From: mclaren
Subject: technology and intonation
--
A tenth century text on organ building laid
out the rules for pipe length exactly as
Pythagoras would have in the Greek era.
Start with a pipe and call it C. Divide it
Pythagoras would have in the Greek era.
Start with a pipe and call it C. Divide it
into 4 parts, remove one and you have the
pipe for the low F. Divide the C pipe into
3, throw away one part, and the resulting
pipe sounds a G above C. Divide the G
pipe into three, add one part to it, and
the result is D below G. The instructions
continue in the same way, producing
a completely standard Pythagorean scale
that effectively translates the tuning
of a monochord into fixed ratios of
pipe length.
This is a typical reaction to new
technology. As Marshall McLuhan
pointed out, new forms of technology
typically start by taking on the modes
and habits of older forms of tehcnology.
Only gradually does the new technology
and habits of older forms of tehcnology.
Only gradually does the new technology
start to develop unique and novel
modes of use.
For example, early printing presses
used type designed to fool its readers
into thinking the letters had been
written by hand. Each letter was
carefully designed to imitate the
shape of a letter written in ink with
a square-nibbed pen; printers of the 1490s
even used multiple typesets with
different inks to produce the effect
of illumination by scribes with red
ink for special words, etc.
Early television programs imitated
plays; early Internet applications
imitate magazines--for example,
this tuning forum. The world wide
imitate magazines--for example,
this tuning forum. The world wide
web is not limited to ASCII text,
as is this tuning forum, and soon
sounds will be sent attached to
graphics and text as a matter of
course (this still takes too much
bandwidth today--a 44.1 khz stereo
soundfiles demands 10.5 megs of
data per minute).
In the 1450s Duke Philip's organ
designer Henri Arnaut came up with
the idea of modifying the Pythagorean
system to keep as many fifths pure as
possible while still making as many
keys as possible listenable (i.e., triads
without excessive beats). This was
in retrospect a failed attempt to
use the new technology of the modern
in retrospect a failed attempt to
use the new technology of the modern
organ for polyphonic music; meantone
tuning did the opposite of Arnaut's
procedure, keeping thirds just while
shaving bits off each fifth.
Meantone proved so successful that,
according to Alexander J. Ellis and
others, it remained the dominant form
of tuning through the 1840s.
In between the 1500s and the 1840s,
many different peculiar variants of
meantone were tried.
Example: an organ at Bucksburg, build around
1615, boasts 14 keys per octave. Handel's
harpsichord also uses 14 keys to the
octave. I have pictures in my files of many
peculiar-looking keyboards which have as
many as three tiers of keys--one set of
peculiar-looking keyboards which have as
many as three tiers of keys--one set of
ordinary white keys, a second set of
black keys with some extra smaller keys
*in between* B and C, and a third tier of
keys, also blac keys, which reproduce the
conventional black keys but translated
by a comma up. Mersenne's Harmonie
Universelle is full of such illustrations,
but many such keyboards were actually
built. Between 1500 and 1800 there was
no such thing as "a standard keyboard
instrument keyboard"--there were a lot
of different types of keyboards, since
all musical instruments throughout that
period were hand-made.
Such extended meantone keyboards flourished
during the 17th and 18th century, a period
when standardization was not the norm,
during the 17th and 18th century, a period
when standardization was not the norm,
and when musical tuning--like spelling!--
was considered a matter of individual
taste within the overall limits of the
meantone system. (It's important to
remember that because meantone is
a general method in which fifths are
altered to preserve just thirds, there
are *many* different flavors of meantone.
1/3 comma, 1/4-comma, 1/6 comma,
1/11 comma--known as 12-TET--and
variants such as the irregular circulating
temperaments of Marpurg and Werckmeister
and Kirnberger.)
The next great technological leap was made
by Henry Maudslay, who worked at the
smithy in Woolwich Royal Arsenal in the
early late 1700s.
smithy in Woolwich Royal Arsenal in the
early late 1700s.
Joseph Brahma, an entrepeneur who wanted
to build an unpickable lock to cash in on
a highly-publicized series of robberies in
London, hired Maudslay as an apprentice
locksmith. By 1797, Maudslay asked for
a raise of thirty shillings a week (to
support his wife and children) and Brahma
refused, so Maudslay walked out and
started his own workshop on Oxford street
in London.
Maudslay's first product was a new lathe
he had designed.
A lathe is basically a machine which
uses a screw as a moving base for a knife;
the knife can cut wood, or if made of
tempered steel, iron or copper.
The 1800 Maudslay lathe was far larger
tempered steel, iron or copper.
The 1800 Maudslay lathe was far larger
than any of its predecessors (which were
mainly used for ornamental work on small
gewgaws) and his sliding tool-rest
was perfectly mounted on accurately
planed triangular bars. Because Maudslay
was a fanatic for accuracy, he built his
lathes to extraordinarily fine tolerances
for the era; but the big suprise was not
that Maudslay's lathe could turn out more
accurate work faster than any other lathe.
The real shock came when people realized
that they could use Maudslay lathes to
machine extremely accurate and regular
screws and bars for use in *other*
lathes, which in turn could produce
*other* machine tools... Starting with
extremely accurate screws, it is
*other* machine tools... Starting with
extremely accurate screws, it is
possible to build a huge variety of
precision machine tools. These tools
in turn make possible the creation
of even more precise machine tools.
The process builds on itself in much
the same way as the development of
ever-more-powerful silicon chips has
led to silicon compilers which in turn
allow the construction of even more
powerful computer chips by automated
methods.
