That makes sense. I wondered because I do notice when playing along to music, a tuning difference of about 10 cents is quite apparent, but that’s more playing piano or organ parts along with a recording. (And I don’t have a particularly sharp ear, in my opinion.)
I changed my mind. I think a 2 Hz difference, if we’re in the range of A=440, would probably be noticeable to a trained ear, maybe even slightly annoying. I mean, think about it. 2 hz is about 1/6 of a half-step, at that pitch range.
But again, only a roll/tremolo on the marimba, in unison with a string/woodwind/brass instrument, on long, sustained tones.
My school orchestra always had the First chair, first violin play the note that the other strings tuned to. That violin was usually tuned by a pitch pipe or tuning fork.
It wouldn’t be hard to adjust the pitch slightly. Depends on what other instruments are added. Everyone has to to tune to the piano if its used.
If you play two sustained, pure (few harmonics) tones simultaneously, one at 440Hz and the other at 442, you will hear a beat tone of 2Hz. This is too low for humans to detect as a pitch; they will hear it as a twice-per-second pulse, a tremolo, almost like a vibrato.
This is under ideal conditions. Under more practical conditions, such a pitch difference is negligible, even desired (how do you think string sections get their blended sound? From combined, tiny pitch differences between multiple instruments.)
Combine a perfectly-tuned marimba with a horn or woodwind and it’s doubtful if even the best horn or woodwind performers can hit every note within 2 Hz of the marimba anyway, even if the tempo is Largo Molto con Slowest.
Tradition uses an oboe, not a violin.
I would have thought that, too, but then when I saw that’s equal to 8 cents, I’m not so sure. Like I said above, I’ve played along with and recorded to other recordings, and a difference of 10 cents starts becoming obnoxious. The last time I had to record a little country piano part, I had to detune the piano (electronically) by 12 cents for it to sound in tune with the recording. Now, I agree, a couple cents here and there and it lends “thickness” to a sound–that is essentially what the chorus effect does. But once you start hitting close to 10 cents, it just sounds out-of-tune to me. From what I’ve been able to find online 4-5 cents is where the human ear begins to notice.
I was referring to a string orchestra. We rarely performed with any wind or percussion instruments. The band students had their own conductor and performances in the band hall or at pep rallies and games.
Yeah, 2 Hz is about 16 cents at A=440. It’s definitely audible.
Again, though, I really only think this is really noticeable with sustained, single-note rolls in unison with a wind/string instrument.
According to the calculators I’ve found, it’s 8 cents. Try this. It says it’s 7.85-ish cents. Now 16 cents is pretty big (in my opinion). That’s the difference between A444 and A440. Eight cents is a bit more subtle. It’s one of those things that if I play for a few bars with another instrument, I’ll know someone is off, but I wouldn’t be able to tell you which instrument is sharp or flat relative to the other, just that they’re both a bit off. It feels slightly “uneasy.”
Never mind, your math is right.
You were also right in saying that 4-5 cents is the minimum audible difference, AFAIK. That’s what I was always told in school. I’ve never determined it experimentally.
I ran into my informant again yesterday. He had been doing some thinking and told me that there are marimbas and similar instruments tuned to both 441 and 442 Hz, but they are very expensive and only the richest orchestras can afford them.
I think arguing about the audibility, in real life, of a 2 Hz difference, is like arguing about whether strings play in a tempered scale or not. It’s highly subjective and also subject to too many factors that will mask what you are looking for. If you are pairing a marimba with a violin, the marimba will probably be played by repeated, rapid strikes with a mallet and the violinist will, unless told not to, be using a vibrato. And the whole thing is likely mashed up with a orchestra. Expecting even a sophisticated ear to detect a 2 Hz difference is not likely.
Now pair two sine waves at 440 and 442, and everyone can tell.
I agree, for the most part, but I don’t think you need sine waves to tell. Like I said, playing piano along to a recording that is 10 cents off is noticeable, at least to me, and I don’t think I have a particularly great ear. I have a reasonable ear, but I don’t have perfect pitch, or anything like that. Playing around in Logic Pro, it looks like 8 cents is just within the threshold where I hear a “thickening” of the sound instead of out-of-tuneness, for lack of better word, but not enough to start annoying me. Looks like it’s closer to 15 cents where it really annoys me, which actually agrees with al27052’s original post that a 440 instrument is okay up to a 442 orchestra, but beyond that requires a properly tuned instrument.
There’s a big difference between 2 Hz at the 40 Hz level, versus at the 2800 Hz level, which would be close the outer extremes of orchestra sound.