736/729: Difference between revisions
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'''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 | '''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)]]. | ||
== 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. | 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 === | === Sagittal notation === | ||