Phaotic comma: Difference between revisions
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The '''phaotic comma''', or '''phaotisma''' (from Ancient Greek ''pháos'' 'light'), is an [[unnoticeable comma|unnoticeable]] [[13-limit]] ( | The '''phaotic comma''', or '''phaotisma''' (from Ancient Greek ''pháos'' 'light'), 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 == | ||
Revision as of 22:11, 29 November 2024
| Interval information |
phaotisma
The phaotic comma, or phaotisma (from Ancient Greek pháos 'light'), 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.