FWD: Bach's tuning

Paul Hahn wrote:

>> I have never seen (I don't think) 18th-century German ear tuning
>> instruction that use fifths as a tempering device for Equal
>> Temperament.
>> They all used rows of MAJOR THIRDS which were to be made wide!
>> (Sorge gave explicit instructions that each successive third should be
>> made somewhat *wider* than the last.)

> Eh? If one is wider than another, then they're not equal, are they?

Remember that Sorge's were *ear tuning* instructions. Because
frequency doubles with every octave, the beating of any fixed interval
*increases* as the frequency of the lower tone of the pair increases. Although
Sorge's major thirds remain the same size linearly speaking, they would
beat faster with each successive third of the row, hence Sorge's
instructions to make each of the thirds a little wider than the last.

>> Yes, this is the F#-C# fifth in Kirnberger I though III. However, it is not
>> tempered by 1/12 Pythagorean comma; it is tempered by the
>> *schisma.* Kirnberger was not the best mathematician in the world
>> and Marpurg, in fact, corrects Kirnberger's calculations in Marpurg's
>> _Versuch._

>Let me get this straight: you castigate Jorgenson for insisting on .1
>cent accuracy, and now you're making a fuss about a difference of (my
>calculator puts it) .0012817 cents? Sounds like straining at gnats and
>swallowing camels to me.

I was merely pointing out that there is a difference between 1/12 of a
Ditonic Comma and the schisma. For all intents and purposes (thank you,
Michael), they are the same thing and difference between them is
imperceptible in actual tuning... even to your dog.


Aleksander Frosztega



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