15/14: Difference between revisions

Line 21:

* [[26/15]] and [[13/7]]

== ~~Terminology~~ ==

== Theory ==

15/14 is traditionally called a ''diatonic semitone'', perhaps for its proximity (and conflation in systems such as septimal [[meantone]] and [[marvel]]) with the classic diatonic semitone [[16/15]]. However, 15/14 is a ''[[Wikipedia:chromatic semitone|chromatic semitone]]'' in both [[Helmholtz–Ellis notation]] and the [[Functional Just System]], viewed as the apotome [[2187/2048]] altered by [[5120/5103]]. [[Marc Sabat]] has taken to call it the ''major chromatic semitone'' in the same material where [[21/20]] is also named as the minor diatonic semitone<ref>Marc Sabat. [https://masa.plainsound.org/pdfs/crystal-growth.pdf ''Three Crystal Growth Algorithms in 23-limit constrained Harmonic Space'']. Plainsound Music Edition, 2008.</ref>.

15/14 is the difference between certain [[interval qualities]] of thirds and sixths: between (classic) minor and supermajor, and between subminor and (classic) major. These are the pairs of intervals separated by 15/14:

* 7/6 and 5/4 (otonal thirds)

* 6/5 and 9/7 (utonal thirds)

* 14/9 and 5/3 (otonal sixths)

* 8/5 and 12/7 (utonal sixths)

[[36/35]] separates the otonal pairs from the utonal pairs; 4/3 separates the thirds from the sixths.

They can also be organized into pairs of intervals differing by 36/35:

* 7/6 and 6/5 (minor thirds)

* 5/4 and 9/7 (major thirds)

* 14/9 and 8/5 (minor sixths)

* 5/3 and 12/7 (major sixths)

15/14 separates the minor pairs from the major pairs; 4/3 separates the thirds from the sixths.

36/35 separates 15/14 from [[25/24]] on one side and [[54/49]] on the other.

== Approximation ==

@@ Line 21: / Line 21: @@
 * [[26/15]] and [[13/7]]
-== Terminology ==
+== Theory ==
 /14 is traditionally called a ''diatonic semitone'', perhaps for its proximity (and conflation in systems such as septimal [[meantone]] and [[marvel]]) with the classic diatonic semitone [[16/15]]. However, 15/14 is a ''[[Wikipedia:chromatic semitone|chromatic semitone]]'' in both [[Helmholtz–Ellis notation]] and the [[Functional Just System]], viewed as the apotome [[2187/2048]] altered by [[5120/5103]]. [[Marc Sabat]] has taken to call it the ''major chromatic semitone'' in the same material where [[21/20]] is also named as the minor diatonic semitone<ref>Marc Sabat. [https://masa.plainsound.org/pdfs/crystal-growth.pdf ''Three Crystal Growth Algorithms in 23-limit constrained Harmonic Space'']. Plainsound Music Edition, 2008.</ref>.
+/14 is the difference between certain [[interval qualities]] of thirds and sixths: between (classic) minor and supermajor, and between subminor and (classic) major. These are the pairs of intervals separated by 15/14:
+* 7/6 and 5/4 (otonal thirds)
+* 6/5 and 9/7 (utonal thirds)
+* 14/9 and 5/3 (otonal sixths)
+* 8/5 and 12/7 (utonal sixths)
+[[36/35]] separates the otonal pairs from the utonal pairs; 4/3 separates the thirds from the sixths.
+They can also be organized into pairs of intervals differing by 36/35:
+* 7/6 and 6/5 (minor thirds)
+* 5/4 and 9/7 (major thirds)
+* 14/9 and 8/5 (minor sixths)
+* 5/3 and 12/7 (major sixths)
+/14 separates the minor pairs from the major pairs; 4/3 separates the thirds from the sixths.
+/35 separates 15/14 from [[25/24]] on one side and [[54/49]] on the other.
 == Approximation ==