Comments on: Mamuth to Elephant (3)

By: Alexandre Popoff

Alexandre Popoff — Thu, 24 Mar 2022 08:54:39 +0000

Thanks for your comment ! Indeed, I now see that there is a typo in the paper which completely escaped me during the review process, and I’m sorry for that. Obviously, it should be n_m L (n+8)_M as is the case for all generalizations of L, since we want them to coincide with the usual neo-Riemannian operator on major/minor triads.

By: lievenlb

lievenlb — Thu, 24 Mar 2022 07:21:53 +0000

Thanks Alexandre! I based myself on your definition 5.2 in ‘On the use of relational…’ where L is not symmetric for major and minor triads. With the L you suggest I do indeed get as the sizes of the two monoids 473293 and 994624.
I’ll make corrections to the blogpost.

By: Alexandre Popoff

Alexandre Popoff — Wed, 23 Mar 2022 15:34:58 +0000

I meant 473293 (and not 473283) in my comment above….

By: Alexandre Popoff

Alexandre Popoff — Wed, 23 Mar 2022 15:33:54 +0000

I think the mistake lies in the definition of L (before TU).
Given that it is an involution sending C#_M to F_m, shouldn’t it be
PBR([ [ -17 ], [ -18 ], [ -19 ], [ -20 ], [ -21 ], [ -22 ], [ -23 ], [ -24 ], [ -13 ], [ -14 ], [ -15 ], [ -16 ],[ -9 ], [ -10 ], [ -11 ], [ -12 ], [ -1 ], [ -2 ], [ -3 ], [ -4 ], [ -5 ], [ -6 ], [ -7 ], [ -8 ], [ -25 ],[ -26 ], [ -27 ], [ -28 ], [ -29 ], [ -30 ], [ -31 ], [ -32 ], [ -33 ], [ -34 ], [ -35 ], [ -36 ], [ -37 ],[ -38 ], [ -39 ], [ -40 ] ],
[ [ 17 ], [ 18 ], [ 19 ], [ 20 ], [ 21 ], [ 22 ], [ 23 ], [ 24 ], [ 13 ], [ 14 ], [ 15 ], [ 16 ], [ 9 ], [ 10 ],[ 11 ], [ 12 ], [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5 ], [ 6 ], [ 7 ], [ 8 ], [ 25 ], [ 26 ], [ 27 ], [ 28 ], [ 29 ],[ 30 ], [ 31 ], [ 32 ], [ 33 ], [ 34 ], [ 35 ], [ 36 ], [ 37 ], [ 38 ], [ 39 ], [ 40 ] ]) ?

I get 473283 when calculating the monoid size with this definition of L.

By: lievenlb

lievenlb — Tue, 22 Mar 2022 08:18:18 +0000

GAP seems to need a lot more time calculating sizes when using BinaryRelationOnPoints. But yes, I do get the same numbers.

By: Alexandre Popoff

Alexandre Popoff — Mon, 21 Mar 2022 09:47:29 +0000

The difference in monoid sizes is strange. Have you tried with BinaryRelationOnPoints in GAP instead of PBRs (which seem a little bit complicated) ?