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Message: 7800 Date: Wed, 29 Oct 2003 03:36:39 Subject: Re: Linear temperament names? From: Dave Keenan --- In tuning-math@xxxxxxxxxxx.xxxx "monz" <monz@a...> wrote:

> hi Dave and Gene, > first of all, can both of you *PLEASE* take a deep breath > and count to 10 before responding?

Done.

> anyway, aside from personality conflicts, one thing i want > to speak on is the use of vector addition. i have a very > hard time understanding why so many people here consider it > to be "advanced" math. it's just simple addition and subtraction, > and doesn't get more complicated than that unless the reader > *needs* to calculate the ratios from those exponents.

It isn't only vector addition I'm avoiding, but matrix multiplication. I deliberately don't even use the word vector, but simply "list", because the mere introduction of a new word like vector can cause people to _assume_ there's a whole lot of stuff associated with it that they will need to know, and don't. So they give up. Probably the method of fretboard optimisation I'm describing is so complex anyway that it is futile to explain it to non-mathematicians in the available space, but it's worth a try. I'm sure you agree that the main thing is to have lots of diagrams.

> i see no reason why a paper can't simply present a tuning > on a lattice diagram, with a clear explanation of how the > lattice relates to the monzos, and give the reader all the > ratio data in the form of monzos. > > *if* the reader is adventurous enough to try calculating the > ratios for himself, fine. if not, then it doesn't get any > more complicated than addition, subtraction, and comparing > results to lattice-points. that's as "dumbed down" as it gets.

Yes. If my reader is to apply my method for themselves they will need to calculate monzos from ratios, and yes I use lattice diagrams to illustrate the process.

Message: 7801 Date: Wed, 29 Oct 2003 22:28:35 Subject: Re: Linear temperament names? From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Dave Keenan" <d.keenan@b...> wrote:

> I've searched the tuning-math archive for an explanation of the name > "Unidec" and can find none. I've racked my brains for a reason.

The generator can be taken to be an 11/7, which Manuel has listed as a "unidecimal augmented fifth." It may not be a very good name, but if you think that you've waited a long time to say so.

Message: 7802 Date: Wed, 29 Oct 2003 22:33:30 Subject: Re: Linear temperament names? From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Dave Keenan" <d.keenan@b...> wrote:

> Yes. If my reader is to apply my method for themselves they will need > to calculate monzos from ratios, and yes I use lattice diagrams to > illustrate the process.

If they are going to turn monzos into octaves/generators, they will need the information a mapping matrix gives, whether or not presented as a matrix. This idea you have rejected with contempt. What to you propose as a replacement? To be sure, the information can be extracted using the generator size in cents, but that, as I pointed out, is *harder*.

Message: 7803 Date: Wed, 29 Oct 2003 08:22:16 Subject: Re: Linear temperament names? From: monz hi Dave, --- In tuning-math@xxxxxxxxxxx.xxxx "Dave Keenan" <d.keenan@b...> wrote:

> Can we please forget this octave-equivalence war for > a moment and just talk about the names. > > <snip> > > And with the "tuple" words, maybe when it gets big we just > say "29 chains of" instead.

for our software, i was trying to keep interval names as terse as possible, so i decided to trash regular words altogether, and simply use "7al" for "septimal", "11al" for "undecimal", etc. so how about "29al"? you've probably noticed by now that i *refuse* to spell out interval names, always using "2nd", "3rd", etc. i think the arabic numeral conveys the information quicker and more succinctly. -monz

Message: 7804 Date: Wed, 29 Oct 2003 22:37:34 Subject: Re: Linear temperament names? From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Dave Keenan" <d.keenan@b...> wrote:

> How did you get to be such a prick?

I didn't call names, and you began the conversation by telling me to rub it in my hair. My impression still is that you are determined not to listen to opinions other than your own.

Message: 7805 Date: Wed, 29 Oct 2003 22:42:40 Subject: Re: Linear temperament names? From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "monz" <monz@a...> wrote:

> Gene, i'm sorry but i have to agree with Dave that your > explanations are *hardly* the kind non-mathematicians can > make sense out of.

My explanations are not at issue. The question is whether the poor, unfortunate reader is going to be able to easily figure out what the temperament means. Dave apparently will give number of generator steps, periods to the octave, and generator size in cents. From this it is possible to reconstruct the mapping matrix or other means of presenting how to pass from a ratio to its image in the temperament, but why not make it easy?

