Re: Paul Erlich, EULER, GUIDE TONE

>>Message: 5
>> Date: Mon, 8 Mar 1999 18:48:26 -0500
>> From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
>>Subject: Reply to Eduardo Sabat-Garibaldi

>>Some years ago I discovered that the product of the numerator and
>>denominator of any ratio (in its Canonic form) is straight related
with
>>the Rameau Fundamental Bass concept I called this product Indice
>>Armonico (I avoid the Spanish accents because the ASCII symbols
>>not works well everywhere) and was systematized for my purposes.
>>This figure is the number of the harmonic (related with the Rameau
Bass)
>>that is in common with some specific harmonic of the notes.
------------------------------
>Yes, Euler proposed this same harmonic index several centuries ago, and

>Fokker calls the common harmonic the "guide tone". I think Vogel calls
>it something similar.
------------------------------

The reference I have and had about Euler is described in the Helmholtz
book "On the Sens..."., and there the math is much more complex than the
simple product that I propose.
He adds "degrees" and substracts "one". Really I don't understand the
meaning.
I tried to imagine some sort of Logs. (??)
I suspect that this would be the moment to write a book on that matter
but Im not in the better position to compile all the proposals and to
handle properly the mathematic. Who of you ?
BTW, I have the Spanixh version (1961) of the John Redfield book "Music:
a science and an art" (1926), where he propose his own method to
evaluate the musical harmony.

Eduardo