# Talk:MOS scale/WikispacesArchive

# ARCHIVED WIKISPACES DISCUSSION BELOW

**All discussion below is archived from the Wikispaces export in its original unaltered form.**

Please do not add any new discussion to this archive page.

All new discussion should go on Talk:MOS scale.

## 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

## MOS definition

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:

What

Is

The

Name

Of

This

Scale?

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[8]. 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[8] 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 7

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