Layman's terms please!

[Brad Lehman]

>     Tell them that ET has all notes separated by the 12th root of 2,
>     (dividing the octave into 12 parts). Each key signature has
>     identical amounts of
>     dissonance.   All major keys have the same harmonic content, as do
>     the minor keys,  differing only in their pitch centers.
>          Tell them it is a way to erase all the harmonic differences
>     between the keys, and that it is a tuning perfectly suited to the 
 >     music composed upon it,
>     (1900 and later).  Tell them that it is a tuning based on a
>     mathematical
>     concept, and arose as a result of factory standardization.  It is
>     like off-the-rack
>     clothing, designed to fit as broad a range of users without being
>     optimum for any of them.


Well said.

Another uncommonly straightforward and valuable resource, describing the 
musical and technical issues in layman's terms, is Ross Duffin's new 
book.  _How Equal Temperament Ruined Harmony (and Why You Should Care)_, 
W W Norton, 2007.

Publication details:
http://www2.wwnorton.com/catalog/fall06/006227.htm
http://www.amazon.com/Equal-Temperament-Ruined-Harmony-Should/dp/0393062279

It's an easy read in two or three hours, designed for musicians at all 
levels, and enlivened with musical illustrations, commissioned cartoons, 
and historical vignettes.  It does especially well at explaining the 
inter-relationships between keyboard tunings and non-keyboard tunings, 
and showing how the "circle of fifths" is really a spiral that doesn't 
overlap itself.  It also has clear explanations of pure intervals 
(simple ratios), the commas, and major and minor semitones(!).

On page 163 as its Appendix it includes a table of cent values, giving 
the sizes of 24 different intervals: compared by columns for "Just", 
"ET", "Bach WT", "Sixth-Comma" and "55-Division".

It doesn't bother with the relatively unimportant/uninteresting 
measurements of equal-temperament intervals, in Hz, to whatever decimal 
places.  This book focuses on presenting concepts that affect the ways 
musicians actually play and sing, toward listening to and understanding 
intonation as a set of relationships.

======

Also, there's my own 2006 article "Bach's Art of Temperament" as an 
attempt to address the big concepts, without getting bogged down in 
arithmetical stuff.
http://www-personal.umich.edu/~bpl/larips/art.html

That one shows how the Do-Re-Mi's tie into the scale structure of tuning 
by fifths (whether pure or tempered).  It also has a short section 
describing the seven general strategies in historical keyboard temperaments.


Bradley Lehman
http://www.larips.com