From: Tuning Digest
To: monz@juno.com
Date: Sun, 29 Nov 1998 11:02:24 -0500 (EST)
Subject: TUNING digest 1596
TUNING Digest 1596
Topics covered in this issue include:
1) Re: HAPPY THANKSGIVING
2) Re: Orpheus and the Undertones, Subharmonics, Utonalities etc.
3) Re: Tuning "innovations" and rediscoveries
4) Re: TUNING digest 1595
5) Thank you
6) RE: Paul Hahn
7) Re: Tuning "innovations" and rediscoveries
8) more explanation of finity and bridging
9) Re: Tuning "innovations" and rediscoveries
----------------------------------------------------------------------
Topic No. 1
Date: Sat, 28 Nov 1998 11:06:05 -0500 (EST)
A great turkey day to all USers and an enthusiastic well-wishing to all
other global cohabitants. We do have an amazing relationship on this
list. I suspect there are few other lists that mean as well for each
other as this one does.
There are several things I'd like to address, but am a bit unsure as to
wether to write several short monographs as Gary Morrison prefers, or a
more paragraphic approach. To keep my thoughs more cohesive, I'll dig in
for this holiday/weekend.
The AFMM is now planning a Wall-To-Wall Microtonal Concert - likely on
May 23rd - for about 12 hours of music. It's conceiveable to have "2"
days (May 22) if warranted by a plethora of significants works. There are
already planned 2 other concerts in May (on the 20th and 23rd). Things
are really shaping up well, with a blow out orchestra concert on
October 11 -- including the Columbus Day premiere of Julian Carrillo's
"Colubmus Symphony."
Due to the newer generations of microtonal preferring composers and
performers, all along continuing to play the pioneering masters, and while
regularly polishing off the gems in the extant repertoire, a
"Wall-To-Wall" became the answer. AFMM President suggests callig it the
Microthon.
Please consider sending tapes and scores to my attention if you would
like to participate, especially if you can be in New York. It is great if
you will perform in your own piece. There is no real money available for
this endeavor in terms of "pay." Thanks to a $500 grant from the Virgil
Thomson Foundation, we have the impetus to produce an important event.
Combined with the strong support we continually receive from the New York
State Council on the Arts, we already have the publicity in place for the
concert, nestling it between 2 Thursdays. It should certainly attract
the New York City imagination.
Now about "subharmonics": are these properly the same as "difference
tones," thus produceable as the mathematical difference heard as a result
of 2 higher pitches rubbing up against each other?
Isn't the octave, what Partch once called the "aura," carved up in actual
music to include the 6/5 from the very the same organic core as the 5/4?
Could there even be a major withour a minor? In any tuning? The
Utonality
is every bit as real as the harmonic Otonality, and
consequently, harmonic in itself. It bears no real distinction. It is
not an "other" set of tones. Mirror inversions are as real on the
mathematical plane as what they mirror on the mathematical plane, and
clearly in the imagination realm. Hence, composition with the undertone
series. Every bit as real as the overtone series, except not in every
acoustic situation.
Johnny Reinhard
------------------------------
Topic No. 2
Date: Sat, 28 Nov 1998 12:52:40 -0500
I'm not sure what to make of that suggestion. Being an
equal-temperament,
clearly Bohlen's tuning approximates the same subharmonics as it does
harmonics, and equally accurately.
------------------------------
Topic No. 3
Date: Sat, 28 Nov 1998 13:16:54 -0500
Interesting observation. I'd have to play with it a bit, but my
immediate inclination would be to guess that 128:81 is complex enough a
relationship that it would be more readily perceived as an off 8:5 than as
something in itself. That's how 88CET's minor sixth has struck me anyway.
I take it that that's not your experience?
I personally haven't had a chance to read XH 17 yet. Bizzy bizzy... I
hope that I am not to infer from this fragment of Heinz Bohlen's article, that
he views 88CET as a competitor, or in any other way a threat, to his tuning.
If so, I personally don't see any reason to see it that way. In fact, they
even have some properties in common, beyond which each has its own useful
capabilities.
------------------------------
Topic No. 4
Date: Sat, 28 Nov 1998 14:34:32 -0800
It think this is right. But I think that tracking step sizes and holding
each of the (octave-equivalent) absolute pitches of a scale in short-term
memory may produce different subjective experiences. Of course, both often
go on at once...
