128/125: Difference between revisions
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Revision as of 12:14, 13 September 2020
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.