ancient Greek consonance

[Marion:]
> You're saying that the Greeks sounded this ratio in their music,
> but didn't consider it consonant? Does that mean that the only
> "consonant" ratios were 3/2 and 4/3?

If no one minds, I can step in here and say, 'yes', if you're
not counting 'octaves', those were the only consonant ratios.

The Greeks considered the proportions 6:8:9:12:16:18:24
to contain all the consonances: 4/3, 3/2, 2/1, 3/1, and 4/1.

They gave one-word names to all these ratios, to signify
the fact of their consonance:

4/1 bisdiapason (basically, 'double diapason')
3/1 (can't remember this one)
2/1 diapason thru all [strings]
3/2 diapente thru 5 [strings]
4/3 diatessaron thru 4 [strings]

In the diagram below the 9/8s are the 'tones of disjunction'
between the tetrachords.

24 \ \ \
\ | | |
/ 3:4 | | |
18 2:3 \ | \ |
> 8:9 | | 1:2 | |
16 / 2:3 | | |
\ | | | |
/ 3:4 | | | |
12 \ / / | 1:4
\ | \ | |
/ 3:4 | | | |
9 2:3 \ | 1:3 |
> 8:9 | | | | |
8 / | 1:2 | |
\ 2:3 | | |
/ 3:4 | | | |
6 / / / /

Joseph L. Monzo....................monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html

|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |

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