Actually, it will solve most of it for guitarists, because the tuning problems that most guitarists blame on equal temperament are actually coming from their bad intonation. The fourths and fifths in equal temperament are not nearly as bad as they imagine. The equal temperament fifth is only 1.955 cents sharper than the pure fifth (3/2 ratio). Just under 2 cents.
Guitar intonation that is accurate to 2 cents is very good, I would say above average.
Another way to look at the pitch error in the ET perfect fifth is as a percentage of the pitch, which is about -0.169 %.
Suppose a 1200 Hz tone (quite a high note, somewhere between D6 and D#6) is played together with one that is 0.169 % flat. That flat one will have a frequency of 1198 Hz. The difference is 2 Hz, and so a 2 Hz beat will be heard: two volume swells per second.
Much lower down, at 120 Hz, that will be 0.2 Hz: two volume swells every ten seconds. Basically nothing. It makes no difference to guitar chords played in the first four fret box down by the nut.
The equal temperament error is worse for some other intervals; the ET major third is a percent sharp, or around 13.6 cents, which is a lot. It is pretty jarring, even in lower registers.
That's not what the submitted article is about; tuning in such a way as to fixing the tiny error in the fourths/fifths will not repair the major third.
Actually, it will solve most of it for guitarists, because the tuning problems that most guitarists blame on equal temperament are actually coming from their bad intonation. The fourths and fifths in equal temperament are not nearly as bad as they imagine. The equal temperament fifth is only 1.955 cents sharper than the pure fifth (3/2 ratio). Just under 2 cents.
Guitar intonation that is accurate to 2 cents is very good, I would say above average.
Another way to look at the pitch error in the ET perfect fifth is as a percentage of the pitch, which is about -0.169 %.
Suppose a 1200 Hz tone (quite a high note, somewhere between D6 and D#6) is played together with one that is 0.169 % flat. That flat one will have a frequency of 1198 Hz. The difference is 2 Hz, and so a 2 Hz beat will be heard: two volume swells per second.
Much lower down, at 120 Hz, that will be 0.2 Hz: two volume swells every ten seconds. Basically nothing. It makes no difference to guitar chords played in the first four fret box down by the nut.
The equal temperament error is worse for some other intervals; the ET major third is a percent sharp, or around 13.6 cents, which is a lot. It is pretty jarring, even in lower registers.
That's not what the submitted article is about; tuning in such a way as to fixing the tiny error in the fourths/fifths will not repair the major third.