Message: 7806 Date: Wed, 29 Oct 2003 23:12:43 Subject: Re: UVs for 46-ET 11-limit PB From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote:

> i grouped a few quartets of 11-limit commas together at random, and > after a couple of 72s, found that 9801:9800, 3025:3024, 441:440 and > 176:175 together give 46. then i tried multiplying and dividing pairs > of these to get simpler ratios (being sure to keep 4 linearly > independent ones at each stage); one possibility is 896:891, 385:384, > 125:126, and 176:175.

If you TM reduce this, you get the 11-limit TM basis for h46, namely [121/120, 126/125, 176/175, 245/243]. A Fokker block for this can be obtained from q[i] = (81/80)^i (121/120)^round(-19i/46) (126/125)^round(-24i/46) (176/175)^round(38i/46) (245/243)^round(31i/46) This gives the following scale: 1 [0, 0, 0, 0, 0] 55/54 [-1, -3, 1, 0, 1] 36/35 [2, 2, -1, -1, 0] 25/24 [-3, -1, 2, 0, 0] 35/33 [0, -1, 1, 1, -1] 15/14 [-1, 1, 1, -1, 0] 11/10 [-1, 0, -1, 0, 1] 10/9 [1, -2, 1, 0, 0] 198/175 [1, 2, -2, -1, 1] 25/22 [-1, 0, 2, 0, -1] 7/6 [-1, -1, 0, 1, 0] 90/77 [1, 2, 1, -1, -1] 6/5 [1, 1, -1, 0, 0] 11/9 [0, -2, 0, 0, 1] 216/175 [3, 3, -2, -1, 0] 5/4 [-2, 0, 1, 0, 0] 14/11 [1, 0, 0, 1, -1] 9/7 [0, 2, 0, -1, 0] 33/25 [0, 1, -2, 0, 1] 4/3 [2, -1, 0, 0, 0] 1188/875 [2, 3, -3, -1, 1] 15/11 [0, 1, 1, 0, -1] 7/5 [0, 0, -1, 1, 0] 140/99 [2, -2, 1, 1, -1] 10/7 [1, 0, 1, -1, 0] 22/15 [1, -1, -1, 0, 1] 875/594 [-1, -3, 3, 1, -1] 3/2 [-1, 1, 0, 0, 0] 50/33 [1, -1, 2, 0, -1] 14/9 [1, -2, 0, 1, 0] 11/7 [0, 0, 0, -1, 1] 8/5 [3, 0, -1, 0, 0] 175/108 [-2, -3, 2, 1, 0] 18/11 [1, 2, 0, 0, -1] 5/3 [0, -1, 1, 0, 0] 77/45 [0, -2, -1, 1, 1] 12/7 [2, 1, 0, -1, 0] 44/25 [2, 0, -2, 0, 1] 175/99 [0, -2, 2, 1, -1] 9/5 [0, 2, -1, 0, 0] 20/11 [2, 0, 1, 0, -1] 28/15 [2, -1, -1, 1, 0] 66/35 [1, 1, -1, -1, 1] 48/25 [4, 1, -2, 0, 0] 35/18 [-1, -2, 1, 1, 0] 108/55 [2, 3, -1, 0, -1]

Message: 7807 Date: Wed, 29 Oct 2003 15:22:07 Subject: Re: UVs for 46-ET 11-limit PB From: Carl Lumma

>If you TM reduce this, you get the 11-limit TM basis for h46, namely >[121/120, 126/125, 176/175, 245/243]. A Fokker block for this can be >obtained from > >q[i] = (81/80)^i (121/120)^round(-19i/46) (126/125)^round(-24i/46) >(176/175)^round(38i/46) (245/243)^round(31i/46)

Whoa, the makings of an intelligible method, safe to try at home. What's i? And where has 81/80 come from? The TM basis has 4 commas, which should be enough to enclose an 11-limit block. -Carl

Message: 7808 Date: Wed, 29 Oct 2003 23:50:21 Subject: Re: Linear temperament names? From: Dave Keenan --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote:

> --- In tuning-math@xxxxxxxxxxx.xxxx "Dave Keenan" <d.keenan@b...> wrote: >

> > I've searched the tuning-math archive for an explanation of the name > > "Unidec" and can find none. I've racked my brains for a reason.

