
The octave – history of a discovery - monort
http://www.neuroscience-of-music.se/Octave-History.htm
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monort
If you are interested in how music works, I recommend to read this paper about
music theory from physics point of view:

[http://arxiv.org/html/1202.4212v1/](http://arxiv.org/html/1202.4212v1/)

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nitrogen
I've noticed that intervals whose beat frequency is a subharmonic of one of
the notes in the interval, or a subharmonic of a small integer multiple of one
of the notes, are particularly consonant. Is there any discussion of beat
frequencies in that paper?

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ewoodrich
There's some discussion here:

[http://arxiv.org/html/1202.4212v1/#sec_5_1_0](http://arxiv.org/html/1202.4212v1/#sec_5_1_0)

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ambrop7
I can't help myself but every time I hear "octave", I think fencepost error.

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theoh
It might make you feel better to split the octave into two parts and eliminate
the interval in the middle, i.e. Do-re-mi-fa, pause, So-la-ti-do. Each of
those four note sections has the same intervals. So arguably it's closer to
being a "pi vs. 2pi" problem. (I am not really serious)

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nitrogen
Isn't _fa_ a half step down from being exactly between _do_ and _do '_?

As far as the fencepost error, it helps to remember that musical intervals are
multiplicative, rather than additive. An octave above _do_ is _f_Hz_ ( _do_ )
• 2. Half an octave ( _fa#_ ) would be _f_ •sqrt(2). Generalized to a twelve
tone scale, each half step is _f_0_ •2^(1/12), dividing the octave into twelve
equal _multiplicative_ intervals.

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theoh
I'm not saying fa is half way, I'm saying you can take the scale in two
sections which are just transposed versions of the same intervals. This is not
helpful, but it is true.

Pretty sure you can't get out of the fact that do appears twice by invoking
multiplicative rather than additive logic: two octaves played together
contains 3 dos, 3 octaves contains 4, etc.

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unhammer
"In a large-scale anatomical study of the auditory thalamus (medial geniculate
nucleus of the thalamus) in the cat Kent Morest found …"

"For the rabbit Justin Cetas …"

Some lovely garden-path sentences :-)

