Ancient Greek music

[pythagoras.lym]

Has anyone done any research on ancient Greek music? I got a few books viz.west's book"ancient Greek music", Greek musical writings vol. 1 and 2. Aristoxenus' books on harmony and rhythm, and philodemus book de musica. And I was wondering if anyone wants to have a productive discussion to try to figure out this very Interesting subject? What do y'all think?

[pythagoras.lym]

I also checked out a book/cd called symposium on ancient Greek music where they go through Greek musical intervals and
Other interesting aspects like different Greek instruments. I've also worked through Kepler's harmony of the world. So, I'd like to get into some discussions regarding these things.
So, if anyones interested, email me or respond to this message.

[annis]

Are you interested in this material for your own compositional purposes? To ancient Greek scholars, music theory was a branch of mathematics.

For a very thorough treatment of Greek (and some Greek-inspired Arab) music theory, from the perspective of a modern composer interested in just intonation, John Chalmers' Divisions of the Tetrachord cannot be beat.

[pythagoras.lym]

Yes, I am, actually, and also for general historical investigation. Thank you for the book. It will prove very useful. I have done some work on the Pythagorean Musical system trying to figure out the development of Musical Systems. From Ancient times up through Bach's Well-tempered Klavier, which I believe is not, as most scholars say, the Equal Tempered system we have in use today. I have a hypothesis that Bach knew that one could never have a "perfect" system and that when Bach composed the Well-Tempered Klavier, he was thinking of tuning using the natural ability of a singer to "adjust" the intonation to make the intervals fit ('αρμονία).

Well, thanks again.

[cb]

hi, i actually took an interesting uni course on this very subject, the development of musical systems prior to pythag, coincidence. i googled the professor's name and found an article which may interest you (and also contains a reference to me, another coincidence):

http://www.springerlink.com/content/20516375j8625861/

cheers, chad

[annis]

From Ancient times up through Bach's Well-tempered Klavier, which I believe is not, as most scholars say, the Equal Tempered system we have in use today.

It was well-tempering he used for that, not 12ET (12-tone equal tempered).

I have a hypothesis that Bach knew that one could never have a "perfect" system and that when Bach composed the Well-Tempered Klavier, he was thinking of tuning using the natural ability of a singer to "adjust" the intonation to make the intervals fit ('αρμονία).

I'm curious to know why you think this needs to be hypothesized. Bach was well aware of tuning issues, including the trade-offs between the sweeter-sounding just intervals versus the ability to modulate to remote keys. It's reported he made life difficult for his organ tuner. And while singers and players of fretless instruments get training in these intonation issues to this day, the WTK is a demonstration of a way to try to get sweet intonation and remote modulation together on a normal fixed-pitch instrument, like a harpsichord. There's no way to adjust the intonation of a harpsichord during a performance (though it might, depending on the weather, adjust its own tuning by surprise).

[pythagoras.lym]

Interesting, annis.

I'm confused. What exactly is well-tempering? I assume you don't believe the crazy, wild and frankly stupid hypothesis of the little spiral on top of the WTK page...hehe

I read that scholars think that Bach used equal-tempering to be used to play in all keys. But I thought that Bach would never sacrifice the real intonation for that. I mean, isn't there a natural limitation to a fixed instrument? I've read through Kepler's Harmony of the World, and in Book 3, Kepler runs into some difficulties when encountering a second octave. The comma comes into play and all that...

Well, Bach obviously knew about the different tunings of his day, and the impossibility of a fixed system on a klavier. Maybe he wanted it to be SUNG or played on fretless instruments. Maybe it's a joke. well-tempered klavier...

I suppose we can discuss this more fully. It'd be fun.

[annis]

I'm confused. What exactly is well-tempering?

Equal tempering isn't really possible without certain kinds of technology. Since that hadn't been invented yet, there were several well-tempering schemes which approximated equal tempering. They removed the nastier harmonic howlers from the remote keys while still leaving different keys with distinct characters. If you take a tune in Cmaj and transpose it to Abmaj on a modern piano, they sound basically the same, except for being in a slightly different pitch. 19th century composition manuals sometimes talk about the character of different keys. In a 12tet system, that makes no sense, but in a Pythagorean — or a well-tempered — system, Ab will sound different than C. In fact, one of the complaints at the beginning of the 20th century about going to 12tet was that it was bland and characterless.

But I thought that Bach would never sacrifice the real intonation for that.

Why not? This is part of my question from before — why do you think Bach cared about perfectly Pythagorean intonation in his harmonies? By his time modulation to different keys was firmly established as a structural element in music. Well-tempering gave him access to those resources in keys with more accidentals.