14/13: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

| Name = tridecimal 2/3-tone, trienthird, tridecimal supraminor second, sinaic

~~| Ratio = 14/13~~

| Color name = 3uz2, thuzo 2nd

~~| Monzo = 1 0 0 1 0 -1~~

~~| Cents = 128.29824~~

| Name = tridecimal 2/3-tone, ~~ ~~trienthird, ~~ coffee interval~~

| Color name =

~~| FJS name = M2713~~

| Sound = jid_14_13_pluck_adu_dr220.mp3

}}

'''14/13''', the '''2/3-tone''' or '''trienthird''' (one-third third)~~, nicknamed the '''coffee interval''',~~ is a somewhat exotic 13-limit interval measuring about 128.3¢, which is almost exactly 1/3 of a [[5/4]] major third- a stack of three trienthirds falling short of a 5/4 major third by a [[10985/10976|cantonisma]].

'''14/13''', the '''tridecimal 2/3-tone''' or '''trienthird''' (one-third third) is a somewhat exotic 13-limit interval measuring about 128.3¢, which is almost exactly 1/3 of a [[5/4]] major third- a stack of three trienthirds falling short of a 5/4 major third by a [[10985/10976|cantonisma]].

The trienthird was a favorite interval of [[Wikipedia:Avicenna|Avicenna]] (Ibn Sina) for his scale constructions, and may be considered a smaller size of neutral second (a second between major and minor).

The trienthird was a favorite interval of [[Wikipedia:Avicenna|Avicenna]] (Ibn Sina) for his scale constructions, and may be considered a smaller size of neutral second (a second between major and minor). Thus intervals close in size to it have been called '''sinaics''' by [[Zhea Erose]]. It may be called the '''tridecimal supraminor second''' as well, analogous to [[21/13]] being the ''tridecimal supraminor sixth''.

In [[13-limit]] [[~~Just Intonation~~]], 14/13 represents the difference in size between the tridecimal minor third of [[13/11]] and undecimal major third of [[14/11]]. It is also the difference between [[13/10]] and [[7/5]]; [[13/12]] and [[7/6]]; [[13/9]] and [[14/9]], and of course [[13/8]] and [[7/4]] and the inversions of the above. As it combines the primes 7 and 13, it appears in JI subgroup tunings involving those primes.

In [[13-limit]] [[just intonation]], 14/13 represents the difference in size between the tridecimal minor third of [[13/11]] and undecimal major third of [[14/11]]. It is also the difference between [[13/10]] and [[7/5]]; [[13/12]] and [[7/6]]; [[13/9]] and [[14/9]], and of course [[13/8]] and [[7/4]] and the inversions of the above. As it combines the primes 7 and 13, it appears in JI subgroup tunings involving those primes.

== See also ==

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* [[Gallery of just intervals]]

~~[[Category:13-limit]]~~

~~[[Category:Interval]]~~

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

~~[[Category:Ratio]]~~

[[Category:Second]]

[[Category:Neutral second]]

[[Category:Supraminor second]]

[[Category:Semitone]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
+| Name = tridecimal 2/3-tone, trienthird, tridecimal supraminor second, sinaic
-| Ratio = 14/13
+| Color name = 3uz2, thuzo 2nd
-| Monzo = 1 0 0 1 0 -1
-| Cents = 128.29824
-| Name = tridecimal 2/3-tone, <br>trienthird, <br>coffee interval
-| Color name =
-| FJS name = M2<sup>7</sup><sub>13</sub>
 | Sound = jid_14_13_pluck_adu_dr220.mp3
 }}
-'''14/13''', the '''2/3-tone''' or '''trienthird''' (one-third third), nicknamed the '''coffee interval''', is a somewhat exotic 13-limit interval measuring about 128.3¢, which is almost exactly 1/3 of a [[5/4]] major third- a stack of three trienthirds falling short of a 5/4 major third by a [[10985/10976|cantonisma]].
+'''14/13''', the '''tridecimal 2/3-tone''' or '''trienthird''' (one-third third) is a somewhat exotic 13-limit interval measuring about 128.3¢, which is almost exactly 1/3 of a [[5/4]] major third- a stack of three trienthirds falling short of a 5/4 major third by a [[10985/10976|cantonisma]].
-The trienthird was a favorite interval of [[Wikipedia:Avicenna|Avicenna]] (Ibn Sina) for his scale constructions, and may be considered a smaller size of neutral second (a second between major and minor).
+The trienthird was a favorite interval of [[Wikipedia:Avicenna|Avicenna]] (Ibn Sina) for his scale constructions, and may be considered a smaller size of neutral second (a second between major and minor). Thus intervals close in size to it have been called '''sinaics''' by [[Zhea Erose]]. It may be called the '''tridecimal supraminor second''' as well, analogous to [[21/13]] being the ''tridecimal supraminor sixth''.
-In [[13-limit]] [[Just Intonation]], 14/13 represents the difference in size between the tridecimal minor third of [[13/11]] and undecimal major third of [[14/11]]. It is also the difference between [[13/10]] and [[7/5]]; [[13/12]] and [[7/6]]; [[13/9]] and [[14/9]], and of course [[13/8]] and [[7/4]] and the inversions of the above. As it combines the primes 7 and 13, it appears in JI subgroup tunings involving those primes.
+In [[13-limit]] [[just intonation]], 14/13 represents the difference in size between the tridecimal minor third of [[13/11]] and undecimal major third of [[14/11]]. It is also the difference between [[13/10]] and [[7/5]]; [[13/12]] and [[7/6]]; [[13/9]] and [[14/9]], and of course [[13/8]] and [[7/4]] and the inversions of the above. As it combines the primes 7 and 13, it appears in JI subgroup tunings involving those primes.
 == See also ==
@@ Line 20: / Line 15: @@
 * [[Gallery of just intervals]]
-[[Category:13-limit]]
-[[Category:Interval]]
-[[Category:Just interval]]
-[[Category:Ratio]]
 [[Category:Second]]
 [[Category:Neutral second]]
+[[Category:Supraminor second]]
 [[Category:Semitone]]