15/8: Difference between revisions

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{{Infobox Interval

| Name = classic~~/just~~ major seventh

| Name = just major seventh, classic(al) major seventh, ptolemaic major seventh

| Color name = y7, yo 7th

| Sound = jid_15_8_pluck_adu_dr220.mp3

}}

In [[5-limit]] [[just intonation]], '''15/8''' is the '''classic major seventh''' 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]].

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.

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* [[16/15]] – its [[octave complement]]

* [[Gallery of just intervals]]

== Notes ==

[[Category:Seventh]]

[[Category:Major seventh]]

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 {{Infobox Interval
-| Name = classic/just major seventh
+| Name = just major seventh, classic(al) major seventh, ptolemaic major seventh
 | Color name = y7, yo 7th
 | Sound = jid_15_8_pluck_adu_dr220.mp3
 }}
 {{Wikipedia|Major seventh}}
-In [[5-limit]] [[just intonation]], '''15/8''' is the '''classic major seventh''' 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]].
+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.
@@ Line 12: / Line 12: @@
 * [[16/15]] – its [[octave complement]]
 * [[Gallery of just intervals]]
+== Notes ==
+<references/>
 [[Category:Seventh]]
 [[Category:Major seventh]]