Systematic comma names explained - Revision history

FloraC: /* Johnston */ explain how this works

2024-12-21T08:27:36Z

Johnston: explain how this works

← Older revision		Revision as of 08:27, 21 December 2024
Line 75:		Line 75:

	== Johnston ==		== Johnston ==
	=== 19th partial chroma, 29th partial chroma, etc. ===		=== 19th-partial chroma, 29th-partial chroma, etc. ===
	These are commas named according to [[Ben Johnston's notation]].		These are commas named according to [[Ben Johnston's notation]]. In general, the ''p''-th-partial chroma is the formal comma that translates a basic interval to an interval of the corresponding harmonic, or "partial". For example, the 19th-partial chroma is the difference between 6/5 and 19/16, so that using it on a 6/5 minor third converts it to 19/16.

	{{todo\|inline=1\|complete section\|research\|comment=explain how, exactly, Ben Johnston's notation is used to name them (the Ben Johnston notation page doesn't explain it, nor do any of its internal or external links)}}		{{todo\|inline=1\|complete section\|research\|comment=explain how, exactly, Ben Johnston's notation is used to name them (the Ben Johnston notation page doesn't explain it, nor do any of its internal or external links)}}

FloraC: /* Closing error */ rework this section to more concisely explain the rules

2024-12-21T08:22:22Z

Closing error: rework this section to more concisely explain the rules

← Older revision		Revision as of 08:22, 21 December 2024
Line 21:		Line 21:

	== Closing error ==		== Closing error ==
	=== 31-comma, 21-23-comma, etc. ===		=== 31-comma, 21-23-comma, 11-3/5 comma, etc. ===
	These types of comma names show the [[closing error]] of a specific [[interval]] in a specific [[edo]].		These types of comma names show the [[closing error]] of a specific [[interval]] in a specific [[edo]]. In general, an ''n''-''m''-comma, where ''n'' is a positive integer and ''m'' is a frequency ratio, is the difference between a stack of ''n'' instances of ''m'' and a number of octaves. ''m'' can be an integer, which means it is a harmonic. If the harmonic in question is the third harmonic (3/1), then it is left out of the comma name.

	~~For example~~, ~~the ''31-~~5-comma~~'' is the difference between~~ a stack of 31 5/4's (~~5/4 is the~~ octave ~~reduces harmonic 5)~~, ~~and 10 octaves, which~~ is ~~tempered out in 31edo~~.		An interval with a bigger denominator than numerator, like 3/5, indicates a negative interval. 3/5 for example is about -884 cents. A comma can still temper a stack of these. Just imagine it like a stack of 5/3's but going down instead of up. (In an edo, intervals that go down still wrap back around every octave, so this is possible.)

	If the ~~harmonic in question~~ is the reduced ~~third~~ harmonic ~~(3/2~~), ~~then it~~ is ~~left~~ out ~~of the comma name~~. ~~For example~~ the 31-comma is the difference between a stack of 3/2's and a stack of octaves ~~in 31edo~~.		For example, the ''31-5-comma'' is the difference between a stack of thirty-one 5/4's (5/4 is the octave-reduced harmonic 5) and 10 octaves, which is tempered out in 31edo. Meanwhile, the 31-comma is the difference between a stack of thirty-one 3/2's and eighteen octaves. As another example, the 11-3/5-comma is the difference between a stack of eleven 3/5's and minus eight octaves.

	These kinds of names can sometimes be mistaken for sagittal names (discussed later on this page) and vice versa, so be wary of that.		These kinds of names can sometimes be mistaken for sagittal names (discussed later on this page) and vice versa, so be wary of that.

	~~=== 11-3/5 comma, 45-7/5 comma, etc. ===~~
	These are the same type of name as above, but they involve stacks of intervals that are not octave reduced harmonics. For example 7/4 is an octave reduced harmonic, so a comma tempering a stack of those would be an ''n''-7 comma, but 7/5 is ''not'' a reduced harmonic, so a comma tempering a stack of those would be an ''n''-7/5 comma rather than just ''n''-7.

	An interval with a bigger denominator than numerator, like 3/5, indicates a negative interval. 3/5 for example is about -884 cents. A comma can still temper a stack of these. Just imagine it like a stack of 5/3's but going down instead of up. (In an edo, intervals that go down still wrap back around every octave, so this is possible.)

