Invisible Haircut

> Joe Monzo's Invisible Haircut

[Erlich:]
> I really like this tune!

[Lumma:]
> Isn't it killer?

Thanks, guys. I really appreciate the kind words.

We've been slammed for "so many numbers, so little music",
and I feel that to a large extent I'm dropped into that
category, so I figured it was time I had better get some
good microtonal music "out there".

[Lumma:]
> Have you heard his 24Tune?
> It's on his webpage under list of works.

> I actually like it better than invisible haircut.

You told me you like the "24-Eq Tune", Carl, but
I'm really surprised that you don't like "Invisible
Haircut" more. Not that I'm trying to slight the
other tune, but I wrote that mainly because I felt
24-Eq had been criticized "unjustly", and I took
it as a challenge to write something that sounded
good in that tuning.

"Invisible Haircut", on the other hand, was really
an inspiration. It just popped into my head and/or
fingers one day, and immediately, as soon as I'd
played it, I could imagine all the different just
ratios swirling about.

[Erlich:]
> This type of transcription, with 11 and 13 and 19
> identities, leads to a pronounced "periodicity buzz"
> in the otonalities that is radically different from
> the jazz aesthetic but has a flavor that can certainly
> grow on you (Kami Rousseau had some similar transcriptions
> on his web page . . .

I'm quite happy with the way my "justification" of it
turned out. The "periodicity buzz" in that V/V - V - I
progression really does it for *me*!

> Also, the progression from the 126/95-Otonality to
> the 9/5-Otonality is quite nice as a V-I, even though
> the root rises by a fourth of 529 cents (or drops by
> a fifth of 671 cents).

These are the two chords that really display
that "buzz". I thought I'd go into a little
more detail about Paul's observation about the
size of the intervals.

I'm adding the following "minor" chord into this
description. Altho my harmonic analysis (on the
webpage) of the "Eb minor" chord is as a 27/20-Utonality,
it can also be thought of in the traditional sense
as a "minor" chord built upwards on "Eb" 6/5.

Here's a diagram, in cents (rounded to 2 decimal
places), of the "root" movement of these three chords,
and the intervals of both the V-I skips, and the
stepwise movement in the (Schenkerian) "prolongation"
from the 126/95 to the 6/5:

126/95 9/5 6/5
488.91 1017.59 315.64
| \ / \ / |
| 671.31 498.04 |
\________ 173.27 __________/

I believe the reason this works so well
is because there is a "xenharmonic bridge"
at play here. The difference between
126/95 and 4/3 is the interval 190/189
[= 9.13+ cents]. If we analyze the intervals
in the above progression with 4/3-Otonality
substituted for the 126/95-Otonality, we get:

4/3 9/5 6/5
498.04 1017.59 315.64
| \ / \ / |
| 680.44 498.04 |
\________ 182.40 __________/

Although it's not your usual Pythagorean [3-limit]
bass-line, this is a "root"-movement that would be
familiar to most people, since it occurs in the
(implied) JI/meantone diatonic scale.

The II (supertonic - "minor") is *the* problem chord
in (implied) 5-limit diatonic music. Sometimes the
II-degree has to be tuned to 9/8 to be consonant with
the Dominant (V), sometimes tuned to 10/9 to be consonant
with the Subdominant (IV).

Notwithstanding Paul's observation about how my chords
here are "radically different from the jazz aesthetic",
jazz harmony was very much how I was thinking when I
wrote this tune.

In jazz , the standard chord progressions are strings
of V-I's, and that's what I did in this little section.
Thus, we can assume a local tonicization of the "Eb" 6/5
in the above progression.

In the "key of Eb 6/5", the "I" is 6/5, the "V" is 9/5,
and the "II" (the "V of V") is, in this case, 4/3.

So I think that it's entirely possible that we're
"hearing" 4/3 for 126/95, as well as perceiving a
more familiar 40/27 skip for the 28/19 actually heard
between "F" and "Bb", and a 10/9 step for the 21/19
actually heard between the "F" and "Eb", by making
use of the 9-cent xenharmonic bridge from the 3- to
the 19-limit.

BTW, I didn't plan any of this - it "just" worked
out that way. I figured out the JI "translation" years
ago by writing out pages full of common-tone chord
progressions. It was only much later that I
"saw that confounded bridge".
[pun intended, for Led Zeppelin fans]

I wish I could draw a lattice of it here to simplify
the explanation (and because it's *beautiful*!),
but 19-limit is too complex (and too big).

Other small 3--19 bridges were implied in the
Chromatic and Enharmonic genera of the ancient
Greek Eratosthenes, c. 200 BC, and in the Chromatic
genus of Boethius, c. 505 AD, and have also popped
up in my explanation of Marchetto's "fifth-tone"
theories, c. 1318. (c. - I mean see, my website)

I'd like to point out that, tho I already admitted
this was a transcription (since it was first composed
on a 12-Eq keyboard), the sound of the JI version you
hear was very much in my head from the moment I wrote
it. This is the case for a lot of 12-Eq music I've
written over the last ten years.

The entire reason I developed my lattice theory is
because I despaired of having an instrument that could
give me all the pitches I wanted, and the lattice
diagram model was the best way for me to understand
and internalize the musical relationships.

Associating the visual mapping with the sound of
the intervals was the only way I could make sense
of the vast array(s) of ratios in the musical fabric.
So even as I write or play in 12-Eq, I'm hearing
(in my head) ratios that I can visualize on the lattice.

Having instruments available now in 17-, 19-,
22-, and 31-Eq helps a bit, because at least it
gives me some more of the sounds, but I still think
in JI and sure wish I could afford a Microzone!
(or even a Clavette!) It would take a lot of the
work out of what I'm doing . . .

("justified" another of my old tunes last night)

-Monzo
http://www.ixpres.com/interval/monzo/homepage.html

Listen to "Invisible Haircut" at:
http://www-math.cudenver.edu/~jstarret/haircut.html
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[Erlich:]
> It is magical how JI transcription happened
> to "work" on this one.

[Lumma:]
> Ackg! JI can always work this well, no magic.

[Erlich:]
> If you read the "Invisible Haircut" page itself,
> you'll see that Joe says he could not apply this
> kind of JI trascription to works of other composers
> that he tried it on.

I had been thinking about responding to this
earlier and now you kind of pushed me into the ring.

As far as JI working "magically" in my tune:
I have to side with Carl on this. I enjoy writing
and especially improvising in different kinds of
ETs and other tunings too, but with JI I can
always find *exactly* the pitch I'm looking for.

I should have been more specific when I talked
about how this "justification" didn't work for
other composers. I've tried to use 7-limit ratios
for Mozart and couldn't make it work, and there
are 12-Eq tunes that I've tried to interpret
rationally and I just can't do it.

By it "working", what Paul and I mean is that
in ETs you are able to write repeated phrases
that cycle back to the same point, and in JI
there are usually commatic shifts involved in
repeated cycling.

I suppose what the Mozart experiment proved is
that Mozart was pretty much thinking in 5-limit/meantone,
because higher-limit intervals just sounded "off".
(I even tried 19s in Mozart)

I think the main reason it "worked" in "Invisible
Haircut" is because I unconsciously made use of
the 3--19 bridge, so the root movement can be
perceived basically as Pythagorean or 5-limit.
The bridge is what made the magic.

- Monzo
http://www.ixpres.com/interval/monzo/homepage.html
___________________________________________________________________
You don't need to buy Internet access to use free Internet e-mail.
Get completely free e-mail from Juno at http://www.juno.com/getjuno.html
or call Juno at (800) 654-JUNO [654-5866]