Tridecapyth comma - Revision history

Godtone: small correction

2026-06-06T18:24:41Z

small correction

← Older revision		Revision as of 18:24, 6 June 2026
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	}}		}}

	The '''tridecapyth comma''' ({{Monzo\|legend=1\| 28 -20 0 0 0 1 }}, [[ratio]]: 3489660928/3486784401), also described as the ''tridecaschisma'' (~~after the 2.3.~~13 ~~temperament~~), 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.		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 ==		== Temperaments ==

Hkm: /* Tridecapyth */

2026-06-06T15:51:34Z

Tridecapyth

← Older revision		Revision as of 15:51, 6 June 2026
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	=== Tridecapyth ===		=== Tridecapyth ===
	{{ See also \| No-fives subgroup temperaments#Temperaments with a 2.3.13 gene }}		{{ See also \| No-fives subgroup temperaments#Temperaments with a 2.3.13 gene }}
	Tempering out this comma in the 2.3.13 subgroup leads tridecapyth, which can be seen as a way of giving a mapping of prime 13 to any temperament with an extremely accurate tuning of its fifth (like the [[53edo]] tuning of [[schismic]]). Interestingly, the mapping is ''so'' accurate that more optimized ~~tuning~~ of schismic that use a flatter fifth are not accurate enough to preserve the mapping; for 118edo we get the 118f [[val]] that takes the second-best, flat mapping of prime 13, and the same is true for [[171edo]] where we get the 171f val. However, due to its small note count, [[41edo]] technically uses this mapping too, so that the val sum 41 + 53 = [[94edo]] also uses this mapping, suggesting it's of interest to flatter tunings of [[garibaldi]] with fifths tending close to pure; this corresponds to the extension of garibaldi called [[cassandra]]. If we add this mapping to 5-limit schismic instead we get [[tridecaschismic]].		Tempering out this comma in the 2.3.13 subgroup leads tridecapyth, which can be seen as a way of giving a mapping of prime 13 to any temperament with an extremely accurate tuning of its fifth (like the [[53edo]] tuning of [[schismic]]). Interestingly, the mapping is ''so'' accurate that more optimized tunings of schismic that use a flatter fifth are not accurate enough to preserve the mapping; for 118edo we get the 118f [[val]] that takes the second-best, flat mapping of prime 13, and the same is true for [[171edo]] where we get the 171f val. However, due to its small note count, [[41edo]] technically uses this mapping too, so that the val sum 41 + 53 = [[94edo]] also uses this mapping, suggesting it's of interest to flatter tunings of [[garibaldi]] with fifths tending close to pure; this corresponds to the extension of garibaldi called [[cassandra]]. If we add this mapping to 5-limit schismic instead we get [[tridecaschismic]].

	[[Subgroup]]: 2.3.13		[[Subgroup]]: 2.3.13

Godtone: /* Tridecapyth */ link

2026-06-06T15:35:56Z

Tridecapyth: link

← Older revision		Revision as of 15:35, 6 June 2026
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	== Temperaments ==		== Temperaments ==
	=== Tridecapyth ===		=== Tridecapyth ===
			{{ See also \| No-fives subgroup temperaments#Temperaments with a 2.3.13 gene }}
	Tempering out this comma in the 2.3.13 subgroup leads tridecapyth, which can be seen as a way of giving a mapping of prime 13 to any temperament with an extremely accurate tuning of its fifth (like the [[53edo]] tuning of [[schismic]]). Interestingly, the mapping is ''so'' accurate that more optimized tuning of schismic that use a flatter fifth are not accurate enough to preserve the mapping; for 118edo we get the 118f [[val]] that takes the second-best, flat mapping of prime 13, and the same is true for [[171edo]] where we get the 171f val. However, due to its small note count, [[41edo]] technically uses this mapping too, so that the val sum 41 + 53 = [[94edo]] also uses this mapping, suggesting it's of interest to flatter tunings of [[garibaldi]] with fifths tending close to pure; this corresponds to the extension of garibaldi called [[cassandra]]. If we add this mapping to 5-limit schismic instead we get [[tridecaschismic]].		Tempering out this comma in the 2.3.13 subgroup leads tridecapyth, which can be seen as a way of giving a mapping of prime 13 to any temperament with an extremely accurate tuning of its fifth (like the [[53edo]] tuning of [[schismic]]). Interestingly, the mapping is ''so'' accurate that more optimized tuning of schismic that use a flatter fifth are not accurate enough to preserve the mapping; for 118edo we get the 118f [[val]] that takes the second-best, flat mapping of prime 13, and the same is true for [[171edo]] where we get the 171f val. However, due to its small note count, [[41edo]] technically uses this mapping too, so that the val sum 41 + 53 = [[94edo]] also uses this mapping, suggesting it's of interest to flatter tunings of [[garibaldi]] with fifths tending close to pure; this corresponds to the extension of garibaldi called [[cassandra]]. If we add this mapping to 5-limit schismic instead we get [[tridecaschismic]].

