Phaotic comma: Difference between revisions
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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 == | ||
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== Etymology == | == 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 | 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"). | ||
== See also == | == See also == | ||
Revision as of 00:42, 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").