Demisemitones

I wrote:

>> I now use the term "demisemitone" for intervals with dimensions
>> of q and r-q, although I would rather call them quartertones.

Gary Morrison wrote:

> I may have lost track of the "p"s and "q"s, but I think I understood you
> to suggest that the distance between a minor second and an augmented octave
> should be viewed as roughly a quartertone?

There is a difference between a fifth and a twelfth, so there is
also a difference between an octave and a unison. In this case,
we're talking about the difference between an augmented unison
and a minor second. Augmented octave indeed ...

I introduced the term "demisemitone" for this concept, to avoid
confusion with other meanings the word "quartertone" has
acquired.

> If so, I don't think that's a good idea. In 24TET for example, the
> distance between an augmented unison (e.g., C-C#) and a minor second (e.g.,
> C-Db) is zero, not a quartertone. In 19TET, that difference is the same as
> chromatic half-step.

The definition only applies to syntonic meantones. 24tet, as
opposed to 12tet, is not such a scale, so a demisemitone can
be defined as 1 step. In general, I would define a demisemitone
as the approximation of the septimal comma. This is consistent
with 7/4 being a subminor seventh, and an augmented sixth in
a syntonic meantone.

> When you deal with quarter-steps, you have to add the ideas of
> half-augmentation and half-diminishment, and consequently subminors,
> neutrals, and supramajors. If you don't, you're almost certainly going to
> run into inconsistent terminology.

Yes, fine with me.



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