Systematic comma names explained

This page aims to document some of the methods of systematically naming commas, to help the reader make a bit more sense of some of the comma names out there.

This page does not cover common names for commas, it only covers names that were generated using some systematic process.

Pseudo-systematic names

Trienstonic, hendecatonic, etc.

Often, these are commas that generate a fractional-octave temperament, but this type of name is not actually systematic. Usually these types of commas are named after the temperament, and not the other way around. To learn about some of these temperament names, visit Temperament naming.

Trientone, hexadecatone, etc.

These are commas that are a fraction of a whole tone (~200 cents or ~9/8). For example, a trientone is about one third of a whole tone. A hexadecatone is about one sixteenth of a whole tone.

This method of naming is only semi-systematic, as there is still a level of subjectivity and vagueness involved, but it's still worth mentioning because it is used often.

Closing error

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 5/4s (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.

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".

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 5/3s but going down instead of up. (In an EDO, intervals that go down still wrap back around every octave, so this is possible.)

Todo: review double check this is correct

Sagittal

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

These types of comma names are derived from sagittal notation.

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.

Many comma pages with sagittal names were named using the spreadsheet File:CommaNamer.xls, which was made in 2004.

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

• 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)
• 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)
• 111.9 to 115.5 = apotome
• 115.5 to 118.2 = schisma-plus-apotome
• 118.2 to 125.4 = kleisma-plus-apotome
• 125.4 to 148.9 = comma-plus-apotome
• 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
• 225.6 to 229.2 = double-apotome
• Over 229.2 = 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).

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: expand 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

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

These are commas named according to Ben Johnston's notation.

Todo: expand 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.

Todo: expand please explain this type of comma name

Prima, secunda, etc.

Todo: expand please explain this type of comma name

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

Todo: expand please explain this type of comma name; are these all the same type of name, or multiple different categories? Are they systematic?

87-fold, as in 87-fold starling comma

Todo: expand please explain this type of comma name; is it systematic?