At 12:32 AM 5/15/2005, Jason Kanter wrote:
>Once upon a time...
Well, a good try - but not quite. Let's see what we can clarify here...
First, some context. We must remember that:
1. Tuning/tempering applies to all musical instruments (and voices too) -
not just keyboards. Everyone who plays and sings and builds wind
instruments must decide how to tune intervals.The singers and players do it
on the fly - the builders in the shop. Until the 18th century, keyboards
were secondary - and followed the lead of whatever else was out there. They
were accompaniment - not solo - instruments.
2. Until the 19th century, musicians tuned their own keyboard instruments.
And - as musicians do - they tuned whatever sounded good to them. All the
"temperaments" with their fancy names were published by music theoreticians
and mathematicians (the fields are related), who needed fodder for their
manuscripts. Case in point - nobody knows for sure what particular
temperament J.S. Bach actually used - and it is said that he was able to
tune his doubles (at least 3 sets of strings) in 15 minutes (so ET is not
likely...) and so the arguments continue... The professional tuner who
neither plays nor builds instruments does not really appear until the 19th
century.
3. The idea that an octave can be divided into equal segments was known
since ancient times - in the Ancient Western world to the Pythagoreans (who
were the musical/mathematical secret society of ancient Greece), Medieval
and Renaissance Europe had access to these sources, and at times the
"equal" temperament was used when needed. (more later)
>First there was "Pythagorean" or "just" tuning, favoring perfect fifths and
>consequently with very noisy major thirds. Music didn't use major thirds
>much. If you tune perfect fifths (and fourths) CGDAE, you wind up with a CE
>major third that is 21.5 cents expanded, as opposed to the 13.7 cents
>expanded that we are so accustomed to in our equal temperament. These major
>thirds are called "Pythagorean".
A couple things here:
Throughout the earlier Medieval era, vertical harmony (2 or more notes sung
or played simultaneously as chords) was not used. So "intervals" were
strictly melodic concepts. In addition, music was based on the hexacord -
not the octave. In other words, only six - not all seven scale tones were
used. No need to close the circle (or octave)... After "vertical" (chordal)
harmony was introduced in Paris (in the organum at Notre Dame), "chords" as
such still were not a real concept (they didn't really become such until
the early Baroque) - they were formed "accidentally" as counterpoint
melodies intersected. In all "important" places (cadences and other points
of emphasis) these had to be fifths or (later) fourths - considered the
only consonant ("perfect") intervals. Thirds - along with everything else -
were deemed dissonant, and avoided at such places (though they were common
throughout the music where there was no emphasis). The Pythagorean tuning
served these musical needs just fine. The thirds were supposed to sound
lousy and there was no need to close the octave - so the "wolf" interval
did not matter.
Later on, the seventh scale tone comes into use - closing the octave and
creating the "wolf" interval. Additional accidentals are introduced to
form harmonies over more scale tones, and that barbaric music using
vertical thirds and sixths (GASP!!!) - apparently coming from England -
invades the continent. (It was called "fauxbourdon" - false bass, where the
bass is separated from the upper voices by those pesky imperfect thirds and
sixths - instead of the perfect fifths and fourths like it should oghta be,
humph....) And so the "wolf" becomes a problem and there is a need for
better sounding thirds.
>Then, early Renaissance, musical sensibility in Europe flip-flopped and
>composers started experimenting with "sweet" major thirds (just/pure or at
>least a lot slower-beating than the Pythagorean third). Note - to tune a
>perfect 5:4, beatless major third, where CE is pure, you therefore have to
>narrow all four of the fifths CGDAE substantially (averaging about 5 cents
>narrow, as compared to the 1.96 cents narrow that we are now accustomed to).
>There developed a number of variations called "meantone" tuning. Generally,
>eight of the 12 major thirds in meantone were tuned to be pretty clean, --
>but the remaining four thirds (usually BD#, F#A#, C#F, and AbC) were
>unplayably harsh (some expanded by 40 cents or more), and one of the fifths
>(usually AbEb) was very wide (actually a diminished sixth) and such a
>horrible sound that it was called the "wolf".
Well, my friend, this is where the chronology just isn't as you present it.
