Systematic comma names explained: Difference between revisions
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== 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 | 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 | 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. | ||
From this spreadsheet, these are the cent values of the size categories up to one decimal place: | |||
* Less than 1.8 cents = schismina ('' | * Less than 1.8 cents = schismina (or ''atom'') | ||
* 1.8 to 4.5 = schisma ('' | * 1.8 to 4.5 = schisma (or ''skisma, skhisma'') | ||
* 4.5 to 11.7 = kleisma ('' | * 4.5 to 11.7 = kleisma (or ''semicomma'') | ||
* 11.7 to 35.2 = comma ('' | * 11.7 to 35.2 = comma (or ''diaschisma, diaskhisma, chroma'') | ||
* 35.2 to 45.1 = | * 35.2 to 45.1 = small diesis (or ''minor diesis, 1/5-tone, chroma'') | ||
* 45.1 to 56.8 = diesis ('' | * 45.1 to 56.8 = medium diesis (or ''diesis, 1/4-tone, chroma, enharmonic-diesis, enharmonic'') | ||
* 56.8 to 68.6 = | * 56.8 to 68.6 = large diesis (or ''major diesis, 1/3-tone'') | ||
* 68.6 to 78.5 = | * 68.6 to 78.5 = small semitone (or ''chromatic semitone'') | ||
* 78.5 to 102.0 = | * 78.5 to 102.0 = medium semitone (or ''limma'') | ||
* 102.0 to 111.9 = | * 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 = | * 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 = | * 170.5 to 182.3 = large-diesis-plus-apotome | ||
* 182.3 to 192.2 = | * 182.3 to 192.2 = small-semitone-plus-apotome | ||
* 192.2 to 215.6 = | * 192.2 to 215.6 = medium-semitone-plus-apotome | ||
* 215.6 to 225.6 = | * 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). | ||
{{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, | |||
== Johnston == | == Johnston == | ||