Diesis: Difference between revisions

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The '''diesis''' (/ˈdaɪəsɪs/ ''DY-ə-sis''; plural ''dieses'') ~~most~~ commonly refers to:

The '''diesis''' (/ˈdaɪəsɪs/ ''DY-ə-sis''; plural ''dieses'') is a small interval that has several related definitions. Most commonly, it refers to [[128/125]], the ''augmented comma'' a.k.a. ''lesser diesis'', though rarely and if the context is clear, it can refer to [[648/625]], the ''diminished comma'' a.k.a. ''greater diesis''.

* [[128/125]], the ''augmented comma'' or ''lesser diesis'';

** rarely, [[648/625]], the ''diminished comma'' or ''greater diesis'';

* By extension, a melodic unit of about the size of 128/125 (≈ 41¢). See [[Diesis (interval region)]];

* By extension, the difference between two enharmonic notes in a scale. See [[Diesis (scale theory)]].

In ~~addition~~, ~~there~~ are a ~~number~~ of ~~archaic usages~~ in [[~~Ancient Greek music~~]]:

== History ==

* [[~~256~~/~~243~~]], ~~known as~~ the ~~limma today;~~

The earliest usage of the term ''diesis'' was due to {{w|Philolaus}} in [[ancient Greek music]] to refer to an interval that is known as the [[256/243|limma]] today. Another usage, also in ancient Greek theory and notably used by {{w|Aristoxenus}}, would refer to a number of [[quartertone]]-sized intervals. In more recent times, {{w|Marchetto da Padova}} used it for fifth-tones, and finally, the modern diesis centered around [[31edo|1\31]] is due to [[Adriaan Fokker]].

* ~~A variety~~ of ~~quartertones~~.

== As an interval region ==

As an interval region, the diesis is a small melodic unit of about an augmented comma's size. The specific range varies considerably among musicians, but is generally agreed to be roughly 30–60 cents.

=== Just intervals ===

Some just intervals have been named according to this sense of diesis.

* [[Porcupine comma]], or ''maximal diesis'' (49.2{{c}})

* [[Magic comma]], or ''small diesis'' (29.6{{c}})

* [[Tetracot comma]], or ''minimal diesis'' (27.7{{c}})

* [[49/48]], the ''large septimal diesis'' (35.7{{c}})

* [[50/49]], the ''small septimal diesis'' or ''septimal tritonic diesis'' (35.0{{c}})

This is not to be confused with the related sense of the same term introduced next, for which the [[648/625|major diesis (648/625)]] was named while being way wider than the "maximal diesis".

== As a diatonic interval category ==

In the [[5L 2s|diatonic]] scale, the diesis, more specifically '''enharmonic diesis''', is the distance between two [[enharmonic]] notes in a scale. In terms of diatonic degrees, it is the diminished second or inverse diminished second, whichever is positive in size. An example of a diesis is the interval between C♯ and D♭. The diesis spans twelve [[perfect fifth]]s, and is observed in any tuning whose perfect fifth is not the same as [[12edo]]'s. Notes related by the diesis are said to be ''enharmonic'' to each other.

=== Just intervals ===

If the fifth represents the just interval [[3/2]], the diesis or inverse diesis represents the [[Pythagorean comma]]. In [[meantone]], the diesis approximates a class of [[comma]]s separated by the syntonic comma ([[81/80]]), among which [[128/125]], the augmented comma, is notable for being tuned pure in [[quarter-comma meantone]]. Therefore ''diesis'' traditionally refers to the augmented comma by default. Other dieses according to this definition are

* [[648/625]], the major diesis, tuned pure in [[1/3-comma meantone]].

* [[2048/2025]], the diaschisma, tuned pure in [[1/6-comma meantone]].

* [[32805/32768]], the schisma, tuned pure in 1/12-comma meantone.

This is not to be confused with the related sense of the same term introduced in the section above, for which a number of other intervals are named despite not being reached through twelve fifths.

=== Generalization ===

The diesis can be generalized to any [[mos scale]] as the '''mosdiesis''', defined as {{nowrap| {{!}}L - 2s{{!}} }}, i.e. the difference between a large step and two small steps. In terms of [[stepspan]], it is usually the diminished mosstep or inverse diminished mosstep, whichever is positive. However, in ''n''L 1s scales, it is the double-diminished mosstep or inverse thereof since the small step itself is diminished. Except for ''n''L 1s scales, it is the diminished mosstep in [[soft]] {{nowrap|(L:s < 2:1)}} scales and the inverse diminished mosstep in [[hard]] {{nowrap|(L:s > 2:1)}} scales. It vanishes in basic {{nowrap|(L:s {{=}} 2:1)}} scales.

== Normal diesis ==

The '''normal diesis''' (~~≈ ~~38.7¢) is an [[interval size measure]] defined as one step of [[31edo]].

The '''normal diesis''' (~38.7{{c}}) is an [[interval size measure]] defined as one step of [[31edo]].

