17/15: Difference between revisions

(3 intermediate revisions by 3 users not shown)

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 ==

Line 19:

Line 15:

* [[Gallery of just intervals]]

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

~~[[Category:Interval ratio]]~~

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

[[Category:Second]]

~~[[Category:Listen]]~~

[[Category:Whole tone]]

[[Category:Diatismic]]

@@ 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 ==
@@ Line 19: / Line 15: @@
 * [[Gallery of just intervals]]
-[[Category:17-limit]]
-[[Category:Interval ratio]]
-[[Category:Just interval]]
 [[Category:Second]]
-[[Category:Listen]]
 [[Category:Whole tone]]
+[[Category:Diatismic]]