6/5: Difference between revisions
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| Monzo = 1 1 -1 | | Monzo = 1 1 -1 | ||
| Cents = 315.64129 | | Cents = 315.64129 | ||
| Name = classic minor third | | Name = classic/just minor third | ||
| Color name = g3, gu 3rd | | Color name = g3, gu 3rd | ||
| FJS name = m3<sub>5</sub> | | FJS name = m3<sub>5</sub> | ||
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In [[5-limit]] [[ | In [[5-limit]] [[just intonation]], '''6/5''' is the '''classic''' or '''just minor third''', measuring about 315.6[[cent|¢]]. It is sharp of the [[Pythagorean]] minor third of [[32/27]] (about 294.1¢) as well as the 300¢ minor third of [[4edo]], [[12edo]] and all other 4n-[[EDO|edos]]. It arises in the [[harmonic series]] between the 5th and 6th overtones and appears in the [[5-limit]] otonal triad of 4:5:6. A 5-limit minor triad in just intonation can be written 10:12:15, with 6/5 falling between 10 and 12, [[5/4]] falling between 12 and 15, and [[3/2]] falling between 10 and 15. | ||
In higher-limit JI, 6/5 is only one of many minor thirds. A popular one in the [[7-limit]] is [[7/6]] (about 266.9¢), the septimal subminor third, which is [[36/35]] (about 48.8¢) flat of 6/5. Another in the [[13-limit]] is [[13/11]] (about 289.2¢), which is [[66/65]] (about 26.4¢) flat of 6/5. Both of these are more complex intervals than 6/5 and have their own character to them. | In higher-limit JI, 6/5 is only one of many minor thirds. A popular one in the [[7-limit]] is [[7/6]] (about 266.9¢), the septimal subminor third, which is [[36/35]] (about 48.8¢) flat of 6/5. Another in the [[13-limit]] is [[13/11]] (about 289.2¢), which is [[66/65]] (about 26.4¢) flat of 6/5. Both of these are more complex intervals than 6/5 and have their own character to them. | ||
== Approximation == | |||
It is very accurately approximated by [[19edo]] (5\19), and hence the [[enneadecal]] temperament. | It is very accurately approximated by [[19edo]] (5\19), and hence the [[enneadecal]] temperament. | ||
== See also == | == See also == | ||
* [[5/3]] – its [[octave complement]] | * [[5/3]] – its [[octave complement]] | ||
* [[5/4]] – its [[fifth complement]] | * [[5/4]] – its [[fifth complement]] | ||
* [[10/9]] – its [[fourth complement]] | * [[10/9]] – its [[fourth complement]] | ||
* [[Gallery of | * [[Gallery of just intervals]] | ||
* [[List of superparticular intervals]] | |||
* [[Wikipedia: Minor third]] | * [[Wikipedia: Minor third]] | ||
* [[:File:Ji-6-5-csound-foscil-220hz.mp3]] – another sound example | * [[:File:Ji-6-5-csound-foscil-220hz.mp3]] – another sound example | ||
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[[Category:Interval]] | [[Category:Interval]] | ||
[[Category:Just interval]] | [[Category:Just interval]] | ||
[[Category:Ratio]] | |||
[[Category:Third]] | [[Category:Third]] | ||
[[Category:Minor third]] | [[Category:Minor third]] | ||
[[Category:Superparticular]] | [[Category:Superparticular]] | ||
[[Category:Over-5]] | [[Category:Over-5]] | ||
Revision as of 13:49, 9 September 2021
| Interval information |
reduced
[sound info]
In 5-limit just intonation, 6/5 is the classic or just minor third, measuring about 315.6¢. It is sharp of the Pythagorean minor third of 32/27 (about 294.1¢) as well as the 300¢ minor third of 4edo, 12edo and all other 4n-edos. It arises in the harmonic series between the 5th and 6th overtones and appears in the 5-limit otonal triad of 4:5:6. A 5-limit minor triad in just intonation can be written 10:12:15, with 6/5 falling between 10 and 12, 5/4 falling between 12 and 15, and 3/2 falling between 10 and 15.
In higher-limit JI, 6/5 is only one of many minor thirds. A popular one in the 7-limit is 7/6 (about 266.9¢), the septimal subminor third, which is 36/35 (about 48.8¢) flat of 6/5. Another in the 13-limit is 13/11 (about 289.2¢), which is 66/65 (about 26.4¢) flat of 6/5. Both of these are more complex intervals than 6/5 and have their own character to them.
Approximation
It is very accurately approximated by 19edo (5\19), and hence the enneadecal temperament.
See also
- 5/3 – its octave complement
- 5/4 – its fifth complement
- 10/9 – its fourth complement
- Gallery of just intervals
- List of superparticular intervals
- Wikipedia: Minor third
- File:Ji-6-5-csound-foscil-220hz.mp3 – another sound example