128/125: Difference between revisions

| Name = diesis, augmented comma, enharmonic diesis, enharmonic comma, cyberisma

The 41.059 cent interval of '''128/125''' is called the '''diesis''' or '''augmented comma'''; it represents the gap between a stack of three [[5/4]] just major thirds and the [[octave]], or in other words 2/(5/4)³.

 

If the diesis is treated as a musical interval in its own right as opposed to tempering it out, it is approximately a quarter-tone and so can be used to introduce [[7-limit]] and [[11-limit]] harmony into 5-limit scales.  

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 meantone it appears as the difference between sharps and flats, e.g. between D# and Eb. It is also called '''enharmonic diesis''' or '''enharmonic comma''' for this reason.  

Tempering out this comma leads to [[augmented]] temperament. See [[augmented family]] for the family where it is tempered out.

=== Walker temperament ===

Walker temperament flattens the octave in order to temper out the difference between 2^10 and 10^3, which is an occurrence of the diesis. [[40ed10]] is an example of Walker temperament. It was created by Vector Graphics (Jay Walker) before he even knew what temperament was, as an attempt to align powers of 2 and powers of 10. In the context of Walker temperament, the augmented comma can be called the '''cyberisma,''' after its appearance in computing.

 

 

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