3/2: Difference between revisions
merge done; remove notice |
m Cleanup; +links |
||
| Line 5: | Line 5: | ||
| Cents = 701.95500 | | Cents = 701.95500 | ||
| Name = just perfect fifth | | Name = just perfect fifth | ||
| Color name = w5, wa 5th | | Color name = w5, wa 5th | ||
| FJS name = P5 | | FJS name = P5 | ||
| Sound = jid_3_2_pluck_adu_dr220.mp3 | |||
}} | }} | ||
'''3/2''', the '''just perfect fifth''', is the largest [[superparticular]] [[ | '''3/2''', the '''just perfect fifth''', is the largest [[superparticular]] [[interval]], spanning the distance between the 2nd and 3rd harmonics. It is an interval with low [[harmonic entropy]], and therefore high consonance. | ||
Variations of the [[Perfect_fifth|fifth]] (whether just or not) appear in most music of the world. On a harmonic instrument, the third harmonic is usually the loudest one that is not an octave double of the fundamental. Treatment of the perfect fifth as consonant historically precedes treatment of the major third (see [[5/4|5:4]]) as consonant. 3:2 is the simple JI interval best approximated by [[ | Variations of the [[Perfect_fifth|fifth]] (whether just or not) appear in most music of the world. On a harmonic instrument, the third harmonic is usually the loudest one that is not an octave double of the fundamental. Treatment of the perfect fifth as consonant historically precedes treatment of the major third (see [[5/4|5:4]]) as consonant. 3:2 is the simple JI interval best approximated by [[12edo]], after the [[octave]]. | ||
Producing a chain of just perfect fifths yields Pythagorean tuning. Such a chain does not close at a circle, but continues infinitely. [[12edo]] is a system which flattens the perfect fifth by about 2 cents so that the circle close at 12 tones. Meanwhile, [[meantone]] temperaments are systems which flatten the perfect fifth such that the major third generated by four fifths upward be closer to 5:4 | Producing a chain of just perfect fifths yields Pythagorean tuning. Such a chain does not close at a circle, but continues infinitely. [[12edo]] is a system which flattens the perfect fifth by about 2 cents so that the circle close at 12 tones. Meanwhile, [[meantone]] temperaments are systems which flatten the perfect fifth such that the major third generated by four fifths upward be closer to 5:4 – or, in the case of [[quarter-comma meantone]] (see [[31edo]]), identical. | ||
In composition, the presence of perfect fifths can provide a "ground" upon which unusual intervals may be placed while still sounding structurally coherent. Systems excluding perfect fifths can thus sound more "xenharmonic". | In composition, the presence of perfect fifths can provide a "ground" upon which unusual intervals may be placed while still sounding structurally coherent. Systems excluding perfect fifths can thus sound more "xenharmonic". | ||
| Line 76: | Line 76: | ||
== See also == | == See also == | ||
* [[4/3]] – its [[octave complement]] | * [[4/3]] – its [[octave complement]] | ||
* {{OEIS|A060528}} – a list of EDOs with increasingly better approximations of 3:2 (and by extension 4:3) | * [[Fifth complement]] | ||
* {{OEIS|A005664}} – denominators of the convergents to log<sub>2</sub>(3) | * [[Gallery of just intervals]] | ||
* [[Wikipedia: Perfect fifth]] | |||
* {{OEIS| A060528 }} – a list of EDOs with increasingly better approximations of 3:2 (and by extension 4:3) | |||
* {{OEIS| A005664 }} – denominators of the convergents to log<sub>2</sub>(3) | |||
[[Category:3-limit]] | [[Category:3-limit]] | ||