Fwd: Another musical algorithm.

--- In MicroMadeEasy@yahoogroups.com, "robert thomas martin"
<robertthomasmartin@...> wrote:

Another musical algorithm for making microtonal transformations is:

C = zero cents
G = x
D = 2x
A = 3x

E = y
B = x + y
F# = 2x + y
C# = 3x + y

Ab = 2y
Eb = x + 2y
Bb = 2x + 2y
F = 3x + 2y

Choose any values for x and y.

Subtract multiples of 1200 when the results exceed 1200(an octave).

--- End forwarded message ---

Robert Thomas Martin wrote:

> Choose any values for x and y.

> Subtract multiples of 1200 when the results exceed 1200(an octave).

Have you heard of the Euler's monochord scale? It's just one of these -- with the sole exception that the chain starts on F, not C. One generator is the "x" of 3/2 (i.e. ~701.955 cents) and another one is the "y" of 5/4 (i.e. ~386.314 cents).

Scala can create these "Euler-Fokker genera" with the "Eulerfokker" command with whatever intervals and whatever number of dimmensions (or generators) you choose. Some of them sound really cool -- About two years ago, I've actually made some music which I then retuned from one such "genus" to another so that I had different versions of the piece.

Petr

--- In tuning@yahoogroups.com, Petr Parízek <p.parizek@...> wrote:
>
> Robert Thomas Martin wrote:
>
> > Choose any values for x and y.
>
> > Subtract multiples of 1200 when the results exceed 1200(an
octave).
>
> Have you heard of the Euler's monochord scale? It's just one of
these -- with the sole exception that the chain starts on F, not C.
One generator is the "x" of 3/2 (i.e. ~701.955 cents) and another one
is the "y" of 5/4 (i.e. ~386.314 cents).
>
> Scala can create these "Euler-Fokker genera" with the "Eulerfokker"
command with whatever intervals and whatever number of dimmensions
(or generators) you choose. Some of them sound really cool -- About
two years ago, I've actually made some music which I then retuned
from one such "genus" to another so that I had different versions of
the piece.
>
> Petr
>
From Robert. I don't know anything about Euler or Fokker but I've
used this simple algorithm countless times when carrying out music
experiments. It has always seemed an untuitively logical way of
going about things. I have made a note of "Euler's monochord scale"
and "Euler-Fokker genera" for future research. I design and/or
collect simple musical algorithms which can be used to generate
microtonal transformations of 12tet music and I am always on the
lookout for new ideas. Please supply some useful links if you can.
And thankyou.

> From Robert. I don't know anything about Euler or Fokker but I've
> used this simple algorithm countless times when carrying out music
> experiments. It has always seemed an untuitively logical way of
> going about things. I have made a note of "Euler's monochord scale"
> and "Euler-Fokker genera" for future research. I design and/or
> collect simple musical algorithms which can be used to generate
> microtonal transformations of 12tet music and I am always on the
> lookout for new ideas. Please supply some useful links if you can.
> And thankyou.

www.xs4all.nl/~huygensf/doc/efg-e.html

http://tonalsoft.com/enc/e/euler-genus.aspx

Petr

PS: Don't know why the first link doesn't appear to be a link. Please copy and paste it in your browser.

PP

--- In tuning@yahoogroups.com, Petr Parízek <p.parizek@...> wrote:
>
> PS: Don't know why the first link doesn't appear to be a link. Please
copy and paste it in your browser.
>
> PP
>
From Robert. Thanks for the links. If I find anything I can actually
understand then I will try to "dumb it down" for all the
mathematically challenged musicians like myself.