From: Tuning Digest
To: monz@juno.com
Date: Fri, 27 Nov 1998 11:00:51 -0500 (EST)
Subject: TUNING digest 1594
TUNING Digest 1594
Topics covered in this issue include:
1) Paul Erlich
2) Drew Skyfyre
3) Paul Hahn
4) TUNING digest 1593
5) Orpheus and the Undertones, Subharmonics, Utonalities etc.
6) Hahn's ASCII lattice
7) Vocal Fry
8) Many Tones
9) Mozart's tuning
10) Janko Keyboard
11) the hunt for Mozart's tuning
12) Cognitive Limits
13) visit to LA
----------------------------------------------------------------------
Topic No. 1
Date: Thu, 26 Nov 1998 13:25:47 -0800
Bah! He could have been using well temperament without being obligated to
use all of its resources. Also, a simple analysis of what "keys" a work
requires is not all there is to it. 1/4 comma meantone is really quite a
different beast than something like Werkmeister.
The point is that Mozart in his life must have played on keyboards that
were horribly out of tune. He must have played on meantone instruments.
And most of the time he was probably playing in some well temperament. To
ask "what did the composer use" is like asking Indonesians to write down
their tunings. These well temperaments were part of the musical
consciousness of the time. It is okay if we want to write them down, as
long as we don't fool ourselves about who wrote them down. Sure, we know
about Werkmeister because somebody back then wrote it down. But the idea
harpsichord tuners in the 18th century were accurately tuning any
particular one of these book tunings....
In this case none; I was considering only just intervals.
In general: Surprise me.
Yes, and I posted a reply.
I could see trying these. I'm going to be getting my first MIDI keyboard
in a week or two. It should be fun. In the long run, however, I have
serious problems with these mappings. In the 12-of-22 mapping, patterns on
the keys and patterns in the tuning will not match up. In the tuning
described in your paper, I can't span the interval of equivalence with one
hand.
Darreg called this last objection a "pseudo-problem". McLaren went off on
me about how playing octaves was a piano-era orchestration effect that's no
longer necessary with the advent of electronic timbres. But there are lots
of other reasons why one might want to be able to span a reasonable amount
of the tuning with one hand...
Wilson's 22-tone generalized mappings are the best I've seen for 22 so far.
I hope to design a similar keyboard around the decatonic (as opposed to
diatonic) scale, and then have it built. This shoud be really fun.
Carl
------------------------------
Topic No. 2
Date: Thu, 26 Nov 1998 13:42:51 -0800
Wow! Missed that. Thanks for pointing it out!
Carl
------------------------------
Topic No. 3
Date: Thu, 26 Nov 1998 14:00:32 -0800
I missed Paul Hahn's post (until now) to Tuning Digest 1592 (along with the
other posts past # 15) because it was mixed up in a bunch...
By my count too! For some reason, I have listed in my notes that the
12-out-of Stellated Hexany has 31 consonances. But you are right, it only
has 30 (the same number as either of the truss tunings in my article). I
must have mis-counted.
I think I missed your tuning because I was looking mostly at stuff that fit
roughly within the 12tET pitch classes (I didn't consider any tunings with
the 64:63 comma). This tuning has two hexanies, but only four tetrads. So
the 12-out-of Stellated Hexany still wins for complete chords, but you win
the double-dog dare!
Carl
------------------------------
Topic No. 4
Date: Thu, 26 Nov 1998 16:30:55 -0500
Re: Mozart's tunings.
I agree that there were probably a great deal of ad hoc temperaments in use
in the late eighteenth century ranging from meantones to well-temperaments
(and probably a lot of bad tunings -- akin to the recent Siberian example).
However, the instrument most likely to have been tuned with great care was
the organ, and it is certain that Mozart's organ works would have been
played in meantone, and 1/6-comma meantone at that.
