15/8: Difference between revisions

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{{Infobox Interval

~~| JI glyph =~~

| Ratio = 15/8

| Monzo = -3 1 1

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| Sound = jid_15_8_pluck_adu_dr220.mp3

}}

In [[5-limit]] [[just intonation]], '''15/8''' is a '''major seventh''' of about 1088.3¢. It is also the 15th ~~overtone~~ ([[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 '''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]].

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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[[Category:5-limit]]

~~[[Category:Interval]]~~

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

~~[[Category:Ratio]]~~

[[Category:Seventh]]

[[Category:Major seventh]]

[[Category:~~Listen]]~~

[[Category:Octave-reduced harmonics]]

~~[[Category:Overtone~~]]

[[Category:Pages with internal sound examples]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| JI glyph =
 | Ratio = 15/8
 | Monzo = -3 1 1
@@ Line 9: / Line 8: @@
 | Sound = jid_15_8_pluck_adu_dr220.mp3
 }}
-In [[5-limit]] [[just intonation]], '''15/8''' is a '''major seventh''' of about 1088.3¢. It is also the 15th overtone ([[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 '''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]].
 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 18: / Line 17: @@
 [[Category:5-limit]]
-[[Category:Interval]]
-[[Category:Just interval]]
-[[Category:Ratio]]
 [[Category:Seventh]]
 [[Category:Major seventh]]
-[[Category:Listen]]
+[[Category:Octave-reduced harmonics]]
-[[Category:Overtone]]
 [[Category:Pages with internal sound examples]]