Double octave divided into 47 steps

Hello all!

Happy to see the list working again. Here I'm going to repeat my obviously
lost message of December 13 for a third time:

"Ever heard of a scale that divides the double octave into 47 steps? It is
non-octave, naturally, and its equal-tempered version accomodates 7- and
13-limit intervals exceptionally well. I came across it when playing a little
with "Pythagorean" scale approaches. For those interested I put it up on the
Net:
http://members.aol.com/bpsite/pythagorean.html "

My best wishes for the New Year to you all!

Heinz Bohlen

>Hello all!

Hello Heinz,

>Happy to see the list working again. Here I'm going to repeat my obviously
>lost message of December 13 for a third time:
>
>"Ever heard of a scale that divides the double octave into 47 steps? It is
>non-octave, naturally, and its equal-tempered version accomodates 7- and
>13-limit intervals exceptionally well. I came across it when playing a little
>with "Pythagorean" scale approaches. For those interested I put it up on the
>Net:
>http://members.aol.com/bpsite/pythagorean.html "
>
>My best wishes for the New Year to you all!

This is simply every other step of 47 tET. I've played with a number
of these scales which are multiple octaves divided by an odd number of
steps. One of my favorites is three octaves divided by 19, or every
third step of 19 tET.

Randy
**************************************************************************
* Randy Winchester * randy@mit.edu * PO Box 426074, Cambridge, MA 02142 *
* (617) 253-7431 * http://web.mit.edu/randy/www *
**************************************************************************

Hello Heinz,

My apology. Actually, I did see the article on your web site shortly
after the first time your message was posted. Very interesting!

I wasn't thinking as clearly the next time I saw your article and my
mind immediately went to equal divisions of multiple octaves -
something that I had been pondering recently.

HPBohlen@aol.com wrote:
>You answered that dividing the double octave into 47 steps "is simply every
>second step of 47 tET". If you look up the website that I suggested (
>http://members.aol.com/bpsite/pythagorean.html ) you will find that it is by
>far not that simple. The scale I came across is a scale of just intervals,
>many of them 7- or 13-limit, and it is decidedly non-octave (i.e. there is no
>relationship to any ET-scale). It contains a fair number of triades and
>tetrades, as for instance 1/1 - 7/4 - 5/2 - 13/4, 1/1 - 10/7 - 13/7 - 16/7,
>1/1 - 13/10 - 8/5, thus there is some real potential for harmonies. It is just
>accidental and fortuitous that dividing the double octave into 47 equal steps
>presents a very good approximation for many of the scales intervals.

Randy
**************************************************************************
* Randy Winchester * randy@mit.edu * PO Box 426074, Cambridge, MA 02142 *
* (617) 253-7431 * http://web.mit.edu/randy/www *
**************************************************************************