1323/1280: Difference between revisions

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Created page with "1323/1280, the septimal 2/7-tone, is a 7-limit ratio very close to the step of 21edo. == Theory == If taken as a comma to be tempered, it produces greenwood. If it is..."
 
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1323/1280, the septimal 2/7-tone, is a 7-limit ratio very close to the step of [[21edo]].
{{Infobox Interval
|Ratio = 1323/1280
|Name = septimal 2/7-tone, septimal 21st-octave
|Color name = Lzzg2, lazozogu 2nd
|Comma = yes
}}
'''1323/1280''', the '''septimal 2/7-tone''', is a 7-limit ratio very close to the step of [[21edo]].


== Theory ==
== Theory ==
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 produces [[akjayland]] and temperaments like 441 & 1848.
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.
 
[[Category:Commas named after their interval size]]

Latest revision as of 07:02, 3 November 2024

Interval information
Ratio 1323/1280
Factorization 2-8 × 33 × 5-1 × 72
Monzo [-8 3 -1 2
Size in cents 57.2031¢
Names septimal 2/7-tone,
septimal 21st-octave
Color name Lzzg2, lazozogu 2nd
FJS name [math]\displaystyle{ \text{m2}^{7,7}_{5} }[/math]
Special properties reduced
Tenney height (log2 nd) 20.6915
Weil height (log2 max(n, d)) 20.7392
Wilson height (sopfr(nd)) 44
Comma size medium
Open this interval in xen-calc

1323/1280, the septimal 2/7-tone, is a 7-limit ratio very close to the step of 21edo.

Theory

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.