chopi and otherwise

besides Erv's mavila, i personally found that the following recurrent sequence does remarkably well in terms of many african balophones in the near 7 equal range.
A+B=E, as found in Meru # 5. also called Meta Ptolemy.
generator (when converged) = .287760787077=345.31294449 cents.
As the most interesting scales of the recurrent sequences tend to be those before it actually converges a subjective observation by actually using said objects), it works quite well and illustrates the capacity to tune such animals by ear.
the chart included shows in application to a real object.
Tuning by Venancio Mbande from southern Mozanbique
Being the one of the last, if not the last chopi tuner in Vibrations per second, being way they are heard, since no one hears in cents ( except Johnny!). interestingly when applying recurrent sequence analysis to the slendros found in kunst, there was also a tendency to be in the neighborhood of being two v.p.s. sharp. whether this is caused to do to some stretching of the harmonics in the bars impossible to say without really looking. but would be the first one i would try.
Note No. Herz
1'' 1004
7' 924
6' 843
5' 756.2
4' 691.1
3' 616.2
2' 562
1' 508.7
7 462
6 418.6
5 375.6
4 341
3 307
2 278.7
1 253.8
7, 230
6, 207.5
5, 188
4, 170
3 153

153+188=341!
170+207.5=377.5 1.9 sharp
188+230=418 .6 flat
207.5+253.8=461.3 .7 flat
230+278.7=508.7!
253.8+307=560.8 1.2 sharp
278.7+341=619.7 3.5 sharp
307+375.6=682.6 8.5 flat not good at all
341+418.6=759.6 3.4 sharp
375.6+462=837.6 5.4 flat ?
418.6+508.7=927.3 3.3 sharp
462+562=1024 /2 512 3.3 sharp
508.7+616.2=1124.9 /2=562.45 .45 sharp
562+691.1=1253.1 /2=626.55 not good at all
616.2+756.2=1372.4 /2= 686.2 4.9 flat not good at all
691.1+843= 1534.1 /2= 767.05 10.85 sharp not good at all
756.2+924=1680.4 /2= 840 3 flat
843+1004=1847 /2= 923.5
924
1004

(this evaluation is very critical, beyond what one might consider acceptable tolerances, but maybe more might be gained if others took similar approach as opposed to giving the impression that the
answers have been found)

Now all the measurements that are bad involve 4' 691.1. Now if this pitch would
have been originally been
tuned to 682.6 as the pattern would imply and a sliver fell off or whatever caused it
to raise in pitch we would
have for the top of the instrument the following;

562+682.6=1244 /2=622 6.1 sharp??
616.2+756.2= 1372.4 /2= 686.2 3.6 sharp
682.6+843= 1525.6 /2=762.8 6.6 sharp ????
Better but no cigar if the original pitch could have been even a little higher or
halfway between the present pitch
it would fit.

there could be genuine musical reasons for having this pitch out, since much of their tuning is based on speech ( just like partch did latter on) and the inflection might be of not such a pleasant nature)
these comments on tolerances are not meant as "answers , as much as possible line of inquiry to fluctuations.

Erv called his original series on this Meta Ptolemy because one of his first seedings of it were 10-12-15-18-22-27-33-40. Stephan Taylor had me tune a diatonic set of wooden bars to this for use as an african scale.
-- Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles