On 03 Mar 2014, at 09:50, Kim Jones wrote:
On 3 Mar 2014, at 6:49 pm, Bruno Marchal <[email protected]> wrote:
On 03 Mar 2014, at 08:32, Kim Jones wrote:
On 2 Mar 2014, at 11:03 pm, Bruno Marchal <[email protected]> wrote:
On 02 Mar 2014, at 11:13, Kim Jones wrote:
Kim Jones B. Mus. GDTL
On 1 Mar 2014, at 7:43 pm, Bruno Marchal <[email protected]>
wrote:
and I chose numbers as people are familiarized with them.
Bruno
How about music? Music is just a bunch of numbers.
Well, you can't say that. Especially to a literally minded
stubborn mathematician :)
I do agree that the relation between math and music are very deep
and profound though.
Yes. Tell me: are the following equivalent statements to a
literally-minded stubborn mathematician like you:
4 + 1 = 5
1 + 4 = 5
2 + 3 = 5
3 + 2 = 5
They are equivalent in many senses, and not equivalent in many
other senses.
They are equivalent semantically, but then with classical
semantics, all true statement are equivalent.
I mean that if you have the truth that 4+1 = 5 then 1+4=5. That is:
(4+1= 5 <-> 1+4=5) is true.
They are deductively equivalent in RA, PA, ZF, etc. because such
theories can prove the equivalence above.
They are not equivalent in any procedural sense. adding 1 to 4 is
not the same thing than adding 4 to 1. It happens that the result
is the same, but the procedure is not.
In fact "equivalent" means nothing, if you don't stipulate the
relation of equivalence applied.
because to a lateral-thinking, alternative-seeking musical thinker
like moi they are not.
OK. But I need your equivalence relation.
Equivalent in the “musical sense” would mean strict invariance
“to the ear”.
You only have to perform (ie clap or tap out) 4 + 1 followed by 1
+ 4 to see ( ie hear -> ratiocinate) that they are not equivalent
in the musical sense.
OK, in the musical sense, assuming "+" introduce a time delay in
the claps, they are not.
“ + “ adds no time delay. All the numbers are “butt to
butt”. A time delay would signify a number. Curiously, the only
sonic way you can perform 4 + 1 is to differentiate these two
entities somehow. We do this by making the first clap of any group
loud and all successive claps soft. So 4 + 1 comes out as (F =
‘forte’ loud, p = ‘piano’ soft) FpppFFpppFFpppFF etc.
Try 3 + 2 (X3) and swap immediately to 2 + 3 (X2)
Comes out as:
FppFpFppFpFppFpFpFppFpFpp (remember no gabs between claps. A gap
is a number. Silence is structured in music.)
Do it really fast and continually and then later on smoke a joint
and listen to Dave Brubeck’s “Take Five” which you have kind of
just prepared your neurons for.
I think this is used in musinum.
http://reglos.de/musinum/
Give me a shout if you cannot clap these sentences accurately.
Actually, your clap view of numbers make 1+x non equivalent with x
+1 useful for the infinite ordinals.
1 + omega = omega
that is clap followed by clap clap clap clap ... is considered as
equivalent to clap clap clap ...
The "+" does not add delay, for the ordinal, unless there are an
infinity, and so:
omega + 1 is not = to omega,
clap, clap, clap, clap, ...., clap ≠ clap, clap, clap,
clap, ....,
That's a different rhythm indeed.
Bruno
Yes. Actually, an interesting “law” of music is that when dealing
with isochronic stresses “beats” - the invisible number structure
that orders all music linearly (can be explicit or virtually
undiscernible depending on the music)
is that STRONG is always followed by WEAK.
Thus, ‘1’ is ALWAYS a strong (ie loud) beat. With a field of 3
beats (‘waltz-time’) this gets interesting because you now have
FppFppFpp which when you perform it suggests a circle. The old
conductors would wave their arms in a circle to conduct 3/4 time in
the past. What is it, Bruno, about 3 beats to the bar that
precisely, irrefutably describes to my mind a circle?
You tell me.
Bruno
K
K
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