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 augmented fourth (729/512)]]. | ||
== Sagittal notation == | == 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 | 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. The symbols being used in Helmholtz-Ellis notation are virtually identical to up and down arrows, and the authors attribute them to [[James Tenney]] and {{w|John Cage}}, who have possibly used them for [[72edo|1\72]]. | ||
=== 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| !~ }}. | |||
[[Category:Commas named after music theorists]] | |||
[[Category:Commas named after composers]] | |||
Latest revision as of 20:15, 29 July 2025
| 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 augmented 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. The symbols being used in Helmholtz-Ellis notation are virtually identical to up and down arrows, and the authors attribute them to James Tenney and John Cage, who have possibly used them for 1\72.
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 .