Perfect fourth: Difference between revisions
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{{About|the [[interval region]]|the just perfect fourth|4/3}} | |||
A '''perfect fourth (P4)''' 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. Another common range is the even stricter diatonic range, from 480 to ~514 cents, which corresponds to [[diatonic perfect fourth]]s that can be used to generate a [[5L 2s|diatonic scale]]. | |||
A '''perfect fourth (P4)''' 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. | |||
== In just intonation == | == In just intonation == | ||
=== By prime limit === | === 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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=== 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 [[Circular temperament|circular temperaments]] in general | ** The 3-limit [[Circular temperament|circular temperaments]] in general | ||
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* [[Mavila]], the temperament sharpening 4/3 such that three 4/3s stack to [[6/5|5/4]] | * [[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 | * Various historical [[Well temperament|well temperaments]] generated by tempered 4/3s or 3/2s, equivalent to 12edo as compton and meantone | ||
{{Navbox intervals}} | {{Navbox intervals}} | ||