Paul Erlich experiment details

Ed Borasky wrote:

>If you're going to play with CSound, I *highly* recommend buying "The
CSound
Book" from MIT Press. It has *two* CDs and includes CSound, a number of
tutorials, oodles of sample code and some student compositions.

Ummm, actually, I just ordered this last night. They sure make it
"easy"
at Amazon.com. One click and straight to the stored credit card.
Whoopie!
Wonderful...

And Darren Burgess wrote:

Joe,

Please send me the info regarding the Erlich experiment and I will
program
the csound orchestra and score to do it. I will comment it so that you
can
understand how it works, and generate the mp3 file for upload to the
tuning
lab. Should be interesting to compare it to the results from the 'z.
Is
there anything specific I need to know when I encode the MP3

Darren

Hi Darren!

This is really great. Thanks for the help, and I will be VERY
interested
in the results! I thought I would just send you the info. privately,
but
then I thought it might be nice to post it again to the list, to
"refresh"
the memories of anyone inclined to listen to the experiment at the lab.
If
people know this, they can just "scroll through" quickly.

Basically, we are using 22-tET with, of course, the following cents
value
(using Scala) considering each step, of course, as 54.545 cents:

0: 1/1 0.000 unison, perfect prime
1: 54.545 cents 54.545
2: 109.091 cents 109.091
3: 163.636 cents 163.636
4: 218.182 cents 218.182
5: 272.727 cents 272.727
6: 327.273 cents 327.273
7: 381.818 cents 381.818
8: 436.364 cents 436.364
9: 490.909 cents 490.909
10: 545.455 cents 545.455
11: 600.000 cents 600.000
12: 654.545 cents 654.545
13: 709.091 cents 709.091
14: 763.636 cents 763.636
15: 818.182 cents 818.182
16: 872.727 cents 872.727
17: 927.273 cents 927.273
18: 981.818 cents 981.818
19: 1036.364 cents 1036.364
20: 1090.909 cents 1090.909
21: 1145.455 cents 1145.455
22: 2/1 1200.000 octave

Using C with a frequency value of 261.6256, we get then, the following
frequencies in Hz:

0: 261.6256 Hertz 8.00000 oct
1: 269.9997 Hertz 8.04545 oct
2: 278.6420 Hertz 8.09091 oct
3: 287.5608 Hertz 8.13636 oct
4: 296.7652 Hertz 8.18182 oct
5: 306.2641 Hertz 8.22727 oct
6: 316.0671 Hertz 8.27272 oct
7: 326.1838 Hertz 8.31818 oct
8: 336.6244 Hertz 8.36363 oct
9: 347.3992 Hertz 8.40909 oct
10: 358.5189 Hertz 8.45454 oct
11: 369.9944 Hertz 8.50000 oct
12: 381.8373 Hertz 8.54545 oct
13: 394.0593 Hertz 8.59091 oct
14: 406.6724 Hertz 8.63636 oct
15: 419.6893 Hertz 8.68182 oct
16: 433.1228 Hertz 8.72727 oct
17: 446.9864 Hertz 8.77272 oct
18: 461.2936 Hertz 8.81818 oct
19: 476.0588 Hertz 8.86363 oct
20: 491.2967 Hertz 8.90909 oct
21: 507.0222 Hertz 8.95454 oct
22: 523.2511 Hertz 9.00000 oct

Now, out of that, we are extracting pitches for a 12-note scale. We map
the pitches according to the following scheme:

Mapping :
C#: 0
D : 2
Eb: 4
E : 6
F : 7
F#: 9
G : 11
G#: 13
A : 15
Bb: 17
B : 19
C : 20
C#: 22

Now that the 12-note scale is created, we are comparing the following
chords with the corresponding chords in 12-tET.

A dominant seventh chord:

Eb-G-Bb-Db

If we were to place a "mirror" right in the center of the "D" on the
traditional keyboard, gazing into it we would see a "mirror" chord:

Eb-Gb-A-Db

This is the second chord, the "half diminished" seventh, that we are
considering for comparison with 12-tET.

Thanks so much for the help, and I will be VERY interested in hearing
the
results.

The .mp3 file really needs nothing really special for posting:

It must be encoded in MPEG 1.0, Layer III, 128kbps,
44.1khz, and any form of stereo (the usual default).

Again, thanks for the help, and I will enjoy receiving these files.
They
can be attached to my e-mail for uploading at

josephpehrson@compuserve.com

By the way, I will be out of town for about a week. Going to a nice
lake
to do, hopefully, some reading and composing, so I'll have lots of
"catching up" to do when I get back.. since I don't have a laptop!

Perhaps the experiment will be ready for "uploading" by then!

THANKS AGAIN!

Joe

________________ ______ ___ __
Joseph Pehrson