mes@sequent.UUCP (Mike Seyfrit) (11/09/89)
Re: equal temperament systems, etc.
Actually, most "equal" temperment tunings are actually off to some degree
anyhow, if they are laid out by ear. I have both seen and done some research
showing that most piano tunings that attempt to be equal tempered are actually
not quite so equal. In fact, many piano or other keyboard instrument tuners
frequently slant their tunings purposely in some way, for instance, making
the b-f# fifth slightly rougher than the rest. Another thing about tuning
systems is that in concert performance of say, 18th and 19th century works that
involve piano, strings, winds, the tuning is actually quite dynamic. A
c natural in one context is not the same a moment later. This depends
partially on the context (ie, what part of the chord the note represents)
and partially on the perceived motion of the harmony (ie where the note is
in relation to the prevailing key). Additionally, we all make minute
allowances so that prominant intervals, particularly when played without
other supporting harmony, are as beat-free as possible.
I really think that we should seldom speak of "equal temperaments", but,
I guess like Jorgensen or others, "well" or "good" ones. those (in many
views) would be those in which all keys can be played in, though they might not
be the same. That could include the Vallotti, Young 1800, Werkmeister, and
many others. Then we could speak about the "on-the-fly" alterations on each
of these caused by playing "in tune" with the prevailing harmony, and
only then do we have a picture of what is really happening in any context
other than computer-generated scales performed by fixed-pitch instruments.
--
===== Mike Seyfrit phone:503-241-4121 | \ mail:625 NW Everett #228 =
net:{uunet,sun,tektronix)!sequent!mes | \ Portland, OR, 97209 =
===== org: Sequent Computers, Beaverton, OR | / \ =======================mjs@hpfcso.HP.COM (Marc Sabatella) (11/10/89)
>Another thing about tuning >systems is that in concert performance of say, 18th and 19th century works that >involve piano, strings, winds, the tuning is actually quite dynamic. This much is definitely true. If you are playing a piece in C major, a B natural that occurs in a iii resolving to vi is played flatter than in a V resolving to I - ie, unless you are playing piano (which can't easily alter pitch on the fly), you try to play the leading tone sharply. On stringed instruments, this is accomplished simply by moving the finger up; on brass, double reed, and flute it can be accomplished easily by embouchre changes; on single reed instruments (which can easily be played flat with embouchre changes but can't as easily be played sharp) alternate fingerings are often employed. Actually, I wonder if this has anything to do why leading tones are so often trilled in late baroque/early classical piano music - to aid in the perception that the note is sharper than it actually is. >Actually, most "equal" temperment tunings are actually off to some degree >anyhow, if they are laid out by ear. I have both seen and done some research >showing that most piano tunings that attempt to be equal tempered are actually >not quite so equal. In fact, many piano or other keyboard instrument tuners >frequently slant their tunings purposely in some way, for instance, making >the b-f# fifth slightly rougher than the rest. Whether this is true or not I can't say, but there must be some explanation of the commonly perceived "fact" that some keys are "richer", "lighter", "brighter", or "darker" than others. The general tendency is to hear that major keys get "richer" you add sharps to the key signature; minor keys get "darker" as you add flats. This definitely seems to be the case on the piano, although how it is perceived on instruments that are tuned to different keys, I can't say. I personally have a much easier time discerning keys by "color" on the piano than, say, in an orchestra, although the latter is easy if you can single out one instrument and recognize, say, the quality of a clarinet's open Bb, and deduce the key from there. Marc Sabatella
elkies@brauer.harvard.edu (Noam Elkies) (11/10/89)
In article <6335@merlin.usc.edu> alves@aludra.usc.edu (Bill Alves) writes:
:In article <3068@husc6.harvard.edu> [I wrote:]
:> [...] Smileys aside, my point was that if you
:>embark on a radically new tuning (as opposed to a subtle tweaking of a pre-
:>existing one) you'll have to create an entire musical system practically from
:>scratch, and there's a lot more to that than simply setting down a list of
:>frequencies. New instruments, too; existing instruments, after all, evolved to
:>best complement existing tuning systems.
:
:I think this exaggerates the effort required to invent and successfully use a
:new tuning system. [...]
I rather think most practitioners underestimate this effort. Of course
here we could both be right...
:Here are some of the most common solutions:
:[...]
:2) Retune an existing instrument. I've seen composers retune harpsichords, but
: certainly pianos and harps (without using the pedals) could be too. I've
: even seen one percussionist who altered the tuning on his vibraphone by
: tightly winding thick wire on one end of each of the bars.
:
:3) Use continuous pitch instruments in conjunction with specially tuned ones.
