"The concept of tempered tuning (that is, tuning the note spacings so that the pitch relationships in different keys remain constant) isn't all that new. In fact, it's been a common practice applied to tuning instruments like the piano and harpsichord since the 1600s.
In relation to a piano, this means it's actually tuned a little bit sharp from middle C up, and tuned flat from middle C down in order to make the sounds more pleasing.
There are at least 12 or more ways to temper a piano, which vary according to the taste of the player, and different names for each method."
Here again, Feiten’s confusion is evident. He’s confusing Equal Temperament (the blue highlighted statement, which is also incorrect as it happens) with octave stretching (highlighted in red) and the earlier systems of tuning such as mean-tone and Just Intonation, which required retuning of keyboard instruments to suit different keys (highlighted in green). Equal temperament is the default standard tuning for all modern fixed pitch instruments including the guitar and piano, octave stretching is a practice applied only to pianos to counter inharmonicity (an explanation of this will follow) and Mean-tone and Just Intonation have been obsolete for centuries, being resurrected occasionally for authentic performances of music from the pre-classical eras.
One of the more interesting claims made by Feiten is to have followed the practice of “octave-stretching” used by piano tuners. He seems to have naively assumed that this practice is a departure from equal temperament but, yet again, he hasn’t done his homework on the subject.
Inharmonicity is a phenomenon which affects instruments whose primary source for the generation of sound is a vibrating string or bar. Find out about inharmonicity here
Piano strings operate at extreme tension and are of a very heavy gauge. The higher strings are behaving more like bars than strings, and pulling up the true pitch of the higher notes tricks the brain into assessing it as being close to the equal temperament value.
Far from being a departure from equal temperament, this form of tempering tuning is a way of compensating for the instrument's physical limitations so that the illusion of equal temperament pitch is created. The mistake Feiten is making in regard to this is in assuming that the same process needs to be applied to the guitar. In the guitar, inharmonicity is found on the higher frets and predominantly the lower strings, the G and low E being most affected, but a properly undertaken intonation procedure, done by ear, rather than with a tuner, incorporates compensation for any effects of inharmonicity by default. Errors only occur when too much reliance is placed on digital measurement.
