Comma and diesis: Difference between revisions

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"Comma" and "diesis" are two terms used to refer to intervals that are less than about 60 ~~cents~~ in size.

"Comma" and "diesis" are two terms used to refer to intervals that are less than about 60{{cent}} in size.

"Comma" also refers to an interval that is tempered out by any given [[temperament]], but that is not the sense of "comma" that this article covers.

Generally, "comma" refers to an interval flatter than about 30 ~~cents~~, and "diesis" refers to an interval between about 30 and 60 ~~cents~~.

Generally, "comma" refers to an interval flatter than about 30{{c}}, and "diesis" refers to an interval between about 30 and 60{{c}}.

This includes the range of [[Quarter tone|quarter tones]], which, according to systems that determine consonance in terms of proximity to simple just ratios, is one of the most dissonant interval regions.

== In just intonation ==

In just intonation, commas are often seen as the difference between two similar intervals, so it is hard to find intervals within this range that are treated as steps in their own right. The 3-limit interval in this range is the '''Pythagorean comma''' of [[531441/524288]], which can be considered an augmented seventh (octave-reduced), and is about 23 ~~cents~~.

In just intonation, commas are often seen as the difference between two similar intervals, so it is hard to find intervals within this range that are treated as steps in their own right. The 3-limit interval in this range is the '''Pythagorean comma''' of [[531441/524288]], which can be considered an augmented seventh (octave-reduced), and is about 23{{c}}.

For the remainder of this list, I have tried to choose intervals that are '''not''' mostly treated as commas (in the temperament sense). Higher-limit intervals in the comma and diesis range are:

* The 5-limit '''augmented diesis''' is a ratio of 128/125, and is about 41 ~~cents~~.

* The 5-limit '''augmented diesis''' is a ratio of 128/125, and is about 41{{c}}.

** There is also the 5-limit '''magic comma''' of 3125/3072, which is about 30 ~~cents~~.

** There is also the 5-limit '''magic comma''' of 3125/3072, which is about 30{{c}}.

* The 7-limit '''slendro diesis''' is a ratio of 49/48, and is about 36 ~~cents~~.

* The 7-limit '''slendro diesis''' is a ratio of 49/48, and is about 36{{c}}.

* The 11-limit '''quarter tone''' is a ratio of 33/32, and is about 53 ~~cents~~.

* The 11-limit '''quarter tone''' is a ratio of 33/32, and is about 53{{c}}.

* The 13-limit '''minor diesis''' is a ratio of 40/39, and is about 43 ~~cents~~.

* The 13-limit '''minor diesis''' is a ratio of 40/39, and is about 43{{c}}.

== In EDOs ==

The following table lists the best tuning of 128/125, and other dieses or commas if present, in various significant [[EDOs]]. Not included are EDOs (i.e. those smaller than 15) where the best tuning is the unison, or 0c, or those where the best tuning is sharper than 60 ~~cents~~ (i.e. not a diesis or comma).

The following table lists the best tuning of 128/125, and other dieses or commas if present, in various significant [[EDOs]]. Not included are EDOs (i.e. those smaller than 15) where the best tuning is the unison, or 0{{c}}, or those where the best tuning is sharper than 60{{c}} (i.e. not a diesis or comma).

{| class="wikitable"

