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Step 13How to count only Musical Numbers
This is in english but for the purpose of making an algorithm in any program language
or for making a circuit.
First, an example:
The 20 six-bit Binary Musical Numbers in 2 columns.
000111 100011
001011 100101
001101 100110
001110 101001
010011 101010
010101 101100
010110 110001
011001 110010
011010 110100
011100 111000
Notice that binary can count to 63 with 6 bits, but only 20 are "musical",
(by my definition , or physically sound-like). The ratio of musical to total
numbers decreases incredibly as the number of bits goes up. Therefore
they are very countable. Not infinite. In fact, each has a double that
sounds exactly the same all bits different in the other column (which
need not be in another column, just to save 10 lines).
Notice that at the beginning, the count has all the ones on the right,
and ends with the ones on the left. It just so happens that the number
of Musical Numbers for any number of bits is equal to the number in
the middle of the row of Pascal's triangle whose row number is the
number of bits. This is a fascinating unique science.
Ok, one rule for counting this way in binary is:
00001111
Start on the RIGHT and go LEFT until you find 01.
Change that 01 to 10, and push any other 1's you've passed all the way to the right. Stop.
You now have the next musical number.
Do it again and again until all the 1's are on the left side.
11110000
If you are using a circuit, you may bend it by mixing up the bits before and
unmixing them after each count, as simply as "not wiring the bits in the right order".
In a program, you might have a SWAP instruction, or an arbitrary lookup table.
Why? To make really weird counting patterns that sound different.
Another Secret :
TO AVOID COUNTING, You can calculate any sound instantly by remembering
it as a polynomial, and having "the calculator" evalulate it, and then,
Use the combinatorics function "N Choose R". THIS WORKS IN ALL BASES.
What's the trillionth sound that fits in 4 megabytes? Bam!
Boo! (-The ghost of "napster"!)
It's raining ACME anvils, pianos, and dynamite somewhere now, what a beautiful noise!
or for making a circuit.
First, an example:
The 20 six-bit Binary Musical Numbers in 2 columns.
000111 100011
001011 100101
001101 100110
001110 101001
010011 101010
010101 101100
010110 110001
011001 110010
011010 110100
011100 111000
Notice that binary can count to 63 with 6 bits, but only 20 are "musical",
(by my definition , or physically sound-like). The ratio of musical to total
numbers decreases incredibly as the number of bits goes up. Therefore
they are very countable. Not infinite. In fact, each has a double that
sounds exactly the same all bits different in the other column (which
need not be in another column, just to save 10 lines).
Notice that at the beginning, the count has all the ones on the right,
and ends with the ones on the left. It just so happens that the number
of Musical Numbers for any number of bits is equal to the number in
the middle of the row of Pascal's triangle whose row number is the
number of bits. This is a fascinating unique science.
Ok, one rule for counting this way in binary is:
00001111
Start on the RIGHT and go LEFT until you find 01.
Change that 01 to 10, and push any other 1's you've passed all the way to the right. Stop.
You now have the next musical number.
Do it again and again until all the 1's are on the left side.
11110000
If you are using a circuit, you may bend it by mixing up the bits before and
unmixing them after each count, as simply as "not wiring the bits in the right order".
In a program, you might have a SWAP instruction, or an arbitrary lookup table.
Why? To make really weird counting patterns that sound different.
Another Secret :
TO AVOID COUNTING, You can calculate any sound instantly by remembering
it as a polynomial, and having "the calculator" evalulate it, and then,
Use the combinatorics function "N Choose R". THIS WORKS IN ALL BASES.
What's the trillionth sound that fits in 4 megabytes? Bam!
Boo! (-The ghost of "napster"!)
It's raining ACME anvils, pianos, and dynamite somewhere now, what a beautiful noise!
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