Euler

[Rousseau:]
>> Was Euler looking for a tuning in which 36/35 = 0 steps?
>> Do you think he would have been favorable to 12TET?

[me:]
> Definitely not.
>
> Again from my notes, at the end of the same paper,
> [_Conjecture_] Euler suggests that the music of his
> time had already replaced Leibniz's 2/3/5 basis
> with 2/3/5/7.
>
> <blah blah blah ...>

OK, re-reading that has me seeing it from your point
of view. It sounds like Euler *was* interested in a
tuning where these septimal commas vanish.

Perhaps he decided 7 was being used as a factor
in the music of his time *because* of 12-Eq or
meantone temperaments in use at the time which have
these commas vanish.

-monzo

|\=/|.-"""-. Joseph L. Monzo....................monz@juno.com
/6 6\ \ http://www.ixpres.com/interval/monzo/homepage.html
=\_Y_/= (_ ;\
_U//_/-/__/// |"...I had broken thru the lattice barrier..."|
/monz\ ((jgs; | - Erv Wilson |

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Hmmm...just read something in the library today
that really has me confused now.

In a letter Euler wrote to Lagrange in 1759,
he stated that when one hears a 7:8, it is *always*
interpreted as an out-of-tune 8:9.

Of course one must bear in mind the historico-musical
context in which this statement was made.

But it seems to me to directly contradict his other
statement that

[Euler:]
> 36:45:54:65 is indistinguishable from 36:45:54:63
> [= 4:5:6:7].

Even if 36:45:54:65 is a typo for 36:45:54:64,
he is saying here that whatever the tuning of the
top note, if it's close enough in pitch, it will
be perceived as a 7 because of the strong resemblance
of the entire chord to 4:5:6:7.

So why would he call 7:8 a mistuned 8:9?

Perhaps this is just an indication that he changed
his mind over the course of his research. I don't
have the references available to put these two
contradictory statements in their proper chronological
order, but the bit I quoted from Euler stating that
music's basis had become by his time 2/3/5/7 was
written in 1764, 5 years after the letter to Lagrange.

-monzo
http://www.ixpres.com/interval/monzo/homepage.html

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I wrote:

> Perhaps this is just an indication that he changed
> his mind over the course of his research.

Ahh... I see from my translation of Bailhache's paper
on Euler that she noticed his change of opinion, too.

Apparently, he only decided after 1760 that 7 was implied
in the music of his time; before that he based his
theories and calculations on 5-limit.

Webpage on the way soon!

-Monz
http://www.ixpres.com/interval/monzo/homepage.html

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