Comma and diesis - Revision history

Overthink: bold

2026-05-24T18:14:21Z

bold

← Older revision		Revision as of 18:14, 24 May 2026
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	\| Higher region=[[Semitone (interval region)\|Semitone]]		\| Higher region=[[Semitone (interval region)\|Semitone]]
	}}		}}
	"Comma" and "diesis" are two terms used to refer to intervals that are less than about 60{{cent}} in size. In terms of [[interval region]]s, "comma" refers to an interval flatter than about 30{{cent}}, and "diesis" refers to an interval between about 30 and 60{{cent}}. In [[Sagittal notation]], a comma is specifically defined as between half of the [[Pythagorean comma]] {{monzo\| -19 12}} and half of the Pythagorean 17-fifths diesis {{monzo\| 27 -17}}, about 11.7{{c}} to 33.4{{c}}, and a diesis is defined as between the comma upper bound and half of the Pythagorean 19-fifths apotome-plus-comma {{monzo\| -30 19}}, about 68.6{{c}}.		'''Comma''' and '''diesis''' are two terms used to refer to intervals that are less than about 60{{cent}} in size. In terms of [[interval region]]s, "comma" refers to an interval flatter than about 30{{cent}}, and "diesis" refers to an interval between about 30 and 60{{cent}}. In [[Sagittal notation]], a comma is specifically defined as between half of the [[Pythagorean comma]] {{monzo\| -19 12}} and half of the Pythagorean 17-fifths diesis {{monzo\| 27 -17}}, about 11.7{{c}} to 33.4{{c}}, and a diesis is defined as between the comma upper bound and half of the Pythagorean 19-fifths apotome-plus-comma {{monzo\| -30 19}}, about 68.6{{c}}.

	"[[Comma]]" also refers to an interval that is tempered out by any given [[temperament]].		"[[Comma]]" also refers to an interval that is tempered out by any given [[temperament]].

Overthink: - extra newline

2026-05-24T18:12:08Z

- extra newline

← Older revision		Revision as of 18:12, 24 May 2026
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	\| Higher region=[[Semitone (interval region)\|Semitone]]		\| Higher region=[[Semitone (interval region)\|Semitone]]
	}}		}}

	"Comma" and "diesis" are two terms used to refer to intervals that are less than about 60{{cent}} in size. In terms of [[interval region]]s, "comma" refers to an interval flatter than about 30{{cent}}, and "diesis" refers to an interval between about 30 and 60{{cent}}. In [[Sagittal notation]], a comma is specifically defined as between half of the [[Pythagorean comma]] {{monzo\| -19 12}} and half of the Pythagorean 17-fifths diesis {{monzo\| 27 -17}}, about 11.7{{c}} to 33.4{{c}}, and a diesis is defined as between the comma upper bound and half of the Pythagorean 19-fifths apotome-plus-comma {{monzo\| -30 19}}, about 68.6{{c}}.		"Comma" and "diesis" are two terms used to refer to intervals that are less than about 60{{cent}} in size. In terms of [[interval region]]s, "comma" refers to an interval flatter than about 30{{cent}}, and "diesis" refers to an interval between about 30 and 60{{cent}}. In [[Sagittal notation]], a comma is specifically defined as between half of the [[Pythagorean comma]] {{monzo\| -19 12}} and half of the Pythagorean 17-fifths diesis {{monzo\| 27 -17}}, about 11.7{{c}} to 33.4{{c}}, and a diesis is defined as between the comma upper bound and half of the Pythagorean 19-fifths apotome-plus-comma {{monzo\| -30 19}}, about 68.6{{c}}.

TallKite at 02:51, 20 May 2026

2026-05-20T02:51:27Z

← Older revision		Revision as of 02:51, 20 May 2026
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	\| Cents upper=40		\| Cents upper=40
	\| Cents upper wide=60		\| Cents upper wide=60
	\| JI intervals=128/125~~, 81/80~~		\| JI intervals=81/80, 128/125
	\| Complement=(Imperfect) [[octave]]		\| Complement=(Imperfect) [[octave]]
	\| Lower region=[[Unison]]		\| Lower region=[[Unison]]
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	As comma and diesis is the smallest interval class, it may be represented by:		As comma and diesis is the smallest interval class, it may be represented by:

	* Any superparticular interval smaller than 29/28		* Any delta-1 (i.e. superparticular) interval smaller than 29/28
	* Any delta-2 interval smaller than 57/55		* Any delta-2 interval smaller than 57/55
	* Any delta-3 interval smaller than 88/85		* Any delta-3 interval smaller than 88/85

Dave Keenan at 00:40, 25 April 2026

2026-04-25T00:40:57Z

← Older revision		Revision as of 00:40, 25 April 2026
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	}}		}}