Guys, wouldn't any rotation and/or reflection of this figure in the
tetrahedral/octahedral lattice work too?
Should. (I presume you mean only those about which it is symmetrical)
For the entire lattice? I'm pretty new to this, but for rotational
symmetry I count 2 in the (x,y) plane, 4 in the (x,z) plane, and 2 in the
(y,z) plane. For mirror symmetry, I count 4 in each plane.
But while this should give us the maximum possible symmetry for structures
on the lattice, it certainly wouldn't give us the minimum (I don't think
Paul Hahn's structure has all of them). Just moving a structure in the
lattice (called translation?) can change the number of intervals (although
there's probably a symmetry here too -- every 2 steps along any axis?).
I don't know how. But I wish I did... [see next response]
Carl
------------------------------
Topic No. 5
Date: Sat, 28 Nov 1998 22:38:54 +0000
Many thanks to all those very well tempered friends from this list, who
gave me very helpful advice in my e-mail-problem with the list, namely
John Chalmers non12@deltanet.com
Stay in good tuning!
Ibo Ortgies
> > > How long does a hpscd stay tuned?
> > Until someone opens the door.
> AAAARRRRGGGGHHHH!
------------------------------
Topic No. 6
Date: Sat, 28 Nov 1998 15:38:32 -0800 (PST)
On Sat, 28 Nov 1998, Paul H. Erlich wrote [1595.10]:
Indeed, it does, although the restriction of it being 7-limit makes
non-orthogonal rotations fail.
The other two orientations are -
And
There are 6 orientations of the other arrangement with 30 consonances in
it. I'd be happy to work all of them out if anybody sends me the ascii
diagram.
If you're willing to be a bit perverse and use a tuning with an octave
ratio of 7:3 the following is also very consonant:
1 15/14 6/5 9/7 7/5 10/7 3/2 75/49 25/14 5/3 2 15/7 7/3
-Bram
------------------------------
Topic No. 7
Date: Sun, 29 Nov 1998 00:28:00 -0500
Oh, regarding to 88CET's 9-step interval of 792 cents, I just remembered that
I concluded early on in my explorations that it was recognizably perceptible as
an approximation of 19:12.
------------------------------
Topic No. 8
Date: Sun, 29 Nov 1998 06:17:37 -0800
I just saw an old Tuning Digest from September,
with a couple of postings about blues tuning.
I responded to one of the posters, telling him
about my microtonal JI blues-vocal analysis,
and while discussing my disclaimer about the accuracy
of the ratios (which, in my MIDI sequence, I tuned by
ear), I started thinking about my new concepts
and got carried away. I guess it was really meant
for Tuning people to read publicly, so I've added to
it and stuck it here. Hope you find it as enriching
as I have, and hope you can add to it.
-----------------------------------------
Humans perceive the intonational relationships
between musical tones in several different ways. The
two most obvious of these are equal-temperament and
just-intonation. Of course there are also meantone and
well temperaments, whose use was probably initiated by
a twofold desire to provide decent 5-limit consonances
and the possibility of wide modulation, but which became
intonational gestalts in their own right once accepted
into practical usage. Then there are the more unusual
non-just non-equal (and sometimes non-octave) scales,
and others less frequently encountered.
And in keeping with my concepts, "scales" turns
out to be an unusually appropriate word, for as you
can see above, I'm talking about the different ways we
perceive the relationships, implying different methods
of mapping those sounds to some kind of orderly conceptual
framework. This implies different projections and scales
(in the "map" sense).
(My favorite "orderly conceptual framework" is the
prime-factor
lattice diagram. See:
Well, regardless of what relationships the notes
actually have (i.e., even if they're irrational
proportions as in an equal-temperament), we are always
perceiving harmonic relationships between simultaneous
tones - that's simply a function of the musical notes
having periodicity.
Prime factors in these ratios may be very high, but may
be close enough in pitch to ratios of lower prime numbers,
and the musical context may supply enough of an implication
supporting these lower primes, that we will interpret
the higher-prime ratio as one with lower prime factors,
which would probably aid in our understanding the
relationship by making it simpler.
Or it may be the case that a higher prime in any
given instance may provide a more distinctive or unique
quality (affect) than that provided by an interpretation
which favors lower prime factors but higher exponents.
This may help to make the note blend better or stand
out better, depending on context.
