Why does it not matter what octave you're tuning to? If you wind a string to two different octaves of the same note, surely it's going to have a big effect on the sound, no?
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For the extreme bass and treble of a piano, it does matter -- the octave are stretched.– user9480Commented Dec 28, 2018 at 1:20
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4 Answers
Why does it not matter what octave you're tuning to?
If you want to set a string to a certain pitch, of course it does matter what octave you adjust the string to.
Setting a string to A3 (220Hz) is not the same as setting it to A4 (440 Hz). Not only will the sound be different, but you might make the string very hard to play if it is too slack, or break your string (or your instrument!) if it is too tight.
However, "tuning to" can refer to the reference you are listening to while you tune. And because of the phenomenon of octave equivalence, it is possible to listen to A3 as a reference while adjusting an instrument to play A4, as long as you have some way of not getting confused about which octave you are actually adjusting the string to.
This is normally quite easy, because usually an instrument is approximately in tune - the strings might be a semitone out-of-tune at the most. So if you need to tune the A string on your guitar, you can play any A on the piano*, and tune your guitar to the correct A, because you know that you only need to adjust the guitar slightly.
*Notes near the extremes of the piano might not be good choices, because the strings behave in a somewhat 'less-ideal' way.
answered Dec 26, 2018 at 14:31
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I agree, except octave equivalence has little to do with it - especially because the answer to the linked question shows that there is essentially nothing special about the octave other than the high overlap of overtones, which higher pitches from the overtone row have too. A trained musician could use a reference pitch at, say, a fifth from the pitch they’re tuning (like string players). An octave is just the easiest interval (apart from a prime) from the reference pitch. A tenth (or rather a seventeenth) should be possible as well, if you practice a bit (but any higher would be tricky).– 11684Commented Dec 28, 2018 at 9:46
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@11684 I guess it's possible to tune using any reference, if you have sufficient training, or for some people maybe even no reference. The octave is often easier in 12-TET though not just because of overtone similarity, but also because octaves are perfect, while fifths are a little flat. I used to assume that octave equivalence was only due to overtone coincidence but I've also read that there is some physiologically octave-related structure in the "Medial Geniculate"... whatever that is. Commented Dec 28, 2018 at 10:41
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Yes, in 12-TET the octave is easiest (even more so than in other temperaments). That has nothing to do with octave equivalence either - and as I said I agree with your answer except the octave equivalence bit. In 12-TET octaves are the only pure interval so it’s the only interval with which you can use the overtones to tune. If you have to tune a pure interval, you can use higher overtones as well, but the higher the harder to hear. Octaves are easiest because the first overtone is the octave, not because of “octave equivalence” (this in line with the Physics.SE answer you linked to).– 11684Commented Dec 28, 2018 at 11:35
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@11684 to my mind, octave equivalence encompasses everything that makes notes an octave apart seem 'easy to equate' - whether that's the high overlap of overtones, or any deeper physiological reason - and my line of thinking is that in a general sense, those are the same things that make it easy to tune a string to A4 while listening to A3. I didn't want to get too much into the detail of using overtones to tune as I wasn't sure the idea the OP was referring to that technique in particular. Commented Dec 28, 2018 at 12:53
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then I suggest removing the link to Physics.SE since it specifically asks for something deeper than overlapping overtones, my comments being proof of the resulting confusion.– 11684Commented Dec 28, 2018 at 12:57
True enough, sonically. You'll also probably end up with two different guitar parts too. 'Why does it not matter?' - it does.
I think you may be referring to tuning an A string (for example) to an A note - but maybe an A note in a different octave. If so, the frequencies of each note are double or haqlf to arrive at another A. It will be an 'octave copy' of what you need, but for a lot of folk, it's a good reference point. Not as good as the actual note you need to match, but good enough. We do it all the time when singing. If a man and a woman were singing the same melody, they'd be an octave or two apart, without thinking about it. Neither would be trying to reach the other's actual notes, only octave copies thereof.
That apart, it's impossible to 'wind a string to two different octaves'. There's only one string, therefore only one note available. The strings on any instrument are the correct gauge for the notes they're going to be tuned to. Go down an octave and they're too floppy; go up and they're way too tight. Neither move is sensible.
@topomorto provided a very nice answer so I won't repeat what he already wrote.
But... FWIW, it does matter to me in which octave the reference pitch is.
1 (E) 329.63 Hz E4 2 (B) 246.94 Hz B3 3 (G) 196.00 Hz G3 4 (D) 146.83 Hz D3 5 (A) 110.00 Hz A2 6 (E) 82.41 Hz E2
When I tune the low E2 string, I have trouble tuning it to the high E4 string as a reference pitch.
I usually fret string 4 at the 2nd fret for an E3 reference pitch, and also fret the 6 string at the 5th fret for the unison with the open string 5 (A2.)
In this sense the octave does matter to me for tuning. If the reference pitch is 2 octaves away, I can't hear the "beating" between the two pitches as clearly.
answered Dec 26, 2018 at 20:35
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1The 'beats' would hardly be discernible at two octaves apart. I can't even hear them! +1 for beats.– TimCommented Dec 27, 2018 at 8:11
Just to add the boring mathematical basis for the other excellent answers: the reason we have the "octave equivalence effect" is because tones an octave apart, a 2/1 ratio in frequency, are the closest to being the same tone mathematically, a 1/1 ratio, and we hear this similarity.
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That's not accurate --- take a look at the ratio of, say, a minor second. That's much closer to 1:1 but hardly "feels" the same. Commented Dec 28, 2018 at 2:23
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2@CarlWitthoft That's because a minor second is close to it numerically, but not multiplicatively. What we hear as "close" is how well the waveforms sync up. A note one octave up would synchronize every other period. See this explanation– bxk21Commented Dec 28, 2018 at 19:25