... The 179/306 convergent gives rise to my favorite system, 612-et. I define 1/612 octave or 1/51 12-et semitone as a tempered schisma ($). 1C (cent) =...
... I used to just call it a schisma. Cents seem to be pretty well established, but maybe with the "$" notation this could still fly. Keeping some of the...
I've uploaded a zip file for some of these. None of the scales turned out to be epimorphic, though presumably less interesting ones could be found which are....
First let me introduce myself: I am, by profession, a professor of mathematics, and I am also an amateur musician (I play trumpet in a community concert...
... Yes, but there is a balancing act to perform when adjusting an equal-tempered scale to better fit JI: using the least squares technique, it amounts to...
... Well hello, and I hope you will stick around. What sort of mathematics would you regard as your specialties? (Sort of the same nosy question the AMS asks,...
... Now you're talking! Including thirds is absolutely crucial to common-practice music. It makes little sense to ignore thirds and sixths if you are going to...
... I didn't read carefully what you wrote the first time through, and missed that you were working with the 3-limit, and with the fourth, fifth and octave in...
Inspired, if that is the word, by the 14-note blocks with 2048/2025 and 2048/1875 as boundries, which worked out nicely for marvel tempering, I decided to...
Here are the two blocks with the greatest number of (breed tempered) ontonal tetrads resulting from 40353607/4000000 and 40960000/40353607. The commas are...
Dear professor, I agree with Gene Ward Smith's last comments, even though I know that the Western ear for the past century and a half inclines more favorably...
My library of useful tempering functions isn't set up for the 3-limit, because it's just too darn simple. So I may have this wrong, but I get a 0.6 cent...
Let me try to answer as many of the replies as I can in one note: ... My grad school specialty was logic and set theory (advisor was Jim Baumgartner at...
... 3-limit TOP tuning is 0.617 cents, so this agrees. I haven't calculated any least-squares values since I don't know the weighting. ... It seems to me that...
... Ken Ribet at Berkeley here. Have you ever run into the phase "musical set theory", by the way? but in recent years most of my ... Java is a wonderful...
... No, but I'd like to hear of any tuning-math stuff discussed there. ... So are you suggesting there may be a first-order statement of RH in which it is true...
... This isn't really the place for this discussion, but let me just clear up my question a bit. In order for PD to really apply, I would need a statement of...
... backing. ... http://www.mmk.e-technik.tu-muenchen.de/persons/ter/top/scalestretch.html ... Thanks for the link -- that is yet another approach. The...
... that. It's stateable in Peano arthmetic, and I suspect there's a proof out there which does not require any extra set theoretical assumptions. But then,...
... Couldn't you guess what weighting makes sense, and then act surprised if you guessed wrong? Oh, all right then. Weight by the size of the prime interval...
... You're right -- Phrygian mode (E to E on the white keys) computing using the entire scale in the least squares, but unweighted, gave me a shrink of 3.39...
My recollection is that Prof. A.D. Fokker proposed a slightly shrunk 31-tet octave from similar considerations, but I'd have to look up the exact reference. ...
... TOP tuning for 31 is the same in the 5, 7, and 11 limits, and has the octave stretched. Given the flat fifths, this isn't surprising. The stretch is 1.47...
... <gwsmith@s...> ... Just wondering, do you ever get orthogonal vectors when you derive two commas for say, a 7-limit linear temperament? I looked on you ...
... An example would be the Pontiac temperament, where the TM basis is {2401/2400, 65625/65536}. I looked on you ... There certainly are advantages to Fokker...
... derive ... having ... the ... Interesting. Does this also tie into orthogonal projection, where you make the comma(s) disappear? (I need to review that...
... you ... I recalculated for all of the modes (except the hyper- ones), and this is what I got -- first number is unweighted, second is weighted with double...
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