144/143: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
TallKite (talk | contribs)
added color name
BudjarnLambeth (talk | contribs)
mNo edit summary
 
(6 intermediate revisions by 4 users not shown)
Line 1: Line 1:
{{Infobox Interval
{{Infobox Interval
| Name = grossma
| Name = grossma
| Color name = 3u1u1, Thulu comma
| Color name = 3u1u1, thulu 1sn,<br>Thulu comma
| Comma = yes
| Comma = yes
}}
}}


'''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.
'''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 {{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{{nbhsp}}{{sagittal | )~! }}. The upward version is called '''1/143C''' or '''143C up''' and is represented by {{sagittal| )~| }}.


== See also ==
== See also ==
* [[Small comma]]
* [[Small comma]]
* [[List of superparticular intervals]]
* [[List of superparticular intervals]]
* [[Grossmisma]], the difference by which a stack of seven 144/143s falls short of [[21/20]]


[[Category:Grossmic]]
[[Category:Grossmic]]
[[Category:Commas with unknown etymology]]

Latest 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 height (log2 nd) 14.3298
Weil height (log2 max(n, d)) 14.3399
Wilson height (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