129/128: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| Ratio = 129/128
| Ratio = 129/128
| Name = Magikarp comma, 43rd-partial chroma, 43-limit Johnston comma
| Name = 43rd-partial chroma, 43-limit Johnston comma
| Color name = 43o1, fotho unison
| Color name = 43o1, fotho unison
| Comma = yes
| Comma = yes
}}
}}
'''129/128''', the '''Magikarp 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)]].
'''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)]].


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.
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.
== Temperaments ==
Tempering out this comma in the 43-limit leads to the '''Magikarp temperament'''. In the 2.3.43 subgroup, it can be viewed as a diatonic-based temperament in which the perfect fifth represents both [[3/2]] and [[64/43]] (43rd subharmonic).
=== 2.3.43 Magikarp ===
[[Subgroup]]: 2.3.43
[[Comma list]]: 129/128
{{Mapping|legend=1| 1 0 7 | 0 1 -1 }}
: Mapping generators: ~2, ~3
[[Optimal tuning]] (CTE): ~2 = 1＼1, ~3/2 = 700.8959
{{Optimal ET sequence|legend=1| 5, 7, 12 }}
[[Badness]]: 0.000476


== Etymology ==
== Etymology ==
The name ''Magikarp comma'' was named by [[User:Xenllium|Xenllium]] in 2025. It refers to [[wikipedia:Magikarp and Gyarados|Magikarp]] (National Pokédex number #0129), which was in turn named after a fictional character in the ''[[wikipedia:Pokémon|Pokémon]]'' franchise (''Pokémon'' species). Before that, this interval was known as 43rd-partial chroma or 43-limit Johnston comma.
This interval was named the 43rd-partial chroma or 43-limit Johnston comma by [[Stephen Weigel]] in 2023.


== See also ==
== See also ==
Line 36: Line 18:
[[Category:Commas named after composers]]
[[Category:Commas named after composers]]
[[Category:Commas named after music theorists]]
[[Category:Commas named after music theorists]]
[[Category:Commas named after fictional characters]]

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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