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Fwd: Two 21-tone JI scales: detemperings of blackjack   Message List  
Reply | Forward Message #17491 of 17519 |
Lattices

Question:

Has anyone here studied any of these lattices, in relationship to
musical tuning?

1. A2.12 sublattice of the Leech Lattice (one of 23 Neimeier lattices)
2. A1.24 sublattice of the Leech Lattice
3. K12 Lattice
4. Barnes-Walls Lattice
5. Coxeter-Todd Lattice

There first two are based on M12 and M24 respectively, and of course
Leech is just a lattice of S(5,8,24) blown up, K12 I think is the
same as Coxeter-Todd?

Finally, is the A4 or D4 lattice discussed here based on the same
nomenclature as the Dynkin diagrams? (Used for Lie Algebras, et c)

Thanks

PGH
Mon Mar 2, 2009 10:59 pm

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paulhjelmstad
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Forward 		Message #17491 of 17519 |
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Paul I would believe naïvely that an interval like 64/63 is too small to be seen as a step but I would never use that as an argument since it concerns musical... 		Pierre Lamothe
plamothe@...
Send Email 		Sep 13, 2001
6:23 am

... It's 1/44 of an octave, and in some temperings it is larger. It's a single step in the 19,26,31,34 and 41 systems, and certainly a single 19-et step does...
genewardsmith@...
Send Email 		Sep 13, 2001
7:08 am

... Don't assume that the modes beginning with 0 are more important or more special than other modes. Look at my suggestion with superparticular steps. It is...
Paul Erlich
paul@...
Send Email 		Sep 13, 2001
9:02 pm

Paul wrote: << Don't assume that the modes beginning with 0 are more important or more special than other modes. Look at my suggestion with superparticular...
Pierre Lamothe
plamothe@...
Send Email 		Sep 14, 2001
8:36 am

... The relative importance they may have is related to the musical grammar used, which lies outside the considerations of your model. Before the 17th century,...
Paul Erlich
paul@...
Send Email 		Sep 14, 2001
11:10 pm

... "Réseau" is French for "lattice" in the sense we've been using it; "lattice" has another meaning in English-language mathematics which French sensibly...
genewardsmith@...
Send Email 		Sep 15, 2001
12:52 am

Paul, In writing << all possible melodic modes have not the same importance >> I was at hundred miles to think you could take that in the sense of historical...
Pierre Lamothe
plamothe@...
Send Email 		Sep 15, 2001
3:57 am

... To keep things from getting too confusing around here, I'll mention again that a Z-module is the same as an abelian group. ... I think again we could fix...
genewardsmith@...
Send Email 		Sep 15, 2001
6:14 am

... Pierre, "mode" in musicians' parlance means rotation -- a different scale degree becomes the first scale degree, and all others rotated by the same amount....
Paul Erlich
paul@...
Send Email 		Sep 18, 2001
12:35 am

Gene, You give me a precious feedback about English and mathematics. I will use simply the word lattice (to translate "réseau") and the word treillis for the...
Pierre Lamothe
plamothe@...
Send Email 		Sep 16, 2001
7:40 am

... I agree we should not identify lattice with abelian group, we should also require it to be a discrete subgroup of R^n. Two examples are: (1) Note classes...
genewardsmith@...
Send Email 		Sep 16, 2001
10:40 pm

Question: Has anyone here studied any of these lattices, in relationship to musical tuning? 1. A2.12 sublattice of the Leech Lattice (one of 23 Neimeier...
Paul H
paulhjelmstad
Offline Send Email 		Mar 2, 2009
10:59 pm
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