8/5: Difference between revisions

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In [[5-limit]] [[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¢).
In [[5-limit]] [[just intonation]], '''8/5''' is a '''minor sixth''', measuring about 813.7¢. It is the 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¢) 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 ==
== See also ==

Revision as of 22:43, 21 November 2021

Interval information
Ratio 8/5
Factorization 23 × 5-1
Monzo [3 0 -1
Size in cents 813.6863¢
Name classic/just 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

In 5-limit just intonation, 8/5 is a minor sixth, measuring about 813.7¢. It is the 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¢) 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