tuning: Consider this...

[windshieldbug]

Not by itself, perhaps, by with another of the same note you can hear the beats easily, which is what Klaus was describing...

I would posit that no one can accurately "pick out" the difference between two perfectly unison notes and two notes tuned 1 cent apart in a scientific test.

I worked in electronic music while I was in school (and yes, that was back in the Moog days). Since the oscillators were not static, we used a frequency counter to get them "close".

Now I realize that the frequency value of cents changes per note/range, but you could hear quite minuscule differences between "unison" notes (the sawtooth wave form being the most obvious, but that's also the one that's closest to a brass sound).

True, that was at perhaps 30' surrounded by quad Altec-Lansing Voice-of-the-Theaters, but I doubt if a Strobo-Conn could tell you the difference between two simultaneously played notes.

It makes no difference anyway; the proof is in what the musician can hear, and their ability to adjust it on the fly to be synchronous. No one will care how good your ears are, to what level of cents you can distinguish, if you can't make the required adjustment. And if you can, no one will care how big or small the required distance is.

[imperialbari]

As my report told, the hearing situation was very special, and it is no coincidence that I remember this one out of all the many pitch situations I have been through.

Many people say they can hear beats, when pitches don't match. I can hear them, but they are not my main tool. I listen for the matching of overtones. A not too worn E string out of steel has a very pure sound, which translates to lack of fuzzy overtones. Each of the two E strings sounded very pure on their own, but when sounded together there was this fuzz entering the picture. As told I never would have been able to pick out that pitch difference in an ensemble situation or between two different instruments or if vibrato had been applied.

I don't remember whether it was Rubinstein or Horowitz who wanted that little fuzz between the pitch of the three strings of each note in the upper half of a piano. That great player wanted life to the sound. In fact that slight fuzz is part of the human touch to music. If you hear a very pure soprano voice you know that the singer is very young. We associate maturity in singers with some degree of fuzz.

If you want to carry out your pitch increment test with electronically generated sine tones, you will get the result you predict, as there are NO (later edition) overtones to create the fuzz I heard in that very special situation.

As for bloke’s original advise it couldn’t surprise me, as it is old experience that bass lines shall of course be in tune, but that if off then rather flat than sharp. A sharp bass will be perceived aggressive or the rest of the of the ensemble will be perceived dull.

Klaus, who also finds this discussion interesting, but some brasses are calling for my attention right now

[iiipopes]

Years ago I stopped trying to tune the E string of a bass guitar open, and always tune it on the 12th fret harmonic, because it's easier to hear and the overtones, being inherently sharp as discussed earlier, line up better with the rest of the instrument.

I never try to get my Rickenbacker 12 string in "perfect" tune. It defeats the purpose. Now, I don't leave it as wide as a "honky-tonk" piano, which in some cases is purposely de-tuned to get as much whang as possible, but the whole purpose of the additional six strings is for body and depth, same function as a celeste stop on an organ, and so to get it too perfect defeats the purpose, and it stops sounding like a twelve string and more like simply a double-tracked single guitar.

I remember taking the standardized battery of musical aptitude tests in 5th grade, with reel-to-reel played on an old industrial/school grade Wollensack player (the ones that 3M had made to play their Scotch brand recording tape). Supposedly, the pitch difference got down to 4 cents on the comparison tones and the questions were whether the second tone was higher or lower. I remember it was funny that I could hear the tape player (probably playing at 7 1/2 ips, although it could have been at 3 3/4, but that would have been awfully slow for "critical" listening) occasionally wobble the tones slightly, my introduction to those old analog tape terms, "wow" and "flutter," and when I turned my head one way or another the timbre could sound different coming off a different wall of the room, whether the all glass window to the outside or the cinder block room divider walls. But I got them all correct, way beyond anything that could be written off to guessing or random statistical variance. So I have documentary proof that, at least at one time, I could hear at least 4 cents difference, and possibly finer, as I was compensating for the slight change in pitch as the plastic tape spool rotated.

[sloan]

Our Bloke has brought up a most interesting topic: the stretching of octaves in piano tuning. The reason this is done is complex. it is because the overtones from a struck piano string are sharp relative to the fundamental. As a struck piano string vibrates back and forth, it stretches at the peaks of its vibration. It is this stretching of the string that essentially "tunes" the string sharper twice per vibration. The result is that octaves sound out of tune even when the fundamental frequencies of the strings are in the strict 2:1 ratios of perfect octaves.

Every wind player with a smattering of knowledge about the physics of musical instruments should read (and understand) the above paragraph...several times, if necessary.

It describes perhaps the most accessible *physical* system that doesn't behave exactly like the simplified mathematical model everyone learns in the beginning. This model is a wonderful starting point - but you see it raised to the level of an Eastern Religion at times - and it's almost never exactly correct for an actual, physical musical instrument!

It's relatively easy to explain WHY the model is not quite correct for pianos (see above!). Trying to do the same for tubas (undoing all of the already learned assumptions and replacing them with the truth) is much, much, much more difficult and time consuming. All I'll say is "what you may think of as the 'natural' harmonic sequence is, in fact, an engineered, sophisticated, artificial creation designed to match the model." The model does a bad job of explaining the instrument. The model does not describe an original proto-tuba; instead, the tuba has to be carefully designed to come close to matching the model!