WDS: My theory of "what music is" is described here in the too-long and too-short versions respectively: https://dl.dropboxusercontent.com/u/3507527/MusicTh.html https://dl.dropboxusercontent.com/u/3507527/MusicThShort.html NJAS: basically all the OEIS algorithm does to sonify a sequence is to reduce the terms mod 88 to a note on the grand piano keyboard. You then get to adjust how the midi file is played, but "read mod 88" is the basic step. This is very primitive and I wish we had something better. The only kind of rating we have for how the "music" sounds is that there is a keyword "hear" that has been added to some sequences that someone has thought are worth listening to. WDS: OK, typing "hear" into the OEIS search box retrieves the following 88 sequences (actually 87, but I added one NJAS mentioned was worth listening to: A261422). This is actually pretty interesting. I still think it would be better if there were a "music-quality rating system" because the present "if a single human likes it, then it qualifies" system is too vulnerable to deranged humans. But the "hear" keyword is not a bad start. A000045 Fibonacci numbers: F(n) = F(n-1) + F(n-2) with F(0) = 0 and F(1) = 1. A000005 d(n) (also called tau(n) or sigma_0(n)), the number of divisors of n. A000010 Euler totient function phi(n): count numbers <= n and prime to n. A007318 Pascal's triangle read by rows: C(n,k) = binomial(n,k) = n!/(k!*(n-k)!), 0<=k<=n. A000120 1's-counting sequence: number of 1's in binary expansion of n (or the binary weight of n). A001223 Differences between consecutive primes. A003415 a(n) = n' = arithmetic derivative of n: a(0) = a(1) = 0, a(prime) = 1, a(mn) = m*a(n) + n*a(m). A000071 Fibonacci numbers - 1. A064413 EKG sequence: a(1) = 1; a(2) = 2; for n > 2, a(n) = smallest number not already used which shares a factor with a(n-1). A005132 Recaman's sequence: a(0) = 0; for n > 0, a(n) = a(n-1) - n if positive and not already in the sequence, otherwise a(n) = a(n-1) + n. A006995 Numbers whose binary expansion is palindromic. A006577 Number of halving and tripling steps to reach 1 in `3x+1' problem. A030101 a(n) is the number produced when n is converted to binary digits, the binary digits are reversed and then converted back into a number. A005811 Number of runs in binary expansion of n (n>0); number of 1's in Gray code for n. A001317 Sierpinski's triangle (Pascal's triangle mod 2) converted to decimal. A001611 a(n) = Fibonacci(n) + 1. A056239 If n = product_{k >= 1} (p_k)^(c_k) where p_k is k-th prime and c_k >= 0 then a(n) = sum_{k >= 1} k*c_k. A048883 a(n) = 3^wt(n), where wt(n) = A000120(n). A003602 Kimberling's paraphrases: if n = (2k-1)*2^m then a(n) = k. A025480 a(2n) = n, a(2n+1) = a(n). A166133 After initial 1,2,4, a(n+1) is the smallest divisor of a(n)^2-1 that has not yet appeared in the sequence. A001610 a(n) = a(n-1) + a(n-2) + 1. A089911 Fibonacci(n) mod 12. A108618 A quaternion-generated sequence calculated using the rules given in the comment box with initial seed x = .5'i + .5'j + .5'k + .5e; version: "tes". A115368 Decimal expansion of first zero of the Bessel function J_0(z). A093873 Numerators in Kepler's tree of harmonic fractions. A004718 The Danish composer Per Noergaard's "infinity sequence", invented in an attempt to unify in a perfect way repetition and variation: a(2n) = -a(n), a(2n+1) = a(n) + 1, a(0)=0. A245701 Permutation of natural numbers: a(1) = 1, a(A014580(n)) = 2*a(n), a(A091242(n)) = 2*a(n)+1, where A014580(n) = binary code for n-th irreducible polynomial over GF(2), A091242(n) = binary code for n-th reducible polynomial over GF(2). A001612 a(n) = a(n-1) + a(n-2) - 1. A080099 Triangle T(n,k) = n AND k, 0<=k<=n, bitwise logical AND, read by rows. A129760 Bitwise AND of binary representation of n-1 and n. A240830 a(n)=1 for n <= s+k; thereafter a(n) = Sum(a(n-i-s-a(n-i-1)),i=0..k-1) where s=0, k=7. A249814 Permutation of natural numbers: a(1) = 1, a(n) = A249741(A001511(n), a(A003602(n))). A140263 Permutation of nonnegative integers obtained by interleaving A117967 and A117968. A239690 Base 4 sum of digits of prime(n). A240828 a(1)=a(2)=0, a(3)=2; thereafter a(n) = Sum( a(n-i-s-a(n-i-1)), i=0..k-1 ), where s=0, k=3. A241154 a(n)=1 for n <= s+k; thereafter a(n) = Sum(a(n-i-s-a(n-i-1)),i=0..k-1) where s=0, k=5. A086099 a(n) = OR(k AND (n-k): 0<=k<=n), AND and OR bitwise. A105870 Fibonacci sequence (mod 7). A142149 a(n) = XOR{k OR (n-k): 0<=k<=n}. A142151 a(n) = OR{k XOR (n-k): 0<=k<=n}. A240835 a(n)=1 for n <= s+k; thereafter a(n) = Sum(a(n-i-s-a(n-i-1)),i=0..k-1) where s=0, k=4. A248034 a(n+1) gives the number of occurrences of the last digit of a(n) so far, up to and including a(n), with a(0)=0. A258083 Smallest multiple of 3 not appearing earlier that ends with n. A186994 Number of maximal subsets of {1, 2, ..., n} containing n and having pairwise coprime elements. A227876 Write the decimal digits of n and take successive absolute differences; sequence is