128/125: Difference between revisions

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{{Interwiki

| en = 128/125

| de = 128/125

}}

{{Infobox Interval

~~| Ratio = 128/125~~

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

~~| Monzo = 7 0 -3~~

| Color name = g32, trigu 2nd, Trigu comma

~~| Cents = 41.05886~~

| Comma = yes

| Name = diesis, ~~ ~~augmented comma

~~| Color name = g32~~, ~~trigu unison~~, ~~Trigu~~ comma

| ~~FJS~~ name = d2<~~sub~~>5,5,5<~~/sub~~>

| ~~Sound~~ =

}}

The 41.059 cent interval of '''128/125''' is called the '''diesis''' or '''augmented [[comma]]'''; it represents the gap between three [[5/4]] just major thirds and the [[octave]], or in other words 2/(5/4)3. 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 ~~quarter-comma~~ 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. Tempering it out leads to [[augmented]] temperament.

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)3.

== 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.

== Temperaments ==

=== As a comma ===

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

~~This~~ interval ~~can also be called~~ a ~~kilobyte comma~~, ~~since~~ it ~~represents the amount by which the binary definition of kilobyte, 1024 bytes, exceeds the nominal definition of "kilo" prefix, 1000~~.

=== 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.

~~[[Category:5-limit]]~~

== Trivia ==

~~[[Category:Medium commas]]~~

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

~~[[Category:Diesis]]~~

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

~~~~

== See also ==

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

* [[Diesis]] (disambiguation page)

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

[[Category:Augmented]]

[[Category:Sonifications]]

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

@@ Line 1: / Line 1: @@
+{{Interwiki
+| en = 128/125
+| de = 128/125
+}}
 {{Infobox Interval
-| Ratio = 128/125
+| Name = diesis, augmented comma, enharmonic diesis, enharmonic comma
-| Monzo = 7 0 -3
+| Color name = g<sup>3</sup>2, trigu 2nd,<br>Trigu comma
-| Cents = 41.05886
+| Comma = yes
-| Name = diesis, <br>augmented comma
-| Color name = g32, trigu unison, Trigu comma
-| FJS name = d2<sub>5,5,5</sub>
-| Sound =
 }}
-The 41.059 cent interval of '''128/125''' is called the '''diesis''' or '''augmented [[comma]]'''; it represents the gap between three [[5/4]] just major thirds and the [[octave]], or in other words 2/(5/4)<sup>3</sup>. 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 quarter-comma 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. Tempering it out leads to [[augmented]] temperament.
+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.
+== Temperaments ==
+=== As a comma ===
+[[Tempering out]] this comma leads to [[augmented]] temperament. See [[augmented family]] for the family where it is tempered out.
-This interval can also be called a kilobyte comma, since it represents the amount by which the binary definition of kilobyte, 1024 bytes, exceeds the nominal definition of "kilo" prefix, 1000.
+=== 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.
-[[Category:5-limit]]
+== Trivia ==
-[[Category:Medium commas]]
+This interval represents the amount by which the binary definition of kilobyte, 1024 bytes, exceeds the nominal definition of "kilo" prefix, 1000.
-[[Category:Diesis]]
-[[Category:Real-life sonifications]]
-<!-- interwiki: links are being placed in the sidebar -->
+== See also ==
-[[de:128/125]]
+* [[Diesis]] (disambiguation page)
-[[Category:Todo:improve layout]]
+[[Category:Augmented]]
+[[Category:Sonifications]]
+[[Category:Commas named after their interval size]]