meantone tunings with beat synchrony; meta-meantone

again, it seems to me that if one wants to acheive as much beat
synchrony as possible, one would base one's tuning system on the
overtone series of a "subsonic" fundamental which would be the lowest-
common-denominator beat rate.

this seems to be what kraig grady did here:

http://www.anaphoria.com/chordpod.gif

btw, this does not agree with the meta-meantone given in the scala
archives:

! metamean.scl
!
Erv Wilson's Meta-Meantone
tuning
12
!
69.413 cents
191.261 cents
260.674 cents
382.522 cents
504.370 cents
573.783 cents
695.630 cents
765.043 cents
886.891 cents
956.304 cents
1078.152 cents
2/1

a third guess is found at http://www.harmonics.com/lucy/lsd/mean.html

who's right? how is meta-meantone defined?

--- In tuning@yahoogroups.com, "wallyesterpaulrus <wallyesterpaulrus@y...>" <wallyesterpaulrus@y...> wrote:

From the analyis I gave on tuning-math, if you want to get
as much synchronicity for 5-limit chords as possible, you
choose from a small list of "magic" q-values for q-comma meantone;
for example, 1/4-comma, 2/7-comma, 5/18-comma etc.

Let's pick on 2/7-comma for an example. This has a major beat
ratio "b" of about -3/2, and a minor beat ratio "c" of about -1;
where if f, t, m are the fifth, major third and minor third respectively, then b = (6t-5f)/(4t-5) and c = (5m-6)/(5m-4f) =
b/f. If we take the average of the fifth we get from b=-3/2 with the fifth we get from -1, we get a fifth (algebraic of degree 16) which is
indistinguishable from 2/7-comma meantone, differing by
1.9729 x 10^(-7) cents. Even the sternest advocate of exact tuning might be willing to concede there is no discernable difference between this and 2/7-comma. Incidentally, it is in terms of the minor triads, not the major ones, that 2/7-comma meantone really stands out,
with all of its beat rations the same.

Paul wrote:
>again, it seems to me that if one wants to achieve as much beat
>synchrony as possible, one would base one's tuning system on the
>overtone series of a "subsonic" fundamental which would be the lowest-
>common-denominator beat rate.

I don't see how this can be done without losing a major
portion of the equal beating relationships.

>btw, this does not agree with the meta-meantone given in the scala
>archives:

I seem to remember that meta-meantone is Erv's term for equal
beating meantones, so there isn't a single one. It's better if I
remove that scale from the archive. It's a duplicate mode anyway.

Manuel