1323/1280

Interval information

Ratio	1323/1280
Factorization	2-8 × 33 × 5-1 × 72
Monzo	[-8 3 -1 2⟩
Size in cents	57.2031 ¢
Names	larger breedsmic half-apotome, 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 norm (log2 nd)	20.6915
Weil norm (log2 max(n, d))	20.7392
Wilson norm (sopfr(nd))	44
Comma size	medium
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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.

[-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.