15/8: Difference between revisions

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~~'''~~15/8~~'''~~

{{Infobox Interval

|-3 1 1~~>~~

| JI glyph =

| Ratio = 15/8

1088.2687 ~~cents~~

| Monzo = -3 1 1

| Cents = 1088.2687

~~[[File:jid_15_8_pluck_adu_dr220.mp3]] [[:File:~~jid_15_8_pluck_adu_dr220.mp3|~~sound sample]]~~

| Name = major seventh

| Sound = jid_15_8_pluck_adu_dr220.mp3

| Color name = y7, yo 7th

}}

In [[5-limit|5-limit]] [[Just_intonation|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|12edo]].

''Since 15 is a perfect fifth above 10 (15/10 = [[3/2|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|6/5]] with a [[5/4|5/4]] stacked on top of it. Another is the Barbados triad, 10:13:15 -- a [[13/10|13/10]] on bottom and a [[15/13|15/13]] on top. And a particularly uncommon but mentionable example is the [[23-limit|23-limit]] inframinor triad 20:23:30.''

Since 15 is a perfect fifth above 10 (15/10 = [[3/2|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|6/5]] with a [[5/4|5/4]] stacked on top of it. Another is the Barbados triad, 10:13:15 -- a [[13/10|13/10]] on bottom and a [[15/13|15/13]] on top. And a particularly uncommon but mentionable example is the [[23-limit|23-limit]] inframinor triad 20:23:30.

See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]] [[Category:5-limit]]

@@ Line 1: / Line 1: @@
-'''15/8'''
+{{Infobox Interval
-|-3 1 1&gt;
+| JI glyph =
+| Ratio = 15/8
-.2687 cents
+| Monzo = -3 1 1
+| Cents = 1088.2687
-[[File:jid_15_8_pluck_adu_dr220.mp3]] [[:File:jid_15_8_pluck_adu_dr220.mp3|sound sample]]
+| Name = major seventh
+| Sound = jid_15_8_pluck_adu_dr220.mp3
+| Color name = y7, yo 7th
+}}
 In [[5-limit|5-limit]] [[Just_intonation|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|12edo]].
-''Since 15 is a perfect fifth above 10 (15/10 = [[3/2|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|6/5]] with a [[5/4|5/4]] stacked on top of it. Another is the Barbados triad, 10:13:15 -- a [[13/10|13/10]] on bottom and a [[15/13|15/13]] on top. And a particularly uncommon but mentionable example is the [[23-limit|23-limit]] inframinor triad 20:23:30.''
+Since 15 is a perfect fifth above 10 (15/10 = [[3/2|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|6/5]] with a [[5/4|5/4]] stacked on top of it. Another is the Barbados triad, 10:13:15 -- a [[13/10|13/10]] on bottom and a [[15/13|15/13]] on top. And a particularly uncommon but mentionable example is the [[23-limit|23-limit]] inframinor triad 20:23:30.
 See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]      [[Category:5-limit]]