736/729: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
|Ratio = 736/729 | | Ratio = 736/729 | ||
|Name = 23-limit Tenney/Cage comma (HEJI) | | Name = 23-limit Tenney/Cage comma (HEJI) | ||
|Color name = s23o2, satwetho 2nd | | Color name = s23o2, satwetho 2nd | ||
| Comma = yes | | Comma = yes | ||
}} | }} | ||
'''736/729''', the '''23-limit Tenney/Cage comma''', is a 2.3.23 subgroup comma. It is the amount by which 23/16 | '''736/729''', the '''23-limit Tenney/Cage comma''', is a 2.3.23 subgroup comma. It is the amount by which the octave-reduced 23rd harmonic [[23/16]] exceeds the [[729/512|Pythagorean augemented fourth (729/512)]]. | ||
== Sagittal notation == | == Notation == | ||
This interval is significant in the [[Functional Just System]] and [[Helmholtz-Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby 23-limit (vicesimotertial) interval. | |||
=== Sagittal notation === | |||
In the [[Sagittal]] system, this comma (possibly tempered) is represented by the sagittal {{sagittal | |~ }} and is called the '''23 comma''', or '''23C''' for short, because the simplest interval it notates is 23/1 (equiv. 23/16), as for example in F-B{{nbhsp}}{{sagittal | |~ }}. The downward version is called '''1/23C''' or '''23C down''' and is represented by {{sagittal| !~ }}. | In the [[Sagittal]] system, this comma (possibly tempered) is represented by the sagittal {{sagittal | |~ }} and is called the '''23 comma''', or '''23C''' for short, because the simplest interval it notates is 23/1 (equiv. 23/16), as for example in F-B{{nbhsp}}{{sagittal | |~ }}. The downward version is called '''1/23C''' or '''23C down''' and is represented by {{sagittal| !~ }}. | ||
[[Category:Commas named after music theorists]] | [[Category:Commas named after music theorists]] | ||
[[Category:Commas named after composers]] | [[Category:Commas named after composers]] | ||
Revision as of 17:12, 28 November 2024
| Interval information |
736/729, the 23-limit Tenney/Cage comma, is a 2.3.23 subgroup comma. It is the amount by which the octave-reduced 23rd harmonic 23/16 exceeds the Pythagorean augemented fourth (729/512).
Notation
This interval is significant in the Functional Just System and Helmholtz-Ellis notation as the formal comma to translate a Pythagorean interval to a nearby 23-limit (vicesimotertial) interval.
Sagittal notation
In the Sagittal system, this comma (possibly tempered) is represented by the sagittal and is called the 23 comma, or 23C for short, because the simplest interval it notates is 23/1 (equiv. 23/16), as for example in F-B . The downward version is called 1/23C or 23C down and is represented by .