19-comma - Revision history

Eufalesio: Updated color notation

2026-05-01T14:48:44Z

Updated color notation

← Older revision		Revision as of 14:48, 1 May 2026
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	\| Monzo = -30 19		\| Monzo = -30 19
	\| Name = 19-comma, Pythagorean kleisma, Pythagorean inverse double-diminished second		\| Name = 19-comma, Pythagorean kleisma, Pythagorean inverse double-diminished second
	\| Color name = L<sup>3</sup>w-2, trilawa negative 2nd		\| Color name = L<sup>3</sup>w-2, trilawa negative 2nd<br>19wM, newama
	}}		}}
	The '''19-comma''', otherwise known as the '''Pythagorean kleisma''' ({{monzo\|legend=1\| -30 19 }}, [[ratio]]: 1162261467/1073741824), is an interval of about 137.1{{cent}}. It is the amount by which nineteen [[3/2\|perfect fifth]]s exceed eleven octaves, or (3/2)<sup>19</sup>/2<sup>11</sup>. If used as an interval in its own right, it is the '''Pythagorean inverse double-diminished second'''.		The '''19-comma''', otherwise known as the '''Pythagorean kleisma''' ({{monzo\|legend=1\| -30 19 }}, [[ratio]]: 1162261467/1073741824), is an interval of about 137.1{{cent}}. It is the amount by which nineteen [[3/2\|perfect fifth]]s exceed eleven octaves, or (3/2)<sup>19</sup>/2<sup>11</sup>. If used as an interval in its own right, it is the '''Pythagorean inverse double-diminished second'''.

Overthink: /* Temperaments */ close to 13/12

2026-02-15T22:43:13Z

Temperaments: close to 13/12

← Older revision		Revision as of 22:43, 15 February 2026
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	== Temperaments ==		== Temperaments ==
	Treating it as a comma, [[tempering out]] this comma gives rise to [[graywood]], which is supported by edos 19, [[38edo\|38]], [[57edo\|57]], and [[76edo\|76]] in their [[patent val]]s.		Treating it as a comma, [[tempering out]] this comma gives rise to [[graywood]], which is supported by edos 19, [[38edo\|38]], [[57edo\|57]], and [[76edo\|76]] in their [[patent val]]s.

			However, this interval is larger than typical commas, being close to [[13/12]] in size. This interval can be equated to 13/12 by tempering out the [[tridecapyth comma]] with monzo {{Monzo\| 28 -20 0 0 0 1 }}, leading to the [[tridecapyth]] temperament.

	== Terminology ==		== Terminology ==

FloraC: Sectioning, hanson and cata -> kleismic

2025-04-26T12:32:27Z

Sectioning, hanson and cata -> kleismic

← Older revision		Revision as of 12:32, 26 April 2025
Line 4:		Line 4:
	\| Color name = L<sup>3</sup>w-2, trilawa negative 2nd		\| Color name = L<sup>3</sup>w-2, trilawa negative 2nd
	}}		}}
	The '''19-comma''', otherwise known as the '''Pythagorean kleisma''' ({{monzo\|legend=1\| -30 19 }}, [[ratio]]: 1162261467/1073741824), is an interval of about 137.1{{cent}}. It is the amount by which nineteen [[3/2\|perfect fifth]]s exceed eleven octaves, or (3/2)<sup>19</sup>/2<sup>11</sup>. If used as an interval in its own right, it is the '''Pythagorean inverse double-diminished second'''. Treating it as a comma, [[tempering out]] this comma gives rise to [[graywood]], which is supported by edos 19, [[38edo\|38]], [[57edo\|57]], and [[76edo\|76]] in their [[patent val]]s.		The '''19-comma''', otherwise known as the '''Pythagorean kleisma''' ({{monzo\|legend=1\| -30 19 }}, [[ratio]]: 1162261467/1073741824), is an interval of about 137.1{{cent}}. It is the amount by which nineteen [[3/2\|perfect fifth]]s exceed eleven octaves, or (3/2)<sup>19</sup>/2<sup>11</sup>. If used as an interval in its own right, it is the '''Pythagorean inverse double-diminished second'''.

			== Temperaments ==
			Treating it as a comma, [[tempering out]] this comma gives rise to [[graywood]], which is supported by edos 19, [[38edo\|38]], [[57edo\|57]], and [[76edo\|76]] in their [[patent val]]s.

