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 | |||
| Color name = | |||
| 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|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|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]]. | ||
Revision as of 09:30, 15 March 2021
| 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 34 EDO, and by two steps of 53, 59 or 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 temperament.