Ben Deckla, T.D. 886

Ben Denckla bdenckla@media.mit.edu

During the last 25 years I have worked on Dynamic music, and I believe I know
a little about it.
I think Dynamics in Music is not only a concept resulting from the change of
the key of a score and consequently the frequency of the notes changes a
little (about one comma from one to the other), but simply the frequency of
the notes changes due to other reasons, either the choice of the "better"
option INCLUDED IN THE SAME KEY, or aesthetical reasons.
When I coined the expression Gama Dinamica (Dynamic Gamut) I didn't know any
other work (as many others) on this subject, and before, when I read Warren
Creel's paper (Dynamic in Music) I was delighted to know that he used the same
word "Dynamic" for the same idea.
Arthur Benade, speaking in his book about Dynamics, says that it forms "a
never ending proliferation of notes". This is O.K. for the concept.

I know that with only 53 notes/Oct it may solve the problem very accurately
for 3 and 5. Yet good enough for 7. And other digits remain for further study.
The bigger the number of notes/oct the bigger the accuracy. The errors will
always be no more than half the width of the smaller step and in this case no
more than a half comma.

I chose the 1/9 Schisma option (I call it Omega option) to define the numbers
for Dinarra, but for synthesizers 53 tET might be better.

I call Omega the Ninth of a Schisma (about 1/5 of a cent) and the "errors"
are 1 Omega for the very important ratios ( 3/2, 4/3, 5/4, 10/9, 8/5, 9/5 ),
and 2 Om. for the others ( 16/15, 15/8, 9/8, 16/9 ).
The ratios 5/3 and 6/5 are exact.
All of this is for 33 notes (of the 53), the other 20 have their particular
discussion and result. Summing up, about 88 % of all possible ratios are
"Omega ratios".


I calculated these numbers.

1/9 S. 1.0001254 1.0 Om. 0.2 Cent.
1 Cent 1.0005778 4.6 Om. 1.0 Cent

3/2 --- 2 raised (31/53) 1.0000394 0.3 Om. 0.07 Cent.
5/3 --- 2 raised (39/53) 1.0007742 6.2 Om. 1.3 Cent.
5/4 --- 2 raised (17/53) 1.0008137 6.5 Om. 1.4 Cent.


The 53 tET option has all its intervals equal within its type.

For more information I'll be happy to assist you.


Eduardo

Eduardo Sabat-Garibaldi E-mail : esabat@chasque.apc.org
Simon Bolivar 1260 Phone: (05982) 78 09 52
11300 Montevideo FAX : (05982) 29 83 91 (Automatico)
Uruguay

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