Systematic comma names explained: Difference between revisions

=== 31-comma, 21-23-comma, etc. ===

These types of comma names show the [[closing error]] of a specific [[interval]] in a specific [[EDO]].

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'''.

If the harmonic in question is the reduced third harmonic ('''3/2'''), then it is left out of the comma name. For example '''31-comma''' is the difference between a stack of 3/2s and a stack of octaves in 31edo.

This is another type of closing error name. It’s for more complex commas that are created by other commas. It is easiest to understand with a couple examples:

'''87-fold starling comma''' means the difference between a '''stack of octaves''', and a '''stack of 87 starling commas''' (126/125s). This results in an 87th-octave temperament.

'''12-fold wesley comma''' means the difference between a '''stack of octaves''' (in this case 1 octave), and a '''stack of 12 wesley commas''' (78125/73728s).

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 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.

According to the spreadsheet, these are the interval size boundaries in cents up to one decimal place:

* Less than 1.8 cents = schismina (''or atom'')

* 1.8 to 4.5 = schisma (''or skisma, skhisma'')

* 4.5 to 11.7 = kleisma (''or semicomma'')

* 11.7 to 35.2 = comma (''or diaschisma, diaskhisma, chroma'')

* 35.2 to 45.1 = minor-diesis (''or small-diesis, 1/5-tone, chroma'')

* 45.1 to 56.8 = diesis (''or medium-diesis, 1/4-tone, chroma, enharmonic-diesis, enharmonic'')

* 56.8 to 68.6 = major-diesis (''or large-diesis, 1/3-tone'')

* 68.6 to 78.5 = chromatic-semitone (''or small-semitone'')

* 78.5 to 102.0 = limma (''or medium-semitone'')

* 102.0 to 111.9 = diatonic-semitone (''or large-semitone'')

* 148.9 to 158.8 = minor-diesis-plus-apotome (''or neutral second'')

* 158.8 to 170.5 = diesis-plus-apotome

* 170.5 to 182.3 = major-diesis-plus-apotome

* 182.3 to 192.2 = chromatic-semitone-plus-apotome

* 192.2 to 215.6 = limma-plus-apotome

* 215.6 to 225.6 = diatonic-semitone-plus-apotome

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).

 

{{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)}}

=== 19th partial chroma, 29th partial chroma, etc. ===

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|expand|research|comment=please explain this type of comma name}}

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

{{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?}}

[[Category:Comma]][[Category:Terms]]