Paul Erlich auditory experiment

Well, Paul has been doing LOTS of fascinating experiments lately, but
the one listed here is an AUDITORY one that he is kindly encouraging
me to post on my "Tuning Lab" site...

I'm VERY sorry this has been taking so long. One of the files would
not appear on the mp3.com site after about a week... so I uploaded it
AGAIN, and now it is appearing.

THEN, I reordered the files... they are STILL not perfect, since
mp3.com has not moved the 4:5:6:7 JI experiment near the others yet,
as I have wished. I believe they are totally taken up with a new
interface they just rolled out... so updates are abnormally slow.

ANYWAY... it's almost "perfect." Just realize the 4:5:6:7 JI example
should be with the others.

HERE IS THE URL:

http://artists.mp3s.com/artists/140/tuning_lab.html

These examples were all created by Paul on his MATLAB program.

The first example is a JI tetrad 4:5:6:7

The next example is an approximate 4:5:6:7 in Paul's 22-tET

Finally, there is a dominant 7th chord in 12-tET

For me, the beatings grow gradually from JI to 22 to 12... I don't
believe much of an unexpected result...

NEXT, Paul deals with the UTONAL world with a half-diminished 7th:

JI 1/7:1/6:1/5:1/4

THEN, there is an approximation of the same chord 1/7:1/6:1/5:1/4
derived from 22-tET.

FINALLY... Paul compares the utonal half-diminished sevenths with
OTONAL half diminished sevenths:

JI 5:6:7:9

The approximation of 5:6:7:9 in 22-tET

and, finally, a half-diminished 7th in 12-tET.

Results??

Well, I was rather startled as to how similar the utonal and otonal
half-diminished sevenths sounded. It was MUCH different than in the
Daniel Wolf example, where I believed I was hearing chords come "into
focus" in the otonal version.

Paul had an explanation for me:

>Well, there was an important difference in the Daniel Wolf example
--
>the otonal chord there had a bass note that was equivalent to the
>otonal root,while in this example (half-diminished) it doesn't.

Anyway, I hope everyone enjoys the LISTENING experience. For me,
also, it is a crucial point of it all.

I have to admit I have been astonished by Paul's recent posts with
the
tetrads from harmonic entropy space...

His suggestion in the important post #11686:

>Many of the chords above come from a
>standard application of 5-limit JI to tetrads found in the diatonic
>scale (including melodic minor and harmonic minor variants), but
many
>are tempered in a subtle way,and some are downright xenharmonic. An
>excellent exercise for a composer looking for points of stability in
>the infinite realm of microtonal harmony would be to spend some
>time with the chords above.

was not lost on "deaf ears." This study was amazingly exhaustive
(virtually "mind blowing" if you include the graphics, but enough on
that!). What a way to approach consonance! (or concordance, or
whatever...)

I'm only hoping I can persuade Paul to let me post some of these
tetrads as SOUND files on my little "Tuning Lab" mp3.com site! I
want
to HEAR the results of the experiment!

_________ ____ __ _ _
Joseph Pehrson

>Well, I was rather startled as to how similar the utonal and otonal
>half-diminished sevenths sounded. It was MUCH different than in the
>Daniel Wolf example, where I believed I was hearing chords come "into
>focus" in the otonal version.
>
>Paul had an explanation for me:
>
>>Well, there was an important difference in the Daniel Wolf example
>>the otonal chord there had a bass note that was equivalent to the
>>otonal root,while in this example (half-diminished) it doesn't.

That's important, but even more important is the fact that they
really are similar. You're listening to your 5679 chord in JI file
twice, calling it correctly once, and incorrectly calling it the
utonal 4567 in JI the other time. The utonal 4567 in 22 file is
right, however.

At the same time, the file names in the writeup at mp3.com don't match
what the mp3.com server actually gives you. The file names it gives
aren't very descriptive either (they're truncated).

>I have to admit I have been astonished by Paul's recent posts with
>the tetrads from harmonic entropy space...
>
>His suggestion in the important post #11686:
>
>>Many of the chords above come from a standard application of 5-limit
>>JI to tetrads found in the diatonic scale (including melodic minor
>>and harmonic minor variants), but many are tempered in a subtle way,
>>and some are downright xenharmonic. An excellent exercise for a composer
>>looking for points of stability in the infinite realm of microtonal
>>harmony would be to spend some time with the chords above.
>
>was not lost on "deaf ears."

Right on!

-Carl

--- In tuning@egroups.com, Carl Lumma <CLUMMA@N...> wrote:
> >Well, I was rather startled as to how similar the utonal and
otonal
> >half-diminished sevenths sounded. It was MUCH different than in
the Daniel Wolf example, where I believed I was hearing chords come
"into focus" in the otonal version.
> >Paul had an explanation for me:
> >
> >>Well, there was an important difference in the Daniel Wolf example
> >>the otonal chord there had a bass note that was equivalent to the
> >>otonal root,while in this example (half-diminished) it doesn't.
>
> That's important, but even more important is the fact that they
> really are similar. You're listening to your 5679 chord in JI file
> twice, calling it correctly once, and incorrectly calling it the
> utonal 4567 in JI the other time. The utonal 4567 in 22 file is
> right, however.
>

Hi Carl and Paul!

Hmmm. Well, that certainly would explain the similarity, wouldn't it!
I can't believe I did that... I thought I was being so careful.
Well, I will look into it, and change it immediately.
Thanks for the immediate perception!

___________ _____ ___ __ _
Joseph Pehrson