By the way, a few minutes ago I calculated the first terms of the continued
fraction expansion of the twelfth root of 2 (which is infinite and
non-periodic-the continued fraction and the decimal fraction :)).
This gives in a precisely defined meaning the "best" approximations of 2^(1/12)
in
That is not true Rainer, they simply say that the use of cents is a relatively
modern one and anachronistic for dealing with Renaissance music. It is
concomitant with equal temperament (in which a cent = 1/100 of a semitone).
Best,
Matthew
Le 28 juil. 2019 à 10:13, Rainer a écrit :
>
Very entertaining, indeed.
Apparently, they don't have the slightest idea where the concept of cents is
coming from.
Rainer
PS
What these guys say about "complicated numbers" and computers in part two is -
I am afraid to say - bullshit.
These guys are mathematical idiots.
On 27.07.2019
[1]https://www.youtube.com/watch?v=FzRKCUUhqeQ=share
With kind regards,
Met vriendelijke groeten,
Bien cordialement,
Gilbert Isbin
[2]www.gilbertisbin.com
[3]gilbert.is...@gmail.com
--
References
1. https://www.youtube.com/watch?v=FzRKCUUhqeQ=share
2.
REMOVE
- Jon Stansberry
Vantage Point ITAD
__
From: lute-...@new-old-mail.cs.dartmouth.edu
on behalf of Gilbert Isbin
Sent: Sunday, July 28, 2019 4:02:08 AM
To: LS LUTELIST
Subject: [LUTE] This Is
On 27.07.2019 18:21, r.turov...@gmail.com wrote:
Im vortail mit dem Puschel und Muschel.
Most impressive!
Muschel died in October 2002 and Puschel died on 3.03.03.
Rainer
To get on or off this list see list information at
http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html
A cent is 1200 times the logarithm to base 2 of a real number.
And the reason for those "complicated numbers" is the rather elementary fact
that
log(3)/log(2)
is irrational.
By the Gelfond-Schneider theorem it is even transcendental, but this a very
deep celebrated theorem proved in 1934
I believe Isaac Newton did some work with this as well; unfortunately I
don't have a source at hand.
Leonard Williams
-Original Message-
From: Rainer
To: Lute net
Sent: Sun, Jul 28, 2019 10:16 am
Subject: [LUTE] "Equal" temoerament
By the way, a few minutes ago
Galilei arrived at the best approximation with the information and
tools available to him at the time. No other system could be more
appropriate to the (evolving) music of his time. And he had a grasp of
the physical realities of the lute, as well as taste.
RA
You don't understand.
He was lucky that the continued fraction expansion of 2^(1/12) started with such
"simple" fractions.
Rainer
On 28.07.2019 16:53, Ron Andrico wrote:
Galilei arrived at the best approximation with the information and
tools available to him at the time. No
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