128/125: Difference between revisions
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<span style="display: block; text-align: right;">Other languages: [[:de:128/125 Deutsch]]</span><span style="display: block; text-align: left;"> | <span style="display: block; text-align: right;">Other languages: [[:de:128/125|Deutsch]]</span><span style="display: block; text-align: left;"> | ||
</span><span style="display: block; text-align: left;">The 41.059 cent interval of '''128/125''' is called the '''diesis''' or '''augmented [[Comma|comma]]'''; it represents the gap between three [[5/4|5/4]] just major thirds and the [[Octave|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]]. In any tuning with just major, thirds, such as [[Quarter-comma_meantone|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]].</span> [[Category:5-limit]] | </span><span style="display: block; text-align: left;">The 41.059 cent interval of '''128/125''' is called the '''diesis''' or '''augmented [[Comma|comma]]'''; it represents the gap between three [[5/4|5/4]] just major thirds and the [[Octave|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]]. In any tuning with just major, thirds, such as [[Quarter-comma_meantone|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]].</span> [[Category:5-limit]] | ||
[[Category:comma]] | [[Category:comma]] | ||
[[Category:diesis]] | [[Category:diesis]] | ||
Revision as of 00:09, 17 September 2018
Other languages: Deutsch
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. 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.