|+

~~!EDO~~

~~!128/125~~

~~!Other commas and dieses~~

|-

|22

! EDO

|~~54c~~

! 128/125

|

! Other commas and dieses

|-

| 22

| 54{{c}}

|

|-

|24

| 24

|~~50c~~

| 50{{c}}

|

|-

|25

| 25

|~~48c~~

| 48{{c}}

|

|-

|26

| 26

|~~46c~~

| 46{{c}}

|

|-

|27

| 27

|~~44c~~

| 44{{c}}

|

|-

|29

| 29

|~~41c~~

| 41{{c}}

|

|-

|31

| 31

|~~39c~~

| 39{{c}}

|

|-

|34

| 34

|~~35c~~

| 35{{c}}

|

|-

|41

| 41

|~~29c~~

| 29{{c}}

|~~59c~~ ≈ 33/32

| 59{{c}} ≈ 33/32

|-

|53

| 53

|~~45c~~

| 45{{c}}

|~~22c~~ ≈ 81/80

| 22{{c}} ≈ 81/80

|}

@@ Line 1: / Line 1: @@
-"Comma" and "diesis" are two terms used to refer to intervals that are less than about 60 cents in size.
+"Comma" and "diesis" are two terms used to refer to intervals that are less than about 60{{cent}} in size.
 "Comma" also refers to an interval that is tempered out by any given [[temperament]], but that is not the sense of "comma" that this article covers.
-Generally, "comma" refers to an interval flatter than about 30 cents, and "diesis" refers to an interval between about 30 and 60 cents.
+Generally, "comma" refers to an interval flatter than about 30{{c}}, and "diesis" refers to an interval between about 30 and 60{{c}}.
 This includes the range of [[Quarter tone|quarter tones]], which, according to systems that determine consonance in terms of proximity to simple just ratios, is one of the most dissonant interval regions.
 == In just intonation ==
-In just intonation, commas are often seen as the difference between two similar intervals, so it is hard to find intervals within this range that are treated as steps in their own right. The 3-limit interval in this range is the '''Pythagorean comma''' of [[531441/524288]], which can be considered an augmented seventh (octave-reduced), and is about 23 cents.
+In just intonation, commas are often seen as the difference between two similar intervals, so it is hard to find intervals within this range that are treated as steps in their own right. The 3-limit interval in this range is the '''Pythagorean comma''' of [[531441/524288]], which can be considered an augmented seventh (octave-reduced), and is about 23{{c}}.
 For the remainder of this list, I have tried to choose intervals that are '''not''' mostly treated as commas (in the temperament sense). Higher-limit intervals in the comma and diesis range are:
-* The 5-limit '''augmented diesis''' is a ratio of 128/125, and is about 41 cents.
+* The 5-limit '''augmented diesis''' is a ratio of 128/125, and is about 41{{c}}.
-** There is also the 5-limit '''magic comma''' of 3125/3072, which is about 30 cents.
+** There is also the 5-limit '''magic comma''' of 3125/3072, which is about 30{{c}}.
-* The 7-limit '''slendro diesis''' is a ratio of 49/48, and is about 36 cents.
+* The 7-limit '''slendro diesis''' is a ratio of 49/48, and is about 36{{c}}.
-* The 11-limit '''quarter tone''' is a ratio of 33/32, and is about 53 cents.
+* The 11-limit '''quarter tone''' is a ratio of 33/32, and is about 53{{c}}.
-* The 13-limit '''minor diesis''' is a ratio of 40/39, and is about 43 cents.
+* The 13-limit '''minor diesis''' is a ratio of 40/39, and is about 43{{c}}.
 == In EDOs ==
-The following table lists the best tuning of 128/125, and other dieses or commas if present, in various significant [[EDOs]]. Not included are EDOs (i.e. those smaller than 15) where the best tuning is the unison, or 0c, or those where the best tuning is sharper than 60 cents (i.e. not a diesis or comma).
+The following table lists the best tuning of 128/125, and other dieses or commas if present, in various significant [[EDOs]]. Not included are EDOs (i.e. those smaller than 15) where the best tuning is the unison, or 0{{c}}, or those where the best tuning is sharper than 60{{c}} (i.e. not a diesis or comma).
 {| class="wikitable"
-|+
-!EDO
-!128/125
-!Other commas and dieses
 |-
-|22
+! EDO
-|54c
+! 128/125
-|
+! Other commas and dieses
+|-
+| 22
+| 54{{c}}
+|
 |-
-|24
+| 24
-|50c
+| 50{{c}}
 |
 |-
-|25
+| 25
-|48c
+| 48{{c}}
 |
 |-
-|26
+| 26
-|46c
+| 46{{c}}
 |
 |-
-|27
+| 27
-|44c
+| 44{{c}}
 |
 |-
-|29
+| 29
-|41c
+| 41{{c}}
 |
 |-
-|31
+| 31
-|39c
+| 39{{c}}
 |
 |-
-|34
+| 34
-|35c
+| 35{{c}}
 |
 |-
-|41
+| 41
-|29c
+| 29{{c}}
-|59c ≈ 33/32
+| 59{{c}} ≈ 33/32
 |-
-|53
+| 53
-|45c
+| 45{{c}}
-|22c ≈ 81/80
+| 22{{c}} ≈ 81/80
 |}