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Message: 11401 Date: Fri, 16 Jul 2004 01:14:23 Subject: Re: Naming temperaments From: Carl Lumma >The name starts with a word for the number of periods per octave, >if more than one: twin, triple, quadruple, quintuple, 6-fold, >7-fold, .... > >And then the generator is described in terms of the simplest >n-odd-limit consonance (from the diamond) (or its octave inversion >or extension, as required). That is the one that takes the fewest >generators to approximate according to the LTs mapping. > >I use the following words if there is more than one generator to >the consonance: semi, tri, quarter, 5-part, 6-part, .... How do you choose a period/generator representation? -Carl
Message: 11405 Date: Fri, 16 Jul 2004 04:03:06 Subject: Re: Beep and bug From: monz --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote: > The 13-limit temperament 4&9 is a 13-limit extension > of 7-limit beep with TM basis {27/25, 21/20, 33/32, 65/64}. > It has mapping given by > > [<1 2 3 3 3 3|, <0 -2 -3 -1 2 3|] this is great -- a model of how to describe a temperament. i only wish there was a way to distinguish between the periods and the generators without labeling them. -monz
Message: 11406 Date: Fri, 16 Jul 2004 20:15:05 Subject: Re: Naming temperaments From: Carl Lumma At 06:37 PM 7/16/2004, you wrote: >--- In tuning-math@xxxxxxxxxxx.xxxx "Carl Lumma" <ekin@l...> wrote: >> >The name starts with a word for the number of periods per octave, >> >if more than one: twin, triple, quadruple, quintuple, 6-fold, >> >7-fold, .... >> > >> >And then the generator is described in terms of the simplest >> >n-odd-limit consonance (from the diamond) (or its octave inversion >> >or extension, as required). That is the one that takes the fewest >> >generators to approximate according to the LTs mapping. >> > >> >I use the following words if there is more than one generator to >> >the consonance: semi, tri, quarter, 5-part, 6-part, .... >> >> How do you choose a period/generator representation? > >You don't have to. You just base it directly on the map -- any map >that's valid. i.e. the generator doesn't have to be in lowest >(period-reduced terms). So there'll be multiple names for each temperament? >For any of the ET/MOS/DE-based names you need to choose specific >values of period and generator. In most cases, different kinds of >optima do not change the period and generator enough to make much >difference, but I just found that while minimax and RMS versions of >5-limit Diminished can be described as 12&16-LT or 12&28-LT, the TOP >version cannot. It could be described as 12&20-LT or 12&32-LT but 20 >and 32 are not 5-limit consistent, so the best you can do >is 8&12-LT. I think that's why Gene is proposing to use ETs that represent the extreme ranges of the generator. >Back to the map-based method. > >The map tells you how many periods to the octave. That's all you >need to know about the period to know whether the temperament is >twin or triple etc. What about temperaments that map 2 through a combination of both the "period" and generator? >For the rest of it, lets look at the simplest case first -- an LT >with one period to the octave, and one generator to some prime. i.e >there's a "1" (or a "-1") there staring at you from one of the >generators-per-prime slots. > >If the 1 is in the prime-3 slot then it's "fourths". I'll say more >later about differentiating multiple temperaments having the same >name of generator. Hmm... I thought one could refactor these maps is several annoying ways. Thus, the reason for something called hermite normal form -- whatever that is. -Carl
Message: 11410 Date: Sat, 17 Jul 2004 01:37:49 Subject: Re: Naming temperaments From: Dave Keenan --- In tuning-math@xxxxxxxxxxx.xxxx "Carl Lumma" <ekin@l...> wrote: > >The name starts with a word for the number of periods per octave, > >if more than one: twin, triple, quadruple, quintuple, 6-fold, > >7-fold, .... > > > >And then the generator is described in terms of the simplest > >n-odd-limit consonance (from the diamond) (or its octave inversion > >or extension, as required). That is the one that takes the fewest > >generators to approximate according to the LTs mapping. > > > >I use the following words if there is more than one generator to > >the consonance: semi, tri, quarter, 5-part, 6-part, .... > > How do you choose a period/generator representation? You don't have to. You just base it directly on the map -- any map that's valid. i.e. the generator doesn't have to be in lowest (period-reduced terms). And you don't have to decide on specific optimum values of period and generator. That's the beauty of it. For any of the ET/MOS/DE-based names you need to choose specific values of period and generator. In most cases, different kinds of optima do not change the period and generator enough to make much difference, but I just found that while minimax and RMS versions of 5-limit Diminished can be described as 12&16-LT or 12&28-LT, the TOP version cannot. It could be described as 12&20-LT or 12&32-LT but 20 and 32 are not 5-limit consistent, so the best you can do is 8&12-LT. Similarly the minimax and RMS versions can be called 4/16-oct, 8/28- oct, 12/40-oct, ... but the TOP version cannot. It has to be 4/12- oct, 8/20-oct, 12/32-oct, .... Notice that I have not reduced these fractions to lowest terms. This lets