128/125: Difference between revisions

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{{Interwiki

| en = 128/125

| de = 128/125

}}

{{Infobox Interval

| Name = diesis, augmented comma, enharmonic diesis, enharmonic comma

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The 41.059 cent interval of '''128/125''' is called the '''diesis''' or '''augmented comma'''; it represents the gap between a stack of three [[5/4]] just major thirds and the [[octave]], or in other words 2/(5/4)<sup>3</sup>.

The 41.059-[[cent]] interval of '''128/125''' is called the '''diesis''' or '''augmented comma'''; it represents the gap between a stack of three [[5/4]] just major thirds and the [[octave]], or in other words 2/(5/4)<sup>3</sup>.

== ~~Approximation~~ ==

== Approximations ==

~~If the diesis~~ is ~~treated as~~ a ~~musical interval~~ in ~~its own right as opposed to tempering it out~~, ~~it is approximately a quarter~~-~~tone~~ and ~~so can be used to introduce~~ [[7-~~limit~~]] and [[11-~~limit~~]] ~~harmony into 5-limit scales~~.

This interval is fairly accurately represented by a single step in [[28edo|28-]], [[31edo|31-]] or [[34edo]], and by two steps of [[53edo|53-]], [[59edo|59-]] or [[65edo]]. In any tuning with pure octaves and just major thirds, such as [[quarter-comma meantone]], it will be exact. Furthermore, in meantone it appears as the difference between sharps and flats, e.g. between D# and Eb. It is also called '''enharmonic diesis''' or '''enharmonic comma''' for this reason.

~~It is fairly accurately represented by~~ a ~~single step in~~ [[~~28edo|28-~~]]~~, [[31edo|31-]] or [[34edo]], and by two steps of [[53edo|53-]], [[59edo|59-]] or~~ [[~~65edo~~]]. ~~In any tuning with pure octaves and just major thirds, such as~~ [[~~quarter-comma meantone~~]]~~, it will be exact. Furthermore, in meantone~~ it ~~appears as the difference between sharps and flats, e.g. between D# and Eb. It~~ is ~~also called '''enharmonic diesis''' or '''enharmonic comma''' for this reason~~.

== Temperaments ==

=== As a comma ===

[[Tempering out]] this comma leads to [[augmented]] temperament. See [[augmented family]] for the family where it is tempered out.

== ~~Temperaments~~ ==

=== As an interval ===

~~Tempering~~ out ~~this comma leads~~ to [[~~augmented~~]] ~~temperament. See~~ [[~~augmented family~~]] ~~for the family where it is tempered out~~.

If the diesis is treated as a musical interval in its own right as opposed to tempering it out, it is approximately a quarter-tone and so can be used to introduce [[7-limit]] and [[11-limit]] harmony into 5-limit scales.

== Trivia ==

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[[Category:Augmented]]

[[Category:~~Real-life sonifications~~]]

[[Category:Sonifications]]

[[Category:Commas named after their interval size]]

~~~~

~~[[de:128/125]]~~

[[Category:~~Todo:improve layout~~]]

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+{{Interwiki
+| en = 128/125
+| de = 128/125
+}}
 {{Infobox Interval
 | Name = diesis, augmented comma, enharmonic diesis, enharmonic comma
@@ Line 5: / Line 9: @@
 }}
-The 41.059 cent interval of '''128/125''' is called the '''diesis''' or '''augmented comma'''; it represents the gap between a stack of three [[5/4]] just major thirds and the [[octave]], or in other words 2/(5/4)<sup>3</sup>.
+The 41.059-[[cent]] interval of '''128/125''' is called the '''diesis''' or '''augmented comma'''; it represents the gap between a stack of three [[5/4]] just major thirds and the [[octave]], or in other words 2/(5/4)<sup>3</sup>.
-== Approximation ==
+== Approximations ==
-If the diesis is treated as a musical interval in its own right as opposed to tempering it out, it is approximately a quarter-tone and so can be used to introduce [[7-limit]] and [[11-limit]] harmony into 5-limit scales.
+This interval is fairly accurately represented by a single step in [[28edo|28-]], [[31edo|31-]] or [[34edo]], and by two steps of [[53edo|53-]], [[59edo|59-]] or [[65edo]]. In any tuning with pure octaves and just major thirds, such as [[quarter-comma meantone]], it will be exact. Furthermore, in meantone it appears as the difference between sharps and flats, e.g. between D# and Eb. It is also called '''enharmonic diesis''' or '''enharmonic comma''' for this reason.
-It is fairly accurately represented by a single step in [[28edo|28-]], [[31edo|31-]] or [[34edo]], and by two steps of [[53edo|53-]], [[59edo|59-]] or [[65edo]]. In any tuning with pure octaves and just major thirds, such as [[quarter-comma meantone]], it will be exact. Furthermore, in meantone it appears as the difference between sharps and flats, e.g. between D# and Eb. It is also called '''enharmonic diesis''' or '''enharmonic comma''' for this reason.
+== Temperaments ==
+=== As a comma ===
+[[Tempering out]] this comma leads to [[augmented]] temperament. See [[augmented family]] for the family where it is tempered out.
-== Temperaments ==
+=== As an interval ===
-Tempering out this comma leads to [[augmented]] temperament. See [[augmented family]] for the family where it is tempered out.
+If the diesis is treated as a musical interval in its own right as opposed to tempering it out, it is approximately a quarter-tone and so can be used to introduce [[7-limit]] and [[11-limit]] harmony into 5-limit scales.
 == Trivia ==
@@ Line 22: / Line 28: @@
 [[Category:Augmented]]
-[[Category:Real-life sonifications]]
+[[Category:Sonifications]]
+[[Category:Commas named after their interval size]]
-<!-- interwiki: links are being placed in the sidebar -->
-[[de:128/125]]
-[[Category:Todo:improve layout]]