the other side of the f

[Steven D. Majewski]

On Fri, 20 Mar 1998, Les Smith wrote:

> Just for the record, ET goes back to the dawn of civilization, when music
> started with a caveman twanging his bow-string as he sat beside a fire.
> He could only play one note, it was equal with itself, hence the tempera-
> ment was equal. This proves conclusively that ET is therefore the oldest
> Historical Temperament. Case closed :)

I don't know about the one-note scale, but there is a good discussion
about 2,5,7,12,19, & 31-note scales in:

"On Rabbits, Mathematics and Musical Scales" by John S. Allen
<http://web0.tiac.net/users/jsallen/tunings/fibonaci.htm>

[He mentions Joseph Yasser's 1930 book "A theory of evolving tonality",
 which in the light of this discussion, I may look at. ] 

Reading this piece suggests to me that there is a sort of creative
tension at work here. Certainly in something like Jazz, which has 
not only the ET of the piano, but the incommensurability of a ET 
pentatonic blues scale with a 7 or 12 note scale. ( Maybe that's 
why Theolonious Monk's 'wrong' notes sound so *right* ! ) 


You might also take a peek at John Allen's keyboard designs, also 
on his web site. 



- Steve Majewski