An explanation of dwarf scales...?

Hi everyone,

I can't find where online the concept of a dwarf scale was first
introduced. They seem to have mysteriously appeared on the tuning list
somewhere around 2004, and I don't see an introductory explanation on
tuning-math either.

I found this explanation here: http://xenharmonic.wikispaces.com/Dwarves

Does this mean that for some equal temperament, a dwarf scale is a way
to construct an otonal, JI version of the scale up to some prime
limit? What musical features do these scales bring?

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> Hi everyone,
>
> I can't find where online the concept of a dwarf scale was first
> introduced. They seem to have mysteriously appeared on the tuning list
> somewhere around 2004, and I don't see an introductory explanation on
> tuning-math either.

Mysterious appearances is what the tuning-math list is all about; dwarf scales were introduced here:

/tuning-math/message/11461

> Does this mean that for some equal temperament, a dwarf scale is a way
> to construct an otonal, JI version of the scale up to some prime
> limit?

That's one thing you could use it for.

>What musical features do these scales bring?

They tend to be well-supplied with chords, especially otonal ones. Particularly when you start from a decent p-limit equal temperament val, you are likely to get scales with desirable qualities such as constant structure and proper.

If the scale is of composite number size and there is an Euler genus of the right properties, the dwarf construction tends to find it. For instance, the 5-limit scales for the stardard vals for 9, 10, 12 (the Duodene), 15, 18, 21 etc, including 72. If not a genus, you often get a genus with a corner nibbled off such as 7 (Zarleno/Ptolemy diatonic), 13, 17, 19 etc including 31. Another common type is more peculiar: merged Euler genuses. This can be as small as a single note sticking out, but it can be much more dramatic (34, 46, 53, 58.)

I'm concentrating on the 5-limit because Scala will draw the corresponding lattices for you.