Jun. 5, 2016

Temperaments & Tuning, Part VI

(con't from Part V)
Organ tuners, in their travels, no matter where they go, are always needing to deal with that pesky little mathematical anomaly called the [Pythagorean] comma.
It's small (24 Cents) -- not quite a quarter semitone -- but it's too big to fit inside the Circle when intervals are tuned pure, so the tuners have to figure out where to hide it ... where to dump it ... how to divide it and squeeze it in ... somewhere ... among all those pure intervals [See blog, Temperaments & Tuning, Part II].
They find a place to do that, when they make their turn here (photo).
In modern equal-temper tuning, which divides the octave into 12 equally out-of-tune semitones, the perfect 5th (700 cents) is slightly flat of the purely-tuned 5th (702 cents), and the major 3rd (400 cents) is a good bit more sharp than the purely-tuned 3rd (386 cents).
This explains why purely-tuned mixture stops in organs don't always get along nicely with tempered 5ths in unit instruments.
(con't in Part VII)