | |||
|- | |||
|4/3 | |||
|498c | |||
|13/10 | |||
|454c | |||
|15/11 | |||
|537c | |||
|19/14 | |||
|529c | |||
|23/17 | |||
|523c | |||
|- | |||
| | |||
| | |||
| | |||
| | |||
|17/13 | |||
|464c | |||
|21/16 | |||
|471c | |||
|25/19 | |||
|475c | |||
|- | |||
| | |||
| | |||
| | |||
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|} | |||
== In EDOs == | == In EDOs == | ||