20201202, 11:42  #1 
"Viliam Furík"
Jul 2018
Martin, Slovakia
150_{16} Posts 
Prime music
Recently I have started transforming Mersenne primes into music. I wanted to start with M1398269, the first prime GIMPS discovered, but it turned out to be too long for me to turn into music because it would be about 38 hours long and I couldn't find any online tool that could render MIDI file that long. So I went for the largest prime I could safely "musify"  M44497. HERE is a link to my personal Google Drive, where you can find 1 hour, 14 minutes and 24 seconds of prime music.
"Musification" was done by mapping the decimal digits onto the consecutive piano keys, creating a CSV file that was turned into MIDI by a special tool I found. Then I used online renderer to render MIDI into WAV. As I was writing, I realised I can shorten the number of notes, and herby time, by converting the number into a higher base. After a short calculation, using all 88 keys of the piano, I can only shorten it to about 20 hours... Does anybody have an idea, how to shorten the big numbers? Or does anybody know of some tool or method that can musify arbitrarily big numbers? 
20201202, 12:26  #2 
"Oliver"
Sep 2017
Porta Westfalica, DE
7×59 Posts 
If you convert the number to base 2^{88}, then each "digit" represents a combination of pressed keys.

20201202, 12:44  #3 
"Viliam Furík"
Jul 2018
Martin, Slovakia
150_{16} Posts 
Hehe, got ya! Mersenne numbers, expressed in powerof2 bases are repdigits. It would be pretty monotonic song... Except for the beginning (that would be the single different digit  or rather symbol in base 2^{88}).

20201202, 12:50  #4 
"Oliver"
Sep 2017
Porta Westfalica, DE
110011101_{2} Posts 
You are totally correct! My error was, that a base2 repdigit is a near repdigit in base 2^{n}...

20201202, 13:13  #5 
Feb 2017
Nowhere
7×599 Posts 
If you're just using a series of single notes, I suppose you could convert to base 12*k and let the digits represent the notes in a range of k octaves.
(In a piano octave, there are 7 white keys (A, B, C, D, E, F, G) and 5 black keys  C sharp (D flat), D sharp (E flat), F sharp (G flat), G sharp (A flat), and A sharp (B flat).) 
20201202, 14:27  #6  
Nov 2016
2764_{10} Posts 
Quote:


20201202, 14:51  #7 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
2^{10}·3^{2} Posts 

20201202, 16:53  #8 
"Viliam Furík"
Jul 2018
Martin, Slovakia
2^{4}×3×7 Posts 
I said (maybe not in the clearest way) that I did that. I was talking about using all 88 keys, but that still wasn't enough, as it only shortened the time to about half, which is still 20 hours.

20201202, 19:26  #9 
Feb 2017
Nowhere
7×599 Posts 
Hmm. The 88 keys on a piano make about 7 octaves.
The range of human hearing is usually stated as around 20 to 20,000 Hz which is about 10 octaves. So, at 12 notes per octave, that would be about 120 notes, give or take. Using the digits in a base around 120 (assuming the base isn't a power of 2 like 128, of course!) would give you as many notes as you could possibly use, but the number of base120 digits would only be something like 6% less than the number of base88 digits. 
20201202, 19:49  #10  
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
2·5^{2}·97 Posts 
Quote:
Rough draft from faded memories of the basics from school days music class long ago 88 keys 10 fingers usually 2 hands usually code left pinkie finger position offset from leftmost key as ~7 bits to have more than enough symbols for possible positions on the piano keyboard, 6 might not do it, 7 overflows the keyboard, so remap linearly. Code actions of other fingers of same hand as 23 bits cumulative offset each and one each for struck or not, so ~12 bits there; code force of key strikes as 3 bits (0=not struck, 7=hardest), code hold time as 3 bits. 25 bits to here. (I think equal force and duration among the digits of a hand is a reasonable simplification. Do skilled players modulate force or duration of each finger on a hand individually? If so add a few bits each times 4 digits) Assume arms do not cross or hands overlap. Might need still 7 bits for coding offset of right thumb, then code the rest of the hand as for the left above. throw in 3 bits for the possible foot pedal activations assuming 3 pedals. That's 53 bits; 2^53=9,007,199,254,740,992. Round up to 10^16. Consider the decimal representation of a Mersenne number as a base 10^16 score. Start from the MSD, or the LSD? Discard partial note code at the end. Remap the nearly 10% of possible 16decimaldigit codes that exceed 53 bits somehow. Perhaps accumulating ten such into a sum mod 2^53 and then playing that note. I suspect how will not matter much, as the tune will probably sound awful regardless. And unplayable by humans, due to much larger hand excursions between notes than is usual. Someone who actually played could probably come up with something much more plausible. I suggest trying out some encodings with something simpler, like M4253 or a thousand digits of pi, to see how they sound. https://youtu.be/z6ijiDiUKw Recasting it as a duet does not double the number of bits per unit time. It's still going to be much too long. Maybe need a whole orchestra. But that may sound like the chaotic tuning up before a performance, while they're all doing different things, not playing in some sort of harmonious whole. Last fiddled with by kriesel on 20201202 at 20:00 

20201203, 07:19  #11  
Romulan Interpreter
Jun 2011
Thailand
9,161 Posts 
Quote:
Or... if you are Rachmaninov, who had very big hands... 

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