A brief introduction to Harry Partch's 43 note scale

Your best bet to understand this stuff is to get your hands
on "Genesis of A Music" by Harry Partch.  It was most
recently reprinted by DaCapo in New York, but it is again
out of print.  Besides looking for it in libraries, you
might aslo drop DaCapo a note letting them know you'd be
interested in buying a copy if it is reprinted again.

I'll only attempt a thumbnail sketch here.

The pitches of Partch's scale are described as ratios.
This is the ratio of two frequencies (or two strings
lengths if they are otherwise identical) to each other.
This is the method used by all people who work in
just intonation.  Partch's scale can be considered
"extended just intonation".

[Example of ratio notation - what most people call an octave,
is expressed by the ratio pair 1/1 2/1, instead of a a'.  If
you aren't used to it, it may seem awkward.  Once you're used
to it, it's fairly obviously a more straight forward description
of two pitches rather than letter names]

So Partch uses an "11 limit" scale.  He could have used a higher
limit - and then had more notes to deal with.  He says there's
nothing magical about 43 or 11 - it's just the point at which he
felt he had enough of a spread of tonal resources.

[In my own practice, I treat it as a continuum - there are an
infinite number of ratios and they are all potentially useful.
But that reflects that I work in software and Partch worked in
hardware.]

So the ratios of Partch's scale are as follow.  He indicated that
1/1 = 392 Hz, which is the G below A 440.  This is nothing more
than a starting point for measurement.

1/1 the Prime Unity
81/80
33/32
21/20
16/15   a minor second
12/11   a minorish second
11/10   a middling second
10/9    the small major second
9/8	the large major second
8/7
7/6
32/27
6/5     Minor third to 1/1
11/9
5/4     Major third to 1/1.  the pure thirds are a strong facet of this scale
14/11
9/7
21/16
4/3     Fourth to 1/1
27/20
11/8
7/5     tritone
10/7    tritone
16/11
40/27
3/2	Fifth to 1/1
32/21
14/9
11/7
8/5     minor sixth to 1/1
18/11
5/3     major sixth to 1/1
27/16
12/7   seventh-natured         
7/4
16/9   the small minor seventh
9/5    the large minor seventh
20/11
11/6
15/8    the small major sevenths
40/21   a very major seventh
64/33   
160/81
2/1