129/128: Difference between revisions

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{| class="wikitable"
{{Infobox Interval
|+Interval information
| Ratio = 129/128
|Ratio
| Name = 43rd-partial chroma, 43-limit Johnston comma
|129/128
| Color name = 43o1, fotho unison
|-
| Comma = yes
|[[Smonzos and svals|Subgroup monzo]]
}}
|2.3.43 [-7 1 1⟩
'''129/128''', the '''43rd-partial chroma''' or '''43-limit Johnston comma''' is a 2.3.43 subgroup comma. It is the amount by which the octave-reduced 43rd harmonic [[43/32]] exceeds the [[4/3|perfect fourth (4/3)]].
|-
 
|Size in [[Cent|cents]]
This interval is the 43rd-partial chroma (43-limit formal comma) used to express 43-limit intervals in the [[Functional Just System]] and [[Helmholtz-Ellis notation]], as well as extended [[Ben Johnston's notation]]. It is significant to translate a Pythagorean interval to a nearby quadragesimotertial interval.
|13.4727065¢
 
|-
== Etymology ==
|Names
This interval was named the 43rd-partial chroma or 43-limit Johnston comma by [[Stephen Weigel]] in 2023.
|43-limit comma (HEJI)
 
|}
== See also ==
'''129/128''', or the '''43-limit Johnston comma (HEJI)''', is a 2.3.43 subgroup comma. It is the amount by which 43/32 (the 43rd harmonic) exceeds the perfect fourth (4/3). It is significant in [[Helmholtz-Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby 43-limit (prefix???) interval.
* [[Small comma]]
* [[List of superparticular intervals]]
 
[[Category:Commas named after composers]]
[[Category:Commas named after music theorists]]

Latest revision as of 03:29, 11 April 2025

Interval information
Ratio 129/128
Subgroup monzo 2.3.43 [-7 1 1⟩
Size in cents 13.47271¢
Names 43rd-partial chroma,
43-limit Johnston comma
Color name 43o1, fotho unison
FJS name [math]\displaystyle{ \text{P1}^{43} }[/math]
Special properties superparticular,
reduced,
reduced harmonic
Tenney height (log2 nd) 14.0112
Weil height (log2 max(n, d)) 14.0225
Wilson height (sopfr(nd)) 60
Comma size small
Open this interval in xen-calc

129/128, the 43rd-partial chroma or 43-limit Johnston comma is a 2.3.43 subgroup comma. It is the amount by which the octave-reduced 43rd harmonic 43/32 exceeds the perfect fourth (4/3).

This interval is the 43rd-partial chroma (43-limit formal comma) used to express 43-limit intervals in the Functional Just System and Helmholtz-Ellis notation, as well as extended Ben Johnston's notation. It is significant to translate a Pythagorean interval to a nearby quadragesimotertial interval.

Etymology

This interval was named the 43rd-partial chroma or 43-limit Johnston comma by Stephen Weigel in 2023.

See also

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