Greetings,
Ric rites:
> Historically ET was desired as a tuning or
intonation if you will, but the technology to tune it was not developed
until ca 1870. We have the writings of Montal from 1838 that describe ET
almost. <<
It is not quite the same to say "ET was desired as a tuning or
intonation" as it is to say there was a desire to avoid dissonance. We have
a bit of historical support for the view that using all 13.7 cent thirds made
for a harsh tuning (in addition to offering no key character). So, I am not
sure that it was "desired" by musicians and composers. Certainly thought
about, but maybe not really developed until manufacturing and musical
composition created a reason for it.
Montal's instructions are an interesting point. They were in a book
titles "How to Tune Your Own PIano". In them, one is instructed to tune four
contiguous minor 3rds to form the basis of the tuning. Try it! If there was
a non-technical piano owner back then that could come closer than a Young to
ET with these instructions, I would be stunned. It was hard for me and I am
a full time tuner. I don't think his instructions created much exposure for
ET at the time.
>>Indeed Aristoxenes shortly after Pythagoras is reported to have
proposed a common demonator ( twelth root of two?) for each of the notes of
a 12 tone scale. <<
This is perhaps true, though I haven't read of this particular appoach
on his part. There is a scale ascribed to Aristoxenes that calls for equally
spaced semitones. However, the plan calls for 10 equal tones and two large
ones. This creates a different set of intervals than our modern 12ET, but
it earned Aristoxenes the moniker "Father of ET".
> it is reported that Aristoxenes said, "judge beauty by what you hear, ie the
ear, rather than a mathmatical fromula" or something to that effect.<
I have also read this and agree, one reason is to claim the support of
antiquity in urging people branch out; from a formulaic approach to hopefully
becoming familiar enough with a variety to learn something from the
comparisons among them.
>>Modern orchestra
woodwinds, reeds and brass instruments are built and tuned to ET. If you
study the development of musical instrumenets you might wonder how they
tuned flutes in the beginning. <<
Prior to the developement of the screw machine lathe ( Maudsley,1830?) the
orchestral instruments were built to play in a particular key. With no
valves, natural horns played the overtones available within them. Obviously,
the higher in the overtone series you go, the closer the pitches are
together, so at some point up there, a chromatic scale can be formed. This
takes a whole lot of lip!
This all changed following the new machining ability and we saw the rise
of the orchestra instruments like trumpets and horns. (Strings also were made
on these new machines, creating an unprecedented increase in the accuracy and
intonation possible for the forests of violins etc. being employed)
The ability to make consistant instruments with the mandrels and lathes
of the industrial revolution created a new need, how to put them together
intonationally. ET is the perfect compromise. It should be mentioned that
today, professional horn players use embouchere to compromise that "perfect
ET" to shade the pitch of certain notes in any given key. There's that lip
again.
>>The problem also presented itself with
fretted stringed instrumenets. The lute for example demanded a
"proportional" spacing of the frets, or else certain chords would sound out
of tune. <<
The lute tuning was greatly simplified by Mersenne's ratios, prior to that,
a good lutist was expected to be able to shift string pressure to accomodate
the occasional passing dissonance.
>>Sounding two notes at once so they sound pleasing is the key to
intonation. <<
Ah, yes, and what is "pleasing". Utter consonance, everywhere all the
time? Or screeching dissonance,(I know people that buy that for their
music). Is it more pleasing to have all intervals alike, or to have a var
iety?
I believe that the key to intonation is the ability to create contrast,
whether it is a blues singer sliding up to the last ringing harmony,(or
leaving the dang thing flatted as the track fades out, which drives me
nuts!), or one of Bach's tremendous harmonic sunsets after a chaotic organ
exposition. It is the contrast of order and disorder that so often creates
beauty. I have found that the unequal temperaments intensify this effect,
especially if the music was written under their influence.
>>Think how two bamboo flutes could be made so they could be
played together in harmony.
The Greek "Aulos" was such a beast, the pipes are believed to have been
tuned to one another in a variety of scale patterns.
>>Think how early pipe organs could have only 8
pipes to a diatonic octave and have all of those notes sound in harmony.
Two or more pipes sounding together "hath charm" until you try to play a
certain fifth. Why was this?
With the unregulated pressure of the pre 800 organs, the rise and fall of
pitch during a notes sustain was dramatic. Intervals smaller than a
ditesseron or dipente(our fourths and fifths), would have been very difficult
to have used. The third at this time was still regarded as an unusable
discord.
Between the gift of an organ from the Ottomans to Pippen around 730 , and
the turn of the millineum, organ's greatly improved their air control. It is
only natural that around 1000 we see the first accidental in what had been an
seven-tone scale for 15 centuries. Organs could use this added complexity
with their more accurate pitch. Over the next two hundred years, culminating
in the Halberstadt organ, keyboards grew to twelve pitches per octave,
however, there were still seven notes, and five accidentals.
By 1300, the Third had become a concord, English choirs were singing
compositions that used them. Instrument intonation was not far behind,
creating the meantone era by at least the 1400's
>>With keyboard instruments "intonation"
needed to be modified somehow or the notes "tempered" to produce an
acceptible harmony.
>>I like to think ET was desired but difficult to get so
all the other temperments execpt Meantone were developed to make it easier.
Kind of like black and white was developed before color and now every one
wants color. Or Stereo from Hi Fi. Who wants to go back to Hi Fi? No one.
Who wants to go back to black and white? OK some do and I can see
Ok, here is where we part somewhat. I don't think ET was desired. I
think it is the entropic end to a harmonic evolution. The modification of
Pythagorean or Just Intonation that occurred between 1100 and 1400, resulting
in meantone, was an attempt to extract the maximum usable harmony out of a
twelve lever keyboard. This was done by tempering the previously pure
fifths, and placing the pure harmony in the thirds. Polophony was increasing
during this time, and the thirds were more in control of the harmony.
The crux here is that there are a growing number of musicians that see
ET as black and white, and are attracted to the color available in the
earlier tunings. Perhaps in a particularly Aristoxenean way, we may tune
more musically if we listen to physical sensations rather than following a
mathematical formula. (the question is, could we sell those tunings........)
In light of what we know now, I am suggesting that the technician of
today is better prepared for tomorrow if they can offer more than one way to
tune a piano.
Regards to all,
Ed Foote RPT
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