Numeric tables: "Bach/wohltemperirt"

Dear Group members,

Before taking some leave due to priority work and some little trips:

To possibly interested members to the Group, and to save them
from wasting their time generating these tables themselves, I
submit now these tables.

Hopefully, I've pasted the right and correct ones; such operations can
go wrong faster than one could believe!

Kind regards

Herbert Anton Kellner

*************************************************************
TONE FREQ CENT A=440
C 1,00000000000000 0,000000000000 262,862348757554
C#1,05349794238683 90,224995673063 276,924943547052
D 1,11893844642071 194,556809811904 294,126788141275
Eb1,18518518518519 294,134997403838 311,540561490434
E 1,25202324687838 389,113619623808 329,109771373511
F 1,33333333333333 498,044999134613 350,483131676738
F#1,40466392318244 588,269994807675 369,233258062736
G 1,49595350624323 697,278404905952 393,229852283193
Ab1,58024691358025 792,179996538450 415,387415320578
A 1,67387989219341 891,835214717856 440,000000000000
Bb1,77777777777778 996,089998269225 467,310842235651
B 1,87803487031758 1091,06862048920 493,664657060266
C 2,00000000000000 1200,00000000000 525,724697515107

220,000000000000
233,655421117825
246,832328530133
262,862348757554
276,924943547052
294,126788141275
311,540561490434
329,109771373511
350,483131676738
369,233258062736
393,229852283193
415,387415320578
440,000000000000

(Instinctively, I prefer to start "Bach-tables" at C rather than at A!)

Best regards,

Herbert Anton Kellner
* fine
P. S.:
Calculation of beats for those who like to check:
*
(Beats of tempered intervals occur between nearly co-inciding harmonic
overtones).

Let within the triad be
f0 be the fundamental,
fT be the frequency of the third ang
fF the fifths frequency.

The beat frequency of the fifth will the be :
f0*3-fF*2

The beat frequency of the third will the be :
f0*5-fT*4

The crucial ptoportion of beat-ratio - absolute value, of course - in the
B-major triad,
between (B-d#) and (B-f#) is 6 : 1. Approximately, but by far sufficient to
assure accurate tempering. Proof:

Kellner, H.A.: Das ungleichstufige, wohltemperierte Tonsystem. In
"Bach-stunden", Festschrift f�r Helmut Walcha, Hg. W. Dehnhard
und G. Ritter. Evang. Presseverband in Hessen und Nassau,
Frankfurt/Main 1978. page 75-91.

D. C. al fine