15/8: Difference between revisions

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{{Infobox Interval

| ~~JI glyph~~ =

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

| ~~Ratio~~ = ~~15/8~~

| Color name = y7, yo 7th

~~| Monzo = -3 1 1~~

~~| Cents = 1088.2687~~

~~| 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~~]].

In [[5-limit]] [[just intonation]], '''15/8''' is the '''just major seventh''', '''classic(al) major seventh''', or '''ptolemaic major seventh'''<ref>For reference, see [[5-limit]]. </ref> of about 1088.3¢. It is also the [[octave-reduced]] 15th [[harmonic]], and appears as a complex consonance in chords such as [[8:10:12:15]], a just version of a major seventh chord. Since 15/8 = [[3/2]] × [[5/4]], it can be seen as a perfect fifth above a major third or vice versa, and this understanding works in [[12edo]], as the sum of [[~]]3/2 and ~5/4 is 700{{c}} + 400{{c}} = 1100{{c}}, which 15/8 is mapped to.

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, which leads to [[8:10:13:15]] with steps 5/4, 13/10 and 15/13, and contains the [[10:13:15]] barbados triad. A particularly uncommon but mentionable example is the [[23-limit]] seventh chord [[16:20:23:30]].

== Approximation ==

== See also ==

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

* [[8/5]] – its [[twelfth complement]]

* [[Ed15/8]]

* [[Gallery of just intervals]]

~~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.~~

== Notes ==

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

[[Category:Seventh]]

~~[[Category:interval]]~~

[[Category:Major seventh]]

[[Category:~~just_interval~~]]

[[Category:~~ratio~~]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| JI glyph =
+| Name = just major seventh, classic(al) major seventh, ptolemaic major seventh
-| Ratio = 15/8
+| Color name = y7, yo 7th
-| Monzo = -3 1 1
-| Cents = 1088.2687
-| 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]].
+{{Wikipedia|Major seventh}}
+In [[5-limit]] [[just intonation]], '''15/8''' is the '''just major seventh''', '''classic(al) major seventh''', or '''ptolemaic major seventh'''<ref>For reference, see [[5-limit]]. </ref> of about 1088.3¢. It is also the [[octave-reduced]] 15th [[harmonic]], and appears as a complex consonance in chords such as [[8:10:12:15]], a just version of a major seventh chord. Since 15/8 = [[3/2]] × [[5/4]], it can be seen as a perfect fifth above a major third or vice versa, and this understanding works in [[12edo]], as the sum of [[~]]3/2 and ~5/4 is 700{{c}} + 400{{c}} = 1100{{c}}, which 15/8 is mapped to.
+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, which leads to [[8:10:13:15]] with steps 5/4, 13/10 and 15/13, and contains the [[10:13:15]] barbados triad. A particularly uncommon but mentionable example is the [[23-limit]] seventh chord [[16:20:23:30]].
+== Approximation ==
+{{Interval edo approximation|15/8}}
+== See also ==
+* [[16/15]] – its [[octave complement]]
+* [[8/5]] – its [[twelfth complement]]
+* [[Ed15/8]]
+* [[Gallery of just intervals]]
-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.
+== Notes ==
+<references/>
-See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]      [[Category:5-limit]]
+[[Category:Seventh]]
-[[Category:interval]]
+[[Category:Major seventh]]
-[[Category:just_interval]]
-[[Category:ratio]]