736/729: Difference between revisions

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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

|-

| Comma = yes

~~|[[Smonzos and svals|Subgroup monzo]]~~

}}

~~|2.3.23 [5 -6 1⟩~~

'''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)]].

|-

~~|Size in [[Cent|cents]]~~

== Notation ==

~~|16.544342¢~~

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]].

|-

~~|Names~~

=== Sagittal notation ===

|23-limit Tenney/Cage comma (HEJI)

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| !~ }}.

|}

'''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.

[[Category:Commas named after music theorists]]

[[Category:Commas named after composers]]

@@ Line 1: / Line 1: @@
-{| class="wikitable"
+{{Infobox Interval
-|+Interval information
+| Ratio = 736/729
-|Ratio
+| Name = 23-limit Tenney/Cage comma (HEJI)
-|736/729
+| Color name = s23o2, satwetho 2nd
-|-
+| Comma = yes
-|[[Smonzos and svals|Subgroup monzo]]
+}}
-|2.3.23 [5 -6 1⟩
+'''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)]].
-|-
-|Size in [[Cent|cents]]
+== Notation ==
-|16.544342¢
+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]].
-|-
-|Names
+=== Sagittal notation ===
-|23-limit Tenney/Cage comma (HEJI)
+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| !~ }}.
-|}
-'''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.
+[[Category:Commas named after music theorists]]
+[[Category:Commas named after composers]]