17/15: Difference between revisions

Line 1:

~~'''~~17/15~~'''~~

{{Infobox Interval

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

| Icon =

| 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

}}

216.~~6867 cents~~

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.

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

√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.).

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.

== See also ==

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

~~√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.).~~

* [[Gallery of Just Intervals]]

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

[[Category:17-limit]]

[[Category:~~just_interval~~]]

[[Category:Interval]]

[[Category:~~sound_example~~]]

[[Category:Ratio]]

[[Category:Just interval]]

[[Category:Sound example]]

@@ Line 1: / Line 1: @@
-'''17/15'''
+{{Infobox Interval
-|0 -1 -1 0 0 0 1&gt;
+| Icon =
+| 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
+}}
-.6867 cents
+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.
-[[File:jid_17_15_pluck_adu_dr220.mp3]] [[:File:jid_17_15_pluck_adu_dr220.mp3|sound sample]]
+√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.).
-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.
+== See also ==
+* [[30/17]] its [[inverse interval]]
-√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.).
+* [[Gallery of Just Intervals]]
-See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]      [[Category:17-limit]]
+[[Category:17-limit]]
-[[Category:just_interval]]
+[[Category:Interval]]
-[[Category:sound_example]]
+[[Category:Ratio]]
+[[Category:Just interval]]
+[[Category:Sound example]]