Comma and diesis: Difference between revisions

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| Cents upper=40

| Cents upper wide=60

| JI intervals=128/125~~, 81/80~~

| JI intervals=81/80, 128/125

| Complement=(Imperfect) [[octave]]

| Lower region=[[Unison]]

| Higher region=[[Semitone (interval region)|Semitone]]

}}

'''Comma''' and '''diesis''' are two terms used to refer to intervals that are less than about 60{{cent}} in size. In terms of [[interval region]]s, "comma" refers to an interval flatter than about 30{{cent}}, and "diesis" refers to an interval between about 30 and 60{{cent}}. In [[Sagittal notation]], a comma is specifically defined as between half of the [[Pythagorean comma]] {{monzo| -19 12}} and half of the Pythagorean 17-fifths diesis {{monzo| 27 -17}}, about 11.7{{c}} to 33.4{{c}}, and a diesis is defined as between the comma upper bound and half of the Pythagorean 19-fifths apotome-plus-comma {{monzo| -30 19}}, about 68.6{{c}}.

"Comma" and "diesis" are two terms used to refer to intervals that are less than about 60{{cent}} in size. In terms of [[interval region]]s, "comma" refers to an interval flatter than about 30{{cent}}, and "diesis" refers to an interval between about 30 and 60{{cent}}.

"[[Comma]]" also refers to an interval that is tempered out by any given [[temperament]].

The range of dieses largely overlaps with the range of [[quartertone]]s (between 40 and 60{{c}}, reasonably mapped to 1/24edo), which, according to systems that determine consonance in terms of proximity to simple just ratios, is one of the most dissonant interval regions. This also corresponds to an [[interseptimal]] interval range. However, quarter tones are still covered here to provide a resource for them in the same format as the other interval region pages.

In the diatonic scale, the analogous concepts are '''subchromatic''' and '''enharmonic''' steps. A subchromatic step (a "comma") does not change the interval category (for example, in most just notation systems, if you flatten the major third [[81/64]] by an [[81/80]] comma to produce [[5/4]], the latter is still considered a major third). Diatonically, subchromatic steps are '''perfect unisons (P1)''', and there are none that are not a unison in a rank-2 diatonic tuning. An enharmonic step (a "diesis", although this is controversial) changes the interval category to an enharmonic interval (for example, a major third to a diminished fourth, or a chromatic semitone to a diatonic semitone). Similarly, enharmonic steps are ascending or descending '''diminished seconds (d2)'''.

== In just intonation ==

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As comma and diesis is the smallest interval class, it may be represented by:

* Any superparticular interval smaller than 29/28

* Any delta-1 (i.e. superparticular) interval smaller than 29/28

* Any delta-2 interval smaller than 57/55

* Any delta-3 interval smaller than 88/85

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| 24

| 50{{c}}

|

| 50¢ ≈ 33/32

|-

| 25

@@ Line 5: / Line 5: @@
 | Cents upper=40
 | Cents upper wide=60
-| JI intervals=128/125, 81/80
+| JI intervals=81/80, 128/125
 | Complement=(Imperfect) [[octave]]
 | Lower region=[[Unison]]
 | Higher region=[[Semitone (interval region)|Semitone]]
 }}
+'''Comma''' and '''diesis''' are two terms used to refer to intervals that are less than about 60{{cent}} in size. In terms of [[interval region]]s, "comma" refers to an interval flatter than about 30{{cent}}, and "diesis" refers to an interval between about 30 and 60{{cent}}. In [[Sagittal notation]], a comma is specifically defined as between half of the [[Pythagorean comma]] {{monzo| -19 12}} and half of the Pythagorean 17-fifths diesis {{monzo| 27 -17}}, about 11.7{{c}} to 33.4{{c}}, and a diesis is defined as between the comma upper bound and half of the Pythagorean 19-fifths apotome-plus-comma {{monzo| -30 19}}, about 68.6{{c}}.
-"Comma" and "diesis" are two terms used to refer to intervals that are less than about 60{{cent}} in size. In terms of [[interval region]]s, "comma" refers to an interval flatter than about 30{{cent}}, and "diesis" refers to an interval between about 30 and 60{{cent}}.
 "[[Comma]]" also refers to an interval that is tempered out by any given [[temperament]].
 The range of dieses largely overlaps with the range of [[quartertone]]s (between 40 and 60{{c}}, reasonably mapped to 1/24edo), which, according to systems that determine consonance in terms of proximity to simple just ratios, is one of the most dissonant interval regions. This also corresponds to an [[interseptimal]] interval range. However, quarter tones are still covered here to provide a resource for them in the same format as the other interval region pages.
+In the diatonic scale, the analogous concepts are '''subchromatic''' and '''enharmonic''' steps. A subchromatic step (a "comma") does not change the interval category (for example, in most just notation systems, if you flatten the major third [[81/64]] by an [[81/80]] comma to produce [[5/4]], the latter is still considered a major third). Diatonically, subchromatic steps are '''perfect unisons (P1)''', and there are none that are not a unison in a rank-2 diatonic tuning. An enharmonic step (a "diesis", although this is controversial) changes the interval category to an enharmonic interval (for example, a major third to a diminished fourth, or a chromatic semitone to a diatonic semitone). Similarly, enharmonic steps are ascending or descending '''diminished seconds (d2)'''.
 == In just intonation ==
@@ Line 32: / Line 33: @@
 As comma and diesis is the smallest interval class, it may be represented by:
-* Any superparticular interval smaller than 29/28
+* Any delta-1 (i.e. superparticular) interval smaller than 29/28
 * Any delta-2 interval smaller than 57/55
 * Any delta-3 interval smaller than 88/85
@@ Line 51: / Line 52: @@
 | 24
 | 50{{c}}
-|
+| 50¢ ≈ 33/32
 |-
 | 25