: [...]
:
:4) It is also possible to write for all continuous pitch instruments (such as
: a string quartet) and ask them to play in the cracks, [...]
Of course you can easily retune the fundamentals of any number of existing
instruments to your favorite New Tuning. But this still leaves two
problems: First, the Pythagorean overtone structure would remain, whereas
you'd probably prefer to redo the entire harmonic series as well; that's where
you'd spend all this time constructing new instruments. [I realize that
I may be here implicitly invoking a controversial assumption about the
relation between the harmonic series and Western tuning---see below.(*)]
Second, while the instrumentalist will then easily play the notes in
your score, (s)he will need a lot of coaching to play them musically;
I see no reason why musical intuition developed over years in the context
of Western tuning must directly transfer to your new tuning system. [And
it's by no means certain that your instrumentalist does much more than
play the notes in the music (s)he was brought up with, either! :-( ]
:I also take exception to the implication that equal temperament is the result
:of hundreds of years of "evolution" towards the most "perfect" tuning system.
:(Certainly Murray Barbour's book has done a lot towards perpetuating this
:myth).
I do not believe this, and have not read Barbour's book.
:Equal temperament has been known about for a very long time. Composers
:simply haven't wanted to use it until the last 100 to 200 years.
But the various systems that were used were all within a few cents of
each other and of equal temperament, and thus mutually compatible for
many purposes; furthermore, as several posters have noted, the differences
are academic except for rigidly pre-tuned instruments (mostly keyboards
and fretted strings).
:A corollary to this misconception seems to be that it is simply impossible
:(or at least inadvisable to attempt) to create an artistically effective
:tuning system, when 12-tone equal temperament has taken the "heroic efforts"
:of hundreds of composers and theorists hundreds of years to perfect.
Since I disavow the premise, this cannot be a corollary. I would put
it differently, anyway: it's not the tuning system that evolved,
but composition within an essentially constant tuning.
:Ridiculous. While the science of tuning is certainly not easy to grasp, I
:don't think it's any harder than the 16th century counterpoint that under-
:graduates traditionally suffer through. [...]
Why, then, did generations of composers struggle between a theory that
proclaimed the fourth a "perfect" consonance and the third an "imperfect"
one, and their ears that told them otherwise? At any rate I hope that
the exponents of New Tunings are aiming higher than the equivalent of
exercises in species counterpoint...
:My goodness! You don't think we'd go out and create tuning systems
:WILLY-NILLY?
No, and presumably also not just because you can. But this process
of elimination isn't getting me very far. So, out of honest curiosity,
I ask: why do you create tuning systems?
(*) Something I've been wondering about intermittently, and reminded
of by your mention of gamelan music: Gamelan music is dominated by
instruments with an overtone series very different from the familiar
overtone series that dominates most Western music. It also uses
very different tunings, tunings which unlike their Western counterpart
developed (I assume) without knowledge of overtones. Thus it could
make an interesting test case for the perennial debate about the
naturalness of a system of tonality based on the overtone series.
Has any significant research been done into the relation or lack
thereof between gamelan tunings and gamelan overtones?
--Noam D. Elkies (elkies@zariski.harvard.edu)
Department of Mathematics, Harvard Universitycsz@well.UUCP (Carter Scholz) (11/12/89)
In a previous article, Noam D. Elkies (elkies@zariski.harvard.edu)
Department of Mathematics, Harvard University writes:
(*) Something I've been wondering about intermittently, and reminded
of by your mention of gamelan music: Gamelan music is dominated by
instruments with an overtone series very different from the familiar
overtone series that dominates most Western music. It also uses
very different tunings, tunings which unlike their Western counterpart
developed (I assume) without knowledge of overtones. Thus it could
make an interesting test case for the perennial debate about the
naturalness of a system of tonality based on the overtone series.
Has any significant research been done into the relation or lack
thereof between gamelan tunings and gamelan overtones?
<end of quote>
I've played Javanese gamelan for 4 years, have studied with Javanese
musicians, and have investigated the tuning systems & discussed them
at length. The idea of a tuning derived from the overtones of the
instruments is seductive, but will not, I think, hold water. As I
understand it, the tuning is set on the gender, which is a resonated
instrument with a waveform as close to a sine wave as you could ask.
The other, more clangorous instruments are tuned from this reference.
(However, there is still a great deal of empiricism involved in
stretching the octaves, etc. The main point is that the instrument
builder does not seem to be listening to any overtones when determining
the tuning; he sings, and uses the sinusoidal gender for reference.)
Carter Scholz csz@well.uucp