Phaotic comma: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Ratio = 256000/255879 | | Ratio = 256000/255879 | ||
| Name = phaotic comma, phaotisma | |||
| Color name = s3uy<sup>3</sup>1, Sathutriyo comma | |||
| Name = phaotic comma, | | Comma = yes | ||
| Color name = | |||
| | |||
}} | }} | ||
The '''phaotic comma''', or '''phaotisma''' | The '''phaotic comma''', or '''phaotisma''', is an [[unnoticeable comma|unnoticeable]] [[13-limit]] ([[2.3.5.13 subgroup]]) comma with the ratio '''256000/255879''', and a size of approximately 0.82{{cent}}. It separates a stack of two [[81/80|syntonic commas]] from [[40/39]], or three [[27/20]] acute fourths from [[16/13]] (up an octave). It factors into {{nowrap|([[4096/4095]])([[4375/4374]])}} or {{nowrap|([[6656/6561]])([[507/500]])<sup>−1</sup>}}. | ||
== Temperaments == | == Temperaments == | ||
Tempering it out splits 40/39 into two equal halves, each representing 81/80. It leads to a form of '''phaotismic temperament''' in the full 13-limit and '''phaotic temperament''' in the 2.3.5.13 subgroup. | Tempering it out splits 40/39 into two equal halves, each representing 81/80. It leads to a form of '''phaotismic temperament''' in the full 13-limit and '''phaotic temperament''' in the 2.3.5.13 subgroup. | ||
== Etymology == | |||
This comma was finally named by [[Aura]] in 2021 after several failed attempts. Its name comes from the Ancient Greek word [[Wiktionary: φάος #Ancient Greek|''pháos'']] ("light")- a name that was chosen in part to reflect [https://discord.com/channels/332357996569034752/780300193110818826/829357139398361118 an association of certain intervals involved with brightness] on the part of [[User:Godtone|Osmium]]. | |||
== See also == | == See also == | ||
* [[Unnoticeable comma]] | * [[Unnoticeable comma]] | ||
[[Category:Phaotismic]] | [[Category:Phaotismic]] | ||
[[Category:Commas named for their regular temperament properties]] | |||
[[Category:Commas named by translating something into another language]] | |||
Latest revision as of 08:19, 2 January 2025
| Interval information |
phaotisma
The phaotic comma, or phaotisma, is an unnoticeable 13-limit (2.3.5.13 subgroup) comma with the ratio 256000/255879, and a size of approximately 0.82 ¢. It separates a stack of two syntonic commas from 40/39, or three 27/20 acute fourths from 16/13 (up an octave). It factors into (4096/4095)(4375/4374) or (6656/6561)(507/500)−1.
Temperaments
Tempering it out splits 40/39 into two equal halves, each representing 81/80. It leads to a form of phaotismic temperament in the full 13-limit and phaotic temperament in the 2.3.5.13 subgroup.
Etymology
This comma was finally named by Aura in 2021 after several failed attempts. Its name comes from the Ancient Greek word pháos ("light")- a name that was chosen in part to reflect an association of certain intervals involved with brightness on the part of Osmium.