AsaFromNasa wrote: Mon Jul 27, 2026 10:17 pm
If you like Bach and math i would highly recommend Godel Escher Bach by Douglas Hofstadter. It's a fun book and it made a big impression on me when i read it in high school.
What is it about? Would it hold up for a 'mature' reader? I always heard about it, but was wary of this book that just throws a bunch of famous names in the title, and nobody ever articulated what it's really about.
Pythagorean tuning is a fun diversion, but there is more to tuning than 'whole' or 'real' or such. Well, one of the first problems is that it doesn't fit the 12-tone system well, so you must make choice on those matters, i.e from C to F#, do you use the aug4 or dim5? You can go in-between and approach a (2*sqrt(2))/2 ratio, it will sound quite ugly! There were instruments made to solve this by having more keys like the 'cimbalo chromatico', but they are difficult to play and I think were made only rarely by special request.
The harmonic complexity of the instrument you are working with has some effect, so you see many variations of tuning methods for the tonally complex harpsichord. It may also have to do with how easy it is to remember and perform a certain kind of attunement; the lone musician must often tune his keyboard, as wood is constantly expanding/shrinking as humidity changes (can be quite large, depends on how porous the wood is) and metals expand/shrink slightly as temperature changes. Evaluating how good a tuning sounds is not an exact science. My opinion is aligning with historical practice for the piece is the best idea, it makes a huge difference to a piece. To give a very strong example, the Well-Tempered Clavier by Bach was written specifically to demonstrate a particular tuning system (one of the Konigsbergs?) and how it had the unique trait of being harmonious in all of the keys. Many other Baroque keyboard works may be made with specific temperament in mind, though the composer more often does not make note of this, which is cool! To me Baroque is so fascinating because of the experimentation/improvisation, and the irony is that historically informed performance has opened up a whole field of creativity and interpretation for this era.
I feel Pythagorean tuning works nice with a less tonally complex instrument, maybe a string instrument.