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

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:

Not to mention some nonsuperparticular but useful ratios:

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

2080/2079

Temperaments

See also