	== Terminology ==		== Terminology ==
	The term ''Pythagorean kleisma'' seems to be first used by [[Flora Canou]] in 2024, for this is the [[kleisma\|moskleisma]] of the [[Pythagorean tuning\|Pythagorean]] [[5L 2s\|diatonic scale]], where ''kleisma'' (adjective: ''kleismic'') refers to the inverse double-diminished 1-step i.e. \|2L - 3s\|. It is equated with the 5-limit kleisma of [[15625/15552]] along with many other intervals in [[meantone]]. It can also be reasoned as a fitting name as by tempering out this comma alongside the meantone comma ([[81/80]]), we get [[19edo]], which [[support]]s [[~~hanson and cata\|~~kleismic]].		The term ''Pythagorean kleisma'' seems to be first used by [[Flora Canou]] in 2024, for this is the [[kleisma\|moskleisma]] of the [[Pythagorean tuning\|Pythagorean]] [[5L 2s\|diatonic scale]], where ''kleisma'' (adjective: ''kleismic'') refers to the inverse double-diminished 1-step i.e. \|2L - 3s\|. It is equated with the 5-limit kleisma of [[15625/15552]] along with many other intervals in [[meantone]]. It can also be reasoned as a fitting name as by tempering out this comma alongside the meantone comma ([[81/80]]), we get [[19edo]], which [[support]]s [[kleismic]].

	== See also ==		== See also ==
	* [[Large comma]]		* [[Large comma]]

Lériendil at 12:37, 15 October 2024

2024-10-15T12:37:04Z

← Older revision		Revision as of 12:37, 15 October 2024
Line 4:		Line 4:
	\| Color name = L<sup>3</sup>w-2, trilawa negative 2nd		\| Color name = L<sup>3</sup>w-2, trilawa negative 2nd
	}}		}}
	The '''19-comma''', otherwise known as the '''Pythagorean kleisma''' ({{monzo\|legend=1\| -30 19 }}, [[ratio]]: 1162261467/1073741824), is an interval of about 137.1{{cent}}. It is the amount by which nineteen [[3/2\|perfect fifth]]s exceed eleven octaves, or (3/2)<sup>19</sup>/2<sup>11</sup>. If used as an interval in its own right, it is the '''Pythagorean inverse double-diminished second'''. Treating it as a comma, [[tempering out]] this comma gives rise to [[graywood]], which is supported by edos 19, [[38edo\|38]], [[57edo\|57]], and [[76edo\|76]] in their [[patent ~~vals~~]].		The '''19-comma''', otherwise known as the '''Pythagorean kleisma''' ({{monzo\|legend=1\| -30 19 }}, [[ratio]]: 1162261467/1073741824), is an interval of about 137.1{{cent}}. It is the amount by which nineteen [[3/2\|perfect fifth]]s exceed eleven octaves, or (3/2)<sup>19</sup>/2<sup>11</sup>. If used as an interval in its own right, it is the '''Pythagorean inverse double-diminished second'''. Treating it as a comma, [[tempering out]] this comma gives rise to [[graywood]], which is supported by edos 19, [[38edo\|38]], [[57edo\|57]], and [[76edo\|76]] in their [[patent val]]s.

	== Terminology ==		== Terminology ==

Lériendil: referenced graywood

2024-10-15T12:36:27Z

referenced graywood

← Older revision		Revision as of 12:36, 15 October 2024
Line 4:		Line 4:
	\| Color name = L<sup>3</sup>w-2, trilawa negative 2nd		\| Color name = L<sup>3</sup>w-2, trilawa negative 2nd
	}}		}}
	The '''19-comma''', otherwise known as the '''Pythagorean kleisma''' ({{monzo\|legend=1\| -30 19 }}, [[ratio]]: 1162261467/1073741824), is an interval of about 137.1{{cent}}. It is the amount by which nineteen [[3/2\|perfect fifth]]s exceed eleven octaves, or (3/2)<sup>19</sup>/2<sup>11</sup>. If used as an interval in its own right, it is the '''Pythagorean inverse double-diminished second'''.		The '''19-comma''', otherwise known as the '''Pythagorean kleisma''' ({{monzo\|legend=1\| -30 19 }}, [[ratio]]: 1162261467/1073741824), is an interval of about 137.1{{cent}}. It is the amount by which nineteen [[3/2\|perfect fifth]]s exceed eleven octaves, or (3/2)<sup>19</sup>/2<sup>11</sup>. If used as an interval in its own right, it is the '''Pythagorean inverse double-diminished second'''. Treating it as a comma, [[tempering out]] this comma gives rise to [[graywood]], which is supported by edos 19, [[38edo\|38]], [[57edo\|57]], and [[76edo\|76]] in their [[patent vals]].

