8/5: Difference between revisions
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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]], '''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}}). | ||
== Approximation == | == Approximation == | ||
{{Interval edo approximation|8/5}} | |||
== See also == | == See also == | ||
* [[5/4]] – its [[octave complement]] | * [[5/4]] – its [[octave complement]] | ||
Latest revision as of 13:05, 3 November 2025
| Interval information |
classic(al) minor sixth,
ptolemaic minor sixth
reduced subharmonic
[sound info]
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 ¢).
Approximation
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 3 | 2\3 | 800.00 | -13.69 | -3.42 |
| 6 | 4\6 | 800.00 | -13.69 | -6.84 |
| 22 | 15\22 | 818.18 | +4.50 | +8.24 |
| 25 | 17\25 | 816.00 | +2.31 | +4.82 |
| 28 | 19\28 | 814.29 | +0.60 | +1.40 |
| 31 | 21\31 | 812.90 | -0.78 | -2.02 |
| 34 | 23\34 | 811.76 | -1.92 | -5.44 |
| 37 | 25\37 | 810.81 | -2.88 | -8.87 |
| 50 | 34\50 | 816.00 | +2.31 | +9.64 |
| 53 | 36\53 | 815.09 | +1.41 | +6.22 |
| 56 | 38\56 | 814.29 | +0.60 | +2.80 |
| 59 | 40\59 | 813.56 | -0.13 | -0.62 |
| 62 | 42\62 | 812.90 | -0.78 | -4.05 |
| 65 | 44\65 | 812.31 | -1.38 | -7.47 |