> > The generator can be taken to be an 11/7, which Manuel has listed as > a "unidecimal augmented fifth." It may not be a very good name, but if > you think that you've waited a long time to say so.

Sorry about that. I guess I was just too busy with other things like work, family and sagittal, around the time you were posting lists of 11-limit LTs. But it isn't as if lots of people are already using the name, so I don't see a problem with changing it. If I use names in my paper that are only my own construction, I will indicate this. But that doesn't include where I might merely change a hemiwuerschmidt to semiwuerschmidt or trikleismic to triple kleismic. I can't see these causing any confusion. By the way, I have credited you and Graham as follows. Please let me know if this is not accurate: Actually finding the linear microtemperaments with the lowest complexity for a given set of ratios, was extremely difficult until very recently. In mid 2001, prompted by the rediscovery of the Miracle temperament, both Graham Breed and Gene Ward Smith wrote computer programs to search for potentially useful linear temperaments – those having the lowest complexity for a given range of error sizes. Graham Breed has made this extraordinary facility available free online for anyone to use at Linear Temperament Finding Home * [with cont.] (Wayb.). Gene's software uses a different method to generate temperament candidates for testing, and has served as a very important check that Graham's algorithm is not missing anything important.

Message: 7809 Date: Wed, 29 Oct 2003 15:54:00 Subject: Re: Linear temperament names? From: Carl Lumma

>I might merely change a >hemiwuerschmidt to semiwuerschmidt or trikleismic to triple kleismic. >I can't see these causing any confusion.

Use a little imagination. -Carl

Message: 7810 Date: Wed, 29 Oct 2003 17:15:21 Subject: Re: Linear temperament names? From: Carl Lumma

>> >I might merely change a >> >hemiwuerschmidt to semiwuerschmidt or trikleismic to triple kleismic. >> >I can't see these causing any confusion.

>> >> Use a little imagination.

> >Would you care to explain what you mean by that cryptic remark?

Sorry, it wasn't meant to be cryptic.

>Do you mean that you think they _could_ cause confusion?

Sure. I can't count the number of times I've checked out a new subject and observed a terminology difference that wasn't discussed anywhere. It drives me crazy wondering whether they're actually the same.

>I don't think you can accuse me of insisting on rigour or taking the >fun out of naming when I'm accepting names like miracle and magic and >catakleismic, and some based on commas like schismic and kleismic and >wuerschmidt, and others based on generators. But I think we can only >afford the luxury of totally non-descriptive names for the most common >or the best.

That makes sense. But I don't think generators sizes are important, especially re. diatonic names. We've been over this before, and it boggles me how you can support such a program. In my book commas are the way to name linear temperaments, and what we actually need is a systematic way of naming commas. Which, IIRC, you've also tried your hand at. Did it have something to do with komma and/or quoma? If so, I think that's bad, 'cause it isn't phonetic. The "a" vs. "ina" thing I thought went over better.

>If I come up with some obscure temperament and tell you I'm composing >an algorithmic piece in the "Fart" temperament. The first thing you're >going to ask me is "What's that?", and I'll say, "Oh it's generated by >three chains of generators which are one third of a major third".

And once I knew that, I wouldn't soon forget it. It's why fantastic absurdities are so common in advertising.

>But >if we had a system and I said I'm composing a piece in the >"triple-trithirds" temperament, you wouldn't even have to ask.

Oh yes I would. I haven't the foggiest idea what this means, and I hang out here regularly. Does "triple" mean three periods in an octave? And does "tri" mean 3 times the size of a third, or 1/3rd the size of a third? And is it a major or minor third? And even if you answer all these questions I won't necc. be able to get close to the optimal generator. Really a cent of resolution is needed here, or it can mean the difference between maps. -Carl

Message: 7811 Date: Wed, 29 Oct 2003 17:16:35 Subject: Re: UVs for 46-ET 11-limit PB From: Carl Lumma

>> And where has 81/80 come from?

> >81/80 is one step in 46-et.