== See also ==

* [[Chroma]]

* [[Shimmerstep]]

== External links ==

* [http://tonalsoft.com/enc/d/diesis.aspx Tonalsoft Encyclopedia | ''Diesis'']

~~{{Disambiguation}}~~

[[Category:Terms]]

[[Category:MOS scale]]

[[Category:Interval size measures]]

@@ Line 1: / Line 1: @@
 {{Wikipedia}}
-The '''diesis''' (/ˈdaɪəsɪs/ ''DY-ə-sis''; plural ''dieses'') most commonly refers to:
+The '''diesis''' (/ˈdaɪəsɪs/ ''DY-ə-sis''; plural ''dieses'') is a small interval that has several related definitions. Most commonly, it refers to [[128/125]], the ''augmented comma'' a.k.a. ''lesser diesis'', though rarely and if the context is clear, it can refer to [[648/625]], the ''diminished comma'' a.k.a. ''greater diesis''.
-* [[128/125]], the ''augmented comma'' or ''lesser diesis'';
-** rarely, [[648/625]], the ''diminished comma'' or ''greater diesis'';
-* By extension, a melodic unit of about the size of 128/125 (≈&nbsp;41¢). See [[Diesis (interval region)]];
-* By extension, the difference between two enharmonic notes in a scale. See [[Diesis (scale theory)]].
-In addition, there are a number of archaic usages in [[Ancient Greek music]]:
+== History ==
-* [[256/243]], known as the limma today;
+The earliest usage of the term ''diesis'' was due to {{w|Philolaus}} in [[ancient Greek music]] to refer to an interval that is known as the [[256/243|limma]] today. Another usage, also in ancient Greek theory and notably used by {{w|Aristoxenus}}, would refer to a number of [[quartertone]]-sized intervals. In more recent times, {{w|Marchetto da Padova}} used it for fifth-tones, and finally, the modern diesis centered around [[31edo|1\31]] is due to [[Adriaan Fokker]].
-* A variety of quartertones.
+== As an interval region ==
+As an interval region, the diesis is a small melodic unit of about an augmented comma's size. The specific range varies considerably among musicians, but is generally agreed to be roughly 30–60 cents.
+=== Just intervals ===
+Some just intervals have been named according to this sense of diesis.
+* [[Porcupine comma]], or ''maximal diesis'' (49.2{{c}})
+* [[Magic comma]], or ''small diesis'' (29.6{{c}})
+* [[Tetracot comma]], or ''minimal diesis'' (27.7{{c}})
+* [[49/48]], the ''large septimal diesis'' (35.7{{c}})
+* [[50/49]], the ''small septimal diesis'' or ''septimal tritonic diesis'' (35.0{{c}})
+This is not to be confused with the related sense of the same term introduced next, for which the [[648/625|major diesis (648/625)]] was named while being way wider than the "maximal diesis".
+== As a diatonic interval category ==
+In the [[5L 2s|diatonic]] scale, the diesis, more specifically '''enharmonic diesis''', is the distance between two [[enharmonic]] notes in a scale. In terms of diatonic degrees, it is the diminished second or inverse diminished second, whichever is positive in size. An example of a diesis is the interval between C♯ and D♭. The diesis spans twelve [[perfect fifth]]s, and is observed in any tuning whose perfect fifth is not the same as [[12edo]]'s. Notes related by the diesis are said to be ''enharmonic'' to each other.
+=== Just intervals ===
+If the fifth represents the just interval [[3/2]], the diesis or inverse diesis represents the [[Pythagorean comma]]. In [[meantone]], the diesis approximates a class of [[comma]]s separated by the syntonic comma ([[81/80]]), among which [[128/125]], the augmented comma, is notable for being tuned pure in [[quarter-comma meantone]]. Therefore ''diesis'' traditionally refers to the augmented comma by default. Other dieses according to this definition are
+* [[648/625]], the major diesis, tuned pure in [[1/3-comma meantone]].
+* [[2048/2025]], the diaschisma, tuned pure in [[1/6-comma meantone]].
+* [[32805/32768]], the schisma, tuned pure in 1/12-comma meantone.
+This is not to be confused with the related sense of the same term introduced in the section above, for which a number of other intervals are named despite not being reached through twelve fifths.
+=== Generalization ===
+The diesis can be generalized to any [[mos scale]] as the '''mosdiesis''', defined as {{nowrap| {{!}}L - 2s{{!}} }}, i.e. the difference between a large step and two small steps. In terms of [[stepspan]], it is usually the diminished mosstep or inverse diminished mosstep, whichever is positive. However, in ''n''L 1s scales, it is the double-diminished mosstep or inverse thereof since the small step itself is diminished. Except for ''n''L 1s scales, it is the diminished mosstep in [[soft]] {{nowrap|(L:s < 2:1)}} scales and the inverse diminished mosstep in [[hard]] {{nowrap|(L:s > 2:1)}} scales. It vanishes in basic {{nowrap|(L:s {{=}} 2:1)}} scales.
 == Normal diesis ==
-The '''normal diesis''' (≈&nbsp;38.7¢) is an [[interval size measure]] defined as one step of [[31edo]].
+The '''normal diesis''' (~38.7{{c}}) is an [[interval size measure]] defined as one step of [[31edo]].
 == See also ==
+* [[Chroma]]
+* [[Shimmerstep]]
+== External links ==
 * [http://tonalsoft.com/enc/d/diesis.aspx Tonalsoft Encyclopedia | ''Diesis'']
-{{Disambiguation}}
 [[Category:Terms]]
+[[Category:MOS scale]]
+[[Category:Interval size measures]]