15/8: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| JI glyph =
| Ratio = 15/8
| Ratio = 15/8
| Monzo = -3 1 1
| Monzo = -3 1 1
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| Sound = jid_15_8_pluck_adu_dr220.mp3
| 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.
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:5-limit]]
[[Category:Interval]]
[[Category:Just interval]]
[[Category:Ratio]]
[[Category:Seventh]]
[[Category:Seventh]]
[[Category:Major seventh]]
[[Category:Major seventh]]
[[Category:Listen]]
[[Category:Octave-reduced harmonics]]
[[Category:Overtone]]
[[Category:Pages with internal sound examples]]
[[Category:Pages with internal sound examples]]

Revision as of 20:30, 12 December 2021

Interval information
Ratio 15/8
Factorization 2-3 × 3 × 5
Monzo [-3 1 1
Size in cents 1088.269¢
Name classic/just major seventh
Color name y7, yo 7th
FJS name [math]\displaystyle{ \text{M7}^{5} }[/math]
Special properties reduced,
reduced harmonic
Tenney norm (log2 nd) 6.90689
Weil norm (log2 max(n, d)) 7.81378
Wilson norm (sopfr(nd)) 14

[sound info]
Open this interval in xen-calc

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), 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.

See also