How are we supposed to know that? -Carl

Message: 7812 Date: Wed, 29 Oct 2003 19:34:01 Subject: Re: Linear temperament names? From: Carl Lumma

>> That makes sense. But I don't think generators sizes are important, >> especially re. diatonic names. We've been over this before, and it >> boggles me how you can support such a program.

> >So when some minimally-mathematical musician wants to tune up their >synthesizer or whatever, to my new Fart temperament. I should give >them a list of six 19-limit commas and say, "Go to it bud!". Gimme a >break.

No, you should give them the size of the generator in cents, and probably the entire scale, and probably the entire fretboard, and probably the name of a good luthier. :)

>> In my book commas are the way to name linear temperaments,

> >How do you make that work past 5-limit? i.e when there are several >commas.

I was thinking of using the one that's not tempered out. Of course this can be expressed in oompteen ways. One probably just chooses the way with the lowest complexity, but I admit this weakens my suggestion somewhat.

>Go back and read from >Yahoo groups: /tuning-math/message/6875 * [with cont.] >if you want to understand my comma naming system.

>> >If I come up with some obscure temperament and tell you I'm composing >> >an algorithmic piece in the "Fart" temperament. The first thing you're >> >going to ask me is "What's that?", and I'll say, "Oh it's generated by >> >three chains of generators which are one third of a major third".

>> >> And once I knew that, I wouldn't soon forget it. It's why fantastic >> absurdities are so common in advertising.

> >You'll remember the name, but why will you remember what it _is_.

Because I have a hook.

>Did you find some association, some "reason" for the name? I didn't >intend any. I suppose all the "th" sounds in the description?

I don't think association has to be logical. At least not for me.

>> And does "tri" mean 3 times the size of a third, or 1/3rd >> the size of a third?

> >Which seems more likely given that we usually give the generator in >lowest terms, or at least significantly smaller than the octave. And >we're usually interested in how many generators make up common >consonances, not the other way 'round.

I thought you were using tertia for division, or some such.

>> And even >> if you answer all these questions I won't necc. be able to get close >> to the optimal generator. Really a cent of resolution is needed >> here, or it can mean the difference between maps.

> >That's true. But you can only pack so much information into a name. At >least it does get you in the right ballpark.

C'mon. You could just say "700 cents". But that's not much of a name. So you've got to dress it up, and make it more ambiguous in the process. Seems pretty silly to me. -Carl

Message: 7813 Date: Wed, 29 Oct 2003 19:36:12 Subject: Re: Linear temperament names? From: Carl Lumma Sorry; never put anything in here...

>>Go back and read from >>Yahoo groups: /tuning-math/message/6875 * [with cont.] >>if you want to understand my comma naming system.

Ouch. This hurts my brain. I love Paul's names, as shown on the xoomer charts. -Carl

Message: 7814 Date: Wed, 29 Oct 2003 01:38:54 Subject: Re: UVs for 46-ET 11-limit PB From: monz hi Gene, --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote:

> --- In tuning-math@xxxxxxxxxxx.xxxx "monz" <monz@a...> wrote: >

> > i tried to derive a 46-note periodicity-block > > which is a subset of this list, using our software, > > with the following unison-vectors: > > > > [ 3 -6 1 0] > > [-4 -2 0 0] (diaschisma) > > [ 2 -3 1 0] (small septimal comma) > > [ 3 -4 0 -1]

> > First Dave, and now you. Commas and any > other interval, as opposed to an octave class, > should ALWAYS be given with the correct value for 2. > Anything else simply will not do. If I was referee > for Dave's article, it would bounce like a rubber > ball until he fixed that problem.

OK, thanks for pointing that out ... but it's no big deal. here is the matrix of unison-vectors with the exponents of 2 included. ... and also note that the sign for the exponent of 7 in the first comma was incorrect, which is probably why paul got a determinant of 14 rather than 46. 2 3 5 7 11 [ 12 3 -6 -1 0] [ 11 -4 -2 0 0] (diaschisma) [ 1 2 -3 1 0] (small septimal comma) [ 8 3 -4 0 -1] -monz

Message: 7815 Date: Wed, 29 Oct 2003 01:44:58 Subject: Re: UVs for 46-ET 11-limit PB From: monz hi paul, --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote:

> --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> > wrote:

> > --- In tuning-math@xxxxxxxxxxx.xxxx "monz" <monz@a...> wrote: > >

> > > i tried to derive a 46-note periodicity-block > > > which is a subset of this list,

> > > > of course, *any* 46-note subset which has each of > > the 46-equal degrees exactly once is already a > > periodicity block . . .

right, i know that ... but i deliberately left in the duplicates and triplicates to see what you, Gene, et al would come up with.