Godtone: /* Temperaments */ add tridecapyth

2026-06-06T15:34:37Z

Temperaments: add tridecapyth

@@ Line 9: / Line 9: @@
 == Temperaments ==
-Tempering out this comma in the 2.3.13 subgroup leads [[tridecaschismic]], which can be seen as a way of giving a mapping of prime 13 to any temperament with an extremely accurate tuning of its fifth (like the [[53edo]] tuning of [[schismic]]). Interestingly, the mapping is ''so'' accurate that more optimized tuning of schismic that use a flatter fifth are not accurate enough to preserve the mapping; for 118edo we get the 118f [[val]] that takes the second-best, flat mapping of prime 13, and the same is true for [[171edo]] where we get the 171f val. However, due to its small note count, [[41edo]] technically uses this mapping too, so that the val sum 41 + 53 = [[94edo]] also uses this mapping, suggesting it's of interest to flatter tunings of [[garibaldi]] with fifths tending close to pure; this corresponds to the extension of garibaldi called [[cassandra]].
+=== Tridecapyth ===
 == Etymology ==

Godtone: /* Temperaments */ grammatical error

2026-06-06T15:05:29Z

Temperaments: grammatical error

← Older revision		Revision as of 15:05, 6 June 2026
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	== Temperaments ==		== Temperaments ==
	Tempering out this comma in the 2.3.13 subgroup leads [[tridecaschismic]], which can be seen as a way of giving any temperament with an extremely accurate tuning of its fifth (like the [[53edo]] tuning of [[schismic]]). Interestingly, the mapping is ''so'' accurate that more optimized tuning of schismic that use a flatter fifth are not accurate enough to preserve the mapping; for 118edo we get the 118f [[val]] that takes the second-best, flat mapping of prime 13, and the same is true for [[171edo]] where we get the 171f val. However, due to its small note count, [[41edo]] technically uses this mapping too, so that the val sum 41 + 53 = [[94edo]] also uses this mapping, suggesting it's of interest to flatter tunings of [[garibaldi]] with fifths tending close to pure; this corresponds to the extension of garibaldi called [[cassandra]].		Tempering out this comma in the 2.3.13 subgroup leads [[tridecaschismic]], which can be seen as a way of giving a mapping of prime 13 to any temperament with an extremely accurate tuning of its fifth (like the [[53edo]] tuning of [[schismic]]). Interestingly, the mapping is ''so'' accurate that more optimized tuning of schismic that use a flatter fifth are not accurate enough to preserve the mapping; for 118edo we get the 118f [[val]] that takes the second-best, flat mapping of prime 13, and the same is true for [[171edo]] where we get the 171f val. However, due to its small note count, [[41edo]] technically uses this mapping too, so that the val sum 41 + 53 = [[94edo]] also uses this mapping, suggesting it's of interest to flatter tunings of [[garibaldi]] with fifths tending close to pure; this corresponds to the extension of garibaldi called [[cassandra]].

