1188/1183: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
Created page with "{{Infobox Interval | Name = kestrel comma | Comma = 1 }} '''1188/1183''', the '''kestrel comma''', is a small 13-limit comma measuring about 7.30{{cent..."
 
+factorizations
Line 4: Line 4:
}}
}}
'''1188/1183''', the '''kestrel comma''', is a [[Small comma|small]] [[13-limit]] [[comma]] measuring about 7.30{{cent}}.  
'''1188/1183''', the '''kestrel comma''', is a [[Small comma|small]] [[13-limit]] [[comma]] measuring about 7.30{{cent}}.  
In terms of commas, it is the difference between [[176/175]] and [[676/675]]. It factors into ([[540/539]])([[847/845]]) or ([[352/351]])([[729/728]]).


== Temperaments ==
== Temperaments ==

Revision as of 15:13, 5 September 2023

Interval information
Ratio 1188/1183
Factorization 22 × 33 × 7-1 × 11 × 13-2
Monzo [2 3 0 -1 1 -2
Size in cents 7.301715¢
Name kestrel comma
FJS name [math]\displaystyle{ \text{d}{-2}^{11}_{7,13,13} }[/math]
Special properties reduced
Tenney height (log2 nd) 20.4226
Weil height (log2 max(n, d)) 20.4286
Wilson height (sopfr(nd)) 57
Comma size small
Open this interval in xen-calc

1188/1183, the kestrel comma, is a small 13-limit comma measuring about 7.30 ¢.

In terms of commas, it is the difference between 176/175 and 676/675. It factors into (540/539)(847/845) or (352/351)(729/728).

Temperaments

Tempering out this comma in the 13-limit leads to the rank-5 kestrel temperament, and enables kestrel chords.

Etymology

This comma was named by Gene Ward Smith in 2011[1].

Notes