In defense of Rasch.

[snip]

>> But, as any other good scientist, he cannot ignore the*evidence* - that
>> being in this case, that there was a steady growth of the use
>>of equal temperament throughout the 18th century. [snip]

>Well, I'll give you that (though see Jorgenson for an argument that no
>one really tuned accurate ETs until a century or so ago when beat rates
>were calculated and began to be used), but the point is that the
>evidence that _Bach_, specifically, used ET is tenuous to the point of
>nonexistence.

Hardly. Jorgensen's thesis (that ET could never have been tuned
accurately and was therefore never used in the 18th century) is specious.
There are many, many references to tuning ET by ear in the 18th century.
Towards the end of the century, many practical treatises give instruction for
ET and don't even mention unequal temperaments! Even if the results
might have been less than perfect, the intention was clear: To tune Equal
Temperment. And there is no doubt in my mind that ET or a close
approximation was used in the 18th century. Given Jorgensen's criteria for
accuracy, ET doesn't exist on harpsichords in this century! (Member of
this List can surely testify to the tremendous stability of most harpsichords;
how many times have we tuned our instruments before a concert only to
discover that they were out of tune again after removing the tuning
hammer from the last wrest pin?)

[snip, paste]

> BTW, there are only two Pythagorean ditones in Barnes' temperament.

I'm not sure whether it is appropriate to use the term "Pythagorean ditone"
in expressing the 81:64 or Pythagorean major third. True, it can be
argued that the Pythagorean major third is comprised of two major tones
(9:8), and that two *tones* form a *ditone.* But when all 18th-century
writers refer to the ditone, they mean specifically the just major third, 5:4.

Aleksander Frosztega



-------------------------------------------------------
Aleksander Frosztega "Odi summusos; proinde aperte
University of Utrecht dice quid sit quod times."
The Netherlands