From Monz: 2 comments to the Tuning List

Forwarded from Joe Monzo.

-----Original Message-----
From: Joe Monzo [mailto:joemonz@yahoo.com]
Sent: Thursday, February 17, 2000 12:54 PM
To: perlich@acadian-asset.com
Subject: 2 comments to the Tuning List

Hey Paul,

I'm already unsubscribed from the List, but you know
I couldn't stay away completely! I read the latest
Digest on the Archives, and just had to say two
things. Would you please post this for me?

1)
Re: the I-IV-V7-I cadence in different tunings

I had meant to mention something else about my MIDI
file experiment in the post in which I described
my own reactions to the different tunigns.

I hope others can hear this also. My setup uses
an AWE64Value soundcard and it is clearly audible:

Even tho the 'reed organ' patch I used here has
no vibrato, in 2 of the tunings - the 12-EDO and
the meantone - the I and IV chords have an interesting
'chorusing' effect. This effect is completely absent
from the other tunings, which all use JI 4:5:6 for
those chords.

My guess: the timbre of the 'reed organ' patch must
have a strong 5th harmonic (and/or its multiples)
that causes those overtones of the 'root' (1/1 or
4/3, respectively) to clash with the 12-EDO or
meantone 'major 3rd'.

2)
Re: Jerry Eskelin's 'high 3rd' mp3

I listened to Jerry Eskelin's mp3 of the 'high 3rd'
experiment sung by his choir. I'm really glad Jerry
included those interjected 'E's played on the piano,
because (assuming the piano is indeed tuned close
to exact 12-EDO) comparison of the 'E's sung by the
singers does indeed prove that they start at a pitch
which is lower than 12-EDO, and that after the 'G'
is added the pitch of 'E' rises to above 12-EDO.

I think it's fair to say that when it's only the
'C' and 'E' dyad, the 'E' is approximating a 4:5.
Now regarding where that 'E' ends up...

I compared my MIDI-file version of this
http://www.ixpres.com/interval/td/monzo/high3rd.mid
with Jerry's mp3, and to me it sounds like Jerry's
singers aren't ending up on *any* of the 'E's in
my MIDI version.

But I think that the 24/19 'E' [= ~404 cents] comes
closest to what they sing. All the 'E's higher than
that in my MIDI-file sound too sharp, edging up
towards a 'suspended 4th' sound, in comparison to
Jerry's mp3. And of course, the 12-EDO 'E' [400
cents] is not high enough, as proven by the piano.

Now that I've heard Jerry's actual experiment, here's
something very important to consider: this triad has
the '3rd' on top and the '5th' in the middle. So the
simple starting proportions approximate *not* 4:5:6,
but rather 2:3:5, sung on the recording in the order
2 - 5 - 3.

I say that this is an important difference, because
IMO most likely what is happening with the ending
pitch of the 'high 3rd' is that some kind of
interaction concerning summation and/or difference
tones is making the singers sharpen the '3rd' so
that it blends in better (or perhaps one should
just say 'finds a different way to blend nicely',
since 2:3:5 *does* provide a great blend
mathematically!) with the 2:3 [= C:G] after
the 'G' comes in. The math is somewhat different
with the 'high 3rd' on top instead of in the middle.

Busy packing now, there's no way I can spend any
more time on this. Hopefully some of the
mathematicians will chew on this for a while,
so that there will be plenty on the subject for
me to read when I re-subscribe!

-monz
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Joe Monzo wrote,

>My guess: the timbre of the 'reed organ' patch must
>have a strong 5th harmonic (and/or its multiples)
>that causes those overtones of the 'root' (1/1 or
>4/3, respectively) to clash with the 12-EDO or
>meantone 'major 3rd'.

In 12=, yes, but in meantone the 3rd harmonic would be involved in a
stronger chorusing effect than the 5th harmonic.

>Re: Jerry Eskelin's 'high 3rd' mp3

[...]

>I say that this is an important difference, because
>IMO most likely what is happening with the ending
>pitch of the 'high 3rd' is that some kind of
>interaction concerning summation and/or difference
>tones is making the singers sharpen the '3rd' so
>that it blends in better (or perhaps one should
>just say 'finds a different way to blend nicely',
>since 2:3:5 *does* provide a great blend
>mathematically!) with the 2:3 [= C:G] after
>the 'G' comes in. The math is somewhat different
>with the 'high 3rd' on top instead of in the middle.

Joe, interactions involving difference tones (or summation tones, which are
almost never audible) favor the simplest possible otonal representation for
the chord, since then, and only then, will the combinational tones all form
simple ratios with the chord tones. My feeling is that Wim's way of thinking
is on the right track: the soprano will tend to "disappear" into the chord
if singing a just major tenth over the bass (2:5 or 1:5), while she will
"stand out" if she sharpens it a little, the rootedness of the chord being
secure due to that 2:3 perfect fifth below her.

I was going to say, "Anyhow, hopefully someone can analyze Jerry's mp3 and
determine exactly what intervals are in this chord." But then I listened to
it. It's a mess. Each singer is wavering within a large band, and the fact
that multiple singers are singing the "same" pitch, creating erratic beats
with one another (in addition to the technical problem of distinguishing
overtones of low notes from fundamentals of high notes, and dealing with the
beats between the two), is going to make a precise analysis of the intervals
impossible (please don't let that stop anyone from trying to get some
approximate cent numbers, though!). If this is what Jerry considers
"locking", I suggest he re-evaluate his position on the ~1� accuracy of some
synthesizers being insufficient to find the true "locking" intervals. Or is
this just a "student" choir?