On Tue, Feb 1, 2011 at 2:40 AM, genewardsmith ... If you were to actually apply the meantone map to 10-et or 17-et, it wouldn't be reversed there. It just gets...
96027
genewardsmith
Feb 1, 2011 8:03 am
... Yeah, I know, but that's points in a projective plane, and we were talking about fractions of an octave....
96028
Mike Battaglia
battaglia01
Feb 1, 2011 8:04 am
On Tue, Feb 1, 2011 at 2:58 AM, genewardsmith ... OK, so I get this, and have always understood this concept practically, but I think that there's something...
96029
Mike Battaglia
battaglia01
Feb 1, 2011 8:09 am
On Tue, Feb 1, 2011 at 2:55 AM, genewardsmith ... I said dominant over septimal meantone because we don't even get to see any meantone 7-limit action in 5L2s...
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genewardsmith
Feb 1, 2011 8:14 am
... Porcupine is rank two, so there are two vals....
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Mike Battaglia
battaglia01
Feb 1, 2011 8:16 am
On Tue, Feb 1, 2011 at 3:14 AM, genewardsmith ... And the first number of each of those vals is always an MOS that that temperament supports? -Mike...
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Mike Battaglia
battaglia01
Feb 1, 2011 8:20 am
... And hence an MOS can be uniquely identified by a pair of ETs, then each linear temperament can be uniquely identified by an MOS...? -Mike...
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genewardsmith
Feb 1, 2011 8:21 am
... OK, but that means you are starting from a linear temperament and getting to the MOS later on, which I didn't think was the point of the exercise. If we...
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genewardsmith
Feb 1, 2011 8:24 am
... Vals aren't MOS, they are vals. You can make the vals two equal temperament vals, but they don't need to be. Graham gives it both ways....
96035
genewardsmith
Feb 1, 2011 8:26 am
... A pair of et vals defines a rank two temperament, not a MOS. In the 5-limit, that means they also define a comma....
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Mike Battaglia
battaglia01
Feb 1, 2011 8:30 am
On Tue, Feb 1, 2011 at 3:26 AM, genewardsmith ... Maybe I should move this to tuning-math. But OK, so let me try to be clear: - A pair of ET vals defines a...
96037
Mike Battaglia
battaglia01
Feb 1, 2011 8:43 am
On Tue, Feb 1, 2011 at 3:21 AM, genewardsmith ... I was just pointing out that the relationship between MOS's and temperaments aren't completely disparate. I'm...
96038
Petr ParÃzek
petrparizek2000
Feb 1, 2011 9:44 am
... Not sure if both of us are talking about the same thing. More here: http://www.phys.unsw.edu.au/jw/musFAQ.html#endeffect ...
96039
Jacques Dudon
jacques.dudon
Feb 1, 2011 4:00 pm
For Petr (and all) : Improvisation with semitone key opened on one of my harmonic flutes, along with Alain Panteleimonoff (surbahar) and Jacques Deregnaucourt...
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cityoftheasleep
Feb 1, 2011 4:13 pm
... Yes, okay, I was awake all friggin' night thinking about this and I realized this is more of a problem that I at first thought (if that's possible). For...
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genewardsmith
Feb 1, 2011 6:22 pm
... Here's something which may be relevant to this quest. I have a list of 36 7-limit commas which I often use as a sort of standard list. If I do what I...
96042
Petr PaÅ™Ãzek
petrparizek2000
Feb 1, 2011 6:58 pm
Hi Jacques. Thanks for sharing, that definitely sounds interesting. You've reminded me of another event. A few months ago, I was even thinking about a possible...
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Mike Battaglia
battaglia01
Feb 1, 2011 7:42 pm
On Tue, Feb 1, 2011 at 1:22 PM, genewardsmith ... What's your goal here...? To see which EDOs result if you combine various interesting commas with septimal...
96044
Mike Battaglia
battaglia01
Feb 1, 2011 7:59 pm
On Tue, Feb 1, 2011 at 11:13 AM, cityoftheasleep ... But that's only because in the cases I mentioned, the generator is itself in the 3-limit. I don't think a...
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Mike Battaglia
battaglia01
Feb 1, 2011 8:36 pm
... After thinking more about this, it seems like the simpler, more all-encompassing, and overall better goal is to group all of the MOS scales by the...
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genewardsmith
Feb 1, 2011 8:57 pm
... To see where commas flip. If they aren't too simple or too complex, I surmise in a reasonable range for the temperament. Most very complex commas seem to...
96047
Mike Battaglia
battaglia01
Feb 1, 2011 9:04 pm
On Tue, Feb 1, 2011 at 3:57 PM, genewardsmith ... OK, I see. That's pretty similar to what I'm suggesting here then; if really simple commas are flipping for a...
96048
cityoftheasleep
Feb 1, 2011 9:08 pm
... Aren't commas derived from mappings? So if two temperaments share a mapping, don't they share commas as well? ... Kingdom phylum class order family genus...
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Carl Lumma
clumma
Feb 1, 2011 9:08 pm
... The flipping thing has potential. As everybody knows, Bosanquet classified ETs according to the number of steps, positive or negative, certain commas come...
96050
Mike Battaglia
battaglia01
Feb 1, 2011 9:16 pm
... Sure, I just meant that it might be more simple conceptually to think about common mappings, since vals deal with mappings and not commas. Maybe since...
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Mike Battaglia
battaglia01
Feb 1, 2011 9:17 pm
... You might have to supply some of the missing glue here, because the stuff you posted where the ET's fit in lines, and then how it turns out that every...
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genewardsmith
Feb 1, 2011 9:24 pm
... Pythagorean?...
96053
Mike Battaglia
battaglia01
Feb 1, 2011 9:34 pm
On Tue, Feb 1, 2011 at 4:24 PM, genewardsmith ... I think that probably makes more sense than my "diatonic"; suggestion. I still like the idea of calling them...
96054
genewardsmith
Feb 1, 2011 9:44 pm
... It's more or less the same thing as giving a generator which is a fraction of an octave, it seems to me. Say we look at 29/50. Looking at the continued...
96055
Jacques Dudon
jacques.dudon
Feb 1, 2011 11:59 pm
... Some calculations are theorically possible but are very complex in that matter. What I always did was guessing from flutes I made before, making slightly...
