Date: Wed, 06 Oct 2004 18:34:43 -0400
Subject: Re: [CB] [CB Digest]
From: Robert Howe
on 10/6/04 6:30 PM, List Server wrote:
> The Conservatory System is like a shackle forged of keys
with
> finicky adjustments, always off key but never sharply
dissonant. I
> say, embrace notes that shift as you go up and down,
modulate and
> harmonize. It's a bit more tricky with winds or
frets, but
> ultimately more meaningful.
>
> Lawrence de Martin
> Greenwich
It's not the "Conservatory System" (that's an oboe mechanism)
but rather, "Equal Temperment". Just try building a piano or
organ that allows you to shift notes.
Ciao
Robert Howe
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Date: Wed, 06 Oct 2004 16:00:54 -0700
From: "Chuck Guzis"
Subject: Re: [CB] [CB Digest]
On 10/6/2004, Robert Howe wrote:
>It's not the "Conservatory System" (that's an oboe mechanism) but
rather,
>"Equal Temperment". Just try building a piano or organ
that allows you to
>shift notes.
Cheers,
Chuck
---------------------------------------------------------
From: "Oscar Wehmanen"
Date: Wed, 6 Oct 2004 23:40:58 GMT
Subject: [CB] Tuning:
Anyone can hear fifths. Even my tone def ex tended to sing in
parallel fifths. So if you do the obvious tuning thing, and tune
fifths (A-E-B-F#-C#-G#-D#-A#-F-C-G-D-A) with the odd octave
transposition to keep things low enough to hear. (Or go the other way
(down) with the odd octave transposition ...) Any way the A's on the
opposite ends turn out to be different if all the fifths are pure
(perfect, or any other nice word meaning copasetic) One solution is to
keep going to (I think) 21 steps and define the scale there with a
smaller intrinsic error. The basic problem is that 2^ n/ 3 is
never an integer( 2 raised to the power n) It is a mathematical fact.
The standard solution is, make them all out of tune by 1%. The
musician response is, those of us who can adjust will adjust and make
it sound good anyway!
A circle of fourths is the same as fifths. A circle of thirds is
possible, but harder to hear, and leads to a similar situation.
So - How would you like the keywork associated with a 21 step
chromatic scale?>>
Oscar
(713) 729-1972
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Date: Thu, 07 Oct 2004 00:23:44 -0400
Subject: [CB] Mouthpiece sought
From: Robert Howe
I seek a mouthpiece for a euphonium or trombone, marked in
cursive, "C G Conn" (or similar legend). Silver, nickel or brass
OK. This is to replace one that came with the double-belled Conn
euphonium in my colleciton. I lent the euphonium to a "friend" and she
lost my mouthpiece.
Ciao
Robert Howe
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Date: Thu, 7 Oct 2004 11:08:14 -0400
Subject: Re: [CB] tuning & temperament
From: Timothy J Tikker
On Sunday, October 3, 2004, at 06:38 PM, List Server wrote:
> So on to my question: Besides "tempered" (think Bach's
"Wohltempiert
> Klavier"), what are the other intonation systems used in
music -- I'm thinking
> primarily Western music -- and what are the characteristics
of them?
> For example, "raise the leading tone", etc.
Just intonation features pure-tuned intervals. The trouble is
that one can only tune so many of these when one is limited to twelve
tones per octave. For instance, if you chose a just tuning for
the key of C major, you'd essentially be limited to that key, plus just
one or maybe two keys distant along the circle of fifths.
Various musics outside of the modern western classical tradition
use just tuning, e.g. the Scottish highland bagpipes mentioned earlier,
or the classical music of India (north & south). Of course,
these are both traditions of monophonic music accompanied by a drone,
not of polyphony, and also not normally involving shifts of tonic.
Pythagorean tuning consists of tuning a series of pure fifths
until one runs out. The trouble is that the circle of fifths
doesn't close: starting on A, tune A-E-B-F#-C#-G#; then fourths from A
again: A-D-G-C-F-Bb-Eb. G# to Eb is not a fifth but a diminished
sixth, and so does not close the circle. The resulting false
fifth is said to be off by a "comma", called here the Pythagorean comma.
