AJI - Automatic Just Intonation

G'day all

I am Ray Tomes and new here. David Madole might like to know that I am
in New Zealand so that he can add one more country to his statistics. I
found out about your list from Matt Nathan who found my WWW pages
somehow. About now I should admit my general ignorance of music jargon
and explain that I came into all this by the back door and missed out on
getting a party hat at the front :-) so please excuse my lapses.

Some years ago I had the idea that with electronic instruments there was
no need to make the old compromises when choosing a tuning system. Just
as a violinist or singer can adjust frequencies a little from note to
note to get perfect harmony, so can an electronic keyboard instrument if
it "knows" what adjustments are needed. In most cases the logic of this
is trivially easy, but there are some more difficult cases. I took out
a provisional patent on the idea, but after finding that an existing
patent covered part of what I was doing and that it would cost big bucks
for possibly no protection I made it all publicly available free.

I call it "Automatic Just Intonation" or AJI for short (this is a little
play on words for Japanese because "aji" means "taste" in japanese).

The description of the idea is on my WWW pages at
http://www.kcbbs.gen.nz/users/rtomes/aji-main.htm
and there are some worked examples also. Due to not owning fancy enough
instruments I have never fully implemented the idea, so if someone who
has the necessary equipment would like to I would be pleased to work
with them.

Here is the essence of the idea. For any chord played take the spacings
of the note-numbers (counted in semitones) and compare them to a master
list which looks like this [note=12*log(ratio)/log(2)]:

ratio 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 etc
note 0 12 19 24 28 31 34 36 38 40 42 43 44 46 47 48 ...

A flash version of this is at
http://www.kcbbs.gen.nz/users/rtomes/aji-a.gif which if printed and cut
in two is a kind of chord slide rule calculator.

Basically you just go along the "note" line from the left until you find
a pattern that matches the notes played. Suppose we play C-E-G then
these have spacings of 4 and 3 semitones (we could use 0-4-7 as a
pattern as E is 4 semitones above C and G is 7). The first occurence of
this pattern is when we get to ratios 4:5:6 and so those are the correct
ratios for these notes (big surprise!) and we can do the same for any
note combination. Use a non-proportional font (such as courier)

1 111 111 fixed
1...........2......3....4...5..6..7.8.9.0.123.456 etc ratio
| | | | | | | | | | ||| ||| scale

---> | | | sliding
C...E..G chord ... matches here

There are a few catches.

1. Once we get up to ratios in the 20s then more than one ratio lands on
the same note and so we don't know which one it should be. I have given
a lot of thought to this and devised several different schemes.
Basically ratios composed of products of 2s and 3s are preferred and
ratios of 5 and 7 are OK and the rest seldom get a look in.

2. Some combinations such as C-D fit in several places near each other
in the table and can mean a ratio of 7:8, 8:9 or 9:10. With no other
information 8:9 is preferred as being made up of 2s and 3s. However it
also depends on the preceeding notes played.

3. How do we know how to link the notes in one chord to those in the
next in terms of relative frequency? Sometimes there are two
possibilities because two repeated notes have a change in their
relationship (e.g G-A changes from 8:9 to 9:10 when D-G-A is followed by
C-G-A). Do we change G or A?

These and other complications are discussed in my article.

In another post later I will explain my theory of the universe which
proves quite convincingly that the entire universe is nothing but a
giant musical instrument and that everything in it, galaxies, stars,
planets ...atoms and particles are all just the manifestations of the
strongly favoured oscillation modes. Seriously!

-- Ray Tomes -- rtomes@kcbbs.gen.nz -- Harmonics Theory --
http://www.kcbbs.gen.nz/users/rtomes/rt-home.htm

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