Ear training
It was, well, a lot simpler back then (say.... c. 900):
Interval
1. semitone—two tones separated by the smallest distance, so that the space between them is scarcely perceived.
2. whole tone—a more perceptible interval
3. semiditone (minor third)—a little larger
4. ditone (major third)—extends farther than this
5. diatessaron (perfect fourth)—even greater
6. tritone—still ampler
7. diapente (perfect fifth)—supasses these by due amount
8. semitone-plus-diapente (minor sixth)—
9. whole-tone-plus-diapente (major sixth)—extending over the widest space of all, has the last place among these intervals, for you will never find one larger than it or smaller than the first.
Comments
That's pretty funny. I thought Pythagoras had already worked out the whole scale (with some imprecision) quite a long time before that.
Posted by: Paul Baxter | 29.09.04 16:36
Comments
Well, the story about Pythagoras in the blacksmith shop is largely apocryphal. The precise distance of a tone wasn't describe until on a monochord c. 1000. The story of Pythagoras is given to us through Boethius. Intervals and consonances are described (where you get the above list of intervals) but an actual, somewhat objective way of creating the precise distance wasn't.
Posted by: Jeannette | 29.09.04 16:43
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Shows what I know. Stuart Isacoff says that Pythagoras worked out the whole circe of fifths with strings, but it wouldn't surprise me if that was wrong. In _Temperament_ he's got a 12th C manuscript with pictures of Boethius and Pythagoras working on a monochord, but that is obviously well past the time you are talking about. Actually, now that I'm looking at it, B is on the monochord and P is playing with bells.
Posted by: Paul Baxter | 30.09.04 12:50
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Awww, how cute! That picture is probably a medieval reinterpretation of what Boethius and Pythagoras were really doing. They DID come up with intervals, but it wasn't until the monochord that they were able to define a specific pitch to the monochord. I.e. instead of saying that a tone is "a more perceptible distance", they could now say that a tone is "the distance from gamma to A on the monochord". And then this what Boethius says Pythagoras (who lived about a thousand years before B) said. B was a big P fan.
I know for sure that Pythagoras did NOT come up with the circle of fifths, as that is a result of the equal temperament tuning system, not in use until about the 18th c.
I don't know that book (or the author). I'll have to check it out. (Especially to see the cute pic of B and P!)
I only bring all this up, because i'm taking a History of Theory class, and we had a test yesterday. :)
Posted by: Jeannette | 30.09.04 13:07
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Yeah, Hucbald was a real specific, anal-retentive guy, wasn't he? I would absolutely LOVE to know what his singing voice sounded like. =)
Posted by: Erica | 30.09.04 17:06
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Well, by circle of fifths, I merely mean the progession of multiplying frequencies by 3:2. If one was familiar with frquencies/wavelengths (in some form of the idea) its pretty easy to derive that circle--coming up with the 12 tones leading back to an octave.
I'm pretty ignorant of how all that actually happened in history. I just tune the silly pianos.
Posted by: Paul Baxter | 30.09.04 17:50