The earliest example of a "meantone" type temperament is published by
Bartolomeo Ramis de Pareja in 1482. The prototype of the "Well"
temperaments - that you describe below - is published just 36 years later -
1518 - by Henricus Grammaticus (really a German musician by the name of
Henryk Schreiber who, in the fashion of the time, affected a Latin name to
establish his scholarly bona fides). Since scholars typically describe what
is already in use, one can only guess when and where these systems were
first formulated. (I'm not even going to try to deal with the issue of when
the Medieval period ends and the Renaissance starts...)
In fact, not much later than that, the equal temperament shows up in
regular use in Italy. For example, the Italian Renaissance musician
Vincenso Galilei (Florence - 1520-1591, father of astronomer/mathematician
Galileo Galilei - that should give you the time frame) advocated that
fretted stringed instruments (lutes and viols) be tuned in equal
temperament, for obvious reasons - it is a rather complicated task to tie
frets onto a fingerboard at exactly the correct angle to create a usable
unequal temperament - whereas parallel frets give you a passable equal
temperament. Contemporary paintings show instruments with both straight and
slanted frets. Italian Baroque opera orchestras (e.g. Monteverdi -
1567-1643) were actually composed of two separate and distinct sections -
which never played simultaneously, because they required different tuning
systems. Those with fretted stringed instruments (the lute and viol
families) - were tuned in equal (including the keyboards in that section)
and those playing with unfretted strings (the violin family) were tuned in
a meantone (to preserve the "melodious" thirds). Here is clear evidence
that musicians used the Equal Temperament when needed - and avoided it when
they could. It didn't quite meet their other musical requirements...
>Then as keyboard instruments evolved, composers wanted to be able to play in
>more than 8 major and 8 minor keys, so they started experimenting first with
>what is now called "modified meantone" (nine playable keys) and then "well
>temperament" (12 playable keys).
Had nothing to do with keyboard instrument evolution - more with the
evolution of musical tastes. Keyboard instrument evolution actually
attempted to follow the evolution of tuning fashions - see below.
>Basically, still keeping the CE third
>cleaner and sweeter than the other thirds, tuners of "well temperament" took
>meantone's four harsh thirds down to a maximum of 21.5 cents expanded (e.g.
>adopted the "Pythagorean third" as the limit of tolerability) and
>distributed the remaining harshness among the remaining thirds, keeping the
>"white" keys sweeter at the expense of the black keys. This kind of tuning
>produced a distinctive "key color" that was also used consciously by
>composers in the 18th-19th centuries. Over time, from Bach's era to the
>early 20th century (when the math for tuning Equal Temperament was first
>solidified and a reliable ET bearing plan was first developed), the
>differences between the sweetest third and the harshest third were gradually
>reduced, but the key color remained, even though it got fainter as we
>advanced into the Victorian era.
It seems that the Meantones and the Well temperaments co-existed and fought
it out right through to the High Baroque. The various baroque Dance Suites
owe their existence to the meantone temperaments. One property of the
meantone temperaments is that a sharp and flats which in ET or Well are
equivalent in pitch (as in C# - Db) in meantone have different pitches (the
sharp is lower than the flat). Having only 5 keys on which to tune
accidentals, one must choose beforehand which five accidentals to tune on
those keys. Therefore, in order to not have to retune the harpsichord
between dances, a whole suite of them was written in one key. Then, when
the dancers needed a breather, the harpsichord could be retuned for a suite
in a different key... Here the musicians were still trying to hang on to
those beautiful meantone triads - the fifth beating at 2-3 bps is not
significant, as compared to a third beating at 6 or more bps... But
instrument builders tried to push the envelope - and retain the beautiful
triad while allow more keys (harmonies) to be used. So harpsichords are
built with split keys - for a sharp on the front and a flat on the rear (or
vice versa - I don't remember - I worked on a replica back in 1991). A
keyboard is even designed with a "sharp" between the B and C or E and F
keys - to allow for B#, E# and Cb,Fb (which are distinct pitches in
meantone). Here technology follows musical demands and tuning fashion - not
vice versa...
However, the Well system of tempering had a musical property that meantone
did not (besides the usable outer enharmonic keys - which in any case there
was little need of). When the tempered fifths were judiciously placed
around the temperament, an affect was created where the tonic triad of the
C major key had the slowest beating third, and as one went around the
circle of fifths farther away from C in both the sharp and the flat
direction (meaning, more accidentals) the beat rate increased. This
increased "activity" in each of the keys was used to determine its
character - calm and peaceful in the quietest, bright and cheerful in the
slightly more active ones, emotional or restless in the yet noisier ones,
on to painful and tragic in the farther ones and on to excruciating in the
farthest (enharmonic) keys - until you got to the very rarely used farthest
keys which were to denote something akin to the end of the world... Baroque
composers found this means of expression more significant than dynamics - a
change of feeling or emotion was denoted by a key change, whereas dynamics
were used in a more decorative manner...
