AUDIBLE HARMONIC ENTROPY PREVIEW!!

Many of the tetrads of Paul Erlich's extensive Harmonic Entropy
experiment are ready for listening in the Tuning Lab!

True, not *ALL* of them have appeared yet... but the vast majority
have. So, this is a bit of an Audible Harmonic Entropy PREVIEW:

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

This is an exciting experiment... since it's a little like extracting
sonority out of "thin air," although I am certain Paul would not
describe it in this way!

It's nice to have an "audible face" to some of these numbers!
__________ ____ __ __ _ _
Joseph Pehrson

Thanks Joseph! If I were to nit-pick, I'd say two things: first, I wish you
had included the parenthetical remark on the last two tetrads; and second,
the relevant graphic would have been:
http://www.egroups.com/files/tuning/perlich/harment.gif. I'd recommend not
using the lo-fi play option here -- the chords sound pretty horrible that
way. Anyway, Joseph, did any of these chords strike your fancy?

Also, Joseph, there is an error in the description of tetrad #14 -- it
should be 9:10:12:15, not 10:12:15:18. Sorry! Could you correct that?

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:

http://www.egroups.com/message/tuning/13115

No, no... "nit-picking" is what it needs at this point!

> Thanks Joseph! If I were to nit-pick, I'd say two things: first, I
>wish you had included the parenthetical remark on the last two
>tetrads;

I think I'm allowed only a 400 letter description in the box... and
that was a *huge* remark... Well, I'll give it a try, and see how
much of it will post...

and second,
> the relevant graphic would have been:
> http://www.egroups.com/files/tuning/perlich/harment.gif.

I knew I'd get the wrong graphic for this exercise... I will replace
the "big" one. The "little ones" are only decorative, anyway to show
which files go with the experiment.... and you can't really read them.

I'd recommend not
> using the lo-fi play option here -- the chords sound pretty
horrible that way.

You're right. I noticed that.

>Anyway, Joseph, did any of these chords strike your fancy?

Well, actually, many did, but I'm trying to figure out if I can
detect any *AUDIBLE* kind of logic progressing to greater dissonance
as wego up the numerical tetrad chain. I guess the ones at the end
surely sound more dissonant than the ones at the beginning... but,
in-between... I'm not sure I'm hearing it yet.

But, I need to spend some more time with them. I think it's a
fascinating exercise, anyway, and it's great to actually *HEAR* them
now...
________ ___ __ __ _
Joseph Pehrson

Joseph wrote,

>Well, actually, many did, but I'm trying to figure out if I can
>detect any *AUDIBLE* kind of logic progressing to greater dissonance
>as wego up the numerical tetrad chain. I guess the ones at the end
>surely sound more dissonant than the ones at the beginning... but,
>in-between... I'm not sure I'm hearing it yet.

No, no, no. Read that parenthetical remark again. The ordering is biased
toward larger intervals, hence many of the 89 tetrads that I left out could
easily be more consonant than the ones I included, if you got rid of that
bias. If you care about the ordering, what I need to do is repeat the
process using a Tenney instead of a Farey series . . . should get the same
local minima but different ordering . . . otherwise I'd prefer you disregard
the ordering altogether.

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:

http://www.egroups.com/message/tuning/13116

> Also, Joseph, there is an error in the description of tetrad #14 --
it should be 9:10:12:15, not 10:12:15:18. Sorry! Could you correct
that?

This error has now been corrected. In addition, I added the
parenthetical remarks for the "final" two tetrads. I can see it
wasn't quite so "parenthetical" after all! Surprisingly, *ALL* of it
was posted properly... it *HAS* to be over 400 characters...

GRAPHIC:

I added a html reference to the correct harmonic entropy graphic. I
didn't change the big "decorative" one on the page, since I have
enough experience with graphics to know that the "real" one was going
to "break up" and not look "nice" on the page... it's too fragmented.
I tried.

So, the one on the page is only decorative, but there is a prominent
link to the "correct" graphic.

I believe those are the only necessary corrections for now... besides
possible re-ordering (??)
_________ ___ __ __ _
Joseph Pehrson

Thanks so much Joseph! I'm working on the Tenney thing now . . . using
n*d<10000. I wonder why this is taking my computer so long? This is the
Matlab code I use to calculate the series:

function out=tfarey(n)
out=[1 1 1];
for a=1:n-1;
for b=1:floor(n/a);
if length(find(out(:,1)==a/b))==0
out=[out;a/b a b];
end;
end;
end;
[y,i]=sort(out(:,1));
out=[0 0 1;out(i,:);Inf 1 0];

Can anyone suggest a better algorithm?

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:

http://www.egroups.com/message/tuning/13121

>
> No, no, no. Read that parenthetical remark again. The ordering is
biased toward larger intervals, hence many of the 89 tetrads that I
left out could easily be more consonant than the ones I included, if
you got rid of that bias. If you care about the ordering, what I need
to do is repeat the process using a Tenney instead of a Farey series
should get the same local minima but different ordering . . .
otherwise I'd prefer you disregard the ordering altogether.