	=== 87-fold starling comma, etc. ===		=== 87-fold starling comma, etc. ===

BudjarnLambeth: /* 5-comma, 5/7-kleisma, 35/11-kleisma, etc. */

2024-12-21T07:18:16Z

5-comma, 5/7-kleisma, 35/11-kleisma, etc.

← Older revision		Revision as of 07:18, 21 December 2024
Line 77:		Line 77:
	In this context, the term "chroma" implied an absolute 5-exponent of 1 within this system.{{clarify}} (But in wider xenharmonic usage, [[chroma]] is pretty vaguely defined and that does not necessarily apply).		In this context, the term "chroma" implied an absolute 5-exponent of 1 within this system.{{clarify}} (But in wider xenharmonic usage, [[chroma]] is pretty vaguely defined and that does not necessarily apply).

	{{todo\|inline=1\|~~expand~~\|research\|comment=explain how, exactly, the representative commas are chosen (the sagittal notation page doesn't explain it, and nor do any of its internal or external links)}}		{{todo\|inline=1\|clarify\|research\|comment=explain how, exactly, the representative commas are chosen (the sagittal notation page doesn't explain it, and nor do any of its internal or external links)}}

	== Johnston ==		== Johnston ==

BudjarnLambeth: Update todo

2024-12-21T07:17:56Z

Update todo

← Older revision		Revision as of 07:17, 21 December 2024
Line 83:		Line 83:
	These are commas named according to [[Ben Johnston's notation]].		These are commas named according to [[Ben Johnston's notation]].

	{{todo\|inline=1\|~~expand~~\|research\|comment=explain how, exactly, Ben Johnston's notation is used to name them (the Ben Johnston notation page doesn't explain it, nor do any of its internal or external links)}}		{{todo\|inline=1\|complete section\|research\|comment=explain how, exactly, Ben Johnston's notation is used to name them (the Ben Johnston notation page doesn't explain it, nor do any of its internal or external links)}}

	== 35-cycle, 21-cycle, etc. ==		== 35-cycle, 21-cycle, etc. ==

	{{todo\|inline=1\|~~expand~~\|research\|comment=please explain this type of comma name}}		{{todo\|inline=1\|complete section\|research\|comment=please explain this type of comma name}}

	== Prima, secunda, etc. ==		== Prima, secunda, etc. ==

	{{todo\|inline=1\|~~expand~~\|research\|comment=please explain this type of comma name}}		{{todo\|inline=1\|complete section\|research\|comment=please explain this type of comma name}}

	== 34-jubilismic, 23 semitone, 19-minor mediant, etc. ==		== 34-jubilismic, 23 semitone, 19-minor mediant, etc. ==

	{{todo\|inline=1\|~~expand~~\|research\|comment=please explain this type of comma name; are these all the same type of name, or multiple different categories? Are they systematic?}}		{{todo\|inline=1\|complete section\|research\|comment=please explain this type of comma name; are these all the same type of name, or multiple different categories? Are they systematic?}}

	== See also ==		== See also ==
Line 103:		Line 103:
	* [[Glossary]]		* [[Glossary]]
	* [[Acronyms]]		* [[Acronyms]]

	[[Category:Comma]][[Category:Terms]][[Category:Interval naming]]		[[Category:Comma]][[Category:Terms]][[Category:Interval naming]]

BudjarnLambeth: /* See also */ add link to orphaned page

2024-12-02T00:23:16Z

BudjarnLambeth at 01:47, 10 November 2024

2024-11-10T01:47:04Z

← Older revision		Revision as of 01:47, 10 November 2024
Line 102:		Line 102:
	* [[Glossary]]		* [[Glossary]]
	* [[Acronyms]]		* [[Acronyms]]
	[[Category:Comma]][[Category:Terms]]		[[Category:Comma]][[Category:Terms]][[Category:Interval naming]]

BudjarnLambeth: /* See also */ add links to glossary and acronyns

2024-11-05T17:24:58Z

See also: add links to glossary and acronyns

← Older revision		Revision as of 17:24, 5 November 2024
Line 100:		Line 100:
	* [[Temperament naming]]		* [[Temperament naming]]
	* [[:Category:Commas by name]]		* [[:Category:Commas by name]]
			* [[Glossary]]
			* [[Acronyms]]
	[[Category:Comma]][[Category:Terms]]		[[Category:Comma]][[Category:Terms]]

