Meantone, my personal adventure

[Jim Coleman, Sr.]

Hi Richard:

The syntonic comma is that amount (in beats) by which 3 contiguous 3rd fail
to equal an octave. As one explained earlier, there are 4 4ths or 5ths 
encountered in going from C to E (ie, tune a 5th up from C to G, tune a 
4ths down to D, tune a 5th up to A, tune a 4th down to E). Actually in the
old days and according to J. Cree Fisher, they didn't use the 4ths, but 
would tune down an octave and then tune up another 5th etc. The Syntonic
comma is expressed by the number of beats in the C-E resultant 3rd. Now, if
you temper each of 5ths equally so that you come out with a pure C-E 
M3rd, then you have tune 1/4 syntonic comma 5ths.

If you work with the D-G# M3rd and do the same thing, you end up with a 
very wide and busy 3rd Ab-C. This is more than a Pythagorean 3rd, and in 
order to arrive at that same place tuning down the flats side of the circle
of 6ths, the "Wolf tone 5th is usually left with the Ab-Db 5th. There are
many ways people dealt with just where to put the wolf and how much 
wolf, or whether to have two smaller wolves etc. Read about it in the First
book of Owen's.

Now all this is not to be confused with the ditonic comma which is the
amount that 12 successive 5ths overshoot 7 octaves. Our present Equal 
temperament is accomplished by shrinking each 5th by 1/12th of the ditonic
comma. On pianos (with their concommitant inharmonicity) the ditonic comma
is not so great (I mean large, not famous). This is why we can get away with
a Pure 5ths temperament on modern pianos, but not on harpsichords etc.

Do you have available Owen's book on Tuning the Historical Temperaments 
by Ear? In this book he doesn't talk as much about cents, but beats. This 
should be more up your alley. 

Jim Coleman, Sr.



On Thu, 18 Mar 1999, Richard Moody wrote:

> 
> Now if I can just find out how terms like "1/4 syntonic comma" lead to the
> flattening of fiths, in Meantone, and how this was determined by the
> tuners of the times before 1750.  I mean how does 1/4 comma  translate
> into beats per second. Yes I know some where it is written that tuners in
> the 1700's (18th cent) did not listen to beats, yet the organ tuners did. 
> 
> 	The exciting part of historical temperaments is that they can be rendered
> on modern pianos----that the predictions of physists of the 17th and 18th
> century can be translated into cents and therefore plugged into 20th
> century tuning machines.  In the interest in "hearing the music as the
> masters did" one must realize that the instruments on which they heard
> their music  no longer exist execpt as museum pieces or reproductions. 
> Hearing modern pianos tuned according to concepts of their time renders
> the keyboard music of the Baroque and Classical eras in a new light for
> our times.  If performers ask, "Is it possible to tune the modern piano in
> Meantone by ear?", I would hope to have something to offer.  
> 	Now if I can just figure out how much 1/4 syntonic comma flattens fifths
> from the aural perspective.  
> 
> Richard Moody
> 	
>