I have reduced and minimalized this so that a small handful of
nice cheap 4040 and 4051 chips may be all you need.
(and battery, wire, solder, iron, speaker, breadboard, etc.)
HEADACHE WARNING: MATH AHEAD (Only "math heads" need to know.)
At this point the simplest musical calculator using "normal numbers" will use a brute force
method that pulls digits out of thin air using a binary counter, which is not considered a
computer, although it calculates all possible combinations starting with zero. Normal numbers
contain all other numbers, and the ones which can be made by counting contain them all
in order. And this is interesting because files and numbers are both the same thing, strings
of bits. This is well demonstrated in the simplest way I can imagine, in that number which
will play as the calculator song.
We say that Pi has an infinite number of digits, and that the digits are arranged "randomly"
in such a way that it contains an equal number of each number, so it is called Normal
(mathematically speaking). If I was making a Pi player, it would sound like the hiss of
static on a radio, because that is the sound of random. No one says that counting is
random, and a number made by ordinary counting will not skip a number, so we can
be sure that any number can be found in sorted order in it's place, leaving no doubt,
as someone could doubt that Pi has a certain number in it if they looked all over it
and never found what they were looking for.
The number "zero point one two three..." is the simplest demo of the musical number
concept, not necessarily the most practical one. Most understandable. I really feel
like I have to condescend and KISS about my most incredible inventions so people
because of responses like this:Digg my "Holodeck"
The original Pandora's Box instructable had constraints, so that it's output would
never sound like static. This one does not have noise-avoiding constraints, except
that as another demo it is not designed to go so far into the calculation that we
will lose the sense of the pattern in the sound which is the process of counting.
It is very important to imagine that the number one need not be the first sound.
If this particular method of making sound were advanced far enough, then
the number one could actually represent the first song on the popularity chart!
I hope to get deeper into enumeration in future "musical number theory" instructables.
My more current enumeration research actually involves effective skipping of white noise,
so just think, out of all the possible numbers (sound files), what portion of them are noise? (!) .
It is important to realize that the musical number explored in this instructable is
not the only one, and this is not the only method I have invented or will invent
of generating digital sounds. Many are not yet impressed with my 3D projection
system or writing style, but at least I've included older projects which may be
reason to anticipate more and better in the future.
There may be inconsistent flow in the development of this prematurely published
instructable. I provide a link to what part of the Musical Number sounds like as
output by the device I'm now making for you to make.Some 2^(2^(17)) digits of The Number (compressed into mp3)
Listen carefully for beats, voice like sounds (woo!) , bells ... some imagination maybe required!
I'm expecting the finished circuit to consist of a few logic chips, (no uC or uP)
so you'll need a soldering iron, a speaker, and chips which I haven't chosen yet.
You may feel free to experiment with the calculation and playing of numbers as
sound files while I work on making this instructable project.
Calculated BINARY numbers sound much louder as RAW or PCM
when the letter O is used instead of the number zero when stored as text.
(Otherwise you may not hear it at all.)
All your base are belong to you! (Haha. Use whatever base you want. Also,
I recommend using only the alphabet for bases 11 thru 26, or Hexadecimal will be distorted.)
The number that sings about the calculator is in ASCII (see Pandora's Box)
because it used to be in BCD, but that is not a standard (net playable) format.
I know you all laugh at my videos but I will probably demo LOTS of unique sound artifacts.