2080/2079

Interval information

Ratio	2080/2079
Factorization	25 × 3-3 × 5 × 7-1 × 11-1 × 13
Monzo	[5 -3 1 -1 -1 1⟩
Size in cents	0.8325242¢
Name	ibnsinma
FJS name	[math]\displaystyle{ \text{P1}^{5,13}_{7,11} }[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	22.044
Weil height (log2 max(n, d))	22.0447
Wilson height (sopfr(nd))	55
Comma size	unnoticeable
S-expressions	S64 × S65, S78 × S79 × S80
Open this interval in xen-calc

2080/2079, the ibnsinma, is a 13-limit unnoticeable comma measuring about 0.8 cents. It is such a significant comma in the 13-limit being the difference between eight pairs of superparticular ratios:

• 64/63 and 66/65
• 78/77 and 81/80
• 100/99 and 105/104
• 325/324 and 385/384
• 364/363 and 441/440
• 540/539 and 729/728
• 676/675 and 1001/1000
• 1716/1715 and 9801/9800

Not to mention some nonsuperparticular but useful ratios:

• 896/891 and 196/195
• 5120/5103 and 352/351
• 352/351 and 847/845

Or as a relation in the four formal commas defined by Functional Just System:

• ((64/63)(1053/1024)) / ((81/80)(33/32)).

It factors into the following superparticular intervals:

• 4096/4095 and 4225/4224
• 3025/3024 and 6656/6655

In Sagittal notation, it is the default comma represented by two minas or six tinas.

Temperaments

By tempering it out is defined the ibnsinmic temperament, which enables the ibnsinmic chords, the essentially tempered chords in the 21-odd-limit. Another consequence is that it makes fifth complements of 13/11 and 80/63, and of 40/33 and 26/21. You may find a list of good equal temperaments that support this temperament below.

Subgroup: 2.3.5.7.11.13

Mapping:
[⟨1 0 0 0 0 -5],
⟨0 1 0 0 0 3],
⟨0 0 1 0 0 -1],
⟨0 0 0 1 0 1],
⟨0 0 0 0 1 1]]

Mapping generators: ~2, ~3, ~5, ~7, ~11

Template:Val list *

* optimal patent val: 3044

See also

• Unnoticeable comma
• List of superparticular intervals