8/5: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| Icon = [[File:8_5_glyph.png|124px]] <small><br/>[[JI glyphs|JI glyph]]</small>
| Name = just minor sixth, classic(al) minor sixth, ptolemaic minor sixth
| Ratio = 8/5
| Color name = g6, gu 6th
| Monzo = 3 0 -1
| Cents = 813.68629
| Name = minor sixth
| Sound = jid_8_5_pluck_adu_dr220.mp3
| Sound = jid_8_5_pluck_adu_dr220.mp3
| Color name =
}}
}}
{{Wikipedia|Minor sixth}}
In [[5-limit]] [[just intonation]], '''8/5''' is the '''just minor sixth''', '''classic(al) minor sixth''', or '''ptolemaic minor sixth'''<ref>For reference, see [[5-limit]]. </ref>, measuring about 813.7{{cent}}. It is the [[octave-reduced]] fifth [[subharmonic]], and thus the inversion of [[5/4]], the classic major third. It appears in chords where the 1/1 is higher than the 5/4, such as 5:6:8 (a first-inversion major triad). It is a large half step of [[16/15]] (about 111.7{{cent}}) sharp of [[3/2]], and a syntonic comma ([[81/80]], about 21.5{{cent}}) sharp of the [[Pythagorean tuning|Pythagorean]] minor sixth of [[128/81]] (about 792.2{{cent}}).


In [[5-limit]] [[Just intonation|Just Intonation]], 8/5 is a minor sixth, measuring about 813.7¢. It is the 5th subharmonic, and thus the inversion of [[5/4]], the classic major third. It appears in chords where the 1/1 is higher than the 5/4, such as 5:6:8 (a first-inversion major triad). It is a large half step of [[16/15]] (about 111.7¢) away from [[3/2]], and an [[81/80]] (about 21.5¢) away from the Pythagorean ([[3-limit]]) minor sixth of [[128/81]] (about 792.2¢).
== See also ==
* [[5/4]] – its [[octave complement]]
* [[15/8]] – its [[twelfth complement]]
* [[Ed8/5]]
* [[Gallery of just intervals]]
{{todo|expand}}


See: [[Gallery of Just Intervals]]
== Notes ==
<references/>


[[Category:5-limit]]
[[Category:Sixth]]
[[Category:interval]]
[[Category:Minor sixth]]
[[Category:just_interval]]
[[Category:ratio]]

Latest revision as of 23:57, 26 October 2024

Interval information
Ratio 8/5
Factorization 23 × 5-1
Monzo [3 0 -1⟩
Size in cents 813.6863¢
Names just minor sixth,
classic(al) minor sixth,
ptolemaic minor sixth
Color name g6, gu 6th
FJS name [math]\displaystyle{ \text{m6}_{5} }[/math]
Special properties reduced,
reduced subharmonic
Tenney height (log2 nd) 5.32193
Weil height (log2 max(n, d)) 6
Wilson height (sopfr(nd)) 11

[sound info]
Open this interval in xen-calc
English Wikipedia has an article on:

In 5-limit just intonation, 8/5 is the just minor sixth, classic(al) minor sixth, or ptolemaic minor sixth[1], measuring about 813.7 ¢. It is the octave-reduced fifth subharmonic, and thus the inversion of 5/4, the classic major third. It appears in chords where the 1/1 is higher than the 5/4, such as 5:6:8 (a first-inversion major triad). It is a large half step of 16/15 (about 111.7 ¢) sharp of 3/2, and a syntonic comma (81/80, about 21.5 ¢) sharp of the Pythagorean minor sixth of 128/81 (about 792.2 ¢).

See also

Notes

  1. ↑ For reference, see 5-limit.
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