BudjarnLambeth: Add see also

2024-11-03T07:45:45Z

Add see also

← Older revision		Revision as of 07:45, 3 November 2024
Line 96:		Line 96:

	{{todo\|inline=1\|expand\|research\|comment=please explain this type of comma name; are these all the same type of name, or multiple different categories? Are they systematic?}}		{{todo\|inline=1\|expand\|research\|comment=please explain this type of comma name; are these all the same type of name, or multiple different categories? Are they systematic?}}

			== See also ==
			* [[Temperament naming]]
			* [[:Category:Commas by name]]
	[[Category:Comma]][[Category:Terms]]		[[Category:Comma]][[Category:Terms]]

Recentlymaterialized: /* Sagittal */ oops

2024-11-01T00:11:18Z

Sagittal: oops

← Older revision		Revision as of 00:11, 1 November 2024
Line 44:		Line 44:
	== Sagittal ==		== Sagittal ==
	=== 5-comma, 5/7-kleisma, 35/11-kleisma, etc. ===		=== 5-comma, 5/7-kleisma, 35/11-kleisma, etc. ===
	These types of comma names were developed for [[sagittal notation]]. After removing all factors of 2 and 3 from the comma, the [[2.3-equivalent_class_and_Pythagorean-commatic_interval_naming_system\|resulting ratio]] may be broken into smaller factors if it is too complex{{clarify}} and is used as the first part of the comma's name. This ratio is followed by the comma's size category, distinguishing 10 categories below the [[apotome]]. For example, the septimal kleisma [[225/224]] is named '''25/7 kleisma''' (7/25k), and the syntonic comma [[81/80]] is named '''1/5 comma''' (1/5C) or "5-comma" in some sources. Because complementation by the [[pythagorean comma]] (and adjustments by [[mercator's comma]]) risks placing commas and their inversions differing by factors of 2 and 3 in the same size category, this categorization scheme is most rigorously defined only on the simplest representation of the comma in its size category.{{clarify}}		These types of comma names were developed for [[sagittal notation]]. After removing all factors of 2 and 3 from the comma, the [[2.3-equivalent_class_and_Pythagorean-commatic_interval_naming_system\|resulting ratio]] may be broken into smaller factors if it is too complex{{clarify}} and is used as the first part of the comma's name. This ratio is followed by the comma's size category, distinguishing 10 categories below the [[apotome]]. For example, the septimal kleisma [[225/224]] is named '''25/7 kleisma''' (25/7k or 7/25k), and the syntonic comma [[81/80]] is named '''1/5 comma''' (1/5C) or "5-comma" in some sources. Because complementation by the [[pythagorean comma]] (and adjustments by [[mercator's comma]]) risks placing commas and their inversions differing by factors of 2 and 3 in the same size category, this categorization scheme is most rigorously defined only on the simplest representation of the comma in its size category.{{clarify}}

	These sagittal names can be confused on occasion with the closing-error type of name described earlier. For example, [[81/80\|5-comma]] (81/80) is a sagittal name, but the most common meaning of [[31-comma]] uses a closing-error type name (even though "31-comma" is a valid sagittal name for a different interval). These clashes are unfortunate, but not fatal, as a look at the comma's page should reveal which system makes the most sense for interpreting its name.		These sagittal names can be confused on occasion with the closing-error type of name described earlier. For example, [[81/80\|5-comma]] (81/80) is a sagittal name, but the most common meaning of [[31-comma]] uses a closing-error type name (even though "31-comma" is a valid sagittal name for a different interval). These clashes are unfortunate, but not fatal, as a look at the comma's page should reveal which system makes the most sense for interpreting its name.
Line 77:		Line 77:
	In this context, the term "chroma" implied an absolute 5-exponent of 1 within this system.{{clarify}} (But in wider xenharmonic usage, [[chroma]] is pretty vaguely defined and that does not necessarily apply).		In this context, the term "chroma" implied an absolute 5-exponent of 1 within this system.{{clarify}} (But in wider xenharmonic usage, [[chroma]] is pretty vaguely defined and that does not necessarily apply).

