24/17: Difference between revisions

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~~'''24/17'''~~

{{Infobox Interval

|~~3 1 0 0 0 0 -1>~~

| Name = small septendecimal tritone

| Color name = 17u4, su 4th

| Sound = jid_24_17_pluck_adu_dr220.mp3

}}

~~596~~.~~9996 cents~~

In [[17-limit]] [[just intonation]], '''24/17''' is the '''small septendecimal tritone''', measuring very nearly 597¢. It is the [[mediant]] between [[7/5]] and [[17/12]], the "larger septendecimal tritone". The two septendecimal tritones are each 3¢ away from the 600¢ half-octave, and so they are well-represented in all even-numbered [[edo]] systems, including [[12edo]]. Indeed, the latter system, containing good approximations of the 3rd and 17th harmonics, can use the half-octave as 24/17 and 17/12 in close approximations to chords such as 8:12:17 and 16:17:24. [[22edo]] is another good edo system for using the half-octave in this way.

[[~~File:jid_24_17_pluck_adu_dr220.mp3~~]] [[~~:File:jid_24_17_pluck_adu_dr220~~.~~mp3|sound sample~~]]

== Terminology and notation ==

Conceptualization systems disagree on whether [[17/16]] should be a [[diatonic semitone]] or a [[chromatic semitone]], and as a result the disagreement propagates to all intervals of [[harmonic class|HC17]]. See [[17-limit]] for a detailed discussion.

In [[~~17-limit|17-limit]] [[Just_intonation|~~Just ~~Intonation~~]], ~~24/17~~ is ~~the "first septendecimal tritone~~,~~" measuring very nearly 597¢. It is the~~ [[~~mediant|mediant]] between [[7/5|7~~/5]] ~~and~~ [[17/12|17/12]]~~, the "second septendecimal tritone~~.~~" The two septendecimal tritones are each 3¢ away from the 600¢ half-octave, and so they are well-represented in all even-numbered~~ [[~~EDO|EDO~~]] ~~systems~~, ~~including~~ [[~~12edo|12edo~~]]~~. Indeed,~~ the ~~latter system, containing good approximations of the 3rd and 17th harmonics, can use the half-octave as 24/17 and 17/12 in close approximations to chords such as 8:12:17 and 16:17:24.~~ [[~~22edo~~|~~22edo~~]] ~~is another good EDO system for using the half-octave in this way~~.

For 24/17 specifically:

* In [[Functional Just System]], it is an augmented fourth, separated by [[4131/4096]] from the [[729/512|Pythagorean augmented fourth (729/512)]].

* In [[Helmholtz-Ellis notation]], it is a diminished fifth, separated by [[2187/2176]] from the [[1024/729|Pythagorean diminished fifth (1024/729)]].

See: [[~~Gallery_of_Just_Intervals|~~Gallery of ~~Just Intervals~~]]

The term ''small septendecimal tritone'' omits the distinction and only describes its melodic property i.e. the size. It is said in contrast to the large septendecimal tritone of [[17/12]].

== See also ==

* [[17/12]] – its [[octave complement]]

* [[17/16]] – its [[fifth complement]]

* [[Gallery of just intervals]]

[[Category:Tritone]]

@@ Line 1: / Line 1: @@
-'''24/17'''
+{{Infobox Interval
-|3 1 0 0 0 0 -1&gt;
+| Name = small septendecimal tritone
+| Color name = 17u4, su 4th
+| Sound = jid_24_17_pluck_adu_dr220.mp3
+}}
-.9996 cents
+In [[17-limit]] [[just intonation]], '''24/17''' is the '''small septendecimal tritone''', measuring very nearly 597¢. It is the [[mediant]] between [[7/5]] and [[17/12]], the "larger septendecimal tritone". The two septendecimal tritones are each 3¢ away from the 600¢ half-octave, and so they are well-represented in all even-numbered [[edo]] systems, including [[12edo]]. Indeed, the latter system, containing good approximations of the 3rd and 17th harmonics, can use the half-octave as 24/17 and 17/12 in close approximations to chords such as 8:12:17 and 16:17:24. [[22edo]] is another good edo system for using the half-octave in this way.
-[[File:jid_24_17_pluck_adu_dr220.mp3]] [[:File:jid_24_17_pluck_adu_dr220.mp3|sound sample]]
+== Terminology and notation ==
+Conceptualization systems disagree on whether [[17/16]] should be a [[diatonic semitone]] or a [[chromatic semitone]], and as a result the disagreement propagates to all intervals of [[harmonic class|HC17]]. See [[17-limit]] for a detailed discussion.
-In [[17-limit|17-limit]] [[Just_intonation|Just Intonation]], 24/17 is the "first septendecimal tritone," measuring very nearly 597¢. It is the [[mediant|mediant]] between [[7/5|7/5]] and [[17/12|17/12]], the "second septendecimal tritone." The two septendecimal tritones are each 3¢ away from the 600¢ half-octave, and so they are well-represented in all even-numbered [[EDO|EDO]] systems, including [[12edo|12edo]]. Indeed, the latter system, containing good approximations of the 3rd and 17th harmonics, can use the half-octave as 24/17 and 17/12 in close approximations to chords such as 8:12:17 and 16:17:24. [[22edo|22edo]] is another good EDO system for using the half-octave in this way.
+For 24/17 specifically:
+* In [[Functional Just System]], it is an augmented fourth, separated by [[4131/4096]] from the [[729/512|Pythagorean augmented fourth (729/512)]].
+* In [[Helmholtz-Ellis notation]], it is a diminished fifth, separated by [[2187/2176]] from the [[1024/729|Pythagorean diminished fifth (1024/729)]].
-See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]
+The term ''small septendecimal tritone'' omits the distinction and only describes its melodic property i.e. the size. It is said in contrast to the large septendecimal tritone of [[17/12]].
+== See also ==
+* [[17/12]] – its [[octave complement]]
+* [[17/16]] – its [[fifth complement]]
+* [[Gallery of just intervals]]
+[[Category:Tritone]]