There seem to be some confusions on this list about the theory and
practice of Western tunings. So here's the Cliff's Notes:
Until tempered tuning, the intervals (differences between pitches) was
unequal - in a particular key, the pitch distance from a D to an F, for
instance, was not not necessarily the same as from an A to a C.
Intervals were derived from the overtone series, or from integral
relationships between pitches (a string length that is a simple
fractional relationship to another string length, for instance), or from
other natural or arbitrary bases.
Assuming that a piece stayed in the same key or mode (tone-set,
interval-set) throughout, as was common, you needed 7 or so pitches per
octave, though depending on the tuning these would be very particular
pitches, unevenly spaced.
If you then wanted to play the same piece in a DIFFERENT key, you would
need another set of pitches -- since your first set of pitches was
unevenly spaced, you couldn't just re-use the same pitches in a
different order.
To APPROXIMATE a common form of just intonation (untempered, unevenly
spaced tuning) in 12 different keys, you need a TOTAL GAMUT of 72
equally spaced pitches. (This is for 7-limit just, using integral
relationships between pitches that can be expressed as simple fractions
with no integers larger than 7). For any given key, you only need 7
unequally spaced pitches drawn appropriately from this total gamut.
So you could say that the untempered Western system as a whole needs
72-notes per octave, but (and this is the important point) not all at
once. In a given piece, you only need a small subset of that. Music is
created by musicians by ear on the level of the subset -- the adjusting
happens as necessary. The total gamut can be seen as a THEORETICAL basis
to the music, but an actual musician works with adjusting exact
intervals in a particular musical context.
How does this relate to pitch discrimination? Your ear would definitely
hear that a piece is "different" if you played it in just intonation and
then transposed it to another key without availing yourself of the
necessary large gamut of pitches to exactly replicate the uneven just
intervals. In other words, to sound the same you'd need to retune,
listening carefully to adjust the various intervals. Bach used this
feeling of difference to great effect in his works that go through many
keys, such as the Well Tempered Clavier. Since the performer couldn't
retune the instrument between pieces, the music in each different key
would be "out" in subtle and interesting ways, having different effects
on the listener. (Yes, I know he used mean tunings instead of pure just
intonation, but the effect is still there -- and no doubt intentional --
as long as you're not on a tempered keyboard.) The ear --and psyche--
can hear these differences quite well.
Here's another example of how well the ear discriminates pitch, in a
harmonic context this time: if you play a seventh chord (C to B-flat) on
an instrumet in tempered tuning, it is a somewhat dissonant and tense
interval. Now lower the B-flat by just 32 cents (significantly less than
a quarter tone) and it will sound completely different, very consonant
and "settled". This is a "7/4 seventh", where the B-flat is in an
integral relationship of 7/4 to the C. Now lower it again so that you
are 50 cents flat, a quarter-tone down from the original B-flat. Once
again it sounds very dissonant. The ear hears all of this very easily.
That's why exact pitch is important to psychological effect, I think.
But to pull of pitch precision you don't need to have 72 pitches per
octave all stored in your head, just an attitude of listening carefully
to intervals in context.
Hope this clears up some of the confusion.
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