{As an exaggerated example:
On the other hand, considered harmonically,
in an accented triad of 64:81:96 [= 1/1 : 81/64 : 3/2]
the 34 would stand out as a dissonance, whereas
in a triad tuned to 4:5:6 [= 64:80:96 =
1/1 : 5/4 : 3/2], 51 would blend right in as the
low-prime and low-exponent 5-identity of the
1/1-otonality. So in this sense, 34 would be
the choice for a note that raises tension.
- this is a good example of how musical context
determines our perception of the sounds.
Similarly, 5-limit JI gives us at least two
"minor 7ths", which are both obviously related
(according to my ears anyway) to the other 5-limit
ratios, but 71 [= 7/4 = 9.69 Semitones] is a
sound unlike any 5-limit ratio, and I would venture
to argue that 3252 [= 225/128 = 9.77 Semitones]
would most often be perceived as a slightly sharp
71, again, depending on context.}
This aspect ties in with the commonly-accepted idea
that sonance is proportional to differing size of both
prime factor and exponent. It's not necessarily that
the ratio is able to be interpreted more simply, or
more consonantly (or less dissonantly) - that is, simply
by degree of sonance - but rather that the different
interpretations also permit of different types of
sonance.
The important point is that these interpretations are
always fluid and changing, completely dynamic. And
because the infinite quality of numbers permits an
equally infinite spectrum of rational interpretation,
it becomes very difficult, without computer frequency
analysis (and probably even with it), to ascertain
precisely what is the pitch of a certain note.
(I believe that it was Schoenberg's recognition of
this, and his frustration at his inability to organize
his harmonic ideas numerically, thru sheer plenitude
of possibility, that led him to so strongly accept the
12-EQ system as a practical compromise.[*] I'm quite
certain that he had multifarious rational implications
of his harmonies firmly in mind while composing,
whatever those implications were; for this reason
I find him one of the most interesting of theorists
and of composers, plus a lot of his stuff sounds great
- just to prove that I can still like good ol' 12, too.)
In fact, modern research is showing that musical sounds
are not quite as periodic or regular or easily-definable
as was once thought. To me, this provides further
weight to the idea that we are perceiving rational
relationships which are much more complicated than has
previously been described, the main complication being
the fact that time is an essential dimension in which
music must be perceived, and the sounds are changing
all the time.
(Indeed, it is often the case that when
sounds do not change enough to suit our appetite for
stimulation, we find the music boring - as in "electronic-
sounding" timbres with little nuance, or very consonant
slow-moving JI music, etc. - altho both of these can
of course produce good music if used well! [the big hit
"Dah dah dah" by a German group in the 80s, with keyboard
part played on a tiny cheap Casio, and used very recently
in a TV commercial, for the former; the music of La Monte
Young for the latter]
[*] Someone please dig out the old Tuning Digest from
the spring of this year where I talked about Schoenberg
stating that the possibilities were infinite, and citing
book and page number.
- Joe Monzo
------------------------------
Topic No. 9
Date: Sun, 29 Nov 1998 08:40:11 -0500
Forgive me if this is a repeat, but I don't recall this ever having appeared
on the list.
Gary Morrison wrote:
Interesting observation. I'd have to play with it a bit, but my
immediate inclination would be to guess that 128:81 is complex enough a
relationship that it would be more readily perceived as an off 8:5 than as
something in itself. That's how 88CET's minor sixth has struck me anyway.
I take it that that's not your experience?
I personally haven't had a chance to read XH 17 yet. Bizzy bizzy... I
hope that I am not to infer from this fragment of Heinz Bohlen's article, that
he views 88CET as a competitor, or in any other way a threat, to his tuning.
If so, I personally don't see any reason to see it that way. In fact, they
even have some properties in common, beyond which each has its own useful
capabilities.
------------------------------
End of TUNING Digest 1596
I welcome feedback about this webpage: corrections, improvements, good links.
by Johnny Reinhard
by Gary Morrison
by Gary Morrison
by Carl Lumma
by Ortgies.Ibo@t-online.de (Ortgies Ibo)
by bram
by Gary Morrison
by monz@juno.com
by Gary Morrison
From: Johnny Reinhard
To: Tuning Digest
Subject: Re: HAPPY THANKSGIVING
Message-ID:
Director
American Festival of Microtonal Music
318 East 70th Street, Suite 5FW
New York, New York 10021 USA
(212)517-3550/fax (212) 517-5495
reinhard@idt.net
http://www.echonyc.com/~jhhl/AFMM
From: Gary Morrison
To: Tuning Digest
Subject: Re: Orpheus and the Undertones, Subharmonics, Utonalities etc.