	== Terminology ==		== Terminology ==
	The term ''Pythagorean kleisma'' seems to be first used by [[Flora Canou]] in 2024, for this is the [[kleisma\|moskleisma]] of the [[Pythagorean tuning\|Pythagorean]] [[5L 2s\|diatonic scale]], where ''kleisma'' (adjective: ''kleismic'') refers to the inverse double-diminished 1-step i.e. \|2L - 3s\|. It is equated with the 5-limit kleisma of [[15625/15552]] along with many other intervals in [[meantone]]. It can also be reasoned as a fitting name as by [[tempering out]] this comma alongside the [[~~meantone comma~~]], we get [[19edo]], which [[support]]s [[hanson and cata\|kleismic]].		The term ''Pythagorean kleisma'' seems to be first used by [[Flora Canou]] in 2024, for this is the [[kleisma\|moskleisma]] of the [[Pythagorean tuning\|Pythagorean]] [[5L 2s\|diatonic scale]], where ''kleisma'' (adjective: ''kleismic'') refers to the inverse double-diminished 1-step i.e. \|2L - 3s\|. It is equated with the 5-limit kleisma of [[15625/15552]] along with many other intervals in [[meantone]]. It can also be reasoned as a fitting name as by tempering out this comma alongside the meantone comma ([[81/80]]), we get [[19edo]], which [[support]]s [[hanson and cata\|kleismic]].

	== See also ==		== See also ==
	* [[Large comma]]		* [[Large comma]]

FloraC: +link to tempering out and support

2024-10-15T12:08:12Z

+link to tempering out and support

← Older revision		Revision as of 12:08, 15 October 2024
Line 7:		Line 7:

	== Terminology ==		== Terminology ==
	The term ''Pythagorean kleisma'' seems to be first used by [[Flora Canou]] in 2024, for this is the [[kleisma\|moskleisma]] of the [[Pythagorean tuning\|Pythagorean]] [[5L 2s\|diatonic scale]], where ''kleisma'' (adjective: ''kleismic'') refers to the inverse double-diminished 1-step i.e. \|2L - 3s\|. It is equated with the 5-limit kleisma of [[15625/15552]] along with many other intervals in [[meantone]]. It can also be reasoned as a fitting name as by tempering ~~it and~~ the meantone comma, we get [[19edo]], which ~~supports~~ [[hanson and cata\|kleismic]].		The term ''Pythagorean kleisma'' seems to be first used by [[Flora Canou]] in 2024, for this is the [[kleisma\|moskleisma]] of the [[Pythagorean tuning\|Pythagorean]] [[5L 2s\|diatonic scale]], where ''kleisma'' (adjective: ''kleismic'') refers to the inverse double-diminished 1-step i.e. \|2L - 3s\|. It is equated with the 5-limit kleisma of [[15625/15552]] along with many other intervals in [[meantone]]. It can also be reasoned as a fitting name as by [[tempering out]] this comma alongside the [[meantone comma]], we get [[19edo]], which [[support]]s [[hanson and cata\|kleismic]].

	== See also ==		== See also ==
	* [[Large comma]]		* [[Large comma]]

Lériendil: not the disambig page

2024-10-14T23:48:21Z

not the disambig page

← Older revision		Revision as of 23:48, 14 October 2024
Line 7:		Line 7:

	== Terminology ==		== Terminology ==
	The term ''Pythagorean kleisma'' seems to be first used by [[Flora Canou]] in 2024, for this is the [[kleisma\|moskleisma]] of the [[Pythagorean tuning\|Pythagorean]] [[5L 2s\|diatonic scale]], where ''kleisma'' (adjective: ''kleismic'') refers to the inverse double-diminished 1-step i.e. \|2L - 3s\|. It is equated with the 5-limit kleisma of [[15625/15552]] along with many other intervals in [[meantone]]. It can also be reasoned as a fitting name as by tempering it and the meantone comma, we get [[19edo]], which supports [[kleismic]].		The term ''Pythagorean kleisma'' seems to be first used by [[Flora Canou]] in 2024, for this is the [[kleisma\|moskleisma]] of the [[Pythagorean tuning\|Pythagorean]] [[5L 2s\|diatonic scale]], where ''kleisma'' (adjective: ''kleismic'') refers to the inverse double-diminished 1-step i.e. \|2L - 3s\|. It is equated with the 5-limit kleisma of [[15625/15552]] along with many other intervals in [[meantone]]. It can also be reasoned as a fitting name as by tempering it and the meantone comma, we get [[19edo]], which supports [[hanson and cata\|kleismic]].

