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The Mathematics of Music
Posted:
Apr 22, 1994 9:44 PM
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Invisible friends,
I forgot to mention something in reference to MicheleFanelli and George Matthews
messages.
> Michele Fanelli wrote :
>
> > It is not unreasonable to suppose, by analogy with what is known about
> > the dependency of the strength of sensory stimulus to the INTENSITY of
> > excitation, that the response of our hearing system to FREQUENCY is
> > proportional to the LOGARITHM of the frequency of the sound. So, it
> > should be natural that the intervals of the scale should be linearly
> > dependent on the log of frequency ....[cut]
>George E. Matthews
>The BASE of the logarithm is ARBITRARY (which may be D G Morin's point),
>but why use anything larger than the NEXT natural number after 1?
As I pointed out in previous messages (based on the Encyclopedia Britannica) :
So long as music consists of melody WITH harmony, consonance plays the main part in the
determination of successive pitches in a scale.
So the base of the logarithm "is not necessarily" the fundamental principle for arranging
the successive pitches.
I'm not proposing to use a BASE larger than the next natural number after 1.
As you can see, the chords I pointed out in my previous messages were not arranged by
means of logarithms.
Those chords are :
[1/1 , 2/2]
[3/3 , 3/2, 3/1]
[4/4 , 4/3 , 4/2, 4/1]
[5/5, 5/4, 5/3, 5/2, 5/1]
[6/6, 6/5, 6/4, 6/3, 6/2, 6/1]
By using only the sequence [6/6, 6/5, 6/4, 6/3, 6/2, 6/1] you can construct a "perfect"
musical instrument (i.e. the guitar) whose chords are "perfect" and most of them do not
appear in our modern keyboards.
>Although I know no music theory, I would suppose that consonance IS harmony.
Yes, it is.
In reference to the question :
> How many points do we need to construct a curve?
It is clear that having no equation for explaining consonance, Pythagoreans as well as
any other terrestrial person certainly need as much points as they can in order to
understand the amazing secret of euphony.
I understand that the answers for my question were given from the point of view of the
mathematician rather than that of a person who is trying to collect some data at the
"laboratory",
for it is fairly clear that only GOD does not need any point, AT ALL, to figure out any
phenomena.
Domingo
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Apart from all the above, I would like to express my HAPPINESS for President Fujimori
actions.
A new South America is born and certainly holds its own and new Philosophy.
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"ALL THE MEANS ARE MEDIANTS, say, 'RATIONAL MEANS'
Domingo Gómez MorÃÂn
http://www.etheron.net/usuarios/dgomez/default.htm
Caracas, Venezuela.
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