The Western music system uses 12 different notes to represent pitch; C, C#/D♭, D, D#/E♭, E, F, F#/G♭, G, G#/A♭, A, A#/B♭ and B. These notes then repeat each “octave” (an octave is how the sets of 12 notes are divided) with notes of each new octave having twice the pitch of the last. This exponential property's also consistent within octaves; each new note being 2^(1/12) times the frequency of the last. This allows us to model the frequency of notes as b x 2^(x/12), b being the frequency of the base note and x the number of semitones (notes) above b.
In the Western music system, b is defined as A4 (the note A in the fourth octave) at 440Hz (oscillating 440 times per second). Using this formula and value of b, we can convert numbers from our series into musical notes, however large numbers in our series will generate incredibly high pitch notes outside of our hearing range. To avoid this, we first take the modulus 12 of x (dividing x by 12 and only keeping the remainder) before using it. This means that we can't hear what octave the note is in but this is fine as equivalent notes across octaves sound similar already.
According to the Collatz Conjecture, all Hailstone Series will eventually reach 1 regardless of the starting number. However, despite it's simplicity, no-one has been able to prove this true or false.
To calculate Hailstone Series, start with a positive integer (whole number). If it is even, divide by 2 to get the next term, otherwise multiply by 3 and add 1. Then repeat indefinitely.
All Hailstone Series found so far, eventually reach some power of 2, causing them to repeatedly half until they drop to 1. 1 then becomes 4, which drops to 2 and then 1 again. The sequence starting with 3 (the sequence below 6 that takes the longest to reach 1) is as follows: 3, 10, 5, 16, 8, 4, 2, 1, 4, 2, 1...
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