Checking high-register intonation with a tuner
I have recently started checking my intonation with a tuner and I notice that, high up on the E-string, I seem to hear that I'm in tune while the tuner says I'm sharp by about 25 cents. I'm wondering if I should trust my ear or the tuner. (Piano tuners use stretch tuning [Railsback curve] where the upper register is tuned sharp to compensate for inharmonicity. A short steel E-string would be expected to exhibit inharmonicity.)
I have had the same experience with the old fashioned method of comparing to open strings (somehow I can't get any value out of the tuner for intonation purposes, only for tuning). It seems one tends to play sharp up there unless one corrects oneself.
Tuners are inherently inexact for the same reason that pianos are always very slightly out of tune on every note.
Jeffrey, the inharmonicity that requires stretch tuning on a piano only applies to freely vibrating strings. On a bowed string, all the partials are harmonic.
Thanks for that clarification, Han. This explains why I observe that bowed natural harmonics are in tune according to the tuner.
If you want to believe your ears, just listen for the waves in the intonation. Even if you hit a D on the E string on the tuner in-tune but the rest of your strings have gone flat, you're still "out of tune" where it counts - with yourself.
In all my psycho-acoustical readings, it is found by experiment that on average our ears are only "linear" over the middle range, e.g. for notes in the treble and bass clefs (plus a couple of ledger-lines). Higher notes sound progressively flatter than they "should", and lower ones sound sharper.
Our brains have a marvelous analog computer that converts the exponential frequency curve into a linear perceived pitch function. But it is not perfect. So we don't tune to the electronic tuner for the high notes.
I've been playing around with it. I notice that if a higher octave follows a lower octave, the higher octave typically sounds a bit flat. But if I play them together, they sound good. If I sharpen the higher octave, it sounds better following the lower octave, but terrible if played together with the lower octave. From this, I conclude that in most cases (especially playing with others), the tuner should be followed more than the ear.
another experiment-- Tune your open E to the same E on the piano. Then compare the double-octave harmonic E with the same note on the piano. That double-harmonic E at the very end of Schaherezadhe will sound flat. The last time I did that solo, I tuned my E string sharp before starting the 4th movement.
I don't think it is the tuner. Comparing with open strings is a time honored and still valid way to check yourself. When you play "solo" in the high register I don't see a reason why it should be different from when the lower octave goes along (or any other note to complement the chord). If you play an A-Major scale and the A at the top (in 7th position if you want to count) is not a perfect double octave higher than the open A string you are playing too sharp and your hearing may be off as well.
"... I observe that bowed natural harmonics are in tune according to the tuner."
Inharmonicity gets worse with higher-numbered partials. It's a more of a problem on low strings because they are capable of producing lots of high partials. Higher-pitch strings like an E string are probably not producing many of these higher partials.
If you're playing for an audience of electronic tuners, I recommend practicing with a tuner.