Still curious to see if Gene might approve of this idea, which will surely revolutionize our naming system and thus possibly our field, and then potentially...
Steinhaus showed that with a single generator, on cannot have more than 3 size intervals, most of theserepeat two sets of intervals too. -- /^_,',',',_...
... It's just popped in my mind because I've been experimenting with multiples of 25/24, 128/125, 81/80. If I'm not mistaken, 12l + 7m + 3s then gives 2/1. ...
He's saying that a scale formed by a generator which isn't an MOS will have three step sizes at most and never more than that. It's called the Three Gap...
Thanks (Mike) for bringing this up. Back in December I suggested something called kernelnaming might solve these problems. Graham sent me a dump of his...
Basically one only has to find the set of any three numbers that add up to the number of tones one wants in the scale. for instance if we want 9 tones we have...
... This includes a lot of 'dupes' like (-4 1 1) & (4 -1 -1). These get the same under my proposal http://groups.yahoo.com/group/tuning/message/102083 But...
Last post, continued from http://groups.yahoo.com/group/tuning/message/104670?var=0 So, Hermite bases may be better for this than LLL bases. ... These names...
... Sorry, I attached my replies to a weird spot in this thread. I generally agree that prime limits should be privileged subgroups and that names should show...
Mainly I think the names coming out of my spreadsheet are too consonanty. I did a quick scan of the trivial names and didn't see too many things I couldn't...
... Interesting! I think it's a neat idea, although I admit it I'd like it better if the syllables were a bit smoother. Then again, I'm all for changing...
... The Hermite sequence always works, so if we agree on that then we're done. But the original definition uses builds the sequence iteratively with TM...
... Hurrah. So then, keeping in mind with that, then one common objection is that sometimes people don't want temperaments to share names, like 2.3.5.7...
... I'm not sure if this is what you want; it's Hermite form with the columns reversed. For instance, this maps {81/80, 126/125} to {81/80, 59049/57344}. It's...
... Depends what we mean by extension. I think people are using "2.3.5 meantone" and "2.3.5.7 meantone" to refer to different rank 2 temperaments. In my...
... Yeah, you're talking about extensions that preserve codimension and alter rank; I was talking about extensions that preserve rank and alter codimension....
... There seems to be a tradeoff between the max complexity of the commas in the sequences and having related temperaments share the beginnings of their...
... That's basically what's happening now. It does have some things going for it. What on Graham's list are you objecting to? Just the clever alternate...
