Euler Harmonics and drift in 4D space

[Monzo TD 184.1]
>My English translation of Patrice Bailhache's
>_Music as Mathematics: Leonhard Euler_ is at:

>http://www.ixpres.com/interval/monzo/euler/euler-en.htm

I am going to have to study this carefully because it has a lot of
interesting stuff in it. The table of numbers is the nearest thing that
I have seen to my harmonics calculations outside of vedic literature.
The calculations are not the same, but must have some similarities as
many of the same numbers are there.

>I submitted a posting about this interesting idea a couple of
>months ago, calling modulation along the 3 and 5 axes (the
>kind we're used to hearing or implying) 'lateral modulation'
>and modulation along the 7 and 11 (and higher?) axes 'vertical
>modulation'.

>The terminology is loosely based on tonal lattice diagrams,
>since the 3 x 5 axes form a grid.

I also think of the 3 and 5 making the grid and the 7 as vertical.
Of course we humans can't see extra orthogonal dimensions so sometimes I
think of 2 as vertical (but very closely stacked).

>I've noted also in my book that older concepts of tonal
>expansion were based on a lateral or horizontal expansion
>of pitch resources, while La Monte Young is perhaps the
>foremost explorer of the vertical expansion (using whole
>groups of primes into the 200s).

Ah, Pythagorean versus Galilean!

Personally I don't think that any primes beyond 23 are important in
music of themselves. However some may come about as a result of special
modulations such as a 48 frequency modulated by a 1 will give a prime 47
(and a 49) due to the interaction. This raises another aspect of
variations about the JI important notes and is another enormous topic in
its own right - expect a post about that soon.

>Many times here I've talked about how for so many years as
>I worked in isolation, I thought I'd 'invented' lattice diagrams
>and lots of other aspects of my theory.

>Getting on the Tuning List has shown me that work like this
>has been done before, and it's a delight to be able to argue
>aspects of it with others who know all about it.

I know the feeling well, but mainly in relation to physics ideas.
The most wonderful thing about internet is that it allows people who
have thoughts that only one in a million have to find the other members
of that group around the world.

-- Ray Tomes -- http://www.kcbbs.gen.nz/users/rtomes/rt-home.htm --
Cycles email list -- http://www.kcbbs.gen.nz/users/af/cyc.htm
Alexandria eGroup list -- http://www.kcbbs.gen.nz/users/af/alex.htm
Boundaries of Science http://www.kcbbs.gen.nz/users/af/scienceb.htm