15/8: Difference between revisions

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In [[5-limit]] [[just intonation]], '''15/8''' is the '''just''', '''classic(al)''', or '''ptolemaic major seventh'''<ref>For reference, see [[5/4]]. </ref> of about 1088.3¢. It is also the 15th [[harmonic]] ([[octave-reduced]]), and appears as a complex consonance in chords such as 8:10:12:15, a just version of a major seventh chord. Since 15 is 3×5, it can be seen as a perfect fifth above a major third or vice versa, and this understanding is compatible with the 1100¢ interval of [[12edo]].

Since 15 is a perfect fifth above 10 (15/10 = [[3/2]]), ~~[[List of root-3rd-P5 triads in JI|root-3rd-P5 triads]]~~ can be formed with the 10th harmonic as ~~root~~ and 15th harmonic as ~~perfect fifth~~. The simplest and most familiar example is the ~~classic minor triad~~ 10:12:15 ~~– a [[~~6/5~~]] with a [[~~5/4~~]] stacked on top of it~~. Another is the ~~Barbados triad~~, 10:13:15 ~~– a [[~~13/10~~]] on bottom~~ and ~~a [[~~15/13~~]] on top~~. ~~And a~~ particularly uncommon but mentionable example is ~~the~~ [[23-limit]] ~~inframinor triad~~ 20:23:30.

Since 15 is a perfect fifth above 10 (15/10 = [[3/2]]), seventh chords can be formed with the 10th harmonic as major third and 15th harmonic as major seventh. The simplest and most familiar example is the classical major seventh chord 8:10:12:15 with steps 5/4, 6/5 and 5/4. Another example replaces the 12 with 13, as 8:10:13:15 with steps 5/4, 13/10 and 15/13. A particularly uncommon but mentionable example is a [[23-limit]] seventh chord 16:20:23:30.

== See also ==

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 In [[5-limit]] [[just intonation]], '''15/8''' is the '''just''', '''classic(al)''', or '''ptolemaic major seventh'''<ref>For reference, see [[5/4]]. </ref> of about 1088.3¢. It is also the 15th [[harmonic]] ([[octave-reduced]]), and appears as a complex consonance in chords such as 8:10:12:15, a just version of a major seventh chord. Since 15 is 3×5, it can be seen as a perfect fifth above a major third or vice versa, and this understanding is compatible with the 1100¢ interval of [[12edo]].
-Since 15 is a perfect fifth above 10 (15/10 = [[3/2]]), [[List of root-3rd-P5 triads in JI|root-3rd-P5 triads]] can be formed with the 10th harmonic as root and 15th harmonic as perfect fifth. The simplest and most familiar example is the classic minor triad 10:12:15 – a [[6/5]] with a [[5/4]] stacked on top of it. Another is the Barbados triad, 10:13:15 – a [[13/10]] on bottom and a [[15/13]] on top. And a particularly uncommon but mentionable example is the [[23-limit]] inframinor triad 20:23:30.
+Since 15 is a perfect fifth above 10 (15/10 = [[3/2]]), seventh chords can be formed with the 10th harmonic as major third and 15th harmonic as major seventh. The simplest and most familiar example is the classical major seventh chord 8:10:12:15 with steps 5/4, 6/5 and 5/4. Another example replaces the 12 with 13, as 8:10:13:15 with steps 5/4, 13/10 and 15/13. A particularly uncommon but mentionable example is a [[23-limit]] seventh chord 16:20:23:30.
 == See also ==