	== See also ==		== See also ==
	* [[Large comma]]		* [[Large comma]]

Godtone: support for the name

2024-10-14T22:29:12Z

support for the name

← Older revision		Revision as of 22:29, 14 October 2024
Line 7:		Line 7:

	== Terminology ==		== Terminology ==
	The term ''Pythagorean kleisma'' seems to be first used by [[Flora Canou]] in 2024, for this is the [[kleisma\|moskleisma]] of the [[Pythagorean tuning\|Pythagorean]] [[5L 2s\|diatonic scale]], where ''kleisma'' (adjective: ''kleismic'') refers to the inverse double-diminished 1-step i.e. \|2L - 3s\|. It is equated with the 5-limit kleisma of [[15625/15552]] along with many other intervals in [[meantone]].		The term ''Pythagorean kleisma'' seems to be first used by [[Flora Canou]] in 2024, for this is the [[kleisma\|moskleisma]] of the [[Pythagorean tuning\|Pythagorean]] [[5L 2s\|diatonic scale]], where ''kleisma'' (adjective: ''kleismic'') refers to the inverse double-diminished 1-step i.e. \|2L - 3s\|. It is equated with the 5-limit kleisma of [[15625/15552]] along with many other intervals in [[meantone]]. It can also be reasoned as a fitting name as by tempering it and the meantone comma, we get [[19edo]], which supports [[kleismic]].

	== See also ==		== See also ==
	* [[Large comma]]		* [[Large comma]]

Francium: +color name

2024-07-27T09:31:32Z

+color name

← Older revision		Revision as of 09:31, 27 July 2024
Line 2:		Line 2:
	\| Monzo = -30 19		\| Monzo = -30 19
	\| Name = 19-comma, Pythagorean kleisma, Pythagorean inverse double-diminished second		\| Name = 19-comma, Pythagorean kleisma, Pythagorean inverse double-diminished second
			\| Color name = L<sup>3</sup>w-2, trilawa negative 2nd
	}}		}}
	The '''19-comma''', otherwise known as the '''Pythagorean kleisma''' ({{monzo\|legend=1\| -30 19 }}, [[ratio]]: 1162261467/1073741824), is an interval of about 137.1{{cent}}. It is the amount by which nineteen [[3/2\|perfect fifth]]s exceed eleven octaves, or (3/2)<sup>19</sup>/2<sup>11</sup>. If used as an interval in its own right, it is the '''Pythagorean inverse double-diminished second'''.		The '''19-comma''', otherwise known as the '''Pythagorean kleisma''' ({{monzo\|legend=1\| -30 19 }}, [[ratio]]: 1162261467/1073741824), is an interval of about 137.1{{cent}}. It is the amount by which nineteen [[3/2\|perfect fifth]]s exceed eleven octaves, or (3/2)<sup>19</sup>/2<sup>11</sup>. If used as an interval in its own right, it is the '''Pythagorean inverse double-diminished second'''.

Lériendil at 19:36, 25 July 2024

2024-07-25T19:36:49Z

← Older revision		Revision as of 19:36, 25 July 2024
Line 6:		Line 6:

	== Terminology ==		== Terminology ==
	The term ''Pythagorean kleisma'' seems to be first used by [[Flora Canou]] in 2024, for this is the [[kleisma]] of the [[Pythagorean tuning\|Pythagorean]] [[5L 2s\|diatonic scale]], where ''kleisma'' (adjective: ''kleismic'') refers to the inverse double-diminished 1-step i.e. \|2L - 3s\|. It is equated with the 5-limit kleisma of [[15625/15552]] along with many other intervals in [[meantone]].		The term ''Pythagorean kleisma'' seems to be first used by [[Flora Canou]] in 2024, for this is the [[kleisma\|moskleisma]] of the [[Pythagorean tuning\|Pythagorean]] [[5L 2s\|diatonic scale]], where ''kleisma'' (adjective: ''kleismic'') refers to the inverse double-diminished 1-step i.e. \|2L - 3s\|. It is equated with the 5-limit kleisma of [[15625/15552]] along with many other intervals in [[meantone]].

	== See also ==		== See also ==
	* [[Large comma]]		* [[Large comma]]