128/125: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

| Ratio = 128/125

| Monzo = 7 0 -3

| Cents = 41.05886

| Name = diesis, augmented comma

| Name = diesis, augmented comma

| Color name =

| FJS name = d25,5,5

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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~~]].

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 comma''' for this reason. Tempering it out leads to [[augmented]] temperament.

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.

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
 | Ratio = 128/125
 | Monzo = 7 0 -3
 | Cents = 41.05886
-| Name = diesis, augmented comma
+| Name = diesis, <br>augmented comma
 | Color name =
 | FJS name = d2<sub>5,5,5</sub>
@@ Line 10: / Line 9: @@
 }}
-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]].
+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 comma''' for this reason. Tempering it out leads to [[augmented]] temperament.
 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.