intonation question: 5th sharp, 17th flat

[bobsax]

Really cool stuff mega fiddle
Thanks for educating. That after all is why many of us are here.

 

[Turnaround]

1 cent error is what you call in tune, at least at bass frequencies, and if your reference is perfect
equally tempered intervals. I cent is 1/100 of a semitone. The 5th fret on the G string is about 130 Hz.
A 1 cent error is a frequency difference of about 0.08 Hz

Many of us detect errors in intonation as the beats we hear between two notes at slightly different frequencies. In the case above, there would be less than 1 beat every ten seconds. Might as well call it in tune.

 

[megafiddle]

hgregs -
bobsax -

Thanks, glad it helped.

I should correct and explain this a little better (from post #17):

1 cent error is what you call in tune, at least at bass frequencies, and if your reference is perfect
equally tempered intervals.

I don't mean to say that a cent has a different significance for equally tempered notes. It doesn't.
I should have said, "if your goal is perfect equally tempered intervals."

Basic tuners use an equally tempered scale as their main tuning temperament. Some offer alternate
tuning temperaments like just intonation. But most all of us use equally tempered. Therefore most,
(I think) would consider being within 1 cent of equally tempered to be dead on.
I mentioned it because not everyone considers perfect equal temperament to be "in tune".

Many of us detect errors in intonation as the beats we hear between two notes at slightly different frequencies. In the case above, there would be less than 1 beat every ten seconds. Might as well call it in tune.

Good point about the beat frequencies.
I mentioned that 1 cent was "in tune" at bass frequencies because at low frequencies, 1 cent amounts
to a very small difference in Hz and therefore a very slow beat frequency. At higher frequencies, that
same size cent error amounts to a larger difference in Hz and a faster beat frequency.

Just as the frequency difference between octave notes is larger at the high end of the scale, the frequency
difference for 1 cent is also larger at the high end:

55 A to 110 A - 55 Hz difference
880 A to 1760 A - 880 Hz difference

1 cent at 55 A - 0.03 Hz
1 cent at 1760 A - 1.01 Hz

When the two notes are not heard simultaneously and cannot produce a beat frequency, the error might
have to be as large as 5 cents to be heard as out of tune. This seems to be a commonly accepted value
for the threshold of pitch perception.

*

 

[pedrodelawasp]

I just liked someone's comment on here, not realising the thread is two years old!

Informative discussion, none the less.

 

[walterw]

I just liked someone's comment on here, not realising the thread is two years old!

dammit! i was ready to respond before i realized this.

oh well, maybe this'll be useful for archival purposes:

went back and checked my relief on the G string (holding the 1st and 12th fret down, and the string holds a business card at the 5th fret) - i'm guessing the relief is ok.

that's probably too much relief, it should be more like a sheet of notebook paper between 1st and 12th.

hell, if the fretwork is good enough i'll shoot for that same "sheet of notebook paper" gap between first fret and last fret.

 

[GrumpiusMaximus]

Fretted instruments are always a compromise.

You're never going to be perfectly in tune the whole way up the neck on all the frets. In fact, 'in tune' is a harder concept to understand than many think. The basic mathematical principle of an 'octave' being twice the frequency of the first pitch class is basically right but not the whole truth. Fundamentally, A=440 (or 442) and the octave A would be 880 or 884 but depending on which instrument you're playing, that's not quite the case. Pianos stretch the upper frequencies of their tuning so that a (say) theoretical fundamental of 1200's octave would be tuned at (say) 2404 rather than just a simple double.

What I'm basically trying to say is that get the intonation as good as you can but don't sweat one cent here or there. It's even harder to hear on bass frequencies (as long as you don't have any beating going on) than with mids and highs (anything with significant 1K-10K harmonic content - Fletcher-Munson curves and all that) and that setting the intonation at the 12th and looking for any errant issues with the nut (if you have a sharp 1st fret) and the 17th will do you just fine. Don't sweat 1 or 2 cents here and there - nobody will notice and if they do, they're either bullshitting or have exceptional pitch differentiation.

As a side point, Violinists playing solo tend to play in a different temperament than they do when accompanying others precisely because they can play 'between' the notes. If you get into more advanced theory, you'll learn that (say) an Eb is not quite the same as a D#. It's not something you have to worry about but it does explain the woes we have with tuning and intonation.