Systematic comma names explained: Difference between revisions

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== Sagittal ==

=== 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.

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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 ==

@@ Line 44: / Line 44: @@
 == Sagittal ==
 === 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.
@@ 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).
-{{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 ==