Is it accurate to tune with harmonics higher than the third harmonic on the double bass?

Question

I typically play an A4 with my tuner when I am tuning because that is the note that the violin would be playing.

On the bass, I would be playing the A harmonic on the D-string in fourth position. If I set my tuner to simply record my intonation, the note I play is consistently flatter than 220 Hz, even though it feels in tune against a drone. If I then play the harmonic an octave above that (somewhere F on the D string), that high A is recorded more correctly 440Hz.

I know that pianos and plucked instruments exhibit stretched tunings because of inharmonic strings, but I had thought I read somewhere that bowed instruments have perfectly lined up overtones because of the bow action, but I don't know if this still applies to playing the harmonics themselves.

So what I'm asking is: Is it okay to use harmonics as high as the 6th (5th?) harmonic to tune the instrument? Why or why not? If not, should I tune by ear, playing the lower A harmonic and the A440Hz; or should I train myself to get the tuner to line up to 220Hz?

Answer 1

How high the harmonic is above the open string isn’t the primary issue, it’s the natures of the partials themselves. The 2nd partial harmonic an octave higher should be a true octave above the open string. This will be true, therefore, of all doublings of two. The fourth, eighth and (if you can find it) sixteenth partials have the same relationship to the open string, factoring out octave differences. The third partial, octave and a P5th harmonic is, of course, perfectly in tune with the overtone series of the string (give or take the inevitable flaws and discrepancies of an actual physical string). If you’re trying to be in tune with equal temperament, then this will technically be about two cents sharp, but in most circumstances this difference is insignificant. That’s why most string players feel perfectly happy using it to tune.

As with the second partial, any doubling of this partial has the same relationship, so the sixth partial (and twelfth, if you can find it) is just as usable as the third. However—and this is the part of your question I most wanted to address—the fifth (or tenth or twentieth), 2 octave and a M3rd partial is probably not usable for tuning purposes unless you’re working within a just intonation setting. This will be somewhere around 14 cents lower than an equal tempered equivalent. You only asked about going up to the sixth, but the seventh is also unlikely to be usable unless you’re in a just-intonation setting.

So, TL;DR, using up to the sixth partial should be fine, except for the fifth.

Answer 2

I think it depends on what you are tuning to. In an orchestra? usually, you tune to the 1st violin? Playing in a jazz combo you would usually tune to the piano if you have an upright or a grand. If you playing rock, make sure everyone tunes to a tuner. Playing along with recordings? well that's a little different, I've often had to adjust my tuning to be in tune with the recording. Its al relative I guess. in regard to the harmonics, I would say whatever you are able to hear most clearly. I had an old teacher who used to say "its close enough for jazz" then count off a tune.