the sum of all digits at each level of the pyramid. A249346 The exponent of the highest power of 6 dividing the product of the elements on the n-th row of Pascal's triangle. A051933 Triangle T(n,m) = Nim-sum (or XOR) of n and m, read by rows, 0<=m<=n. A075877 Powering the decimal digits of n (left-associative). A126759 a(0) = 1; a(2n) = a(n); a(3n) = a(n); otherwise write n = 6i+j, where j = 1 or 5 and set a(n) = 2i+2 if j = 1, otherwise a(n) = 2i+3. A243493 Value of Matula-Goebel signature at the fixed points of A069787: a(n) = A127301(A243490(n)). A243658 a(0)=0; thereafter a(n) = noz(n+a(n-1)), where noz(n) = A004719(n). A256229 Powering the decimal digits of n (right-associative). A257213 Least d>0 such that floor(n/d) = floor(n/(d+1)). A258200 First differences of A258024. A125886 a(1) = 1, a(n) = smallest positive number b not among a(1)..a(n-1) such that the last digit of b = the first digit of a(n-1). A131813 a(n+1) = number of preceding terms that are contained in a(n) in binary; a(0)=0. A137655 Working in base 3, a(n+1) = number of preceding terms that are contained in a(n); a(0)=0. A140266 Inverse permutation to A140265. A169669 (first digit of n) * (last digit of n) in decimal representation. A227538 Smallest k such that a partition of n into distinct parts with perimeter k exists. A256489 First differences of A257509: a(n) = A257509(n+1) - A257509(n). A068636 a(n) = Min(n, R(n)), where R(n) (A004086) = digit reversal of n. A068637 a(n) = Max(n, R(n)), where R(n) (A004086) = digit reversal of n. A104325 Number of runs of equal bits in the Dual Zeckendorf (binary) representation of n. A117154 Floretion with FAMP code 1teszapsumseq[C*B] with C = - .5'j + .5'k - .5j' + .5k' - 'ii' - .5'ij' - .5'ik' - .5'ji' - .5'ki' and B = - .5'i + .5'j - .5i' + .5j' - 'kk' - .5'ik' - .5'jk' - .5'ki' - .5'kj'. A119953 Y = X = 'i + .25(ii + jj + kk + e); Z = 'i - i' + .5(jj + kk - jk + kj) + e. See pdf-file for an exact definition (this sequence gives an initial term 1); Version "jes". A123456 Ludwig van Beethoven, Bagatelle No. 25, "Fuer Elise". A126626 A floretion-generated sequence based on the iterative procedure defined in the link given. A144488 Ludwig van Beethoven, Bagatelle No. 25, "Fuer Elise". A240827 a(n) = n for 1<=n<=6; thereafter a(n) = a(n-a(n-3))+a(n-a(n-6)). A242353 Number T(n,k) of two-colored rooted trees of order n and structure k; triangle T(n,k), n>=1, 1<=k<=A000081(n), read by rows. A248756 a(n) = smallest k such that a(n-k) and n have the same number of 1's in their binary expansions, or a(n) = n if no such k exists. A254868 Recaman [-, +, *]-sequence with seed 6 and step 4. A261684 Array T(n,k) = lunar product n*k (n >= 0, k >= 0) read by antidiagonals. A261422 Number of ordered triples (u,v,w) of palindromes such that u+v+w=n. A073334 The so-called "rhythmic infinity system" of Danish composer Per Noergaard. A117153 The floretion + .25'i + .25'j + .25'k + .25i' + .25j' + .25k' + .25'ii' + .25'jj' + .25'kk' + .25'ij' + .25'ik' + .25'ji' + .25'jk' + .25'ki' + .25'kj' + .25e. A126949 Moduli n for which -1 is a power residue for some power greater than 2: i.e. m^k == -1 mod n for some k>1 and some m>1. A190906 GCD(n! / floor(n/2)!^2, 3^n) A235431 The smallest positive number that must be added to or subtracted from the sum of the first n primes in order to get a prime. A240829 a(1)=-1, a(2)=0, a(3)=1; thereafter a(n) = Sum(a(n-i-s-a(n-i-1)),i=0..k-1) where s=0, k=3. A247074 a(n) = phi(n)/(product_{primes p dividing n } GCD(p - 1, n - 1)). A254873 Recaman [divide, -, +, *]-sequence with seed 14 and step 2. A212952 Decimal expansion of 3*sqrt(3)/16. A215459 Arises in quick gossiping without duplicate transmission. A255253 Complete list of siteswaps (indecomposable ground-state in concatenated decimal notation organized first by sum of digits and then by magnitude). A255877 a(n) = (2n-2)^3 +(2n-2) - 1. Can we draw any conclusions from this list? Almost all even of these especially musical sequences still are pretty horrible as music. The musical ones seem to include a suspiciously large amount of... 1. Most obviously, sequences with a lot of "note propinquity," i.e. most internote-transitions are short-distances. Examples A000005, A000010, A000120, A000120, A005811, A003602, A166133, A115368, A093873, A004718, A235431, ... 2. Fibonacci and its ilk, e.g. A000045, A001610, A001612 3. sequences invented by actual composers e.g. Beethoven and Noergaard: A123456, A144488, A073334,... 4. Recaman sequences. 5. Various 2D tables read by rows. 6. Floretions (whatever they are). My music theory (actually other people's music theories too...) would predict (1) and obviously (3). Also (5) seems plausible. I'm not sure about (4). For (2) it is mysterious to me why those should be good music (if they are). Some of Noergaard's sequences seem particularly interesting and it ought to be possible to define similar recurrences to his, but designed to enjoy additional musical properties...