Scale generators

Traditional JI scale generating methods are not suitable for
generating exact JI scales to be played on current musical
instruments.

There are matrix methods, which multiply sets of frequency
ratios, and there are cycle methods which multiply a single ratio
iteratively. All of them quickly generate a lot of scales, but
they are, for the greater part, scales that can not be accurately
reproduced on contemporary instruments. Also, these methods are
mostly indifferent to the consonance of the scales they produce.

I use three methods which produce scales that will actually play
on a given instrument, and which tend to select consonant scales.

One obvious ploy, is to design an algorithm that only considers
scales that can be represented on some target hardware. My
lcm60, filscal, and fil5 utilities fall into this category.
lcm60 searches through all the 5 limit scales that can be played
on the sound blaster and picks out those with more than a given
number of lcm60 chords. In order to do this in a reasonable
length of time, I had to resort to an exotic form of arithmetic,
adding and subtracting factors instead of multiplying and
dividing. That is the reason I have only so far done this for 5-
limit scales. Going to 7-limit would expand the search space and
make the programming more difficult.

The fill method, starts with some arbitrary number, or numbers,
and then searches through all the possible remaining notes, and
selects the one which has the smallest LCM's with the existing
notes. This procedure is iteratively applied until the scale is
filled. fil5 restricts possible choices to 5-limit candidates.

The lcmscal, and nulcm utilities select scales with lower LCMs.
While it is true that a scale with a low LCM may not necessarily
produce chords with a low LCM, there seems to be enough
correlation to make the method useful.

Marion

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Helmut Wabnig writes

>I like listening to midi music, because it is free of "interpretation",
>which does not interest me.
>

Now there's an interesting idea! I wonder, Helmut, what you can mean by
""interpretation"". All notated music was certainy mean to be subjected to
"interpretation"
(in the sense that the score is not a literal representation of the music)
If this is so, what you're listening to is a MIDI interpretation, no?

- David

___________________________________________________
David Worrall
Founding Head, Australian Centre for the Arts & Technology (ACAT)
Institute of the Arts, Australian National University.
PO Box 804 Canberra, ACT 2601 AUSTRALIA
Tel: +61 6 249 5640 Fax: +61 6 247 0229
http://www.anu.edu.au/ITA/ACAT/drw/Welcome.html
___________________________________________________



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