Comma and diesis: Difference between revisions

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''This article is about "comma" and "diesis" as interval regions. For other senses of these two words, see [[comma]] and [[diesis]].''

: ''This article is about "comma" and "diesis" as interval regions. For other senses of these two words, see [[comma]] and [[diesis]].''

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

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

In terms of [[~~Interval~~ region~~|interval regions~~]], "comma" refers to an interval flatter than about 30{{c}}, and "diesis" refers to an interval between about 30 and 60{{c}}.

In terms of [[interval region]]s, "comma" refers to an interval flatter than about 30{{c}}, and "diesis" refers to an interval between about 30 and 60{{c}}.

The range of dieses largely overlaps with the range of [[~~Quarter tone|quarter tones~~]] (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.

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 just intonation ==

=== By prime limit ===

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}}.

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:

For the remainder of this list, I{{who}} 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{{c}}.

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* Any delta-3 interval smaller than 88/85

== In ~~EDOs~~ ==

== 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 0{{c}}, or those where the best tuning is sharper than 60{{c}} (i.e. not a diesis or comma). Note that this does not depend on how each ~~EDO~~ tunes the intervals that 128/125 might be derived from, only on which edostep is closest to 128/125's size.

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). Note that this does not depend on how each edo tunes the intervals that 128/125 might be derived from, only on which edostep is closest to 128/125's size.

{| class="wikitable"

|-

! ~~EDO~~

! Edo

! 128/125

! Other commas and dieses

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The role of commas and dieses in regular temperaments is often as the intervals that are tempered out (i.e. equated to 0 cents). Discussing that is not within the scope of this article; you may learn more at [[Regular temperament]].

However, there are, rarely, temperaments generated by commas. One example is [[slender]], where ten [[49/48]]~~<nowiki/>~~s ~~equal~~ [[5/4]].

However, there are, rarely, temperaments generated by commas. One example is [[slender]], where a stack of ten [[49/48]]'s equals [[5/4]].

== In ~~moment-of-symmetry~~ scales ==

== In mos scales ==

Intervals less than 100{{c}} generate the following [[~~MOS~~]] scales:

Intervals less than 100{{c}} generate the following [[mos]] scales:

These tables start from the last monolarge ~~[[MOS]]~~ generated by the interval range.

These tables start from the last monolarge mos generated by the interval range.

~~MOSes~~ with more than 12 notes are not included.

Scales with more than 12 notes are not included.

{| class="wikitable"

|-

! Range

! ~~MOS~~

! Mos

|-

| 0–100{{c}}

@@ Line 1: / Line 1: @@
-''This article is about "comma" and "diesis" as interval regions. For other senses of these two words, see [[comma]] and [[diesis]].''
+: ''This article is about "comma" and "diesis" as interval regions. For other senses of these two words, see [[comma]] and [[diesis]].''
 "Comma" and "diesis" are two terms used to refer to intervals that are less than about 60{{cent}} in size.
@@ Line 5: / Line 5: @@
 "[[Comma]]" also refers to an interval that is tempered out by any given [[temperament]].
-In terms of [[Interval region|interval regions]], "comma" refers to an interval flatter than about 30{{c}}, and "diesis" refers to an interval between about 30 and 60{{c}}.
+In terms of [[interval region]]s, "comma" refers to an interval flatter than about 30{{c}}, and "diesis" refers to an interval between about 30 and 60{{c}}.
-The range of dieses largely overlaps with the range of [[Quarter tone|quarter tones]] (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.
+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 just intonation ==
 === By prime limit ===
-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}}.
+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:
+For the remainder of this list, I{{who}} 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{{c}}.
@@ Line 28: / Line 28: @@
 * Any delta-3 interval smaller than 88/85
-== In EDOs ==
+== 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 0{{c}}, or those where the best tuning is sharper than 60{{c}} (i.e. not a diesis or comma). Note that this does not depend on how each EDO tunes the intervals that 128/125 might be derived from, only on which edostep is closest to 128/125's size.
+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). Note that this does not depend on how each edo tunes the intervals that 128/125 might be derived from, only on which edostep is closest to 128/125's size.
 {| class="wikitable"
 |-
-! EDO
+! Edo
 ! 128/125
 ! Other commas and dieses
@@ Line 81: / Line 81: @@
 The role of commas and dieses in regular temperaments is often as the intervals that are tempered out (i.e. equated to 0 cents). Discussing that is not within the scope of this article; you may learn more at [[Regular temperament]].
-However, there are, rarely, temperaments generated by commas. One example is [[slender]], where ten [[49/48]]<nowiki/>s equal [[5/4]].
+However, there are, rarely, temperaments generated by commas. One example is [[slender]], where a stack of ten [[49/48]]'s equals [[5/4]].
-== In moment-of-symmetry scales ==
+== In mos scales ==
-Intervals less than 100{{c}} generate the following [[MOS]] scales:
+Intervals less than 100{{c}} generate the following [[mos]] scales:
-These tables start from the last monolarge [[MOS]] generated by the interval range.
+These tables start from the last monolarge mos generated by the interval range.
-MOSes with more than 12 notes are not included.
+Scales with more than 12 notes are not included.
 {| class="wikitable"
 |-
 ! Range
-! MOS
+! Mos
 |-
 | 0–100{{c}}