> > (by the way, i don't agree with your reckoning of > > "equally close" . . .)

i know ... you use the hexagonal reckoning rather than the rectangular one i used. i considered doing that from the start, but it was just easier for me to do the one i did since i'm still using Excel for this kind of stuff.

> >

> > > using our software, > > > with the following unison-vectors: > > > > > > [ 3 -6 1 0] > > > [-4 -2 0 0] (diaschisma) > > > [ 2 -3 1 0] (small septimal comma) > > > [ 3 -4 0 -1] > > > > > > > > > and the software gave me a nice 46-note > > > periodicity-block, but it was entirely > > > in the [3,5]-plane.

> > > > the determinant of this matrix is 14, so i'm not sure how you're > > getting a 46-note periodicity block out of it!

a sign in the first comma was reversed. its complete [2,3,5,7,11]-monzo should be [12 3 -6 -1 0] . see my post to Gene.

> i grouped a few quartets of 11-limit commas together > at random, and after a couple of 72s, found that > 9801:9800, 3025:3024, 441:440 and 176:175 together > give 46. then i tried multiplying and dividing pairs > of these to get simpler ratios (being sure to keep > 4 linearly independent ones at each stage); one > possibility is 896:891, 385:384, 125:126, and 176:175. > the matrix of these: > > -4 0 1 -1 > -1 1 1 1 > -2 3 -1 0 > 0 -2 -1 1 > > now i looked at the periodicity block defined by the > unit hypercube lying between 0 and 1 (instead of the > usual -.5 and .5) along each of the four transformed > coordinate axes using the matrix above: > > numerator denominator > 55 54 > 33 32 > 25 24 > 16 15 > 275 256 > <etc., snip> > > this has plenty of ratios with factors of 7 and 11 -- > hopefully it's close to what you need!

thanks ... but it would be easier for me to tell if instead of ratios the notes had already been factored into monzos. if anyone else cares to do it for me, that would be nice! ;-) -monz

Message: 7816 Date: Wed, 29 Oct 2003 01:57:51 Subject: Re: Linear temperament names? From: monz hi Dave and Gene, --- In tuning-math@xxxxxxxxxxx.xxxx "Dave Keenan" <d.keenan@b...> wrote:

> --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> > wrote: >

> > How can you simultaneously maintain you are dumbing down > > *and* increase the number of mathematical hoops you expect > > your readers to jump through? If you want to make things > > easy, you are going about it in a very, very bad way.

> > You have absolutely no idea how I am going about it. > All you know is the format in which I am tabulating the > mappings. I have to say, you would be the last person > I would ask for advice on explaining things to > non-mathematicians. > > <snip> >

> > > So when the period _is_ the octave these are all zero > > > and I prefer to omit them. It's easier to omit them > > > without confusion if they come _last_. I do not > > > want to use any vector or matrix math in the article.

> >

> > > It's pitched at an audience with more basic math skills.

> > > > So that is why you insist on making the math difficult??

> > Again you have no idea what math I'm using, so I don't > know where you get off with this sort of arrogant nonsense. > > <snip> >

> > What is this--pledge week for microtonalists? If they > > understand your article without the secret decoder ring > > they are in? In any case sloppy is sloppy.

> > How did you get to be such a prick?

first of all, can both of you *PLEASE* take a deep breath and count to 10 before responding? and if you're still angry, turn off the computer and respond later. it would be stupid if you pissed each other off any further. just cool it, please. there *are* valuable comments being made in this discussion. Gene, i'm sorry but i have to agree with Dave that your explanations are *hardly* the kind non-mathematicians can make sense out of. i know that when you post a list of data output from your programs, it's valuable information. but your presentation of it is so cryptic that if i haven't read every single word posted to that thread, i don't have the foggiest idea what those lists of numbers mean, and i simply file it away for "future reference" ... and unfortunately have yet to reach the future in which i can understand it. anyway, aside from personality conflicts, one thing i want to speak on is the use of vector addition. i have a very hard time understanding why so many people here consider it to be "advanced" math. it's just simple addition and subtraction, and doesn't get more complicated than that unless the reader *needs* to calculate the ratios from those exponents. i see no reason why a paper can't simply present a tuning on a lattice diagram, with a clear explanation of how the lattice relates to the monzos, and give the reader all the ratio data in the form of monzos. *if* the reader is adventurous enough to try calculating the ratios for himself, fine. if not, then it doesn't get any more complicated than addition, subtraction, and comparing results to lattice-points. that's as "dumbed down" as it gets. -monz

