144/143: Difference between revisions

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Dave Keenan (talk | contribs)
Sagittal notation: Changed "simplest ratio" to "simplest interval". Changed colons to slashes and dash. Gave the truly-simplest (2,3-free) interval in addition to the octave-reduced interval. Replaced hair-space with nbhsp template call.
BudjarnLambeth (talk | contribs)
mNo edit summary
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[[Category:Grossmic]]
[[Category:Grossmic]]
[[Category:Commas with unknown etymology]]

Revision as of 23:14, 15 November 2024

Interval information
Ratio 144/143
Factorization 24 × 32 × 11-1 × 13-1
Monzo [4 2 0 0 -1 -1
Size in cents 12.0644¢
Name grossma
Color name 3u1u1, thulu 1sn,
Thulu comma
FJS name [math]\displaystyle{ \text{A1}_{11,13} }[/math]
Special properties square superparticular,
reduced
Tenney norm (log2 nd) 14.3298
Weil norm (log2 max(n, d)) 14.3399
Wilson norm (sopfr(nd)) 38
Comma size small
S-expression S12
Open this interval in xen-calc

144/143, the grossma, is a 13-limit small comma. It is the difference between the 11/9 and 16/13 neutral thirds, and between the 12/11 and 13/12 neutral seconds. Teff is a temperament of note that targets it.

Sagittal notation

In the Sagittal system, the downward version of this comma (possibly tempered) is represented by the sagittal and is called the 143 comma, or 143C for short, because the simplest interval it notates is 143/1 = 11×13 (equiv. 143/128), as for example in C-D⁠ ⁠. The upward version is called 1/143C or 143C up and is represented by .

See also