Note that the Equal Temperament has neither property - beautiful "clean"
thirds or significant key differences - so until the 2nd third of the 19th
century it simply did not meet the needs of musicians, except in rare
cases. It was mostly rejected as an aesthetic and musical choice. Why it
became dominant when it did (if you consider the "quasi-equal" temperaments
of the 19th century as "equal") is a very interesting question - and has to
do with several simultaneous developments in musical tastes, society and
technology. Some of these reasons I read about, some I heard posited by
people whom I respect, and some are my own conjectures:
Technological/musical - The rise of the metal plate modern piano (and its
rise to prominence as a solo and "workhorse" instrument) is probably a very
significant factor. The heavily strung, high-tension instrument with its
high inharmonicity tends to obliterate all the subtle "tuning niceties" of
the Well temperaments - they are just not as apparent. The high tension on
the strings also tends to make the fundamental stronger relative to the
middle overtones. Thus, whereas in a lighter strung harpsichord or early
piano the middle overtones lend the quiet, "pure" or near-pure thirds a
certain beauty - as the coincident partials support each other or gently
clash - in the modern high tension piano they are too weak - so these
intervals in Meantones and Wells sound "dull" and "boring". The briskly
beating equal temperament thirds help make the sound of the thirds
interesting where activity in the middle overtones is too soft. This might
be why piano makers in the 19th century - such as Broadwood - actively
advocated the ET over the older tuning systems - it made the pianos sound
"better".
Musical - as musical fashion changed in the 19th century, key differences
became less significant - while being able to get out to the farthest keys
(and stay there for a while before going back) became more desirable. As
compositional skill became more and more equated with the ability to
quickly and cleverly modulate as far away as possible from the home key and
then back again - for no particular reason except that one could - key
differences pretty much lost their meaning, and more so when music farther
evolved (or possibly devolved) into rampant chromaticism...
Social - With the rise of the middle classes - the businessmen and the
professionals - secular music migrated from the nobleman's parlor or dining
hall to the concert hall. The rising bourgeoisie sought to ape the
nobility's ways, and so the subscription concert became the place of
performance. The niceties of the older temperaments were lost in the larger
halls - and lost on the nouveau riche audiences who, while aping the ways
of the nobility did not necessarily acquire the cultural refinement that
would allow them to appreciate the finer points of music - such as
temperament niceties...
Finally, the heavily strung, high-tension, high-friction modern piano
required the services of a professional tuner. Whereas before, twirling
harpsichord or fortepiano tuning pins wasn't any more complicated or
demanding than twisting violin or guitar pegs (and it was simple enough to
do a quick touchup between songs, dances or movements) , the newfangled
instruments presented issues of "setting the string" ,"torquing the pin"
and "stability" - in other words, one actually had to learn and perfect
"tuning hammer technique". Musicians for the most part were happy to leave
that to professionals who were willing to train in this craft. Since
training was already required - the much more complex task of setting a
temperament that required 12 tempered fifths (rather than 4 or 6) could
also be learned in the process. So there arose a class of people willing
and able to tune ET - we, the tuners.
ET, by the way was still resisted in the late 19th century - an older
musician returning to England from France writes in 1877 that life is hell,
since that "ugly" equal temperament seems to have taken over everywhere -
and makes the organs sound like hell's trumpet.
Footnote: I heard that about 12 years ago in Boston, when one of Steinway's
concert tuners from the New York area - Ludwig, originally from Romania -
gave a lecture at the local Steinway dealer's, somebody tried to show him
how to tune a meantone (Boston is the hotbed for that sort of
thing). After watching the demonstration, Ludwig said that that's how they
originally taught him to tune pianos in Romania...
>Hope this helps. I write from memory and may have some of the minor details
>wrong -- Ed Foote or others, please correct me -- but I believe this is
>pretty accurate.
I write a lot from memory too, but the names and the dates I looked up. And
some of this I got directly from people who play and research that older
stuff for a living...
Israel Stein
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