	"Comma" and "diesis" are two terms used to refer to intervals that are less than about 60{{cent}} in size. In terms of [[interval region]]s, "comma" refers to an interval flatter than about 30{{cent}}, and "diesis" refers to an interval between about 30 and 60{{cent}}. In Sagittal notation, a comma is specifically defined as between half of the Pythagorean comma [-19 ~~12⟩~~ and half of the ~~pythagorean~~ 17-fifths diesis [27 -~~17⟩~~, about 11.7{{c}} to 33.4{{c}}, and a diesis is defined as between the comma upper bound and half of the ~~pythagorean~~ 19-fifths apotome-plus-comma [-30 ~~19⟩~~, about 68.6{{c}}.		"Comma" and "diesis" are two terms used to refer to intervals that are less than about 60{{cent}} in size. In terms of [[interval region]]s, "comma" refers to an interval flatter than about 30{{cent}}, and "diesis" refers to an interval between about 30 and 60{{cent}}. In [[Sagittal notation]], a comma is specifically defined as between half of the [[Pythagorean comma]] {{monzo\| -19 12}} and half of the Pythagorean 17-fifths diesis {{monzo\| 27 -17}}, about 11.7{{c}} to 33.4{{c}}, and a diesis is defined as between the comma upper bound and half of the Pythagorean 19-fifths apotome-plus-comma {{monzo\| -30 19}}, about 68.6{{c}}.

	"[[Comma]]" also refers to an interval that is tempered out by any given [[temperament]].		"[[Comma]]" also refers to an interval that is tempered out by any given [[temperament]].

Dave Keenan: Added Sagittal's specific bounds, for consistency with the Kleisma (interval region) article.

2026-04-25T00:26:33Z

Added Sagittal's specific bounds, for consistency with the Kleisma (interval region) article.

← Older revision		Revision as of 00:26, 25 April 2026
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	}}		}}

	"Comma" and "diesis" are two terms used to refer to intervals that are less than about 60{{cent}} in size. In terms of [[interval region]]s, "comma" refers to an interval flatter than about 30{{cent}}, and "diesis" refers to an interval between about 30 and 60{{cent}}.		"Comma" and "diesis" are two terms used to refer to intervals that are less than about 60{{cent}} in size. In terms of [[interval region]]s, "comma" refers to an interval flatter than about 30{{cent}}, and "diesis" refers to an interval between about 30 and 60{{cent}}. In Sagittal notation, a comma is specifically defined as between half of the Pythagorean comma [-19 12⟩ and half of the pythagorean 17-fifths diesis [27 -17⟩, about 11.7{{c}} to 33.4{{c}}, and a diesis is defined as between the comma upper bound and half of the pythagorean 19-fifths apotome-plus-comma [-30 19⟩, about 68.6{{c}}.

	"[[Comma]]" also refers to an interval that is tempered out by any given [[temperament]].		"[[Comma]]" also refers to an interval that is tempered out by any given [[temperament]].

MisterShafXen at 12:48, 22 November 2025

2025-11-22T12:48:06Z

← Older revision		Revision as of 12:48, 22 November 2025
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	\| 24		\| 24
	\| 50{{c}}		\| 50{{c}}
	\|		\| 50¢ ≈ 33/32
	\|-		\|-
	\| 25		\| 25

VectorGraphics at 01:30, 15 May 2025

2025-05-15T01:30:46Z

← Older revision		Revision as of 01:30, 15 May 2025
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	The range of dieses largely overlaps with the range of [[quartertone]]s (between 40 and 60{{c}}, reasonably mapped to 1/24edo), which, according to systems that determine consonance in terms of proximity to simple just ratios, is one of the most dissonant interval regions. This also corresponds to an [[interseptimal]] interval range. However, quarter tones are still covered here to provide a resource for them in the same format as the other interval region pages.		The range of dieses largely overlaps with the range of [[quartertone]]s (between 40 and 60{{c}}, reasonably mapped to 1/24edo), which, according to systems that determine consonance in terms of proximity to simple just ratios, is one of the most dissonant interval regions. This also corresponds to an [[interseptimal]] interval range. However, quarter tones are still covered here to provide a resource for them in the same format as the other interval region pages.

	In the diatonic scale, the analogous concepts are '''subchromatic''' and '''enharmonic''' steps. A subchromatic step does not change the interval category (for example, in most just notation systems, if you flatten the major third [[81/64]] by an [[81/80]] comma to produce [[5/4]], the latter is still considered a major third). Diatonically, subchromatic steps are '''perfect unisons (P1)''', and there are none that are not a unison in a rank-2 diatonic tuning. An enharmonic step changes the interval category to an enharmonic interval (for example, a major third to a diminished fourth, or a chromatic semitone to a diatonic semitone). Similarly, enharmonic steps are ascending or descending '''diminished seconds (d2)'''.		In the diatonic scale, the analogous concepts are '''subchromatic''' and '''enharmonic''' steps. A subchromatic step (a "comma") does not change the interval category (for example, in most just notation systems, if you flatten the major third [[81/64]] by an [[81/80]] comma to produce [[5/4]], the latter is still considered a major third). Diatonically, subchromatic steps are '''perfect unisons (P1)''', and there are none that are not a unison in a rank-2 diatonic tuning. An enharmonic step (a "diesis", although this is controversial) changes the interval category to an enharmonic interval (for example, a major third to a diminished fourth, or a chromatic semitone to a diatonic semitone). Similarly, enharmonic steps are ascending or descending '''diminished seconds (d2)'''.

