Who says E.T. is the best way to solve octave divisions?

[Frank Emerson]

>Why is equal temperament the only way to solve the dividing of octaves?
 
It is not the only way.  In modern music we have made it the only way we know and use, but historically there have been other, better ways.
 
>I know that the beautifully mathematical solution on paper sounds and works fine, but what if >there a way we could be missing out on something, such as better sounding music?
 
We ARE missing out on something, quite a lot, actually!  I have not read the book recommended  by Paul Bruesch, but it sounds fascinating.  I must read it myself.  My comments may be outdated by more recent research, but I can tell you of my experience with historical temperaments, although I have moved on to other things in my more recent work experience.  
 
Years ago, I assisted Owen Jorgensen in preparing a dozen keyboard instruments for his “temperament recital” at a university where I worked at the time.  In his recital, among other things, he played selections in every major and minor key from Bach’s Well-Tempered Clavier.  In the lecture portion of the recital, Owen made reference to the writings of early musicians and composers who expressed their particular preferences for certain keys.  This has long been puzzling to modern musicians, who know no temperament other than ET, in which the only difference from one key to another is the fundament frequency of the tonic in each key, upon which all of the other tones of the scale are built on precisely the same pitch relationships.  This is certainly not the case in any temperament other than ET.  Prior to Owen Jorgensen’s research, and probably to this day, most musicologists believe(d) that Bach’s Well-Tempered Clavier was a promotion of ET, as the only temperament which would allow for pre-tuning an instrument which could then be played in all keys, and that the earlier temperaments, mean-tone temperaments, could be used in only a few keys.  Owen contradicted this notion with his argument that there was an entire class of temperaments that had been overlooked by musicologists.  This class of temperament was called Well Tempered scales, which, by the was, was prescribed by Bach in the title of his work, The Well-Tempered Clavier.  What distinguished well tempered scales from the others, is that the division of the octave allowed for performing in all keys, but, unlike ET, preserved distinctively different sounds in the various keys.  
 
Returning to your question, “are we missing out on something,” I would say, for one, we are missing out on a fair measure of the genius that is Bach.  His writing in the key of C emphasizes and “shows off” the beauty of the clean Major 3rd intervals, while his writing in the key of C# plays off of the raucous, disturbing sound of the rough 3rds.  The character of his writing matches the inherent character of the key, but only when an appropriate tuning is used.  I am sure other examples can be found, if sought out, in the works of other early composers.
 
>Haven’t we manipulated string lengths and diameters to force E.T. to sound well?
 
Well, I wouldn’t say that.  The scale design of pianos has evolved over the centuries to accommodate different pitch standards, higher tensions, and a more powerful sound, but not necessarily to accommodate a particular temperament, although ET has been assumed to be the only choice for many decades.  The sound quality of a modern piano may suffer from tuning to a lower pitch, but the subtle difference in the overall balance of things, that occurs with temperaments other than ET, do not detectably alter the sounds of individual notes, in isolation.  Of course, there are markedly audible differences in intervallic relationships.  Although there is much to be said for playing “period” music on “period” instruments, tuned to “period” temperaments, one can legitimately tune a modern instrument to an early temperament, and recapture much of the composers original intent for his music.

Frank Emerson


----- Original Message ----- 
From: 
To: pianotech at ptg.org
Sent: 10/21/2007 12:39:36 PM 
Subject: Who says E.T. is the best way to solve octave divisions?


Greetings,

         Why is equal temperament the only way to solve the dividing of octaves? I know that the beautifully mathematical solution on paper sounds and works fine, but what if there a way we could be missing out on something, such as better sounding music? Havent we manipulated string lengths and diameters to force E.T. to sound well? What information am I missing here?

Julia Gottshall
Reading, PA  






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