736/729: Difference between revisions
Dave Keenan (talk | contribs) →Sagittal notation: Changed "simplest ratio" to "simplest interval". Changed colons to slashes and dash. Gave the truly-simplest (2,3-free) interval in addition to the octave-reduced interval. Replaced hair-space with nbhsp template call. |
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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 == | ||
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| !~ }}. | 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]] | |||