1323/1280: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
|Ratio = 1323/1280 | |Ratio = 1323/1280 | ||
|Name = septimal 2/7-tone, septimal 21st-octave | |Name = larger breedsmic half-apotome, septimal 2/7-tone, septimal 21st-octave | ||
|Color name = Lzzg2, lazozogu 2nd | |Color name = Lzzg2, lazozogu 2nd | ||
|Comma = yes | |Comma = yes | ||
}} | }} | ||
'''1323/1280''', the '''septimal 2/7-tone''', is a 7-limit ratio | '''1323/1280''', the '''septimal 2/7-tone''', is a 7-limit ratio, the product of ([[405/392]])·([[2401/2400]]), extremely close to the step of [[21edo]] and less close but very close still to [[sqrt(2187/2048)]] a. It is also the difference between: | ||
== | * [[49/45]] and [[256/243]] | ||
* [[2187/2048]] and [[405/392]] | |||
* [[9/8]] and [[160/147]] | |||
== Temperaments == | |||
If taken as a comma to be tempered, it produces [[greenwood]]. If it is taken as a period and assigned to 1\21 of the octave, it serves as a period in the [[akjayland]] temperament. | If taken as a comma to be tempered, it produces [[greenwood]]. If it is taken as a period and assigned to 1\21 of the octave, it serves as a period in the [[akjayland]] temperament. | ||
{{Monzo|-169 63 -21 42}} is a comma that results from the difference of 21 instances of this interval with the octave. For EDOs N up to ~5000, it is tempered out if and only if 21 divides N. | {{Monzo|-169 63 -21 42}} is a comma that results from the difference of 21 instances of this interval with the octave. For EDOs N up to ~5000, it is tempered out if and only if 21 divides N. | ||
Tempering out 2401/2400 equates 1323/1280 with 405/392 and merges them into half an apotome. | |||
[[Category:Commas named after their interval size]] | [[Category:Commas named after their interval size]] | ||
Latest revision as of 17:08, 3 October 2026
| Interval information |
septimal 2/7-tone,
septimal 21st-octave
1323/1280, the septimal 2/7-tone, is a 7-limit ratio, the product of (405/392)·(2401/2400), extremely close to the step of 21edo and less close but very close still to sqrt(2187/2048) a. It is also the difference between:
Temperaments
If taken as a comma to be tempered, it produces greenwood. If it is taken as a period and assigned to 1\21 of the octave, it serves as a period in the akjayland temperament.
[-169 63 -21 42⟩ is a comma that results from the difference of 21 instances of this interval with the octave. For EDOs N up to ~5000, it is tempered out if and only if 21 divides N.
Tempering out 2401/2400 equates 1323/1280 with 405/392 and merges them into half an apotome.