82/81: Difference between revisions

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Created for HEJI
 
Francium (talk | contribs)
Added Infobox Interval
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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⟩
|-
|Size in [[Cent|cents]]
|21.242402¢
|-
|Names
|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.
'''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.

Revision as of 10:01, 24 September 2023

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 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.