Message: 7817 Date: Wed, 29 Oct 2003 02:53:48 Subject: Re: Linear temperament names? From: Carl Lumma

>For musical types octave-equivalence is a given.

It is?

>I was asking for help with the names. That's all. You have chosen >not to explain your proposed names, or point me to earlier >explanations, instead going on with this ridiculous rant.

Didn't he say he uses names because they have already been used? -Carl

Message: 7818 Date: Wed, 29 Oct 2003 03:11:56 Subject: Re: Linear temperament names? From: Dave Keenan I'm sorry about that last message. I lost it. But you do seem to have that effect on people, Gene. :-) I should have waited a bit longer before hitting the send button. You won't believe this, but within minutes of me sending that message I got a phone call from my mum (mom) telling me about this book she had just been reading on non-agressive communication! Freaky. Can we please forget this octave-equivalence war for a moment and just talk about the names. I've searched the tuning-math archive for an explanation of the name "Unidec" and can find none. I've racked my brains for a reason. I assume it is an abbreviation for "unidecimal" which means relating to the number 11. It doesn't give rise to an 11 note DE scale so it can't be that. It's generator can be described as an approximation to 7:11, but it can also be described as 11:14 or 5:9 or 9:10, so that doesn't seem like a good reason. It is a good 11-limit temperament, but so are many others, so that doesn't seem like a good reason. "Twin minortones" sure looks like a better name to me. And I'm interested in your responses (and those of anyone else) to the other questions I raised regarding prefixes for multiple chains (fractional-octave periods) versus prefixes for generators which are fractions of common intervals or other named generators. I suggest for the former: twin (or double), triple, quadruple, quintuple, sextuple, septuple, octuple, nonuple, decuple, undecuple, duodecuple, etc. (as separate words, not prefixes), and for the latter: semi-, tri-, quarter-, penta-, hexa-, hepta-, octa-, ennea-, deca-, undeca-, dodeca- etc. as actual prefixes. Hopefully most of these will be very rare, except semi-. There is of course a problem with tri- penta- etc. since these usually mean multiples instead of fractions, but there's a worse problem with third, fifth etc, since these usually refer to intervals. But I suggest that third- fifth- etc should be used in place of tri- penta- etc when applied to the word "tone". And with the "tuple" words, maybe when it gets big we just say "29 chains of" instead.

Message: 7819 Date: Thu, 30 Oct 2003 16:33:43 Subject: Re: UVs for 46-ET 11-limit PB From: Manuel Op de Coul Gene wrote:

>namely

> >[121/120, 126/125, 176/175, 245/243]. A Fokker block for this can

I found this one too, but thought it was too uneven. Paul's block is better in that regard. I wonder though if an 11-limit 46-note PB in which the four primes occur and which is strictly proper exists. Manuel

Message: 7820 Date: Thu, 30 Oct 2003 16:28:29 Subject: Re: UVs for 46-ET 11-limit PB From: Paul Erlich that does look more like what monz wanted, hope he takes a look. --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote:

> --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...>

wrote:

>

> > i grouped a few quartets of 11-limit commas together at random,

and

> > after a couple of 72s, found that 9801:9800, 3025:3024, 441:440

and

> > 176:175 together give 46. then i tried multiplying and dividing

pairs

> > of these to get simpler ratios (being sure to keep 4 linearly > > independent ones at each stage); one possibility is 896:891,

385:384,

> > 125:126, and 176:175.