you extract the number of periods per octave as the GCD of numerator and denominator. Back to the map-based method. The map tells you how many periods to the octave. That's all you need to know about the period to know whether the temperament is twin or triple etc. For the rest of it, lets look at the simplest case first -- an LT with one period to the octave, and one generator to some prime. i.e there's a "1" (or a "-1") there staring at you from one of the generators-per-prime slots. If the 1 is in the prime-3 slot then it's "fourths". I'll say more later about differentiating multiple temperaments having the same name of generator. If the 1 is in the prime-5 slot then it's "major thirds" or just "thirds" (assuming the convention that if it's not explicitly called minor or neutral or anything else, then it's major). If the 1 is in the prime-7 slot then it's "supermajor seconds". If the 1 is in the prime-11 slot then it's "super fourths". If there is 1 or -1 generators to more than one prime then you give them both, as in "fourth thirds". If there is no 1 or -1 _directly_ as entries in the generator mapping, then you look for two entries which differ by 1. e.g. Kleismic has <0 6, 5]. If the difference of 1 generator is between 3's and 5's then it's "minor thirds"; between 5's and 7's it's "augmented fourths"; between 3's and 7's it's "subminor thirds"; between 3's and 11's it's "neutral seconds";", between 5's and 11's it's "narrow neutral seconds"; between 7's and 11's it's "narrow supermajor thirds". It starts to get a bit hairy with those "narrow"s and "supermajor"s and we might prefer to just give the approximated ratio. Or you might prefer to give that every time. If we're looking at 9 or 11-limit temps then we also have to double the number in the 3's slot and see if anything differs from that by 1. If the difference of 1 is between 9's and prime 5's it's "narrow major seconds", although we could probably drop the "narrow" since it unlikely we'd ever have a generator that approximates an 8:9; between 9's and prime 7's it's "supermajor thirds"; between 9's and prime 11's it's "neutral thirds". Again if there's more than one, list them all, e.g. "minor major thirds". If you can't find any 1's or differences of 1 then go looking for 2's or differences of 2, in exactly the same way, and put "semi" in front of whatever you find. If no 2's then 3's and put "tri" or "tripartite" or "3-part" (I used to say "tertia") in front. If the n-limit diamond ratio with the fewest generators has 4 generators then put "quarter" in front. After that "5-part", "6- part" etc. But you also have to check that you're describing the correct octave inversion or octave extension of the diamond ratio, so that when you divide it into however many equal parts you really do get something that is a valid generator. For example if you have 1 generator to the prime-3 then you could call it fourths or fifths, but with 2 generators to the prime 3 then you have to check whether your generator is a semifourth or semififth. Only one of those will be correct. And with 4 generators to the prime-3, the generator might even be a quarter eleventh or quarter twelfth. When it comes to LTs with more than one period to the octave, you have to be a little more careful. You the have to look at the periods per prime as well as the generators per prime. You have to ensure that, as well as having the minimum number of generators, the diamond ratio being approximated has a number of periods which corresponds to an integral number of octaves, i.e. that comes to zero when taken modulo the number of periods in the octave. I note that Erv Wilson uses this kind of terminology for LTs, at least "semifourths" and "semififths".
Message: 11413 Date: Sat, 17 Jul 2004 03:34:56 Subject: Re: Naming temperaments From: Dave Keenan --- In tuning-math@xxxxxxxxxxx.xxxx Herman Miller <hmiller@I...> wrote: > > Right. But why _is_ this 11/27 and not 20/49? > > It could be either one: a 27-note scale with an approximate 11/27 > generator or a 49-note scale with an approximate 20/49 generator. But a > 27-note scale is simpler, and it's good to have an idea of the simplest > useful scale associated with a temperament. Note that in the 11- limit > these represent different temperaments: > > 11/27 [<1, 2, 6, 2, 1|, <0, -1, -9, 2, 6|] > 20/49 [<1, 2, 6, 2, 10|, <0, -1, -9, 2, -16|] It's not only different limits that cause this sort of problem, it's also different optimisation criteria at the same limit. TOP and minimax-beat-rate are two extremes that will sometimes give generators so different as to correspond to different ET/MOS/DEs. Any time the generator happens to be very close to some small- denominator fraction of an octave this will be a problem, e.g. with 5-limit Diminished, as I mentioned in another post in this thread. Is there any way we are ever going to agree on which octave fraction is most representative of the temperament. It seemed like Gene was nailing that down somewhat with p-optimal, but then along came TOP (or was it copoptimal? -- I have no idea what that is). > 4/46 gives you [<2, 3, 5, 7|, <0, 1, -2, -8|], not pajara (see > http://www.microtonal.co.uk/diaschis.htm *). Oops. Sorry. That should have been 8/46. But even so, that's only good for "5-limit pajara" or diaschismic. My question was whether we all agree we should use the smallest possible value