Tridecapyth comma: Difference between revisions

The tridecapyth comma (monzo: [28 -20 0 0 0 1⟩, ratio: 3489660928/3486784401) is an unnoticeable 13-limit comma which measures roughly 1.43 cents. It is the interval by which 13/8 exceeds a stack of twenty perfect fifths (3/2) octave reduced, and by which 16/13 falls short of a stack of four Pythagorean limmas (256/243). It is perhaps more easily conceptualized as reaching 13/4 through (9/8)¹⁰. In terms of commas, it is the amount by which tridecimal quartertone (1053/1024) is greater than a stack of two Pythagorean commas.

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-The '''tridecapyth comma''' is the [[13-limit]] [[unnoticeable comma]] '''3489660928/3486784401''', which measures roughly 1.43 [[cent]]s.  It is the interval which, when tempered out, not only equates [[13/8]] with a stack of twenty [[3/2]] perfect fifths octave-reduced, and, consequently, a stack of four [[256/243]] Pythagorean limmas with [[16/13]], but also a stack of two [[Pythagorean comma]]s with the [[1053/1024]] tridecimal quartertone.
+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.
+[[Category:Commas named for the intervals they stack]]
+[[Category:Commas named after polymaths]]

Latest revision as of 13:06, 24 April 2025