131072/130321: Difference between revisions

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{{Infobox Interval|Ratio=131072/130321|Name=Undecivesimal Diminished Comma|Comma=yes}}
{{Infobox Interval
| Ratio = 131072/130321
| Name = Undevicesimal diminished comma, Hunt 19-cycle comma
| Color name = s19u<sup>4</sup>-2, Saquadnu comma
| Comma = yes
}}
'''131072/130321''', known as the '''undevicesimal diminished comma'''<!-- This is a placeholder until a reasonable name is coined. -->, is a [[19-limit]] small comma that marks the difference between four [[19/16]] minor thirds and the [[2/1|octave]], or between four Boethius commas ([[513/512]]) and a [[Pythagorean comma]]. This comma can be used in various subgroups to generate highly accurate quarter-octave period temperaments.


'''131072/130321''', known as the '''Undevicesimal Diminished Comma''', <!-- The name "Undevicesimal Diminished Comma" is a placeholder until a reasonable name can be coined. -->is a [[19-limit]] small comma that marks the difference between four [[19/16]] minor thirds and the [[2/1|octave]].  This comma can be used in various subgroups to generate highly accurate quarter-octave period temperaments.
It is tempered out by any edo divisible by 4 up to [[240edo|240]].


Equal temperaments that temper out this comma in the 19-limit include [[8edo|8]], [[12edo|12]], [[16edo|16]], [[20edo|20]], [[32edo|32]], [[80edo|80]], and [[92edo|92]].
[[Category:Commas with placeholder names]] <!-- for "undevicesimal diminished comma" -->
 
[[Category:Commas named systematically]] <!-- for "Hunt 19-cycle comma" -->
[[Category:Commas with placeholder names]]

Latest revision as of 14:41, 10 February 2025

Interval information
Ratio 131072/130321
Subgroup monzo 2.19 [17 -4
Size in cents 9.947935¢
Names Undevicesimal diminished comma,
Hunt 19-cycle comma
Color name s19u4-2, Saquadnu comma
FJS name [math]\displaystyle{ \text{d}{-2}_{19,19,19,19} }[/math]
Special properties reduced,
reduced subharmonic
Tenney height (log2 nd) 33.9917
Weil height (log2 max(n, d)) 34
Wilson height (sopfr(nd)) 110
Comma size small
Open this interval in xen-calc

131072/130321, known as the undevicesimal diminished comma, is a 19-limit small comma that marks the difference between four 19/16 minor thirds and the octave, or between four Boethius commas (513/512) and a Pythagorean comma. This comma can be used in various subgroups to generate highly accurate quarter-octave period temperaments.

It is tempered out by any edo divisible by 4 up to 240.