2601/2600: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
Fredg999 category edits (talk | contribs)
Kaiveran (talk | contribs)
m ever have one of those nights when you're desperate to do something, ANYTHING, rather than the things you're supposed to be doing
Line 4: Line 4:
| Cents = 0.66573
| Cents = 0.66573
| Name = septendecimal sixth-tones comma
| Name = septendecimal sixth-tones comma
| Color name =
| Color name =17oo3ugg2, sosothugugu 2nd
| Sound =  
| Sound =  
}}
}}

Revision as of 05:25, 17 May 2022

Interval information
Ratio 2601/2600
Factorization 2-3 × 32 × 5-2 × 13-1 × 172
Monzo [-3 2 -2 0 0 -1 2
Size in cents 0.6657312¢
Name septendecimal sixth-tones comma
Color name 17oo3ugg2, sosothugugu 2nd
FJS name [math]\displaystyle{ \text{d2}^{17,17}_{5,5,13} }[/math]
Special properties square superparticular,
reduced
Tenney norm (log2 nd) 22.6891
Weil norm (log2 max(n, d)) 22.6897
Wilson norm (sopfr(nd)) 69
Open this interval in xen-calc

2601/2600 is a 17-limit (also 2.3.5.13.17 subgroup) superparticular comma measuring about 0.67 cents. It may be properly described as the septendecimal sixth-tones comma, since it is the difference between 51/50 and 52/51, the two 17-limit sixth-tones. Another prominent identity is the little gap between 18/13 and a stack of two 20/17's.

In terms of commas, it is the difference between the following pairs:

Temperaments

Tempering out this comma results in 26/25 being split into two equal parts, each representing 51/50~52/51, and enables the related essentially tempered chords.

See also