Ok, here goes another fracas in the temperament wars! The modern grand piano can be tuned in any of the historical approaches, from mean-tone to Victorian style equal,(I know, I know, "equal" is a term that is relative, debatable, controversial, and, to some, inflammatory.). I only use equal temperament for recording studios, in which the key of the song may be moved up or down a half-step to suit the vocalist's preference. Was told that they didn't want the 'feel' to change just because of a half-step modulation. Virtually all of my classical customers prefer something else. Even several jazz artists here prefer the well-tempered sound. Who would have guessed?
When we depart from "equal" we can follow the past templates of various forms that follow Werckmeister's general philosophy. That is, correlating the tonic thirds of the keys with the circle of fifths. This means that the keys with the most accidentals have the widest tonic third and the keys with the least have the smallest thirds. All thirds are either Just or tempered. I know of no tuning that uses a "narrow" third.
You are referencing Murry Barber's early work. This was greatly expanded by one of his students, Owen Jorgensen, in his big red book "Tuning". It lists a lot of previous tuning schemes, as well as giving some historical context.
The unequal temperaments create their difference by the progressive size, (hence, dissonance), of the thirds. Modern ears will usually discern a third that is wider than 15 cents,(ET has all thirds at exactly 13.7 wide). The larger thirds beat faster and create more musical tension. The smaller thirds, such as found in the keys of C, F, Bb, G, create a less stimulative, more consonant sound. Virtually all tunings from 1700 on follow this same progression of dissonance, with C being the calmest and F# being the most edgy. A Young temperament is evenly ordered from a 5.3 cent C-E third to a 21.5 cent F#-A#. This 21.5 cents is the full syntonic comma and was commonly the maximum amount of tempering used in the genre.
I would direct you to Rollingball.com for a full examination of the alternatives. The web sites on my signature will also add some fuel to the journey.
Last edited by Ed Foote; 02/23/21 08:13 PM.