A couple of things: Estampie natalis
by Vaclav Nelhybel(Hey Shos, I think this guy would be Bio material....................no pun intended), 1976. Accompaniment: Piccolo, violins/violas, cello, minor percussion, handbells.
Piano tuning. Selma, you're method would work, but doesn't account for the real subtleties: Relative humidity, minute flaws in the strings, and construction irregularities by virtue of inconsistency of the cast iron plate from piano to piano(they are individually sand cast to this day), and inconsistencies associated with the wood structure of the piano, from the frame to the soundbaord, variances which will occur due to the inconsistencies of the plate from piano to piano. The other huge factor is the fact tuned intervals and octaves are not pure; they are stretched or contracted slightly to give the piano brilliance of tone.
Humidity is a huge factor in the performance of a piano, because it is mostly made of wood. If a piano is freshly tuned, then the humidity is raised, it will actually go up in pitch because the paino will swell.
As for the construction irregularities, all of them combined will change the tambre of each piano, even if they came of the production line one after the other., and to date there is no machine built that is able to discern the tonal "sweet spot" for a given instrument better than the human ear.
As for the impurity of intervals, there are two instances where they occur while tuning: Tuning the temperment section and tuning octaves. The temperment is the middle approximately three octaves of the keyboard, and they are tuned first. If you've ever looked at the strings of a piano, you'll notice that most notes, from the mid bass up have three strings for each note, or unison
. The mid-bass has two per unison, then the low bass has one per unison. The compunding of strings as the pitch goes up is for volume and richness. While tuning the temperment, the outer strings of those unisons are muted, and then, after A440 is set, intervals are tuned up and down the keyboard off of A440, in 4ths and 5ths, and 3rds and 6ths.
A short explanation of string vibration is needed at this point. As a string vibrates, it produces secondary vibrations at higher frequencies than the fundamental vibration, or pitch. The secondary vibrations are called partials, harmonics,
,and continue pretty much infinitely up the frequency spectrum. If you've ever listened to an out of tune piano, when you play a note, most often you'll hear it make a kind of wah-wah-wah-wah sound instead of a steady pitch. This is called beating
, and occurs when two strings of slightly dissimilar frequencies vibrate simultaneously. It might help to think of them as sine waves with slightly different curves, and where the curves cross, they tend to cancel each other out, causing a variances in amplitude, or volume of sound.
Back to tuning intervals. The reason 4ths, 5ths, 3rds, and 6ths are used to tune different pitches is that those intervals have partials in common somewhere up the frequency ladder. For instance, tuning A with D, which is an interval up of a 4th, or down of a 5th, will have an overlapping or common pitch merely one octave up from the highest note in the interval. It should be noted that each partial beats twice as fast as the pitch below it, so if the coinciding A above the D and A being tuned is 4 beats per second, the next partial above that(probably an F# above that A) will beat at 8 beats/second. That being the case, the real art to tuning as purely as possible is to listen for the highest partial possible, and tuning it as beatless as possible. However, when tuning intervals, if it is tuned beatless, the interval will sound flat. Therefore, 4ths and 3rds are tuned narrow
, where the higher note is ever so slightly flatter than pure, while 5ths and 6ths are tuned wide
, where the upper note is tuned ever so slightly sharper than pure. This acheives a desired amout of octave stretching
in the temperment, meaning that each successive note up the scale is minutely sharp compared to the octave below it. If it's done right, you will only hear a very slow beat in the highest partial you can hear, and the net result is brilliance of tone in the piano.
Once the temperment is tuned, the mutes are pulled one string at a time, and the unisons are then tuned. This is the instance where the highest partial is tuned as beatless as possible. When it's done right, the unison sounds positively buttery rich on a good piano.
Beyond the temperment section, the piano is tuned unison by unison, first up the scale, stretching the octaves slightly more as we move up the keyboard, then tuning the lower notes, progressing downward, not worrying too much about attempting to stretch octaves, because the lower notes have so many partials within the range of hearing that the needed brilliance is already there.
Having said all of that, there is still one more factor that will affect the whole process: The idiosyncrasies peculiar to each piano by nature of its materials. No matter how consistently cast iron plates may be cast, due to the variances of the crystalline matrixes when they cool, along with minutes flaws in the metal, no two plates are even similar. I was told that looking at a line of plates waiting to be assembled is pretty shocking: They look positively warped and bent relative to each other. Because of that alone, the stresses inside the piano are distributed slightly differently from piano to piano, and since the combined tension of all the strings comes to 18-20 tons, that becomes a considerable variable. And then, factors such as a knot in the wood, or the angle of a bridge pin can color the tone of a pitch, which to date is only discernable through careful listening with the human ear.
To the best of my knowledge, there is still no machine produced that can account for all of those variables better than the human ear.
Now you know why a piano tuner needs to have relative quiet while he's tuning.
PS. That's why I can't tune anymore. The tinnitis produces a constant high frequency that interferes with my ability to listen to high partials. I tried tuning my piano once to see if I still could - boy, was that a mistake!
PPS. Another reason piano tuining should not be attempted by novices is the tension I referred to earlier. Aside from popping strings if they're pulled too tight, it is crucial to check the fasteners attaching the plate to the wooden frame of the piano. Both work in concert to support the tension of the strings, and neither is sufficient to hold the tension alone. I've heard of recently tuned pianos literally exploding internally because the plate snapped in two from the increase in tension without making sure it was stillsecurley bolted to the wooden frame. In one case, I heard the bottom half of the broken plate was actually driven through the bottom of the piano and 2" into a hardwood floor.
Anyone still awake at this point?
<small>[ 12-24-2005, 01:49 AM: Message edited by: OperaTenor ]</small>