There is everything to be said for Ed Foote's approach, to keep trying and
choose the tuning that with which you personally agree best. I suspect that
the virtues he finds in well-temperaments on modern instruments might just
become vices when applied to a period-style instrument. In my experience,
1/4 comma meantone is excellent for Haydn and Mozart on a fortepiano, whose
spectrum is exceptionally bright. The Mozart Sonata specialist Mitsuko
Uchida tunes her (modern, but heavily re-regulated) piano herself in 1/4
comma meantone, adjusting the position of the wolf according to the key.
I believe, however, that there is a more compelling argument for the
appropriateness of meantone to Mozart within the music itself. Paul Erlich
wrote:
[Erlich, TD 1593.4:]
Kelletat argues, in general, for a meantone Mozart and well-tempered (as
proto-ET and specifically Kirnberger) Beethoven. Kelletat's percentage
count given here does not distinguish between keys used in expositions and
developments. A closer look at the Sonatas will show quickly that the
favored meantone keys are the expository keys and the extreme keys are
saved for development sections. The Mozartian development section had the
function of extreme contrast, reaching areas of furthest harmonic remove
from the exposition in relatively compact time spans. This contrast is
undoubtedly hightened by the more extreme variations (indeed, perhaps even
wolves) in intonation found in meantone. Beethoven, on the other hand,
luxuriated in expositions of great enough length to support the
introduction of wholly new topoi such that memory of the tonic area and
its intonational qualities would have much reduced and the need for
contrast overwhelmingly satisfied by the textural changes introduced by the
new topoi. In turn, the longer duration of the development sections would
have likely been better appreciated in a well temperament.
There are additional historical arguments to be made (i.e. hand horn charts
and Berlioz's concertina in meantone) but they have already been hashed
about on this list.
------------------------------
Topic No. 5
Date: Thu, 26 Nov 1998 16:30:52 -0500
Paul Erlich wrote:
I'm under no illusions about the physics of undertone series. They are
relatively rare and short lived among the real, existing (as the used to
say in the DDR) musical sounds. They seem to be chiefly associated with
forcing enough extra energy into the vibrating body to cause it to vibrate
at integer dividends of the fundamental. The vocal "fry" (singing while
inhaling, and mentioned in the past by Mr. Erlich), bowing a stringed
instrument with extremly concentrated pressure (Allen Strange), and
possibly percussion attacks (Albrecht Schneider) are associated with this
phenomenon. I know of no attempts to get the system to drive beyond the
second or third subharmonics -- anyone know anymore?
I give utonalities and otonalities an amount of equal status only in the
regard that any set from either series can be renotated in terms of the
other series. (Thus a chord in the ratio 10:12:15 can also be notated as
/6:/5:/4). I've had some, admittedly highly speculative, ideas about how
we process such sonorities and what this could mean compositionally.
As a composer, I find the using models of spacing found in harmonic, equal,
and subarmonically divided tone spaces to be extremely useful. This is NOT
the same as putting them on equal terms but positioning them as terms of
contrast to the predominant harmonic construction. It is again a highly
speculative matter, but I have the notion that one could reconstruct the
principles of voice leading and construct a theory of orchestration (or
more broadly, timbre) on this basis of this spacing idea.
------------------------------
Topic No. 6
Date: Thu, 26 Nov 1998 14:06:07 -0800
Paul Hahn wrote:
That's the best ASCII lattice I've seen yet.
For my version, check the TD archives.
- Joe Monzo
------------------------------
Topic No. 7
Date: Fri, 27 Nov 1998 06:30:21 +0800
The vocal fry is not a result of singing while inhaling. It can
be done either inhaling or exhaling, but exhaling is easier.
To get this sound yourself, first sing the lowest pitch you can.
While singing it, RELAX your throat -- a tremendous amount. If
you are getting the effect, it will probably sound very gravelly.
Try to relax even more and maybe focus the sound. If you can
get this to work from these instructions (without a live demo) you
should hear a sound an octave below the original pitch at the same
time that you continue to hear the original pitch. It will
probably stay gravelly -- it takes some practice to make it smoother.
