DeMorgan numbers & graph

[Richard Moody]

Hi Ron K. ,
    Thanks for the cents numbers of the DeMorgan and the Young.
They appear as the tonality center for the key of  A.  The traditional
tonality center is Middle C for historical temperaments.   Most
were figured from fifths up from MC to G# and then 5ths down from MC to Eb.
Meantone for instance follows this  sequence. Most of the other
historical temps start at MC also.  Which means the cents reading should
show MC at 0.    The reason showing A at 0 cents is for
modern machine tuners so they can render a temperament where A4 ends up as
440cps. Since modern orchestras tune at A440 then if they are to play with a
piano tuned in other than ET, the reasoning  (I am guessing) is that A4
should still be A440.
There is a debate on this because middle C has been the traditional starting
point for scales and temperaments. Thus if an HT, for example Meantone, was
tuned from C4 at its ET value of 261.6 then A4 would end up at 435.5
But if the orchestra wants A440 then the cents readings for the HT has to be
altered to give A4 = 0,  which makes C4 = ?
    The advantage of having C4 at 0 is that then you can see how the fifths
from C are formed.   If they are regular, then each fifth would have the
same difference.  If irregular then you could spot  the "irregularity".
Also the tuning sequences, or instructions are given from C, so with C
as 0 it makes following them much easier.   Finally, for temps with other
than C as 0 one must be sure they are indeed centered from C and not simply
tranposed to A as the tonal center, wich would really mess up the "color of
the keys"
    If a historical tuning is to be presented with the cents designations of
A4 at  0 cents, I would hope that  temperament would also be given with C at
0 cents for the sake of musicology and the study of history.
    Some times it seems like a race to implore  players to tune to  anything
but ET, ie a "Try yet another temperament", leaving the real history
expiring in the dust.  ---ric.


----- Original Message -----
From: Ron Koval <drwoodwind@hotmail.com>
To: <pianotech@ptg.org>
Sent: Tuesday, June 13, 2000 11:09 AM
Subject: DeMorgan numbers & graph


> Hi all
>
> I went and looked up the numbers for Augustus DeMorgan (1843) temperament.
> c-2.8
> C#-2.8
> D-.5
> D#-4.4
> E 0
> F-3.8
> F#-1.5
> G-1.5
> G#-3.8
> A 0
> A#-4.4
> B-.5
>

> Ron Koval
>