Temperament questions (belated from 4/05/08)

[Brad Lehman]

I have some articles and other resources at
http://www.larips.com
with hundreds of footnotes out to other reading material as well.

In the regular meantone temperaments of various sizes, the eleven 5ths 
are all the same size as one another (i.e. "regular") but the leftover 
diminished 6th doesn't close the circle; it's much too wide.  Eight of 
the major triads turn out to be usable and four not.

Only very few of the major or minor scales are fully usable for tonal 
music, since the neighboring notes to most of them (such as the 
frequently used note D# in A minor, or the Ab in Bb major) aren't 
present.  These regular temperaments therefore lead to some oddly 
out-of-tune moments whenever things are misspelled...but if one sticks 
with the correctly-spelled twelve notes, things are very consonant and 
resonant.

One of my sub-pages about those regular temperaments:
http://www-personal.umich.edu/~bpl/larips/meantone.html

"Well-temperament" as a term is grammatically abominable.  :)


Brad Lehman


KeyKat88 at aol.com wrote:
> Greetings,
>  
>            In the Alfred edition of the _Bach's Well Tempered Clavier_, 
> edited by Willard A. Palmer, it states the following:
>  
>           "/Meantone temperament/, the system in general use before the 
> adoption of the /well-temperament/, favored specific keys. A sharp could 
> not function as a flat and vise-versa. ... Meantone temperament is 
> actually more in tune in the keys it favors than our present day system 
> (E.T.) in any key."
>  
>           If this is true, then how can this be?
>  
> 1.  Are the intervals of the approx 1BPS for the 4ths and the 3:5BPS 
> for 5ths different in meantone?              How does he mean "more in 
> tune" than our present day system? 
>  
> 2. Does this "more in tune-ness" have to do manipulating the comma 
> differently in some keys?
>  
> 2. Are there any books to read that will set me straight on this 
> subject?    
>  
> 3. Can I tune my old upright to meantone to hear this sort of thing, 
> or will the "modern" scale design of it not allow a meantone tuning to 
> be properly executed and heard as true? 
>  
> Thank You,
> Julia Gottshall
> Reading, PA