I'm looking up pure mathematics again. I tried to find a good algorithm for integer bases of a null space (which is to say finding unison vectors). It turns...
Hi Graham, Don't know if this helps, but there are two chapters on lattice basis reduction here: http://www.cs.berkeley.edu/~karp/greatalgo/ The one that's...
... Hi Carl, I don't usually top-post but you did:) So I am going to read this lecture and try to get back in the loop here. I need to ask a really naive...
... It's a good reference, but it doesn't mention null spaces, or exactly what kinds of lattices the algorithm works for. After that it talks about integer...
... What's a Leech Lattice?-) These are the "lattices" as defined in group theory, although you can also see them as linear algebra with integers. A group...
Sorry, the complexity of a temperament class is the (hyper)volume of the (hyper)parallelapiped with the vals and origins as the corners. Not the distance to...
... Hi Paul! Around here the space usually dictates the lattice. We've worked with tonespace, chordspace (the dual to chordspace), tuningspace, valspace...
... I think you're calling tonespace "ratio space" here. I think I got the bit about its dual wrong. What I called chordspace is I think just a different...
... "Ratio space" is what i thought it was called when I originally joined the tuning list. A space containing ratios. For harmonic timbres that'd be like a...
Graham wrote; ... I'm sure it's been called many things, but tonespace is the most widely used -- McLaren, Monzo, Erlich, and others. ... Huh? ... It's Gene's...
... I see it's in Monz's dictionary, anyway, looking like ratio space. ... From earlier in this thread, "The idea of a tonespace is that all consonant dyads...
... really ... connection ... tuningspace, ... ask), ... are ... using. ... tonespace ... 1. ... Cool. Is there any chance this work might tie into a TOE? Is...
... Show me. ... You say stuff like this in your pdfs too, but from my perspective it's way out in left field. Simple rationals are approximately the most...
... Physics TOE? I doubt it. Though I am hoping some of Lisi's extra particles show up when the LHC finally starts running. ... Probably. ... I don't know. ...
... Great. So we are dealing with continuous groups. There is some correspondence between some of the sporadic groups and some of the Lie groups. I am into M12...
... I don't know how I'm supposed to show the absence of a constraint on a concept without a formal definition. Tone-space, at least, is defined and described...
... It is interesting, anyway. Euclidean distances on the FCC lattice use a quadratic norm: (2 1 1) (1 2 1) (1 1 2) which is like a variance but adding...
2008/12/5 Paul H <phjelmstad@...>: <snip> ... I'm missing (at least) one of your messages in this thread, so I'm not sure of the context. Anyway, the...
I did RMS calculations for arbitrary sets of intervals here: http://x31eq.com/composite.pdf The simplest way of adapting that to odd-limits is to average over...
... not ... there's ... in ... this ... That ... visualize ... them ... Interesting. So, is a continuous group, really just an infinite group? I am trying to...
... I checked Wikipedia, and it says that Lie groups are differentiable manifolds. I know about them because they're used in physics. The tuning space with a...
Maybe the most interesting and informative way to approach the topology would be to position the "notes" on a spiral around a "deformed" cylinder. I am not...
... group? ... etc. ... a ... duals) ... I also perused Wikipedia, and it appears at least that infinite groups can be continuous, of course, the obvious case...
... differentiable ... The ... is ... same ... metric) ... work. ... Here is a connection from Wikipedia: Thus, compact connected Lie groups have been...
... Where are these defined? "Continous group" takes me to the Lie algebra page and "infinite group" takes me to Group Theory. Neither actually defines the...
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