I have heard Joan LaBarbara do this and get a smoother sound, and
even get an octave and a fifth below the low tone.
Best,
Lydia Ayers
------------------------------
Topic No. 8
Date: Thu, 26 Nov 1998 19:05:02 -0800
[Paul Erlich]
Could you elucidate?
[Paul Erlich]
Yes compositional context makes a huge difference. But you can't have your
cake and eat it too. If you use less, in whatever way, you're using less.
I tried to make the chart reflect this.
[Stephen Soderberg]
Miller's paper addresses (if in a limited way) the issue of chunking, and
is available at...
http://www.well.com/user/smalin/miller.html
My interpretation into the realm of music seems to be that while chunking
works (and I think it works a lot better than Miller does!), some type of
experience is still dropping off. I tried to represent this in the chart
and the notes that went with it.
[Stephen Soderberg]
This is quite true. But it is hoped that a strictly melodic test can say
something about the contribution of the melody to these types of musics...
It's difficult to write about chunking clearly, because you can chunk
chunks, and you've got to be carefull about what level you're talking
about. How all this works in the cognitive process is one of the greatest
unanswered questions in pyschology, and its application in music is even
more sketchy. I certainly don't have many answers. I whipped up the chart
pretty quickly, and I'm surprised it is holding up to my second thoughts on
the matter as well as it is. As it is, I need more time to think about it,
especially as regards the excellent feedback from Stephen Soderberg.
Carl
------------------------------
Topic No. 9
Date: Thu, 26 Nov 1998 17:14:35 -0800
I wrote:
I've never heard of this - please give more details.
OK - a TD mix-up. I've seen Manuel's posting.
Johnny Reinhard wrote:
I would certainly prefer to think that "Mozart was conceptualizing
in Just Intonation", but at this point, I'm not sure if it was the
author of the article I cited who gave a 17-tone scale, or if that
was how I conceptualized it after I read the article. I really can't
say more as I don't have the reference.
Wow - now there's an idea for an AFMM piece!
- Joe Monzo
------------------------------
Topic No. 10
Date: Thu, 26 Nov 1998 23:02:23 -0300
Manuel Op de Coul wrote:
Can any of the listers tell me where in the Web could I get some
detailed image of this kind of keyboard?
I tried hard: the searchers got thousands of sites about Janko Keyboards
but computer keyboards, to type. Only one reference to a piano in an
English museum, and the image was a photo of said piano from far away...
Best regards
Carlos
------------------------------
Topic No. 11
Date: Fri, 27 Nov 1998 02:30:07 -0800
- Joe Monzo
------------------------------
Topic No. 12
Date: Fri, 27 Nov 1998 07:31:33 -0800
[Carl Lumma:]
[Steve Soderberg:]
This doesn't take into account (unless I'm missing something -- a
distinct
possibility) the mind's characteristic ability to recognize (and
organize
into) patterns. It may not be as "instantaneous" as Miller's tests
suggest (and I admit I don't know the study -- I'm going on the present
description and similar ones I've heard), but seven stones are nearly
immediately organized into four-plus-three ... Or is that 22 + 31 ?
[...and the rest of this great post to its ending:]
Perhaps this is the main reason I like using complex
lattice diagrams to model tonal systems in prime-factor
form. Music modelled on them creates beautiful,
elegant and complex patterns that are easily recognized
and remembered, enabling visualization of very large
tonal systems, far beyond the 11-limit.
The old 3- and 5-limit structures are ordinary rectangular
"brick houses", but the high-limit lattices are beautiful
multi-angular edifices.
The outlines of these funky-shaped houses describe the
finity of the system.
[a digression:]
I prefer to think of the patterns as resembling maps of
the galaxies. About three years ago I saw a television
program that related how, with the aid of the Hubble
Telescope, astronomers had come to some kind of a consensus
that the galsaxies are grouped into clusters which lie along
something like vectors, between which lie nothing but totally
empty space. It was likened to an enormous cosmic spider web.
