736/729: Difference between revisions

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I added a page explaining that this comma is used in HEJI.
 
Francium (talk | contribs)
Added Infobox Interval
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{| class="wikitable"
{{Infobox Interval
|+Interval information
|Ratio = 736/729
|Ratio
|Name = 23-limit Tenney/Cage comma (HEJI)
|736/729
|Color name = s23o2, satwetho 2nd
|-
}}
|[[Smonzos and svals|Subgroup monzo]]
|2.3.23 [5 -6 1⟩
|-
|Size in [[Cent|cents]]
|16.544342¢
|-
|Names
|23-limit Tenney/Cage comma (HEJI)
|}
'''736/729''', the '''23-limit Tenney/Cage comma''', is a 2.3.23 subgroup comma. It is the amount by which 23/16 (the 23rd harmonic) exceeds the Pythagorean augemented fourth (729/512). It is significant in [[Helmholtz-Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby 23-limit (vicesimotertial) interval.
'''736/729''', the '''23-limit Tenney/Cage comma''', is a 2.3.23 subgroup comma. It is the amount by which 23/16 (the 23rd harmonic) exceeds the Pythagorean augemented fourth (729/512). It is significant in [[Helmholtz-Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby 23-limit (vicesimotertial) interval.

Revision as of 10:09, 24 September 2023

Interval information
Ratio 736/729
Subgroup monzo 2.3.23 [5 -6 1
Size in cents 16.54434¢
Name 23-limit Tenney/Cage comma (HEJI)
Color name s23o2, satwetho 2nd
FJS name [math]\displaystyle{ \text{P1}^{23} }[/math]
Special properties reduced
Tenney norm (log2 nd) 19.0333
Weil norm (log2 max(n, d)) 19.0471
Wilson norm (sopfr(nd)) 51
Open this interval in xen-calc

736/729, the 23-limit Tenney/Cage comma, is a 2.3.23 subgroup comma. It is the amount by which 23/16 (the 23rd harmonic) exceeds the Pythagorean augemented fourth (729/512). It is significant in Helmholtz-Ellis notation as the formal comma to translate a Pythagorean interval to a nearby 23-limit (vicesimotertial) interval.