82/81: Difference between revisions
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+significance in FJS and misc. rework |
+short explanation on its look in HEJI and hopefully this helps to understand the current name |
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'''82/81''', or the '''41-limit Johnston comma (HEJI)''', is a 2.3.41 subgroup comma. It is the amount by which the octave-reduced 41st harmonic [[41/32]] exceeds the Pythagorean major third (ditone) of [[81/64]], and differs from the syntonic comma ([[81/80]]) by [[6561/6560]]. It is significant in the [[Functional Just System]] and [[Helmholtz-Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby quadracesimoprimal (41-limit) interval. | '''82/81''', or the '''41-limit Johnston comma (HEJI)''', is a 2.3.41 subgroup comma. It is the amount by which the octave-reduced 41st harmonic [[41/32]] exceeds the Pythagorean major third (ditone) of [[81/64]], and differs from the syntonic comma ([[81/80]]) by [[6561/6560]]. It is the parent comma for the [[reversed meantone clan]]. | ||
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 quadracesimoprimal (41-limit) interval. In Helmholtz-Ellis notation, the symbols being used are virtually identical to [[Ben Johnston]]'s plus and minus signs representing 81/80. | |||
[[Category:Commas named after composers]] | [[Category:Commas named after composers]] | ||
[[Category:Commas named after music theorists]] | [[Category:Commas named after music theorists]] | ||
Revision as of 18:05, 28 November 2024
| Interval information |
reduced
82/81, or the 41-limit Johnston comma (HEJI), is a 2.3.41 subgroup comma. It is the amount by which the octave-reduced 41st harmonic 41/32 exceeds the Pythagorean major third (ditone) of 81/64, and differs from the syntonic comma (81/80) by 6561/6560. It is the parent comma for the reversed meantone clan.
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 quadracesimoprimal (41-limit) interval. In Helmholtz-Ellis notation, the symbols being used are virtually identical to Ben Johnston's plus and minus signs representing 81/80.