Message-ID: <3660385C.B66C4BF@texas.net>
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)
From: Gary Morrison
To: Tuning Digest
Subject: Re: Tuning "innovations" and rediscoveries
Message-ID: <36603E08.B97E11D9@texas.net>
Both when first reading this and now, my immediate reaction is to
point out that the minor sixth of 128:81, or ~792.18 cents, is a
regular Pythagorean
interval which plays a vital role in 12th-13th
century polyphony
From: Carl Lumma
To: Tuning Digest
Subject: Re: TUNING digest 1595
Message-ID: <4.0.1.19981128114224.00e78870@lumma.org>
Stephen Soderberg made the point I was trying to make here. If you write
a piece in 22 out of 41, you'd better run a lot of 2/41 oct. steps in a
short period of time so that that can be understood as the norm. Then,
the position of the three 1/41 oct. steps will stand out and the entire
scale will be projected
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]
[Erlich, 1595.10:]
Here's where group theory comes in: how many elements does the symmetry
group of this lattice (better known as the face-centered cubic lattice)
have?
>Does that tell us the number of distinct solutions to Carl's challenge?
From: Ortgies.Ibo@t-online.de (Ortgies Ibo)
To: Tuning Digest
Subject: Thank you
Message-ID: <36607B7D.6355@t-online.de>
Judith Conrad jconrad@tiac.net
Manuel op de Coul Manuel.Op.de.Coul@ezh.nl
Paul H. Erlich PErlich@Acadian-Asset.com
Jan Haluska jhaluska@mail.saske.sk
Bob Lee quasar@b0b.com
Carl Lumma clumma@nni.com
Gary Morrison mr88cet@texas.net
Mark Nowitzky nowitzky@alum.mit.edu
William Sethares sethares@eceserv0.ece.wisc.edu
From: bram
To: Tuning Digest
Subject: RE: Paul Hahn
Message-ID:
Guys, wouldn't any rotation and/or reflection of this figure in the
tetrahedral/octahedral lattice work too?
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.
21:20-----21:16-----105:64
/ / \ \ / / \ \ / /
6:5-/---\-3:2-/---\-15:8/
/|\/ \/|\/ \/ |/
/ |/\ /\|/\ /\ /
/ 7:5-------7:4-------35:32
/ / \ \ / / \ \ / /
8:5-------1:1-------5:4 [Diagram by Carl Lumma]
15:14-----15:8------105:64
/ / \ \ / / \ \ / /
10:7-/---\-5:4-/---\-35:32/
/|\/ \/|\/ \/ | /
/ |/\ /\|/\ /\ |/
/12:7-------3:2-------21:16
/ / \ \ / / \ \ / /
8:7-------1:1-------7:4 [Diagram by Carl Lumma]
From: Gary Morrison
To: Tuning Digest
Subject: Re: Tuning "innovations" and rediscoveries
Message-ID: <3660DB5E.FBB6C993@texas.net>
my
immediate inclination would be to guess that 128:81 is complex enough a
relationship that it would be more readily perceived as an off 8:5 than as
something in itself. That's how 88CET's minor sixth has struck me anyway.
From: monz@juno.com
To: Tuning Digest
Subject: more explanation of finity and bridging
Message-ID: <19981129.061744.-170487.2.monz@juno.com>
On the one hand, considered melodically,
a "major 3rd" of 34 [= 81/64 = 4.08 Semitones] is
merely another note in the cycle of powers of 3,
but 51 [= 5/4 = 3.86 Semitones] is a powerful new
identity,
a new odd- or prime-base, 5. It would
provide a whole new set of intervallic relationships
which provide affective information which differs
from that of the intervals in the 3-Limit system.
In this sense, 51 would stand out, which would
make it good as an emphasized melodic note.
monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
From: Gary Morrison
To: Tuning Digest
Subject: Re: Tuning "innovations" and rediscoveries
Message-ID: <36614EBA.4CBAD2E3@texas.net>
Both when first reading this and now, my immediate reaction is to
point out that the minor sixth of 128:81, or ~792.18 cents, is a
regular Pythagorean interval which plays a vital role in 12th-13th
century polyphony
*************************
or try some definitions.
Let me know if you don't understand something.