	== In just intonation ==		== In just intonation ==

VectorGraphics at 01:30, 15 May 2025

2025-05-15T01:30:14Z

← Older revision		Revision as of 01:30, 15 May 2025
Line 16:		Line 16:

	The range of dieses largely overlaps with the range of [[quartertone]]s (between 40 and 60{{c}}, reasonably mapped to 1/24edo), which, according to systems that determine consonance in terms of proximity to simple just ratios, is one of the most dissonant interval regions. This also corresponds to an [[interseptimal]] interval range. However, quarter tones are still covered here to provide a resource for them in the same format as the other interval region pages.		The range of dieses largely overlaps with the range of [[quartertone]]s (between 40 and 60{{c}}, reasonably mapped to 1/24edo), which, according to systems that determine consonance in terms of proximity to simple just ratios, is one of the most dissonant interval regions. This also corresponds to an [[interseptimal]] interval range. However, quarter tones are still covered here to provide a resource for them in the same format as the other interval region pages.

			In the diatonic scale, the analogous concepts are '''subchromatic''' and '''enharmonic''' steps. A subchromatic step does not change the interval category (for example, in most just notation systems, if you flatten the major third [[81/64]] by an [[81/80]] comma to produce [[5/4]], the latter is still considered a major third). Diatonically, subchromatic steps are '''perfect unisons (P1)''', and there are none that are not a unison in a rank-2 diatonic tuning. An enharmonic step changes the interval category to an enharmonic interval (for example, a major third to a diminished fourth, or a chromatic semitone to a diatonic semitone). Similarly, enharmonic steps are ascending or descending '''diminished seconds (d2)'''.

	== In just intonation ==		== In just intonation ==

ArrowHead294 at 10:40, 14 March 2025

2025-03-14T10:40:46Z

← Older revision		Revision as of 10:40, 14 March 2025
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	: ''This article is about "comma" and "diesis" as interval regions. For other senses of these two words, see [[comma]] and [[diesis]].''		: ''This article is about "comma" and "diesis" as interval regions. For other senses of these two words, see [[comma]] and [[diesis]].''
	{{Infobox interval region\|Name=Comma, diesis\|Cents lower=0\|Cents upper=40\|Cents upper wide=60\|JI intervals=128/125, 81/80\|Complement=(Imperfect) [[octave]]\|Lower region=[[Unison]]\|Higher region=[[Semitone (interval region)\|Semitone]]}}		{{Infobox interval region
			\| Name=Comma, diesis
			\| Cents lower=0
			\| Cents upper=40
			\| Cents upper wide=60
			\| JI intervals=128/125, 81/80
			\| Complement=(Imperfect) [[octave]]
			\| Lower region=[[Unison]]
			\| Higher region=[[Semitone (interval region)\|Semitone]]
			}}

	"Comma" and "diesis" are two terms used to refer to intervals that are less than about 60{{cent}} in size. In terms of [[interval region]]s, "comma" refers to an interval flatter than about 30{{c}}, and "diesis" refers to an interval between about 30 and 60{{c}}.		"Comma" and "diesis" are two terms used to refer to intervals that are less than about 60{{cent}} in size. In terms of [[interval region]]s, "comma" refers to an interval flatter than about 30{{cent}}, and "diesis" refers to an interval between about 30 and 60{{cent}}.

	"[[Comma]]" also refers to an interval that is tempered out by any given [[temperament]].		"[[Comma]]" also refers to an interval that is tempered out by any given [[temperament]].

VectorGraphics at 10:25, 14 March 2025

2025-03-14T10:25:13Z

← Older revision		Revision as of 10:25, 14 March 2025
Line 1:		Line 1:
	: ''This article is about "comma" and "diesis" as interval regions. For other senses of these two words, see [[comma]] and [[diesis]].''		: ''This article is about "comma" and "diesis" as interval regions. For other senses of these two words, see [[comma]] and [[diesis]].''
	{{Infobox interval region\|Name=Comma ~~and~~ diesis\|Cents lower=0\|Cents upper=40\|Cents upper wide=60\|JI intervals=128/125, 81/80\|Complement=(Imperfect) [[octave]]\|Lower region=[[Unison]]\|Higher region=[[Semitone (interval region)\|Semitone]]}}		{{Infobox interval region\|Name=Comma, diesis\|Cents lower=0\|Cents upper=40\|Cents upper wide=60\|JI intervals=128/125, 81/80\|Complement=(Imperfect) [[octave]]\|Lower region=[[Unison]]\|Higher region=[[Semitone (interval region)\|Semitone]]}}

	"Comma" and "diesis" are two terms used to refer to intervals that are less than about 60{{cent}} in size. In terms of [[interval region]]s, "comma" refers to an interval flatter than about 30{{c}}, and "diesis" refers to an interval between about 30 and 60{{c}}.		"Comma" and "diesis" are two terms used to refer to intervals that are less than about 60{{cent}} in size. In terms of [[interval region]]s, "comma" refers to an interval flatter than about 30{{c}}, and "diesis" refers to an interval between about 30 and 60{{c}}.