----- Original Message -----
From: Ron Koval <drwoodwind@hotmail.com>
To: <pianotech@ptg.org>
Sent: Wednesday, March 19, 2003 10:39 AM
Subject: temperaments - Ellis
>Any modern ETD user can tell of the
> non-stable nature of the pitch of a struck piano string.
Really? What is this? What degree of cents accuracy is needed to
"observe" this. When a machine shows a string going sharp, then
flat, then sharp again, what does this tell us? Does the string
"read" the same on different blows? Do two machines show the same
"non-stable nature of pitch". If not are we dealing with variance
of the machines, or actual variations of what is being measured?
But what does it matter? Not enough to affect tuning. Other
wise how could we tune at all? If pitch does vary then string
tension formulas would not work.
Ellis claimed his device to be accurate to 1 cent. I think
the Conn devices used in 1937-47 for determination of
inharmonicity were claimed to be within 1 cent.
So yes the data you see from Ellis may have an accuracy of +- .5
cents or = - 1 cent. depending on how the math of tolerance is
computed to reflect, "within one cent".
> Additionally, this
> process would lead to errors,
Yes perhaps, but if so then when does one dismiss Ellis's data?
But to study it at face value, is interesting also. For example,
how could the tuner in line 5 miss C--G by 4 cents? (696).
Actually though he tuned c' --g which is a 4th down according to
Ellis on how the Broadwood tuners proceeded. Which is more
remarkable because the beats of 4ths are double (aprox) with the
same error of the 5th.
But after that he tuned very well, I mean good...; ).
>his main ideas might be
> summarized by:
> The only good interval is a Just interval.
The major premise of the book both of Helmholtz and his translator
was that the octave could be divided into more tones than 12, and
that the 12 tones could be tuned in more ways than one. They were
scientists and as scientists were trying to discover the
scientific foundation of music. Helmholtz explored the
physiological aspects, hence its title, "On the Sensation of Tone"
and then the physical, as in the physics of musical tone. He came
very close to our modern conception of the origin of beats, and
how these beats can be used in tuning in particular of Equal
Temperament. Ellis is the creator or inventor of cents, a way of
using logarithms to express the size of intervals. Here we see ET
forming the basis of cents and cents defining the nature of ET.
Yes there is a mathematical relation. How close to mathematical
perfect is desired, is up to the musician.
For every one who uses a machine and cents to calibrate it,
measure in, or program it; Ellis and Helmholtz is where it all
began.
..................................................................
....
> How does Mr. Ellis come to grips with the reality of tuning a
fixed pitch
> instrument? Convinced by the beauty of the mathematics of >just
.intervals,
> he suggests that the only answer is to venture into
microtonality, the
> splitting of the octave into smaller and smaller intervals,
until any
> interval can be played to the mathematical justness he seeks.
I think if you read more of Ellis and Helmholtz, ( I have never
read the whole work) you will find he was investigating rather
than advocating. Yes he shows what can happen if the octave is
divided into 36, 57, or 117 parts particularly in his chapters
titled, "Musical Intervals", Musical Duodenes", "Experimental Just
Intonation", Mr. Bosanquet's Generalized Fingerboard", "Mr. Paul
White's Harmon, "On Tuning and Intonation"
..................................................................
.............
>
> He goes on to put all tunings in two boxes, which simply leaves
no >room for the Well temperaments.
..................................................................
.................
Exactly, because "Well temperaments" were not known in his time,
much less used by musicians or piano manufacturers. Even with his
measuring devices, no matter how crude they may be judged today,
he could not measure something that did not exist.
........................................................
> On the tuning of ET 36 note scale:
...................................................
No, its a 117 note scheme.....
The reference is, "Hence to tune the Duodenarium of sect. E.
art.18, p. 463, merely by Fifths and major Thirds is quite
hopeless." (p484) [Going to p 462 we see......]
