Tridecapyth comma: Difference between revisions

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The '''tridecapyth comma''' ({{Monzo|legend=1| 28 -20 0 0 0 1 }}, [[ratio]]: 3489660928/3486784401) is an [[unnoticeable comma~~|unnoticeable~~]] [[13-limit~~]] [[comma~~]] which measures roughly 1.43 [[cent~~]]s~~. It is the interval by which [[13/8]] exceeds a stack of twenty [[3/2|perfect fifths (3/2)]] octave reduced, and by which [[16/13]] falls short of a stack of four [[256/243|Pythagorean limmas (256/243)]]. It is perhaps more easily conceptualized as reaching [[13/4]] through ([[9/8]])<sup>10</sup>. In terms of commas, it is the amount by which [[1053/1024|tridecimal quartertone (1053/1024)]] is greater than a stack of two [[Pythagorean comma]]s~~, and~~ the ~~amount~~ by ~~which~~ [[~~262144/255879~~]] ~~exceeds~~ [[~~177147/173056~~]].

The '''tridecapyth comma''' ({{Monzo|legend=1| 28 -20 0 0 0 1 }}, [[ratio]]: 3489660928/3486784401), also described as the ''tridecaschisma'' (from "trideca-" (for 13) + "schisma"), is an [[unnoticeable comma]] in [[13-limit|13-limit just intonation]] which measures roughly 1.43 {{cent}}. It is the interval by which [[13/8]] exceeds a stack of twenty [[3/2|perfect fifths (3/2)]] octave reduced, and by which [[16/13]] falls short of a stack of four [[256/243|Pythagorean limmas (256/243)]]. It is perhaps more easily conceptualized as reaching [[13/4]] through ([[9/8]])<sup>10</sup>. In terms of commas, it is the amount by which [[1053/1024|tridecimal quartertone (1053/1024)]] is greater than a stack of two [[Pythagorean comma]]s.

== Temperaments ==

[[Tempering out]] this comma in the 2.3.13 subgroup leads to the [[tridecapyth]] temperament.

== Etymology ==

This comma was named by [[Aura]] in 2021.

== See also ==

* [[Tridecimal schisma]] (disambiguation page)

[[Category:Commas named for the intervals they stack]]

[[Category:Commas named after polymaths]]

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-The '''tridecapyth comma''' ({{Monzo|legend=1| 28 -20 0 0 0 1 }}, [[ratio]]: 3489660928/3486784401) is an [[unnoticeable comma|unnoticeable]] [[13-limit]] [[comma]] which measures roughly 1.43 [[cent]]s. It is the interval by which [[13/8]] exceeds a stack of twenty [[3/2|perfect fifths (3/2)]] octave reduced, and by which [[16/13]] falls short of a stack of four [[256/243|Pythagorean limmas (256/243)]]. It is perhaps more easily conceptualized as reaching [[13/4]] through ([[9/8]])<sup>10</sup>. In terms of commas, it is the amount by which [[1053/1024|tridecimal quartertone (1053/1024)]] is greater than a stack of two [[Pythagorean comma]]s, and the amount by which [[262144/255879]] exceeds [[177147/173056]].
+The '''tridecapyth comma''' ({{Monzo|legend=1| 28 -20 0 0 0 1 }}, [[ratio]]: 3489660928/3486784401), also described as the ''tridecaschisma'' (from "trideca-" (for 13) + "schisma"), is an [[unnoticeable comma]] in [[13-limit|13-limit just intonation]] which measures roughly 1.43 {{cent}}. It is the interval by which [[13/8]] exceeds a stack of twenty [[3/2|perfect fifths (3/2)]] octave reduced, and by which [[16/13]] falls short of a stack of four [[256/243|Pythagorean limmas (256/243)]]. It is perhaps more easily conceptualized as reaching [[13/4]] through ([[9/8]])<sup>10</sup>. In terms of commas, it is the amount by which [[1053/1024|tridecimal quartertone (1053/1024)]] is greater than a stack of two [[Pythagorean comma]]s.
+== Temperaments ==
+[[Tempering out]] this comma in the 2.3.13 subgroup leads to the [[tridecapyth]] temperament.
+== Etymology ==
+This comma was named by [[Aura]] in 2021.
+== See also ==
+* [[Tridecimal schisma]] (disambiguation page)
 [[Category:Commas named for the intervals they stack]]
 [[Category:Commas named after polymaths]]