Apart from 11 pure fifths and one unusable one, there are 4 nearly pure
major thirds (though in distant triads, if one started tuning the
fifths from A: B major, F#, Db and Ab; the trouble of course is that
one of these triads is spoiled by the bad fifth). The remaining
thirds are uncomfortably wide (i.e. sharp). These however give
wonderfully sharp leading tones... They're called Pythagorean
thirds, and are said to be a syntonic comma wide. This was the normal
tuning in the medieval europe. It must explain the avoidance of
thirds in harmony at the time, and the use of fifths and fourths
instead for polyphony -- think of organum. It's said that
musicians on the european continent thought the British crude for using
the third in their harmony; but perhaps the Brits were actually
using a just intonation that let them do that.
Towards the Renaissance, tunings were developed which allowed
the major third to be used more in harmony. Just tunings and
adaptations of same were used transitionally. Eventually the
favored tuning was 1/4-comma meantone: this consists of narrowing
(i.e. tuning flat,) a series of eight fifths by a quarter-comma (i.e.
taking that discrepancy found in Pythagorean tuning and distributing
this evenly among four fifths, but then doing that all over again with
a second set of four fifths), which allows one to have eight pure major
thirds. The remaining major thirds then become diminished
fourths, e.g. B-Eb, G#-C. The result is that major tonalities
with more than three accidentals in the key signature start to become
impractical, and with five or more accidentals they become
impossible. The tradeoff is that the tonalities which are left
have the beautiful sonority of pure major thirds (which as noted
earlier on this list, give quite flat leading tones).
This deliberate mistuning of intervals is called
"tempering." Thus a "temperament" is a system of tuning which
involves a certain amount of deliberate mistuning of chosen intervals.
Some meantone keyboard instruments had subsemitonia, split accidental
keys which had the front and back halves operating different
pitches. A few organs and harpsichords have been built in modern
times with these, e.g. the Brombaugh organ at Oberlin College, or the
Fisk organ at Wellesley College in Massachussetts. These have Eb
keys with the back half operating D#, and G# keys with the back half
operating Ab (the more commonly used pitch is a the front of the key).
Quarter-comma meantone was used throughout the Renaissance and
even through the 18th century in certain parts of Europe, e.g. France
(Dom Bèdos recommended it in his treatise on organ building
published 1766-78). There are also other meantone systems based
on different distributions of the comma. e.g. 1/5, 1/6...
However, during the Baroque some musicians, especially in
Germany, wanted not to be limited to so few tonalities. A huge
number of tuning systems were proposed which essentially consisted of
blends of Pythagorean and meantone. The best known of these
nowadays are those proposed by Werckmeister and Kirnberger (the latter
a student of J. S. Bach). These allow one to play in all major and
minor keys, but the common keys (i.e. few accidentals in the key
signature) sound better. More specifically, the common keys have
the better major thirds, and the distant ones have the better fifths.
The theoretical possibility of distributing the Pythageorean
comma evenly amongst all twelve fifths -- i.e. equal temperament -- has
been known for centuries. Yet musicians largely avoided it
because, although the fifths sounded nearly pure, all twelve major
thirds were quite out-of-tune, i.e. 2/3 of a syntonic comma wide.
In his treatise on organ building, Dom Bèdos cites 1/4-comma
meantone and equal temperament as two possibilities, but recommends the
latter saying that it is what musicians prefer, ET being favored only
by theorists. So what does "well-tempered" mean? It is now
generally understood that this means a system of tuning in which all
major and minor keys may be used. But this is not necessarily
equal temperament, since there are dozens (probably hundreds) of
possible unequal temperaments which allow all tonalities to be used.
In writing Das Wohltemperirte Clavier, J. S. Bach was showing
the possibility of using all 24 major & minor tonalities. The
common mythology was that he was demonstrating the capabilities of
equal temperament. But it is even more likely that he was in fact
demonstrating the expressive characters of the various-tuned triads in
each tonality.
The modern theoretician Herbert Anton Kellner has developed what
he calls "the Bach temperament," based on his careful study of the use
of intervals in Bach's music, especially WTC. It's a 1/5-comma
system in which one skips a fifth so that the series is distributed
unevenly. The organ in my home is tuned this way, and Bach indeed
sounds very well on it.
