17/15: Difference between revisions

(12 intermediate revisions by 8 users not shown)

Line 1:

'''17/15'''

{{Infobox Interval

|~~0 -1 -1 0 0 0 1>~~

| Name = diatismic whole tone

| Color name = 17og3, sogu 3rd

| Sound = jid_17_15_pluck_adu_dr220.mp3

}}

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.

~~216~~.~~6867~~ cents

== Approximation ==

[[11edo]]'s second degree, measuring approximately 218.2 cents, 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.

~~[[File:jid_17_15_pluck_adu_dr220.mp3]] [[:File:jid_17_15_pluck_adu_dr220.mp3~~|~~sound sample]]~~

~~In [[17-limit|17-limit]] [[Just_intonation|Just Intonation]],~~ 17/15 is ~~the "septendecimal whole tone" measuring about 216.7¢. It is the [[mediant|mediant]] between~~ [[~~9/8|9~~/8]] and ~~[[8~~/~~7|8/7]], as it is (9+8)/(8+7). It is found in the~~ [[~~OverToneSeries|harmonic series~~]] ~~between the 17th~~ and ~~15th overtones. [[11edo|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~~.

== Temperaments ==

The radical interval sqrt(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 [[octave complement]]

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

* [[Gallery of just intervals]]

~~See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]~~ [[Category:~~17-limit~~]]

[[Category:Second]]

[[Category:~~just_interval~~]]

[[Category:Whole tone]]

[[Category:~~sound_example~~]]

[[Category:Diatismic]]

@@ Line 1: / Line 1: @@
-'''17/15'''
+{{Infobox Interval
-|0 -1 -1 0 0 0 1&gt;
+| Name = diatismic whole tone
+| Color name = 17og3, sogu 3rd
+| Sound = jid_17_15_pluck_adu_dr220.mp3
+}}
+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.
-.6867 cents
+== Approximation ==
+[[11edo]]'s second degree, measuring approximately 218.2 cents, 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.
-[[File:jid_17_15_pluck_adu_dr220.mp3]] [[:File:jid_17_15_pluck_adu_dr220.mp3|sound sample]]
+{{Interval edo approximation|17/15}}
-In [[17-limit|17-limit]] [[Just_intonation|Just Intonation]], 17/15 is the "septendecimal whole tone" measuring about 216.7¢. It is the [[mediant|mediant]] between [[9/8|9/8]] and [[8/7|8/7]], as it is (9+8)/(8+7). It is found in the [[OverToneSeries|harmonic series]] between the 17th and 15th overtones. [[11edo|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.
+== Temperaments ==
+The radical interval sqrt(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 [[octave complement]]
+* [[20/17]] – its [[fourth complement]]
+* [[Gallery of just intervals]]
-See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]      [[Category:17-limit]]
+[[Category:Second]]
-[[Category:just_interval]]
+[[Category:Whole tone]]
-[[Category:sound_example]]
+[[Category:Diatismic]]