	{{todo\|inline=1\|expand\|research\|comment=explain how, exactly, the representative commas are chosen (the sagittal notation page doesn't ~~seem to~~ explain it, and nor do any of its internal or external links)}}		{{todo\|inline=1\|expand\|research\|comment=explain how, exactly, the representative commas are chosen (the sagittal notation page doesn't explain it, and nor do any of its internal or external links)}}

	== Johnston ==		== Johnston ==

Recentlymaterialized: /* 5-comma, 5/7-kleisma, 35/11-kleisma, etc. */

2024-11-01T00:09:20Z

5-comma, 5/7-kleisma, 35/11-kleisma, etc.

← Older revision		Revision as of 00:09, 1 November 2024
Line 44:		Line 44:
	== Sagittal ==		== Sagittal ==
	=== 5-comma, 5/7-kleisma, 35/11-kleisma, etc. ===		=== 5-comma, 5/7-kleisma, 35/11-kleisma, etc. ===
	These types of comma names were developed for [[sagittal notation]]. After removing all factors of 2 and 3 from the comma, the resulting ratio may be broken into smaller factors if it is too complex{{clarify}} and is used as the first part of the comma's name. This ratio is followed by the comma's size category, distinguishing 10 categories below the [[apotome]]. For example, the septimal kleisma [[225/224]] is named '''7~~/25~~ kleisma''' (7/25k), and the syntonic comma [[81/80]] is named '''1/5 comma''' (1/5C) or "5-comma" in some ~~early~~ sources. Because the ~~small size of~~ [[~~Mercator~~'s comma]] risks placing ~~two~~ commas ~~related~~ by ~~53 or more 3s~~ in the same size category, this categorization scheme is most rigorously defined only on the simplest representation of the ~~interval~~ in its size category.{{clarify}}		These types of comma names were developed for [[sagittal notation]]. After removing all factors of 2 and 3 from the comma, the [[2.3-equivalent_class_and_Pythagorean-commatic_interval_naming_system\|resulting ratio]] may be broken into smaller factors if it is too complex{{clarify}} and is used as the first part of the comma's name. This ratio is followed by the comma's size category, distinguishing 10 categories below the [[apotome]]. For example, the septimal kleisma [[225/224]] is named '''25/7 kleisma''' (7/25k), and the syntonic comma [[81/80]] is named '''1/5 comma''' (1/5C) or "5-comma" in some sources. Because complementation by the [[pythagorean comma]] (and adjustments by [[mercator's comma]]) risks placing commas and their inversions differing by factors of 2 and 3 in the same size category, this categorization scheme is most rigorously defined only on the simplest representation of the comma in its size category.{{clarify}}

	These sagittal names can ~~occasionally get mixed up~~ with the closing-error type of name described earlier. For example, [[81/80\|5-comma]] (81/80) is a sagittal name, but the most common meaning of [[31-comma]] uses a closing-error type name (even though "31-comma" is a valid sagittal name for a different interval). These clashes are unfortunate, but not fatal, as a look at the comma's page should reveal which system makes the most sense for interpreting its name.		These sagittal names can be confused on occasion with the closing-error type of name described earlier. For example, [[81/80\|5-comma]] (81/80) is a sagittal name, but the most common meaning of [[31-comma]] uses a closing-error type name (even though "31-comma" is a valid sagittal name for a different interval). These clashes are unfortunate, but not fatal, as a look at the comma's page should reveal which system makes the most sense for interpreting its name.

