Tune Smithy Melodies for other sequences in the OEIS

See also: Self Similar Sloth Canon Number Sequences

Van Eck's sequence (A181391 in the OEIS) as a melody with Tune Smithy
The sequence is here: A181391

Played with Tune Smithy, http://tunesmithy.com

HOW THE SEQUENCE IS DEFINED
You look for the last number in the sequence so far. If it is the first occurrence of that number, set the next number to 0. Otherwise, set the next number in the sequence to the number of terms since it's last occurrence.

Example:

0, 0, 1, 0, 2, 0, 2, 2, 1, 6, 0, 5, 0, 2, 6, 5, when you get to this point, the last number is 5, and it repeats another 5 which was 4 terms earlier.. So the next number in the sequence is 4. 0, 0, 1, 0, 2, 0, 2, 2, 1, 6, 0, 5, 0, 2, 6, 5, 4

But now this is the first 4 in the sequence so far, so the next number is 0. 0, 0, 1, 0, 2, 0, 2, 2, 1, 6, 0, 5, 0, 2, 6, 5, 4, 0, The last 0 was 5 terms earlier, so the next number is 5 0, 0, 1, 0, 2, 0, 2, 2, 1, 6, 0, 5, 0, 2, 6, 5, 4, 0, 5, The last 5 was 3 terms earlier so the next number is 3 0, 0, 1, 0, 2, 0, 2, 2, 1, 6, 0, 5, 0, 2, 6, 5, 4, 0, 5, 3 and so it goes on.

ABOUT THE TUNING
The tuning is a pentatonic scale.

Because the numbers go so high in this sequence eventually, I set the scale to "wrap around". I did it so that the pitches go:

1/1 5/4 3/2 5/3 2/1 1/1 ...

That's how you get the octave above the 1/1 as well as the 1/1 both played, and why you get the same note played by numbers that are 6 apart so 0, 6, 12, ... play the same note, the 1/1, and 1, 7, 13, ... play the 5/4, and so on. 5, 11, 17, ... play the 2/1.

Gijswijt's sequence (A090822 in the OEIS) as a melody with Tune Smithy
The sequence is here: A090822. The first 5 occurs at 10^(10^23) - that's the number consisting of 1 followed by 10 to the power 23 zeroes - so you are never going to see a 5 in practise, if you play it all the way from the start, no matter how fast you play it and how long you wait. the other notes.

Played with Tune Smithy

HOW THE SEQUENCE IS DEFINED
The nth number in the sequence gives the number of repeating blocks in the sequence so far, where you are allowed to ignore the beginning of the sequence, as much of it as you like, but it must then repeat exactly from then on.

So for instance, in:

1, 1, 2, 1, 1, 2, 2, 2, 3,

the first few 2s and the 3 are found like (1 ; 1 ) 2 1 1 2 (1 ; 1) 2 (1, 1, 2 : 1, 1, 2), 2 1, 1, 2, 1, 1, (2 ; 2) 2 1, 1, 2, 1, 1,( 2 ; 2 ; 2), 3,

This is the first "interesting" 3: 1, 1, 2, 1, 1, 2, 2, 2, 3, 1, 1, 2, 1, 1, 2, 2, 2, 3, 2, 1, 1, 2, 1, 1, 2, 2, 2, 3, 1, 1, 2, 1, 1, (2, 2, 2, 3 : 2, 2, 2, 3 : 2, 2, 2, 3), 3,

ABOUT THE TUNING
It's just playing the notes of a major chord, so far but in a harmonic series based "just intonation" tuning.

3/2 2/1 5/2 3/2

with the 1/1 set to C (never plays the 1/1 because there is no 0 in the sequence).

If it ever got to a 5 then it would play a 7/4 because it is actually set to play a harmonic series, but we know it is never going to get there in a practical time span :).

You may feel as though you hear a "4" quietly in the gaps between the other notes sometimes before you hear it for real, It's not played at all, no echo. Instead, you are hearing a harmonic of one of the other notes - it's an octave above the 3/2.