The end result of Maudslay's lathe was
that woodworking, metalworking,
manufacture, toolmaking, and factories
were all revolutionized. Maudslay's
lathe changed the nature of warfare
and it made Britain the greatest sea
lathe changed the nature of warfare
and it made Britain the greatest sea
power in the world. It also made possible
the modern orchestra and the modern
piano.
How so?
Napoleonic warfare depended on the fact
that rifles were inaccurate. They were
inaccurate because there was no way
to rifle barrels with precise accuracy or
to turn out standardized gun parts with
high precision at high speed. This meant
that if you shot at an enemy more than
a few score yards away, your shot probably
wouldn't hit. So Napoleonic warfare depended
on masses of infantry marching in lockstep
toward one another until they got close enough
to mow each other down.
Britain became a great sea power when it built
to mow each other down.
Britain became a great sea power when it built
and equipped enough ships to rule the seas; but
this wasn't possible without turning out more
than 1400 block-and-tackle units to haul sails
up and down *on each and every ship* (and that's
only on 3rd-class ships. First-line ships used
> 2000 blocks!). These blocks and winches and
pulleys were made of wood by hand. There
weren't enough carpenters in Britain (or in
Europe) for all the blocks the British navy
needed, and you couldn't run a ship without
'em.
Marc Isambard Brunel came to Maudslay
in 1800 with an idea to turn out these blocks
for the Royal Navy using his new lathe; by 1808,
the first large-scale mass production
facility in the world, Maudslay's factory,
was turning them out by the truckload.
facility in the world, Maudslay's factory,
was turning them out by the truckload.
To string a piano you need huge amounts of
wire, and--even more important--you need
precision machines to build the die through
to draw the wire, and more precision machines
to loop the wire at the ends, and even *more*
precision machines to wind the lower strings.
Maudslay's lathes made it possible to build
such precision machinery, and as a result the piano
rapidly evolved from a relatively thin-voiced
instrument strung at low tension in the 1830s
to a robust instrument with three wires per
note at high tension and wound strings on the
lower octaves by the 1880s--all due to
the tidal wave of change produced in
manufacturing by Madslay's lathe.
Woodwind instrument had always been
nortoriously dicey in their intonation, in large
Woodwind instrument had always been
nortoriously dicey in their intonation, in large
part due to the problems of precisely boring
amd machining wood (essentially the same
problem as rifling a musket barrel). By the 1880s
woodwinds had reached high standards of
precision (though they still depended crucially
on those temperamental reeds). Moreover,
woodwinds plummeted in price along with brass
instruments as precision machine tools
proliferated.
The valves of brass instrument benefited
most of all from Maudslay's lathe because
of the precision tools built to bend and seal
them.
Eventually, wire strings became so common
that they replaced gut strings in the string
instruments, leading to the godawful
screeching-train sound of modern string
instruments, leading to the godawful
screeching-train sound of modern string
instruments and a corresponding increase
in sheer volume (and a precipitous drop
in listenability--the average violin solo
noawdays sounds like a cat being castrated).
--
The upshot of these precision machine tools
was the 12 tone equal tempered scale. Musical
instruments built by mass production could not
be economically individualized so as to accomodate
dozens of different meantone variants. To make
money turning out modern musical instruments,
you must *standardize*--all exactly alike. When you
build only one or two harpischords per year, you
can easliy afford to use exotic three-tier keyboards
fitted to special custom meantone tuning schemes...
but when you build 100 pianos a year you must
settle on a single rigid standard keyboard. As
but when you build 100 pianos a year you must
settle on a single rigid standard keyboard. As
soon as musical instruments became mass-market
commodities, their tuning also had to be standardized
to make a profit for the manufacturer.
The result--as Ivor Darreg pointed out for many
years--was that 12-TET was foisted on the
musical world by musical instrument manufacturers,
rather than by musical theorists, performers,
or composers. As Lou Harrison has pointed out, the
advantages of 12-tet are "almost entirely economic."
In fact Ellis reports that meantone "sounds by far
the sweetest" of all the intonations he tried;
clearly *technology* forced 12 equal tones on
musicians, and they went along *reluctantly.*
With the advent of the digitial synthesizer the
iron fist of 12 made itself manifest in the velvet
glove of digital technology. As Ivor pointed out,
once people started to hear pure unadulterated
glove of digital technology. As Ivor pointed out,
once people started to hear pure unadulterated
exactly precise 12, they fled from it in droves.
Pianos and string instruments strayed gracefully from
12, especially in the upper and lower registers--
the octaves on a piano are systematically stretched,
and vioinists tend to bend pitches whenever
they possibly can.
But with the earliest digital synthesizers, there
was no choice--the intonation was burned into
the ROMs and listeners and composers and
performers were stuck with pure perfect 12.
And the beats drove them crazy, so they slathered
on hockey-rink reverb, they used phase shifting
and multitrack tape and echo... And as soon as
retunable synths appeared, a mass exodus from
12 began in earnest.
Today we're in the middle of that intonational
diaspora. It has been created and supported by
Today we're in the middle of that intonational
diaspora. It has been created and supported by
the technology used in our instruments. As
computers move ever closer to real-time MIDI
generation of Csound-type timbres, it will
become easier and easier to specify with precision
*both* tuning and timbre--and to control the
interaction of the two.
This will produce the next revolution in tuning,
probably within the next generation or two, based
on the ideas of William Sethares, John R. Pierce,
Jean Clause Risset, J. M. Geary and James Dashow.
Hot diggity!
--mclaren
