17/15: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

| Name = diatismic whole tone

~~| Ratio = 17/15~~

~~| Monzo = 0 -1 -1 0 0 0 1~~

~~| Cents = 216.68669~~

| Name = ~~septendecimal~~ whole tone

| Color name = 17og3, sogu 3rd

| Sound = jid_17_15_pluck_adu_dr220.mp3

}}

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 '''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 ==

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

* [[30/17]] – its [[octave complement]]

* [[20/17]] – its [[fourth complement]]

* [[Gallery of just intervals]]

[[Category:~~17-limit~~]]

[[Category:Second]]

[[Category:~~Interval~~]]

[[Category:Whole tone]]

[[Category:~~Ratio]]~~

[[Category:Diatismic]]

~~[[Category:Just interval]]~~

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

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
+| Name = diatismic whole tone
-| Ratio = 17/15
-| Monzo = 0 -1 -1 0 0 0 1
-| Cents = 216.68669
-| Name = septendecimal whole tone
 | Color name = 17og3, sogu 3rd
 | Sound = jid_17_15_pluck_adu_dr220.mp3
 }}
-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 '''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 ==
-* [[30/17]] its [[inverse interval]]
+* [[30/17]] – its [[octave complement]]
+* [[20/17]] – its [[fourth complement]]
 * [[Gallery of just intervals]]
-[[Category:17-limit]]
+[[Category:Second]]
-[[Category:Interval]]
+[[Category:Whole tone]]
-[[Category:Ratio]]
+[[Category:Diatismic]]
-[[Category:Just interval]]
-[[Category:Sound example]]