17/15: Difference between revisions
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We finally have a clearer modifier to describe this interval |
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{{Infobox Interval | {{Infobox Interval | ||
| Name = diatismic whole tone | |||
| Name = | |||
| Color name = 17og3, sogu 3rd | | Color name = 17og3, sogu 3rd | ||
| Sound = jid_17_15_pluck_adu_dr220.mp3 | | Sound = jid_17_15_pluck_adu_dr220.mp3 | ||
}} | }} | ||
In [[17-limit]] [[just intonation]], '''17/15''' is the ''' | In [[17-limit]] [[just intonation]], '''17/15''' is the '''diatismic whole tone''' measuring about 216.7{{cent}}. It exceeds the [[9/8|Pythagorean whole tone (9/8)]] by a [[136/135|diatisma (136/135)]], hence the name. It is the [[mediant]] of 9/8 and [[8/7]], as it is (9 + 8)/(8 + 7). It is found in the [[harmonic series]] between the 17th and 15th [[harmonic]]s. [[11edo]]'s second degree, measuring approximately 218.2¢, is close in size to 17/15 – indeed, the 11edo system has excellent approximations of the 15th and 17th harmonics, and so this harmonic function is plausible in 11edo. | ||
√2/(17/15) is three cents flat of a 5/4 major third, and this or 17/15 itself can be used for a tuning for wizard and its various relatives (lizard, gizzard, etc.). | √2/(17/15) is three cents flat of a 5/4 major third, and this or 17/15 itself can be used for a tuning for [[wizard]] and its various relatives (lizard, gizzard, etc.). | ||
== See also == | == See also == | ||
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* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
[[Category:Second]] | [[Category:Second]] | ||
[[Category:Whole tone]] | [[Category:Whole tone]] | ||
[[Category: | [[Category:Diatismic]] | ||
Latest revision as of 13:44, 1 June 2024
| Interval information |
[sound info]
In 17-limit just intonation, 17/15 is the diatismic whole tone measuring about 216.7 ¢. It exceeds the Pythagorean whole tone (9/8) by a diatisma (136/135), hence the name. It is the mediant of 9/8 and 8/7, as it is (9 + 8)/(8 + 7). It is found in the harmonic series between the 17th and 15th harmonics. 11edo's second degree, measuring approximately 218.2¢, is close in size to 17/15 – indeed, the 11edo system has excellent approximations of the 15th and 17th harmonics, and so this harmonic function is plausible in 11edo.
√2/(17/15) is three cents flat of a 5/4 major third, and this or 17/15 itself can be used for a tuning for wizard and its various relatives (lizard, gizzard, etc.).