8/7: Difference between revisions
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{{Wikipedia|Septimal whole tone }} | {{Wikipedia|Septimal whole tone}} | ||
In [[just intonation]], 8/7 is the '''supermajor second''' or '''septimal major second''' of approximately 231. | In [[just intonation]], 8/7 is the '''supermajor second''' or '''septimal major second''' of approximately 231.2{{cent}}. Although it falls between the familiar major second and minor third of [[12edo]], it generally sounds more like a wide second than a narrow third. It can be found between the 7th and 8th [[harmonic]]s and is thus a [[superparticular]] ratio. In [[7-limit]] JI and higher, it is treated as a consonance, particularly in the context of a chord such as 4:5:6:7:8, where it appears between the harmonic seventh ([[7/4]]) and octave. It differs from the Pythagorean major second of [[9/8]] by [[64/63]], a microtone of about 27.3{{cent}}. It is close in size to one step of 5edo = 240{{cent}}. | ||
A stack of three supermajor seconds is close to a perfect fifth ([[3/2]]). The difference is 1029/1024 (about 8.4{{cent}}), which is tempered out in [[slendric]] and [[31edo]]. | |||
== See also == | == See also == | ||
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* [[7/6]] – its [[fourth complement]] | * [[7/6]] – its [[fourth complement]] | ||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
* [[8/7 equal-step tuning]] | |||
[[Category:7-limit]] | [[Category:7-limit]] | ||
[[Category:Second]] | [[Category:Second]] | ||
[[Category:Supermajor second]] | [[Category:Supermajor second]] | ||
Revision as of 17:43, 23 March 2022
| Interval information |
supermajor second,
septimal major second
reduced,
reduced subharmonic
[sound info]
In just intonation, 8/7 is the supermajor second or septimal major second of approximately 231.2 ¢. Although it falls between the familiar major second and minor third of 12edo, it generally sounds more like a wide second than a narrow third. It can be found between the 7th and 8th harmonics and is thus a superparticular ratio. In 7-limit JI and higher, it is treated as a consonance, particularly in the context of a chord such as 4:5:6:7:8, where it appears between the harmonic seventh (7/4) and octave. It differs from the Pythagorean major second of 9/8 by 64/63, a microtone of about 27.3 ¢. It is close in size to one step of 5edo = 240 ¢.
A stack of three supermajor seconds is close to a perfect fifth (3/2). The difference is 1029/1024 (about 8.4 ¢), which is tempered out in slendric and 31edo.