II
Why Valve Slides Fail to Give Perfect Intonation
DOES 1+2=3? NO! NOT ON VALVE INSTRUMENTS. In other words, the first valve slide plus the second valve slide does NOT equal the third valve slide – the third valve slide is longer than the combined lengths of the other two.
WHY THIS BAD ARITHMETIC? In textbooks you’ll find it stated that the 2nd valve adds a semitone, the 1st valve adds 2 semitones, and the 3rd valve adds 3 semitones; also that valve 2 plus valve 3 equals 4 semitones, that one plus 3 equals 5, and that 2 plus one plus 3 equals 6. This is only approximate, as we shall see. We shall also discover why valves are made as they ar, and why the scale of every valve instrument can be only
approximately correct, why it can be only a
compromise scale.
VALVES IN COMBINATION ARE SHARP. Assume that the 2nd valve adds one semitone, the 1st adds 2 semitones, and the 3rd adds 3 semitones. But one, 2, or 3 semitones respectively are added ONLY when the valves are used
singly. When valves 2 and one are combined, you do not add EXACTLY 3 semitones, for this combination is about .12 of a semitone sharp. Likewise, the combination of 2 and 3 is .16 sharp; of one and 3 is .32 sharp; and of 2, one and 3 is .55 sharp.
IT’S PLAIN ARITHMETIC. Valves used singly may be satisfactory, but when combine them you get sharp results. Let’s see if we can give you some actual figures on the euphonium. For convenience we’ll assume this instrument is 100 inches long, although actually it is somewhat longer. The 2nd valve should add about 6% of this length for a semitone, so we make this valve 6 inches long (6% of 100). The 1st should add about 12%, so we make it 12 inches long; and the 3rd should add about 19%, so we make it 19 inches long.
BUT, when you push down valve one, your horn becomes 112 inches long with the addition of the 1st valve (100 plus 12 equals 112); and when you add valve 2 to this length, you should add 6% of 112, or 6.7 inches. The 2nd valve is fixed at 6 inches, however, so you’re .7 of an inch short, and consequently sharp. (Are you still with us?)
WHEN YOU COMBINE VALVES ONE AND THREE, see what happens. When you push down valve one, your horn becomes 112 inches long. When you add the 3rd valve, you should add about 19% of 112 inches, or 21.28 inches. Actually, however, your 3rd valve is fixed at 19 inches, so you’re over 2 inches short, and consequently sharp.
THE MORE YOU ADD, THE SHARPER YOU GET. If you combine valves one, 2 and 3, the resulting note is nearly a full semitone sharp. As already pointed out, when you combine one and 2, you should add 18.7 inches, but you are short .7 of an inch.
With valves one and 2, your horn
should be 118.7 inches long, and when you add the 3rd valve you should add 19% to this total length, or 22.55 inches. The 3rd valve is fixed at 19 inches, however, and so you are 3.55 inches short. This added to .7 of an inch lost on the one plus 2 combination totals 4.25 inches short. This discrepancy is nearly equal to the total length of valve 2 and would make this 2 plus one plus 3 combination equal to a little over 5 semitones instead of 6 and consequently nearly a semitone sharp.
eufonio.jpg
WHERE THIRD VALVE IS USED. Above are shown all the
regular positions in which the 3rd valve is used. In every instance it is used IN COMBINATION with the 1st valve or 2nd valve, or with both 1st and 2nd valves. Since standard practice calls for the 3rd valve to be used ONLY in combination, its length is calculated for best results when used in combination with other valves and NOT for use singly.
ALLOW FOR SHRINKAGE. We know the 3rd valve in actual usage is going to “shrink” and notes made by using the 3rd valve in combination will be sharp; therefore we make it long enough to allow for this shrinkage. In other words we make the 3rd valve longer than it should be if used by itself (longer than one plus 2) so that it will be of more nearly correct length when used in combination. This can be done because it is not used by itself but only in combination with other valves.
HOW LONG SHALL WE MAKE THE THIRD VALVE SLIDE? This is not an easy problem to solve. If we make it long enough to counteract the .32 of a semitone sharpness of the one plus 3 combination, it will TOO LONG for the 2 plus 3 combination, for this combination is only .16 of a semitone sharp. Furthermore, it will still not be long enough to counteract the .55 sharpness of the 2, one, and 3 combination. That will leave the former combination FLAT and the latter SHARP.
AND WHAT ABOUT THE OTHER TWO VALVES? Not much can be done with valve slides 2 or one, for they are used NOT ONLY in combination
but also singly. A valve cut to proper length for use singly will be to short for use in combination and, conversely, a valve cut to proper length for use in combination will be too LONG for use by itself. Since the use of valves one and 2 singly is more important than their use in combination, their length is fixed primarily for correct intonation when used singly.
YOU CAN’T HAVE YOUR CAKE and eat it, too. Although it is possible to cut the 3rd valve slide long for use in combinations, what is correct for one combination is either too short or too long for others. Also, the 1st and the 2nd valve slides can be cut to correct length for use singly but they will always be too short for use in combinations. What to do? What to do?
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