128/125: Difference between revisions

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~~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|34]] EDO~~, ~~and by two steps of [[53edo|53]], [[59edo|59]] or [[65edo|65]] EDO. In any tuning with just major thirds~~, ~~such as [[quarter-~~comma meantone]], it will be exact. Furthermore, in quarter-comma meantone it appears as difference between sharps and flats, e.g. between D# and Eb. It is also called '''enharmonic comma''' for this reason. Tempering it out leads to [[Augmented_family|~~augmented temperament]].~~

{{Interwiki

| en = 128/125

| de = 128/125

}}

{{Infobox Interval

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

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

| Comma = yes

}}

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

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.

[[~~Category:comma~~]]

[[~~Category:diesis~~]]

== Approximations ==

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

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.

=== 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.

== Trivia ==

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

== See also ==

* [[Diesis]] (disambiguation page)

[[Category:Augmented]]

[[Category:Sonifications]]

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

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-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|34]] EDO, and by two steps of [[53edo|53]], [[59edo|59]] or [[65edo|65]] EDO. In any tuning with just major thirds, such as [[quarter-comma meantone]], it will be exact. Furthermore, in quarter-comma meantone it appears as difference between sharps and flats, e.g. between D# and Eb. It is also called '''enharmonic comma''' for this reason. Tempering it out leads to [[Augmented_family|augmented temperament]].
+{{Interwiki
+| en = 128/125
+| de = 128/125
+}}
+{{Infobox Interval
+| Name = diesis, augmented comma, enharmonic diesis, enharmonic comma
+| Color name = g<sup>3</sup>2, trigu 2nd,<br>Trigu comma
+| Comma = yes
+}}
-[[Category:5-limit]]
+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>.
-[[Category:comma]]
-[[Category:diesis]]
-<!-- interwiki: links are being placed in the sidebar -->
+== Approximations ==
-[[de:128/125]]
+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.
+=== 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.
+== Trivia ==
+This interval represents the amount by which the binary definition of kilobyte, 1024 bytes, exceeds the nominal definition of "kilo" prefix, 1000.
+== See also ==
+* [[Diesis]] (disambiguation page)
+[[Category:Augmented]]
+[[Category:Sonifications]]
+[[Category:Commas named after their interval size]]