82/81: Difference between revisions

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{| class="wikitable"
{{Infobox Interval
|+Interval information
| Ratio = 82/81
|Ratio
| Name = 41-limit Johnston comma (HEJI)
|82/81
| Color name = 41o1, fowo unison
|-
| Comma = yes
|[[Smonzos and svals|Subgroup monzo]]
}}
|2.3.41 [1 -4 1⟩
'''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]].
|-
 
|Size in [[Cent|cents]]
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 are adapted from [[Ben Johnston]]'s plus and minus signs representing 81/80.
|21.242402¢
 
|-
[[Category:Commas named after composers]]
|Names
[[Category:Commas named after music theorists]]
|41-limit Johnston comma (HEJI)
|}
'''82/81''', or the 41'''-limit Johnston comma (HEJI)''', is a 2.3.41 subgroup comma. It is the amount by which 41/32 (the 41st harmonic) exceeds the Pythagorean major third (ditone) of 81/64. It is significant in [[Helmholtz-Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby 41-limit (prefix???) interval.

Latest revision as of 13:43, 12 July 2025

Interval information
Ratio 82/81
Subgroup monzo 2.3.41 [1 -4 1⟩
Size in cents 21.2424¢
Name 41-limit Johnston comma (HEJI)
Color name 41o1, fowo unison
FJS name [math]\displaystyle{ \text{P1}^{41} }[/math]
Special properties superparticular,
reduced
Tenney height (log2 nd) 12.6974
Weil height (log2 max(n, d)) 12.7151
Wilson height (sopfr(nd)) 55
Comma size small
Open this interval in xen-calc

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 are adapted from Ben Johnston's plus and minus signs representing 81/80.

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