	== Etymology ==		== Etymology ==

Godtone: add temperaments section

2026-06-06T15:02:58Z

add temperaments section

← Older revision		Revision as of 15:02, 6 June 2026
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	The '''tridecapyth comma''' ({{Monzo\|legend=1\| 28 -20 0 0 0 1 }}, [[ratio]]: 3489660928/3486784401), also described as the ''tridecaschisma'' (after the 2.3.13 temperament), 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.		The '''tridecapyth comma''' ({{Monzo\|legend=1\| 28 -20 0 0 0 1 }}, [[ratio]]: 3489660928/3486784401), also described as the ''tridecaschisma'' (after the 2.3.13 temperament), 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 [[tridecaschismic]], which can be seen as a way of giving any temperament with an extremely accurate tuning of its fifth (like the [[53edo]] tuning of [[schismic]]). Interestingly, the mapping is ''so'' accurate that more optimized tuning of schismic that use a flatter fifth are not accurate enough to preserve the mapping; for 118edo we get the 118f [[val]] that takes the second-best, flat mapping of prime 13, and the same is true for [[171edo]] where we get the 171f val. However, due to its small note count, [[41edo]] technically uses this mapping too, so that the val sum 41 + 53 = [[94edo]] also uses this mapping, suggesting it's of interest to flatter tunings of [[garibaldi]] with fifths tending close to pure; this corresponds to the extension of garibaldi called [[cassandra]].

	== Etymology ==		== Etymology ==

Godtone: clarify

2026-06-06T14:54:29Z

clarify

← Older revision		Revision as of 14:54, 6 June 2026
Line 6:		Line 6:
	}}		}}

	The '''tridecapyth comma''' ({{Monzo\|legend=1\| 28 -20 0 0 0 1 }}, [[ratio]]: 3489660928/3486784401), also described as the ''~~tridecimal 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.		The '''tridecapyth comma''' ({{Monzo\|legend=1\| 28 -20 0 0 0 1 }}, [[ratio]]: 3489660928/3486784401), also described as the ''tridecaschisma'' (after the 2.3.13 temperament), 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.

	== Etymology ==		== Etymology ==

FloraC: "Tridecimal schisma" is to an extent already in use. Remove from lemma. + etymology

2026-05-04T18:44:25Z

"Tridecimal schisma" is to an extent already in use. Remove from lemma. + etymology

← Older revision		Revision as of 18:44, 4 May 2026
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	{{Infobox Interval		{{Infobox Interval
	\| Ratio = 3489660928/3486784401		\| Ratio = 3489660928/3486784401
	\| Name = tridecapyth comma~~, tridecimal schisma~~		\| Name = tridecapyth comma
	\| Color name = s<sup>3</sup>3o3, trisatho 3rd,<br>Trisatho comma		\| Color name = s<sup>3</sup>3o3, trisatho 3rd,<br>Trisatho comma
	\| Comma = yes		\| Comma = yes
	}}		}}

	The '''tridecapyth comma~~''' or '''tridecimal schisma~~''' ({{Monzo\|legend=1\| 28 -20 0 0 0 1 }}, [[ratio]]: 3489660928/3486784401) 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.		The '''tridecapyth comma''' ({{Monzo\|legend=1\| 28 -20 0 0 0 1 }}, [[ratio]]: 3489660928/3486784401), also described as the ''tridecimal 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.

			== 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 for the intervals they stack]]
	[[Category:Commas named after polymaths]]		[[Category:Commas named after polymaths]]

Hotcrystal0: I think tridecimal schisma is another valid name

2026-05-04T17:52:34Z

I think tridecimal schisma is another valid name

← Older revision		Revision as of 17:52, 4 May 2026
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	{{Infobox Interval		{{Infobox Interval
	\| Ratio = 3489660928/3486784401		\| Ratio = 3489660928/3486784401
	\| Name = tridecapyth comma		\| Name = tridecapyth comma, tridecimal schisma
	\| Color name = s<sup>3</sup>3o3, trisatho 3rd,<br>Trisatho comma		\| Color name = s<sup>3</sup>3o3, trisatho 3rd,<br>Trisatho comma
	\| Comma = yes		\| Comma = yes
	}}		}}

	The '''tridecapyth comma''' ({{Monzo\|legend=1\| 28 -20 0 0 0 1 }}, [[ratio]]: 3489660928/3486784401) 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.		The '''tridecapyth comma''' or '''tridecimal schisma''' ({{Monzo\|legend=1\| 28 -20 0 0 0 1 }}, [[ratio]]: 3489660928/3486784401) 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.

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

Overthink: better linking (MOS:SEAOFBLUE)

2026-03-15T16:56:03Z

better linking (MOS:SEAOFBLUE)

← Older revision		Revision as of 16:56, 15 March 2026
Line 6:		Line 6:
	}}		}}

	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.		The '''tridecapyth comma''' ({{Monzo\|legend=1\| 28 -20 0 0 0 1 }}, [[ratio]]: 3489660928/3486784401) 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.

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