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>.

== Approximations ==

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.

== As a comma ==

== Temperaments ==

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

=== As a comma ===

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

== As an interval ==

=== As an interval ===

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.

== ~~Approximations ==~~

== Trivia ==

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.

~~== Relation to binary~~ ==

This interval represents the amount by which the binary definition of kilobyte, 1024 bytes, exceeds the nominal definition of "kilo" prefix, 1000.

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[[Category:Augmented]]

[[Category:Sonifications]]

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

~~~~

~~[[https://de.xen.wiki/w/128/125]]~~

[[Category:~~Augmented family~~]]

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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>.
+== Approximations ==
+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.
-== As a comma ==
+== Temperaments ==
-Tempering out this comma leads to [[augmented]] temperament. See [[augmented family]] for the family where it is tempered out.
+=== As a comma ===
+[[Tempering out]] this comma leads to [[augmented]] temperament. See [[augmented family]] for the family where it is tempered out.
-== As an interval ==
+=== As an interval ===
 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.
-== Approximations ==
+== Trivia ==
-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.
-== Relation to binary ==
 This interval represents the amount by which the binary definition of kilobyte, 1024 bytes, exceeds the nominal definition of "kilo" prefix, 1000.
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 [[Category:Augmented]]
 [[Category:Sonifications]]
+[[Category:Commas named after their interval size]]
-<!-- interwiki: links are being placed in the sidebar -->
-[[https://de.xen.wiki/w/128/125]]
-[[Category:Augmented family]]