Le 23/06/2016 22:31, S D a écrit :
:-) An acoustic piano is far from an ideal sound generator. In fact,
it is a complex collection of imperfections striving for an
unattainable ideal.
If we wanted a pure sound, we would use a source that produced only
pure waveforms like a sine-wave generator, and perhaps added the
various pure, in-tune harmonic frequencies at various (and diminished)
volumes to the fundamental tone.
A piano has 88 keys and string collections (most notes have 3 strings
per note, bass strings only one wire string with a copper-wire coil
wrapped around it, per note). The strings for any particular note
(tone frequency) are often slightly detuned, so that only the middle
string is more or less perfectly in tune, while the two strings to
either side are detuned slightly in order to make the note's sound
richer and fuller, with beat frequencies and other out-of-tune
artifacts introduced.
In addition, most pianos are "stretch tuned," which means that the
bass notes are intentionally and progressively tuned flatter and
flatter by a small incremental amount, while the treble (high) notes
are tuned incrementally sharper and sharper. This is because the bass
notes have such a low tone that it is their harmonic frequencies that
are heard more clearly by the human ear, and those harmonic
frequencies are often sharp (a higher frequency than they should be if
perfectly in tune). So the bass notes are tuned so that the harmonic
frequencies are heard more in tune while the fundamental frequency is
slightly flat (lower frequency than it should be if it were perfectly
in tune).
Meanwhile, the treble strings, because they are stretched so tightly
in order to produce such a high pitch (frequency, tone), immediately
decay flat (become lower in frequency and out of tune immediately
after they are struck by the piano hammer activated by the key pressed
by the performer. So the treble notes are tuned a little sharp, so
that the decay (the sound as it becomes softer immediately after it is
produced) sounds more in tune.
Add to those out-of-tune compromises the fact that the scale we now
nearly universally use, the equal-tempered 12-tone scale that allows
for playing in any key, is a compromise between the pure tunings of
any specific key, so that nearly every note in the scale of any key is
at least a little out of tune. The intervals of perfect fifths and
perfect fourths, derived from strict mathematical relationships, are
all altered, so that the fourths are stretched (tuned sharper than
they should be) and the fifths are flattened (tuned closer to each of
the two tones than they should be), which means that nearly all music
that we hear, and nearly all instruments that play together in an
ensembles, are ALL out of tune to one degree or another.
In addition to all of that, people usually intentionally introduce
other imperfections into their sounds or music, such as the distortion
frequently used with electric guitar.
Music is a vast collection of imperfections. Regarding modeled pianos,
if the model is too pure and perfect, people complain that it doesn't
sound realistic or authentic. If it models the actual acoustic
instrument's imperfections too well, they complain that it sounds too
"muddy," distorted, not clear or pure enough, etc.
All of this means that it is literally impossible to please a
perfectionist, because there is almost nothing perfect about music or
the production of sound, and also because a perfectionist, if he tries
very hard, can always find something, even the smallest thing, that he
considers imperfect or not ideal. :-) Life must be very hard for the
perfectionist!
However, all that said, our very precisely out-of-tune 12-tone equal
temperament scale, in use for pianos and most orchestral or band
instruments, actually allows for an incredible amount of extremely
complex and beautiful frequency and harmonic relationships that are
impossible when using a completely mathematically pure single-key
scale. Without this "imperfect" tuning, modern music since the time of
Bach, including the beautiful Classical, Romantic, Impressionist and
modern music of Mozart, Beethoven, Chopin, Tchaikovsky, Rachmaninov,
Debussy, Ravel and hundreds of other composers would not be possible.
OK-- I apologize for such a long-winded response! :-)
Please don't apologize!
Really nice to read & learn from your knowledge :)
Maybe you have something to say about the fashion to tune A to 442 Hz?
Greets,
--
Fred,
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