Quote:
Originally Posted by 815C
match the A string 7th fret harmonic to the open E string...
|
You can stop right there.
There are two conditions of getting an instrument to play in tune. The first is related to temperament - what are the desired pitches of the notes - and the second is related to intonation - how consistently close that particular instrument is capable of achieving the desired pitches.
Temperament
Harmonics belong to Pythagorean tuning - they are whole-number divisions of the vibrating string. Frets are placed according to Equal Temperament, a mathematical constant that is a multiple of the 12th root of 2, an non-repeating decimal that is not a whole number.
The ONLY places where the pitches of the two different systems of temperament are the same is the unison and the octave. No other notes will be the same.
Comparing the pitch of a note of one system - say the 7th fret harmonic - that is not an octave or unison, to a note belonging to a different system is like comparing apples to oranges.
The only harmonics that you can use for tuning purposes are the unison and octave(s) of a string. Those can be compared to the pitches of open strings or fretted notes.
Intonation
If the instrument's setup is not sufficient to ensure that the notes consistently get "close enough" to the desired pitches, you will "chase your tail" attempting to get the instrument to play in tune. If the intonation is not well setup, how closely the notes conform to the desired pitches will change depending upon where they are played.
Thus, getting an instrument to play well in tune involves, first, having the instrument setup well enough that the pitches produced are consistently close to the desired pitches. Second, it involves using a self-consistent method of tuning the pitches of the strings - don't use harmonics other than octaves or unisons of the open strings. Then, since Equal Temperament is not what the ear wants to hear, you might want to tweak - or "sweeten" the tuning for particular keys or pieces.