17/15: Difference between revisions

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In [[17-limit]] [[just intonation]], '''17/15''' is the "septendecimal whole tone" measuring about 216.7¢. It is the [[mediant]] between [[9/8]] and [[8/7]], as it is (9+8)/(8+7). It is found in the [[OverToneSeries|harmonic series]] between the 17th and 15th overtones. [[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.

In [[17-limit]] [[just intonation]], '''17/15''' is the '''septendecimal whole tone''' measuring about 216.7¢. It is the [[mediant]] between [[9/8]] and [[8/7]], as it is (9+8)/(8+7). It is found in the [[OverToneSeries|harmonic series]] between the 17th and 15th overtones. [[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.).

== See also ==

* [[30/17]] its [[inverse interval]]

* [[Gallery of just intervals]]

[[Category:17-limit]]

[[Category:Interval]]

[[Category:Interval ratio]]

~~[[Category:Ratio~~]]

[[Category:Just interval]]

[[Category:~~Sound example~~]]

[[Category:Second]]

[[Category:Listen]]

[[Category:Whole tone]]

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 }}
-In [[17-limit]] [[just intonation]], '''17/15''' is the "septendecimal whole tone" measuring about 216.7¢. It is the [[mediant]] between [[9/8]] and [[8/7]], as it is (9+8)/(8+7). It is found in the [[OverToneSeries|harmonic series]] between the 17th and 15th overtones. [[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.
+In [[17-limit]] [[just intonation]], '''17/15''' is the '''septendecimal whole tone''' measuring about 216.7¢. It is the [[mediant]] between [[9/8]] and [[8/7]], as it is (9+8)/(8+7). It is found in the [[OverToneSeries|harmonic series]] between the 17th and 15th overtones. [[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.).
 == See also ==
 * [[30/17]] its [[inverse interval]]
 * [[Gallery of just intervals]]
 [[Category:17-limit]]
-[[Category:Interval]]
+[[Category:Interval ratio]]
-[[Category:Ratio]]
 [[Category:Just interval]]
-[[Category:Sound example]]
+[[Category:Second]]
+[[Category:Listen]]
+[[Category:Whole tone]]