I wonder how much it resembles my lattice diagrams. All this
work I've done with prime-factor music theory has given me an
interest in the ancient idea of "cosmic music". For a
good explanation of this, see
Ernest McClain,
Music
Theory and Ancient Cosmology
Comments on this are appreciated.
- Joe Monzo
------------------------------
Topic No. 13
Date: Fri, 27 Nov 1998 07:36:52 -0800
McLaren and I will be available to meet in LA with
whomever of you are interested, Saturday afternoon
the 27th, around 3:00 or so.
We'd like to get together with as big a group as
possible, so those of you in the Los Angeles area
who'd like to get together say for dinner, email
ASAP.
We'll be available by phone until about 8 am Saturday.
619 231 3673.
- Joe Monzo
------------------------------
End of TUNING Digest 1594
I welcome feedback about this webpage: corrections, improvements, good links.
by Carl Lumma
by Carl Lumma
by Carl Lumma
by Daniel Wolf
by Daniel Wolf
by monz@juno.com
by Lydia Ayers
by Carl Lumma
by monz@juno.com
by Carlos Nogués
by monz@juno.com
by monz@juno.com
by monz@juno.com
From: Carl Lumma
To: Tuning Digest
Subject: Paul Erlich
Message-ID: <4.0.1.19981126112128.00e67540@lumma.org>
By all means I would prefer to know what the composer used. Mozart
sticking to the available keys of meantone at all times would be VERY
strong evidence against well-temperament.
I did say that the 12-out-of Stellated Hexany tuning has the greatest
number of consonant intervals of any possible 12-tone subset of the
7-limit. Did you know this? Or is it incorrect? I have no proof...
What's the largest mistuning you'll allow?
Did you catch my repost of my post from Nov. 17th on
meantone vs. just
(that >is, harmonic mistuning vs. melodic mistuning)?
How about a piano tuned to 12 out of 22 (put 1/22 oct. at e-f and b-c),
or if you want to modulate around all 22 keys, the main keyboard mapping
described in my paper?
From: Carl Lumma
To: Tuning Digest
Subject: Drew Skyfyre
Message-ID: <19981126184216921.AAA411@nietzsche>
Creamware's mega bucks Scope was mentioned.
They also have a card called the Pulsar for
@$1390.
From: Carl Lumma
To: Tuning Digest
Subject: Paul Hahn
Message-ID: <19981126185957750.AAA264@nietzsche>
Carl, I hate to break it to you, but I think you're wrong. The scale you
describe has 30 7-limit consonances, but consider this 3^2 * 5 * 7 genus:
35:24-----35:32-----105:64
/ / \ \ / / \ \ / /
5:3-/---\-5:4-/---\-15:8/
/|\/ \/|\/ \/ |/
/ |/\ /\|/\ /\ /
/ 7:6-------7:4-------21:16
/ / \ \ / / \ \ / /
4:3-------1:1-------3:2 [Diagram by Carl Lumma]
By my count this has 31 7-limit consonances.
From: Daniel Wolf
To: Tuning Digest
Subject: TUNING digest 1593
Message-ID: <199811261631_MC2-61AD-A514@compuserve.com>
...Mozart sticking to the available keys of meantone at all times would be
VERY strong evidence against well-temperament. However, if his music
modulates to other keys during the course of a piece, that would be VERY
strong evidence for well-temperament. Someone who has analyzed a good
deal of Mozart should be able to answer this question. According to
Herbert Kelletat in Manuel's post, Mozart stuck to meantone keys about
80% of the time so he may have been using a well-temperament himself but
realized that many performances by others were bound to use meantone."
From: Daniel Wolf
To: Tuning Digest
Subject: Orpheus and the Undertones, Subharmonics, Utonalities etc.
