128/125: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Ratio = 128/125 | | Ratio = 128/125 | ||
| Monzo = 7 0 -3 | | Monzo = 7 0 -3 | ||
| Cents = 41.05886 | | Cents = 41.05886 | ||
| Name = diesis, augmented comma | | Name = diesis, <br>augmented comma | ||
| Color name = | | Color name = | ||
| FJS name = d2<sub>5,5,5</sub> | | FJS name = d2<sub>5,5,5</sub> | ||
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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) | 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. | 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. | ||
Revision as of 22:24, 12 February 2022
| Interval information |
augmented comma
reduced subharmonic
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 28-, 31- or 34edo, and by two steps of 53-, 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.