ARCHIVED WIKISPACES DISCUSSION BELOW
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Splitting off the MOS catalog?
This article is pretty big, and sometimes I just want the MOS catalog. What about splitting it off? The same comment might be made about the EDO article.
- genewardsmith April 17, 2012, 09:05:22 AM UTC-0700
Good idea I think. Big articles have gone out of fashion as nobody has the time to read.
- xenwolf April 18, 2012, 03:22:51 AM UTC-0700
Shifted a few things around because of the consensus on Multi-MOS and strict MOS and all that, which is I think the best we're going to get. I defined things so that the umbrella class of scales is called "MOS," with these being names for specific subtypes of MOS. I also left in the thing about how some people like to call the larger umbrella term of MOS scales "DE" scales.
Feel free to shift things around if you think anything is confusing.
- mbattaglia1 March 25, 2012, 10:20:51 AM UTC-0700
The 'WITNOTS' Scale
Hi, everybody (:
I put that name, because means:
So, I guess that somebody of you can found a name for this particular MOS: 11L 3s (for me, works well with the name 'Tetradecimal Triatonic').
Bye bye (:
- Osmiorisbendi April 17, 2011, 10:03:10 PM UTC-0700
Error in propriety range
I believe the statement about the range of propriety being (2a+c)/(2b+d) < g < (a+2c)/(b+2d) is incorrect. As a counterexample, take Porcupine. The statement in the article says that the 8-note MOS is only proper if the generator is between 2\17 and 2\15, but Porcupine is proper in 22-equal as you can easily verify.
Perhaps the statement in the article only holds for even-numbered MOSs, or something like that.
- keenanpepper March 20, 2011, 02:44:44 PM UTC-0700
Of course I meant to say perhaps it only holds for odd-numbered MOSs, and not necessarily for even ones.
- keenanpepper March 20, 2011, 04:02:05 PM UTC-0700
I thought about it more and the odd/even thing is certainly wrong. I think the exception to the formula is when one of the numerators is zero, e.g. a = 0. Then when the MOS is of the form LLL...LLLs, the restriction that L < 2S isn't necessary, so the formula fails.
- keenanpepper March 20, 2011, 09:33:38 PM UTC-0700
I've corrected it.
- genewardsmith April 06, 2011, 11:45:49 AM UTC-0700
Theory of MOS scales
My understanding of MOS scales is that they are Well-Formed scales and that these are a subset of Maximally-Even Scales. At least in Erv's original formulation, MOS did not divide the octave evenly. For example, the octatonic scale is Max Even, but not an MOS of 12-tet because it cannot be produced by a cycle of any interval relatively prime to 12. Also a cycle if 8 fifths in 12-tet creates a scale with only two interval sizes, but this scale is not an MOS either.
- jhchalmers June 11, 2010, 12:58:59 PM UTC-0700
I've heard contradictory things about what Erv meant, but my understanding now is that the octatonic scale would count. Eight fifths can be called pseudo-Myhill, which is what Scala does. Is there an easier way to define that than using semiconvergnts
- genewardsmith April 06, 2011, 11:53:15 AM UTC-0700
I've always done it empirically-- taking cycles of generating interval g modulo N (interval of equivalence, usually the octave). Each time a new pair of step intervals appears, there is a new MOS. For G=5 and N=12, we have the following
5 5 2
3 2 3 2 2
1 2 2 1 2 2 2
There is no way the octatonic would arise by this method.
- jhchalmers April 06, 2011, 01:06:45 PM UTC-0700