From: "Gene Ward Smith" <gwsmith@s> ... Something strange must have happened there. The main page loads OK but whenever I try one of the links, I'm told the...
... It's my fault. I would guess there is some kind of website utility which tells you if you have broken links; I'll look for it. Strangely enough, I did add...
. .. .. .. .. .. .. .. .. .. .. Weekly Tuning Community Honor Awards .. last Sunday of every week! .. This week's winner: John Chalmers, for publishing...
... Great work, Gene. A few comments... "" Subsequent commas of the comma sequence are such that the wedge product of these commas is reduced, in the sense...
... That's delightful! Is a full family tree forthcoming? And, I was wondering, would it be constructive for someone to make a big picture of these "middle...
Hi Herman, I'm glad someone's still thinking about this stuff. Good work. I think that it will be very difficult to remember the relative pitch relationships,...
hi Gene, ... wow, i love it! you've suddenly gone all the way round from the abstract mathematical jargon to the most colorful everyday analogy. this is...
Pitch order: O H A P I B Q J C R K D S L E T M F U N G V(O) 7 fifth nominals: F C G D A E B 7 minor-third nominals: E# G# B D F Ab Cb becomes T V B D F...
hi Jacob, ... i don't know how "full" it is ... i'm sure Gene and the others will keep discovering new long-lost relatives! but anyway, i've made a family-tree...
Hi Jacob! ... Erv Wilson's "straight line patterns of the scale tree" shows something like this, except IIRC he only shows octave periods and he isn't talking...
... There were some which didn't get mentioned; there's always this question of when to stop, and what limit to go to. ... Neat! I'd at least add Uncle Injera,...
... This violates one of your rules for comma sequences. I'm guessing you did that to keep from breaking one of the other rules? What's going on here? -Carl...
... The most obvious place to draw the line is at the pivot. From two sister linear temperaments you can define an equal temperament for the next lower prime...
... Why an et? I would have thought they defined a temperament of the same rank (or codimension or whatever we're calling it) as the sisters themselves. For...
This might-should be updated... http://tonalsoft.com/enc/pivot-et.htm ...given the recent thread, it doesn't seem the originating temperaments must be linear,...
... It doesn't violate any of the rules, it violates the claim that there is a unique 5-limit comma for any linear temperament. This is only usually true; I've...
... It seems to be this entire paragraph is violated... "" A comma sequence defines a temperament by means of a sequence of uniquely determined commas at...
... Because we need to draw a boundry. I would have thought they defined a temperament of ... That gives the mother of the two sisters. ... You could for...
... Let's not hurry into this. ***Math warning*** One way to understand this pivot business is that the pivot is determined by the nullspace of the union of...
I think perhaps a better way to write the comma sequence for James Bond would be [1, {25/24, 81/80}]. I think now I'll rewrite the definition of comma sequence...
hi Carl, ... ok, well ... i'm not one of the experts on linear temperaments around here (except for 5-limit meantone). so i defer to others to give me the...
... Hmm... there's not much room between E=9/8 and F=32/27 for two steps, especially if the scale needs to be proper. Maybe F could be 6/5 and E could be...
... This agrees with what I have for kleismic. ... Right. ... I'd say either the 7 or the 13, to be consistent with the 22-ET interpretation (since 22 is also...
... steps, ... OK. Scratch propriety. But maintain pitch order. Or another way of looking at it might be, when E and F get that close together, you have to...