Kirnberger described various systems, the best-known of which
are 1/2 and 1/4-comma. The 1/2-comma was favored in England into
the early 19th century: in 1806 Lord Charles, Earl of Stanhope
introduced a compromise 1/3-comma system, saying that 1/2-comma had
been favored up till then, but some musicians were rejecting it and
moving towards that "ill contrived mode of tuning" called equal
temperament," in which "dull monotony is substituted for pleasing and
orderly variety... modulation from key to key loses, in great measure,
the very object of modulation, which is to relieve the ear." Someone
once crassly wrote that changes in women's clothing fashion represent
the ever-changing outcome of the eternal struggle between a woman's
admitted desire to put on clothes, and her unadmitted desire to take
them off. Whatever truth there may or may not be in that
statement, we do have a very similar eternal struggle in the history of
musical tuning, though both desires are admitted, if not always equally
valued. These are the desire for purity of tuning, and the desire
for freedom of modulation through all tonalities. So long as we
choose to be limited to twelve tones per octave, we can satisfy one or
the other desire fairly completely, or both in part, but not both
entirely. The victory of equal temperament as the standard tuning for
western art music -- which appears to have been established by the
second half of the nineteenth century -- represents the victory of the
desire for free modulation through all keys, which of course is
epitomized in the chromatic music of Wagner and others. It is
also conducive to the atonality of the mid-20th century. However,
not all modern musicians have remained content with that status
quo. Harry Partch, Lou Harrison ("Just intonation is the best
intonation." He also kept his home keyboard in 1/2-comma
Kirnberger, which tuning he specifies for his piano concerto), LaMonte
Young, Douglas Leedy and others have all explored just intonation and
other non-equal tunings in various ways.
- Tim Tikker
---------------------------------------------------------
Date: Thu, 07 Oct 2004 12:12:00 -0700
From: Craig
Subject: Re: [CB] Tuning:
Oscar raises some interesting points. I decided to try
'oversampling' the chromatic octave by a factor of 8, obtaining the
relationship 2 ^ (n/96). I used selected values of n to keep a 12-note
scale. The result was almost identical to just, but the problem is a
lack of an obvious relationship between the values of n. Many are
adjusted slightly from the multiples of 8 one might expect. This
'system' may share just's limitation of being locked to a chosen root
-- I haven't yet run the numbers to see what happens (I chose A=440 for
the first run).
By the way, 2 ^ (n/x) is an integer when n is a multiple of x.
Example: 2 ^ (12/12) = 2, 2 ^ (24/12) = 4, etc.. That is why x defines
the number of steps in the octave. 2 ^ (1/12) is the basic
relationship in 'equal' temp.
The problem with trying to reconcile a perfect fifth with a
perfect octave is that the fifth is f * 1.5, where the octave is f * 2.
The relationship that allows both would be 2 ^ x = 1.500. x = 0.585 is
within the stated accuracy. In terms of integer ratios, x = 31/53 works
nicely. Not exact, but considerably more accurate than 2 ^ (7/12). Now
comes the problem of a keyboard with 53 notes to the octave, along with
knowing which of several C's to play at a given point in time, plus the
question of how to notate it all. Suddenly 'equal' temp seems like a
brilliant compromise...
There is such a thing as too much accuracy. When the beat rate
drops below 1 per second, who can readily detect the error? Consider
also that intonation errors that would make someone like myself shout
"tune it or die!" can be tolerated in certain fast runs. Vibrato covers
a multitude of sins. ;-)
I would love to see the look on a piano tuner's face when
confronted with a 370+ note piano. Wasn't there a movie like that?
Oscar Wehmanen wrote:
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Date: Thu, 07 Oct 2004 12:30:08 -0700
From: "Chuck Guzis"
Subject: Re: [CB] Tuning:
On 10/7/2004, Craig wrote:
>I would love to see the look on a piano tuner's face when
confronted with a
>370+ note piano. Wasn't there a movie like that?
Are you perhaps thinking of the flick "The 5,000 Fingers of Dr.
T"?
Relatively recent research has shown the ear to be a lot more
complex than previously thought. For example, the loudness of a
tone can strongly affect our subjective impression of its pitch.
And contrary to the mathematical model of octaves having a perfect
power-of-2 relationship in frequency, research has shown that humans
tend to like their octaves "stretched" a bit.
Cheers,
Chuck
***End of Contrabass Digest***