> > If you TM reduce this, you get the 11-limit TM basis for h46, namely > [121/120, 126/125, 176/175, 245/243]. A Fokker block for this can be > obtained from > > q[i] = (81/80)^i (121/120)^round(-19i/46) (126/125)^round(-24i/46) > (176/175)^round(38i/46) (245/243)^round(31i/46) > > This gives the following scale: > > 1 [0, 0, 0, 0, 0] > 55/54 [-1, -3, 1, 0, 1] > 36/35 [2, 2, -1, -1, 0] > 25/24 [-3, -1, 2, 0, 0] > 35/33 [0, -1, 1, 1, -1] > 15/14 [-1, 1, 1, -1, 0] > 11/10 [-1, 0, -1, 0, 1] > 10/9 [1, -2, 1, 0, 0] > 198/175 [1, 2, -2, -1, 1] > 25/22 [-1, 0, 2, 0, -1] > 7/6 [-1, -1, 0, 1, 0] > 90/77 [1, 2, 1, -1, -1] > 6/5 [1, 1, -1, 0, 0] > 11/9 [0, -2, 0, 0, 1] > 216/175 [3, 3, -2, -1, 0] > 5/4 [-2, 0, 1, 0, 0] > 14/11 [1, 0, 0, 1, -1] > 9/7 [0, 2, 0, -1, 0] > 33/25 [0, 1, -2, 0, 1] > 4/3 [2, -1, 0, 0, 0] > 1188/875 [2, 3, -3, -1, 1] > 15/11 [0, 1, 1, 0, -1] > 7/5 [0, 0, -1, 1, 0] > 140/99 [2, -2, 1, 1, -1] > 10/7 [1, 0, 1, -1, 0] > 22/15 [1, -1, -1, 0, 1] > 875/594 [-1, -3, 3, 1, -1] > 3/2 [-1, 1, 0, 0, 0] > 50/33 [1, -1, 2, 0, -1] > 14/9 [1, -2, 0, 1, 0] > 11/7 [0, 0, 0, -1, 1] > 8/5 [3, 0, -1, 0, 0] > 175/108 [-2, -3, 2, 1, 0] > 18/11 [1, 2, 0, 0, -1] > 5/3 [0, -1, 1, 0, 0] > 77/45 [0, -2, -1, 1, 1] > 12/7 [2, 1, 0, -1, 0] > 44/25 [2, 0, -2, 0, 1] > 175/99 [0, -2, 2, 1, -1] > 9/5 [0, 2, -1, 0, 0] > 20/11 [2, 0, 1, 0, -1] > 28/15 [2, -1, -1, 1, 0] > 66/35 [1, 1, -1, -1, 1] > 48/25 [4, 1, -2, 0, 0] > 35/18 [-1, -2, 1, 1, 0] > 108/55 [2, 3, -1, 0, -1]

Message: 7821 Date: Thu, 30 Oct 2003 16:54:01 Subject: Re: Linear temperament names? From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:

> In my book commas are the way to name linear temperaments,

even 13-limit linear temperaments? that may be going too far, considering that you'd need 4 commas for each, and various reduction schemes may give different choices for which 4.

> and what > we actually need is a systematic way of naming commas.

and name the temperaments accordingly? based on the above, no thanks.

>Really a cent of resolution is needed > here, or it can mean the difference between maps.

sometimes the difference is even smaller -- look at #4 and #5 here: 4 5 6 9 10 12 15 16 18 19 22 26 27 29 31 35 36... * [with cont.] (Wayb.)

Message: 7822 Date: Thu, 30 Oct 2003 16:58:01 Subject: Re: Linear temperament names? From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:

> I was thinking of using the one that's not tempered out.

then you'll have the same name for tons and tons of them.

> I don't think association has to be logical. At least not for me.

NB this is as true for notation symbols as for names!

Message: 7823 Date: Thu, 30 Oct 2003 09:33:34 Subject: Re: UVs for 46-ET 11-limit PB From: Carl Lumma

>> >> And where has 81/80 come from?

>> > >> >81/80 is one step in 46-et.

>> >> How are we supposed to know that?

> >Surely you can calculate that? What are you asking?

Calculate it from what? One step of 46-et could be lots of things. Why did you pick 81:80? -Carl

Message: 7824 Date: Thu, 30 Oct 2003 09:37:01 Subject: Re: Linear temperament names? From: Carl Lumma

>> I was thinking of using the one that's not tempered out.

> >then you'll have the same name for tons and tons of them.

Didn't I say that in the following sentence? -Carl

7000
7050
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**7800**
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**7800 -**
7825 -