24/17: Difference between revisions

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{{Infobox Interval

| Name = ~~smaller~~ septendecimal tritone

| Name = small septendecimal tritone

| Color name = 17u4, su 4th

| Sound = jid_24_17_pluck_adu_dr220.mp3

}}

In [[17-limit]] [[just intonation]], '''24/17''' is the '''~~smaller~~ 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.

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.

== 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.

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)]].

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 ==

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Name = smaller septendecimal tritone
+| Name = small septendecimal tritone
 | Color name = 17u4, su 4th
 | Sound = jid_24_17_pluck_adu_dr220.mp3
 }}
-In [[17-limit]] [[just intonation]], '''24/17''' is the '''smaller 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.
+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.
+== 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.
+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)]].
+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 ==