Message-ID: <199811261631_MC2-61AD-A512@compuserve.com>
Partch credits Riemann and many others in preceding his
"utonality" concept. The concept has an intersting status
around here, with a few giving it little to no importance
(e.g., Heinz Bohlen), a few giving it near-equal status
with the otonal or "overtone series" concept, such as
Daniel Wolf and (implicitly) Bill Sethares, and most
of us falling somewhere in between.
From: monz@juno.com
To: Tuning Digest
Subject: Hahn's ASCII lattice
Message-ID: <19981126.140612.-133415.7.monz@juno.com>
35:24-------35:16------105:64
.-'/ \'-. .-'/ \'-. .-'/
5:3--/---\--5:4--/---\-15:8 /
/|\ / \ /|\ / \ /| /
/ | / \ | / \ | /
/ |/ \ / \|/ \ / \|/
/ 7:6---------7:4--------21:16
/.-' '-.\ /.-' '-.\ /.-'
4:3---------1:1---------3:2
monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
From: Lydia Ayers
To: Tuning Digest
Subject: Vocal Fry
Message-ID: <199811262230.GAA11550@csnt1.cs.ust.hk>
From: Carl Lumma
To: Tuning Digest
Subject: Many Tones
Message-ID: <19981127000427500.AAA443@nietzsche>
On the many-tones issue, I think the tetrachord structure helps to
reduce the number of independent elements that need to be perceived...
compositional technique can make at least as much difference as an order
of magnitude difference in the number of tones.
This doesn't take into account (unless I'm missing something -- a distinct
possibility) the mind's characteristic ability to recognize (and organize
into) patterns. It may not be as "instantaneous" as Miller's tests
suggest (and I admit I don't know the study -- I'm going on the present
description and similar ones I've heard), but seven stones are nearly
immediately organized into four-plus-three and so on.
Second, a strictly "melodic" test doesn't take into account the full power
of many musics to organize material into recognizable, memorable chunks.
From: monz@juno.com
To: Tuning Digest
Subject: Mozart's tuning
Message-ID: <19981126.171437.-133415.12.monz@juno.com>
And his reaction to a 31-tone (obviously, meantone)
instrument he played on?
To Joe: distinguishing between chromatic and diatonic semitones
is still a far cry from concluding 17 tones. Why not consider
that Mozart was conceptualizing in Just Intonation, rather than
an alternate temperament?
Frank Zappa played on David Rothenberg's 31-tone electronic
instrument: does that mean we should play Zappa's music in 31-tone
during the next century?
monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
From: Carlos Nogués
To: Tuning Digest
Subject: Janko Keyboard
Message-ID: <365E0830.28@hotmail.com>
The museum also has a 12-tone harmonium with a von Janko keyboard
from around 1900, built in Vienna. It has 3 rows of 25 and 3 rows of 24
keys. When you press one key, two more go down, so there are only two
independent rows.
From: monz@juno.com
To: Tuning Digest
Subject: the hunt for Mozart's tuning
Message-ID: <19981127.023015.-133415.27.monz@juno.com>
the wolf (meantone, not daniel) would not occur within a consonant chord
Great pun, Erlich...I'm still laughing
monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
From: monz@juno.com
To: Tuning Digest
Subject: Cognitive Limits
Message-ID: <19981127.073138.-133415.28.monz@juno.com>
(a) It's been shown that average dudes from all over can count how
many
stones you toss on the ground almost instantly- so long as you don't
toss
more than six stones at a time. Since a good deal of the interest of
G.D.
[generalized-diatonic] scales comes from the interaction between parts
in
polyphonic composition, it seems that we'll lose something if we go
above
the 11-limit.
... and so on. Second, a strictly
"melodic" test doesn't take into account the full power of
many musics to organize material into recognizable, memorable
chunks.
I can't "grasp" 10,000 bricks, but I can easily "grasp" a brick house.
monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
From: monz@juno.com
To: Tuning Digest
Subject: visit to LA
Message-ID: <19981127.073655.-133415.29.monz@juno.com>
monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
*************************
or try some definitions.
Let me know if you don't understand something.