So, if I'm understanding you, Paul, then if you use the Tenney series
you would get a progression from the most consonant tetrads to less
consonant ones??

Is there no way you can order them like this given the Farey method
you used?? Otherwise you would have to do the experiment over again
entirely, yes??

It really would make a more interesting experiment if the tetrads
"progressed" from more consonance to less consonance... at least
that's what I think...

Is there no way to order them like that without having to redo the
entire thing??

In the meantime, though... if there is no "progression" with the
present examples, then the numberings should be taken off the chords,
correct??
_________________ ____ __ __
Joseph Pehrson

>I believe those are the only necessary corrections for now... besides
>possible re-ordering (??)

Even after re-ordering, there is a glaring flaw in this "experiment" --
adding diadic discordance vlues is only a piece of the puzzle. No matter how
I calculate diadic discordance, adding diadic discordance values will always
give the same results for 4:5:6:7 and 1/7:1/6:1/5:1/4 (the last two chords
on the page). But we both agree that 4:5:6:7 is, overall, "smoother" than
1/7:1/6:1/5:1/4. The reason falls under the rubric of tetradic harmonic
entropy -- which I don't know how to calculate yet . . .

Joseph wrote,

>Is there no way you can order them like this given the Farey method
>you used??

Not that I know of, until someone can answer one of the "open questions" I
posted (on Monday, I think).

>Otherwise you would have to do the experiment over again
>entirely, yes??

Yup -- I've started the calculations -- ah, the n*d<10000 series and its
mediants just finished -- now to calculate harmonic entropy for the diads
from 0 to 2400 cents . . .

>It really would make a more interesting experiment if the tetrads
>"progressed" from more consonance to less consonance... at least
>that's what I think...

>Is there no way to order them like that without having to redo the
>entire thing??

Even when I'm done redoing it, the ordering won't be right, as it will
ignore the otonal/utonal distinctions, that a true tetradic harmonic entropy
calculation would take into account . . .

>In the meantime, though... if there is no "progression" with the
>present examples, then the numberings should be taken off the chords,
>correct??

Absolutely . . . I should be able to give you the new numberings within a
day . . . assuming none of the chords drop out, new ones don't drop in, and
tunings don't shift . . . in which case I should be able to "MusicMatch" you
some new .mp3s (the program is installing now).

And oh yes, Joseph, some of the bottom 89 are sure to move into the top 36
with the new ordering . . . so I'll definitely be making you some .mp3s . .
.

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:

http://www.egroups.com/message/tuning/13130

> And oh yes, Joseph, some of the bottom 89 are sure to move into the
top 36 with the new ordering . . . so I'll definitely be making you
some .mp3s . .

Paul... I'm sorry, but I'm getting a little confused. After you do
the Tenney sortation *SOME* of the tetrads I have will be part of the
sortation, correct?? Only there will be some others that you will be
adding, yes??

And there *WILL* be some kind of "gradation" away from concordance...
the only inaccuracy being that the distinctions between utonal and
otonal chords are not being recognized appropriately (???)

And please don't forget... ONLY .mp3's this time...

Thanks!
______________ ___ __ _
Joseph Pehrson

I wrote,

>> And oh yes, Joseph, some of the bottom 89 are sure to move into the
>>top 36 with the new ordering . . . so I'll definitely be making you
>>some .mp3s . .

Joseph wrote,

>Paul... I'm sorry, but I'm getting a little confused. After you do
>the Tenney sortation *SOME* of the tetrads I have will be part of the
>sortation, correct?? Only there will be some others that you will be
>adding, yes??

Right . . . before I gave you only the top 36 and left off 89 more. Now,
these will be reshuffled, and the new "top 36" will contain ones you don't
have yet.

>And there *WILL* be some kind of "gradation" away from concordance...
>the only inaccuracy being that the distinctions between utonal and
>otonal chords are not being recognized appropriately (???)

Pretty much . . . and inaccuracy that regards the triadic subsets of the
tetrads as well as the entire tetrads.

>And please don't forget... ONLY .mp3's this time...

You got it!

Guys, this is crazy. Zip those into a single file and get them the hell
off that commercialized-ass mp3.com. There is plenty of server space in
the world, and I don't need to enter my e-mail addresss 30 times to hear
30 seconds sound.

-Carl

Carl wrote,

>Guys, this is crazy. Zip those into a single file and get them the hell
>off that commercialized-ass mp3.com. There is plenty of server space in
>the world, and I don't need to enter my e-mail addresss 30 times to hear
>30 seconds sound.

I don't have to enter my e-mail address even once, and I'm pretty sure I've
deleted all the cookies from my system.

?!?!?