Systematic comma names explained: Difference between revisions

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

These types of comma names ~~are derived from~~ [[sagittal notation]].

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 "5-comma" is ~~actually~~ a sagittal name, ~~even though it looks like~~ the ~~same type~~ of ~~thing as "~~31-comma~~" which is~~ a closing-error type name. 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 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.

Many comma pages with sagittal names were named using the spreadsheet

[[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:

~~Rounded~~ to ~~1 decimal place~~, ~~this was how~~ the ~~spreadsheet named~~ interval size ~~ranges~~:

* 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'')

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

* 11.7 to 35.2 = comma (''or ~~dischisma~~, 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 = minor-diesis (''or minor-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'')

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

* 225.6 to 229.2 = double-apotome

* Over 229.2 = 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).

@@ Line 34: / Line 34: @@
 === 5-comma, 5/7-kleisma, 35/11-kleisma, etc. ===
-These types of comma names are derived from [[sagittal notation]].
+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 "5-comma" is actually a sagittal name, even though it looks like the same type of thing as "31-comma" which is a closing-error type name. 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 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.
 Many comma pages with sagittal names were named using the spreadsheet
 [[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:
-Rounded to 1 decimal place, this was how the spreadsheet named interval size ranges:
+* 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'')
 * 4.5 to 11.7 = kleisma (''or semicomma'')
-* 11.7 to 35.2 = comma (''or dischisma, 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 = minor-diesis (''or minor-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'')
@@ Line 63: / Line 62: @@
 * 215.6 to 225.6 = diatonic-semitone-plus-apotome
 * 225.6 to 229.2 = double-apotome
-* Over 229.2 = 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).