	Many comma pages with sagittal names were named using the spreadsheet		Many comma pages with sagittal names were named using the spreadsheet
	[[File:CommaNamer.xls]], which was made in 2004.		[[File:CommaNamer.xls]], which was made in 2004.
	~~According to the~~ spreadsheet, these are the ~~interval~~ size ~~boundaries in cents~~ up to one decimal place:		From this spreadsheet, these are the cent values of the size categories up to one decimal place:
	* Less than 1.8 cents = schismina (''or atom'')		* Less than 1.8 cents = schismina (or ''atom'')
	* 1.8 to 4.5 = schisma (''or skisma, skhisma'')		* 1.8 to 4.5 = schisma (or ''skisma, skhisma'')
	* 4.5 to 11.7 = kleisma (''or semicomma'')		* 4.5 to 11.7 = kleisma (or ''semicomma'')
	* 11.7 to 35.2 = comma (''or diaschisma, diaskhisma, chroma'')		* 11.7 to 35.2 = comma (or ''diaschisma, diaskhisma, chroma'')
	* 35.2 to 45.1 = ~~minor-~~diesis (''~~or small-~~diesis, 1/5-tone, chroma'')		* 35.2 to 45.1 = small diesis (or ''minor diesis, 1/5-tone, chroma'')
	* 45.1 to 56.8 = diesis (''~~or medium-~~diesis, 1/4-tone, chroma, enharmonic-diesis, enharmonic'')		* 45.1 to 56.8 = medium diesis (or ''diesis, 1/4-tone, chroma, enharmonic-diesis, enharmonic'')
	* 56.8 to 68.6 = ~~major-~~diesis (''~~or large-~~diesis, 1/3-tone'')		* 56.8 to 68.6 = large diesis (or ''major diesis, 1/3-tone'')
	* 68.6 to 78.5 = ~~chromatic-~~semitone (''~~or small-~~semitone'')		* 68.6 to 78.5 = small semitone (or ''chromatic semitone'')
	* 78.5 to 102.0 = ~~limma~~ (''~~or medium-semitone~~'')		* 78.5 to 102.0 = medium semitone (or ''limma'')
	* 102.0 to 111.9 = ~~diatonic-~~semitone (''~~or large-~~semitone'')		* 102.0 to 111.9 = large semitone (or ''diatonic semitone'')
	* 111.9 to 115.5 = apotome		* 111.9 to 115.5 = apotome
			For intervals larger than the apotome, "plus-apotome" names are provided, although they are far less popular:
	* 115.5 to 118.2 = schisma-plus-apotome		* 115.5 to 118.2 = schisma-plus-apotome
	* 118.2 to 125.4 = kleisma-plus-apotome		* 118.2 to 125.4 = kleisma-plus-apotome
	* 125.4 to 148.9 = comma-plus-apotome		* 125.4 to 148.9 = comma-plus-apotome
	* 148.9 to 158.8 = ~~minor~~-diesis-plus-apotome (''or neutral second'')		* 148.9 to 158.8 = small-diesis-plus-apotome (or ''neutral second'')
	* 158.8 to 170.5 = diesis-plus-apotome		* 158.8 to 170.5 = medium-diesis-plus-apotome
	* 170.5 to 182.3 = ~~major~~-diesis-plus-apotome		* 170.5 to 182.3 = large-diesis-plus-apotome
	* 182.3 to 192.2 = ~~chromatic~~-semitone-plus-apotome		* 182.3 to 192.2 = small-semitone-plus-apotome
	* 192.2 to 215.6 = ~~limma~~-plus-apotome		* 192.2 to 215.6 = medium-semitone-plus-apotome
	* 215.6 to 225.6 = ~~diatonic~~-semitone-plus-apotome		* 215.6 to 225.6 = large-semitone-plus-apotome
	* 225.6 to 229.2 = double-apotome		* 225.6 to 229.2 = double-apotome
	Intervals larger than 229.2{{cent}} are outside the scope of this system.		Intervals larger than 229.2{{cent}} are outside the scope of this system.

	In this context, the term "chroma" implied an absolute 5-exponent of 1 within this system. (But in wider xenharmonic usage, [[chroma]] is pretty vaguely defined and that does not necessarily apply).		In this context, the term "chroma" implied an absolute 5-exponent of 1 within this system.{{clarify}} (But in wider xenharmonic usage, [[chroma]] is pretty vaguely defined and that does not necessarily apply).

	~~The spreadsheet advised not to use the "plus-apotome" names unless the interval is being considered first and foremost as a comma and not a scale degree.~~		{{todo\|inline=1\|expand\|research\|comment=explain how, exactly, the representative commas are chosen (the sagittal notation page doesn't seem to explain it, and nor do any of its internal or external links)}}

	{{todo\|inline=1\|expand\|research\|comment=explain how, exactly, ~~sagittal notation is used to name them~~ (the sagittal notation page doesn't explain it, nor do any of its internal or external links)}}

	== Johnston ==		== Johnston ==

← Older revision		Revision as of 00:23, 2 December 2024
Line 98:		Line 98:

	== See also ==		== See also ==
			* [[Comma-prefix names]]
	* [[Temperament naming]]		* [[Temperament naming]]
	* [[:Category:Commas by name]]		* [[:Category:Commas by name]]