15/8 - Revision history

Overthink: more readable wording

2025-12-22T21:53:32Z

Overthink: slight rewrite & expansion

2025-12-22T21:53:00Z

slight rewrite & expansion

← Older revision		Revision as of 21:53, 22 December 2025
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	}}		}}
	{{Wikipedia\|Major seventh}}		{{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 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 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 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 15/8 = [[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, as 8:10:13:15 with steps 5/4, 13/10 and 15/13. A particularly uncommon but mentionable example is a [[23-limit]] seventh chord 16:20:23:30.		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 ==		== Approximation ==
	{{Interval edo approximation\|15/8}}		{{Interval edo approximation\|15/8}}

FloraC: Text replacement - " {{Interval_Edo_Approximation | " to "{{Interval edo approximation|"

2025-11-03T13:04:41Z

Text replacement - " {{Interval_Edo_Approximation | " to "{{Interval edo approximation|"

← Older revision		Revision as of 13:04, 3 November 2025
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	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, as 8:10:13:15 with steps 5/4, 13/10 and 15/13. A particularly uncommon but mentionable example is a [[23-limit]] seventh chord 16:20:23:30.		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, as 8:10:13:15 with steps 5/4, 13/10 and 15/13. A particularly uncommon but mentionable example is a [[23-limit]] seventh chord 16:20:23:30.
	== Approximation ==		== Approximation ==
	{{~~Interval_Edo_Approximation~~ \| 15/8}}		{{Interval edo approximation\|15/8}}

	== See also ==		== See also ==

Pailiaq at 07:49, 3 November 2025

2025-11-03T07:49:30Z

← Older revision		Revision as of 07:49, 3 November 2025
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	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, as 8:10:13:15 with steps 5/4, 13/10 and 15/13. A particularly uncommon but mentionable example is a [[23-limit]] seventh chord 16:20:23:30.		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, as 8:10:13:15 with steps 5/4, 13/10 and 15/13. A particularly uncommon but mentionable example is a [[23-limit]] seventh chord 16:20:23:30.
			== Approximation ==
			{{Interval_Edo_Approximation \| 15/8}}

	== See also ==		== See also ==

BudjarnLambeth: /* See also */ link

2024-10-27T00:01:04Z

FloraC: Reference moved

2023-08-15T10:34:06Z

Reference moved

← Older revision		Revision as of 10:34, 15 August 2023
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	}}		}}
	{{Wikipedia\|Major seventh}}		{{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 [[5/4]]. </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]].		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 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]]), 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, as 8:10:13:15 with steps 5/4, 13/10 and 15/13. A particularly uncommon but mentionable example is a [[23-limit]] seventh chord 16:20:23:30.		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, as 8:10:13:15 with steps 5/4, 13/10 and 15/13. A particularly uncommon but mentionable example is a [[23-limit]] seventh chord 16:20:23:30.

FloraC: +twelfth complement

2023-08-14T11:21:27Z

+twelfth complement

← Older revision		Revision as of 11:21, 14 August 2023
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	== See also ==		== See also ==
	* [[16/15]] – its [[octave complement]]		* [[16/15]] – its [[octave complement]]
			* [[8/5]] – its [[twelfth complement]]
	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]

Aura at 15:24, 25 January 2023

2023-01-25T15:24:23Z

← Older revision		Revision as of 15:24, 25 January 2023
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	}}		}}
	{{Wikipedia\|Major seventh}}		{{Wikipedia\|Major seventh}}
	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]].		In [[5-limit]] [[just intonation]], '''15/8''' is the '''just major seventh''', '''classic(al) major seventh''', or '''ptolemaic major seventh'''<ref>For reference, see [[5/4]]. </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]]), 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, as 8:10:13:15 with steps 5/4, 13/10 and 15/13. A particularly uncommon but mentionable example is a [[23-limit]] seventh chord 16:20:23:30.		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, as 8:10:13:15 with steps 5/4, 13/10 and 15/13. A particularly uncommon but mentionable example is a [[23-limit]] seventh chord 16:20:23:30.

FloraC: Address the irrelevance of the chords

2023-01-12T12:55:03Z

Address the irrelevance of the chords

← Older revision		Revision as of 12:55, 12 January 2023
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	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]].		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.		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, as 8:10:13:15 with steps 5/4, 13/10 and 15/13. A particularly uncommon but mentionable example is a [[23-limit]] seventh chord 16:20:23:30.

	== See also ==		== See also ==

FloraC: Names

2023-01-12T12:46:32Z

Names

← Older revision		Revision as of 12:46, 12 January 2023
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	{{Infobox Interval		{{Infobox Interval
	\| Name = classic~~/just~~ major seventh		\| Name = just major seventh, classic(al) major seventh, ptolemaic major seventh
	\| Color name = y7, yo 7th		\| Color name = y7, yo 7th
	\| Sound = jid_15_8_pluck_adu_dr220.mp3		\| Sound = jid_15_8_pluck_adu_dr220.mp3
	}}		}}
	{{Wikipedia\|Major seventh}}		{{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.		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]]		* [[16/15]] – its [[octave complement]]
	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]

			== Notes ==
			<references/>

	[[Category:Seventh]]		[[Category:Seventh]]
	[[Category:Major seventh]]		[[Category:Major seventh]]

← Older revision		Revision as of 00:01, 27 October 2024
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	* [[16/15]] – its [[octave complement]]		* [[16/15]] – its [[octave complement]]
	* [[8/5]] – its [[twelfth complement]]		* [[8/5]] – its [[twelfth complement]]
			* [[Ed15/8]]
	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]