Systematic comma names explained: Difference between revisions
→Color notation: minor clarifications |
m →Closing error: -abuse of bold |
||
| Line 22: | Line 22: | ||
== Closing error == | == Closing error == | ||
=== 31-comma, 21-23-comma, etc. === | === 31-comma, 21-23-comma, etc. === | ||
These types of comma names show the [[closing error]] of a specific [[interval]] in a specific [[ | These types of comma names show the [[closing error]] of a specific [[interval]] in a specific [[edo]]. | ||
For example, the | 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 ( | If the harmonic in question is the reduced third harmonic (3/2), then it is left out of the comma name. For example the 31-comma is the difference between a stack of 3/2's 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. | 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. === | === 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 | 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 rather than just ''n''-7. | ||
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/ | 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 5/3's but going down instead of up. (In an edo, intervals that go down still wrap back around every octave, so this is possible.) | ||
=== 87-fold starling comma, etc. === | === 87-fold starling comma, etc. === | ||
This is another type of closing error name. | This is another type of closing error name. It is 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 (126/125's). 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 (78125/73728's). | |||
== Sagittal == | == Sagittal == | ||