"This Duodenarium is a table of duodenations, (explained in pages
451-485) which occur even in modern music, though it is impossible
to be certain how far the ambiguities of tempered intonation,
[!tempered intonation!] may mislead the composer to consider as
related, chords and scales which are really very far apart. It
contains an approximative estimate of 117 for the number of tones
in an Octave which would be required to play in just intonation,
and are roughly represented by the 12 tones of equal temperament."
(p. 462)
..............................................................
> that even the laborious and careful training of modern tuners
for >obtaining the very slightly altered fifths and fourths of
equal >temperament can only lead them to absolute correctness 'by
>accident.' (p 484)
...........................................................
YES! This is describing how tuners trained in ET would have
problems tuning the Duodenarium of sect. E. art.18.
Also..."But for major Thirds and minor Sixths there is no [they
would have no] chance at all to get even one interval [of the
Duodenarium] tuned correctly.
...........................................................
>
>
> " In their endeavours to avoid the 'wolves' of meantone
.temperament musicians invented numerous really unequal
temperaments, which it would be uncharitable to resuscitate."
(p 435)
>
> Here is the only mention of another type of temperament....
Proposed by musicians, yet dismissed by Ellis.
..........................................................
Not quite, the very next sentence....
"There is however a really practical unequal temperament which
I call "Unequally Just", but it cannot well be explained till the
Duodenarium has been developed."
Then he proceeds to "Cyclic Temperaments" from which can come
a whole slew of other temperaments. p 435. I dare say that
proponents of "Wells" might find some historic foundations here.
But don't ask me, I don't even know how a "Well" is defined.
..........................................................
> What's more, the temperaments that he [Ellis]
> measured, clearly unequal by his own measurements are lumped
>under the heading of ET to nicely fit into his theories.
..................................................................
That is one theory but here is another. Ellis was not a tuner but
he knew about piano tuning and was close to Hipkins, who claimed
to have introduced ET into the house of Broadwood in 1840's.
Ellis writes,
"It takes a quick man three years to learn how to tune a piano
well in equal temperament by estimation of ear, as I learn from
Mr. A.J. Hipkins. Tuners have not the time for any other method."
("method" I think means tuning ET rather than an other
temperament as they could only tune by ear in those days.)
Then follow the tables called "Specimens of tuning in Equal
Temperament".
Thus we see that Ellis regarded his measurements as genuine
efforts at ET and we see how he regarded his measurements as how
close they came to the ideal. To our modern standards they may
seem "unequal" but how far off are they really? I don't have a
machine to enter these numbers into, but those that do, how to
these temperaments sound?
Also I wonder how aural tuners using the procedures given by
Ellis might compare when measured by modern machines? If a tuner
claims to be tuning ET and submits to measurement by machine, how
can you say by the results of the machine, (of which you express
skepticism) that he is not tuning ET, but something else? There
is no need to rewrite history, simply take the historical record
at its own word.
Of what he measured Ellis wrote.....
"These were all tuned by the modern way of Fifths up and
Fourths down, the object is to make the Fifth up 2 cents to close,
and the Fourth down 2 cents too open. As this interval of 2 cents
lies on the boundary of perception by ear, the difficulty of
tuning
thus with out attending to the beats is enormous. The above
figures shew how very close an approximation is now possible in
pianofortes".
"The order of tuning differs in different houses. Merrs.
Moore & Moore's tuners set c'(4) by a c''(5) fork and then tune
in order: c'(4) g(3) d'4, a3, e'4, b3, f#3, c'#4, g#3, d'#4. Then
begin again and go on as c4, f3, bb3, eb4. The proof of the work
is that e'b4 and d'#4 are identical.
Messers. Broadwood's tuners also set c' from c["?] but then
proceed
c'4, g3, d'4, a3, e'4, b3, f # 3, c'#4, g#3, d'#4, a#3, f3, c4;
with the proof being that the final agrees with the initial c4. In
this case a#--f is taken as Bb--f, that is a Fourth down." (p.
485)
>the crux of
> musical expression; contrast, tension /release, loud /soft,
fast/slow. >This is the chief component of the Well temperaments
that have been described, and are currently being tested by list
members.
>
> Ron Koval
Now if there could some kind of definition of "Well temperament".
----rm
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