of the generator ( the one that's less than half the period) in these octave-fraction-type names? I note that Paul is not doing this in his paper when he gives generators in cents. He is using whatever falls out of a simple algorithm for deriving the mapping from a set of vanishing commas. I note that the number of periods per octave can be obtained as the GCD of numerator and denominator, since we won't be reducing an octave fraction like 8/46. > Pajara is historically associated with 22-ET, of course. But you can > think of the denominator as representing the size of a typical MOS scale > associated with the temperament, rather than an ET. In that case, the > minimum is 10 steps, which matches Paul's decatonic scale. As I've said elsewhere, in the two-ET/MOS/DE method (the two- cardinalities method?) of naming, I'd like the two numbers to give the denominators of two convergents (or semi-convergents) of the generator as an octave fraction, such that one is near the minimum useful generator size and the other is near the maximum. It would be ideal if you could also obtain the typical MOS/DE cardinality by subtracting these two numbers, and obtain a good approximation of an optimum generator by adding them. For example, calling meantone the "12&19-LT" works perfectly. 12-ET and 19-ET are very near the extreme generator values re "harmonic waste". The typical MOS cardinality is 19-12 = 7, and a near optimum occurs at 12+19 = 31-ET. I think at least one of the two numbers should be a convergent, i.e. it should give the cardinality of a Rothenberg-proper MOS/DE for most optimum generator sizes. > >> if you've heard of > >>"superpyth", you take one look at the name and say "Ah yes, *that* > >>temperament". You might not immediately recognize "7/31" > > > > or "9&22", but > > > > Why wouldn't you immediately recognise one of these, if that's what > > you've been used to seeing it called. > > Combinations of numbers aren't especially easy to remember. It would be > like using ZIP codes to refer to cities in the US, instead of names; > they all look alike. Don't you recognise your own zipcode and those of people you regularly send mail to, and similarly phone numbers, although these have many more digits than we're talking about here. It's more like Australian postcodes, which are only four digits. But not even as bad as that. They are generally pairs of only 2 digit numbers taken from a small set of n-limit consistent ETs, whose numbers already have many associations for us. So it's really just associating pairs of already familiar things that we're already used to representing as numbers. And they have the enormous advantage that they are not totally opaque jargon to a newcomer, as are names like sensipent, orson, amity, subchrome, wurschmidt, compton. At least when I see a postcode I've never seen before, I can immediately tell what state it's in, and sometimes I can figure out some towns I know that it must be near. > >>probably anyone who's familiar with it knows the name "orwell". > > > > That's a tautology. > > The pronoun "it" refers to the temperament represented by "7/31" and > "9&22", which happens to be named "orwell". I think it's a fairly safe > assumption that most people who've heard of this temperament will > recognize that name. Only if they have been reading the tuning lists, and even then they may only know that they seen the name but have no way of picking it out of the jargon-diarrhoea that we're swimming in. Imagine if we hadn't learnt that George Secor originally discovered "Miracle", and George Secor turned up on the list for the firs time now. How long would it take him to realise we were talking about his temperament every time we write "miracle". compared to if we were instead calling it the "31&41-LT" or the "7/72-oct-LT"? > (Certainly "19/84" is more familiar, but it implies > a greater degree of complexity, and could easily be overlooked by people > who don't care for highly complex scales.) Yes. 84-ET is outside of most people's familiarity zone. But suppose someone who had independently discovered that temperament turned up on the lists. How long would it take them to figure out "orwell" as opposed to "subminor thirds". Gene complains that some of these descriptive names are "a mouthfull". So what? How many times a day do you find yourself having to say or type them? Anyway, what's a few extra keystrokes for one person in exchange for a whole lot of extra understanding on the part of a whole lot of readers. > >>So you might as well use the name in combination with one > >>or more of the other methods, especially if it's a less familiar > > > > one > > > >>like 3/8 (1/2) 10&16 lemba <<6, -2, -2, -17, -20, 1||. > > > > > > So who needs the "lemba". It adds absolutely nothing, for me. For > > some reason it suggests "unleavened bread" to me. Huh? > > Anyone who's vaguely heard of it, but doesn't know much about it. You > might not know how to recognize a beech tree if you see one, or how it > differs from other trees, but you probably know that the word "beech" > represents a kind of tree. I don't know the mapping of "nonkleismic" off > the top of my head, and probably wouldn't recognize it if I saw it (it's > [<1, -1, 0, 1|, <0, 10, 9, 7|]), but I do recall it being (in theory) a > good temperament. "8/31" might give some idea of its usefulness, but > doesn't distinguish it from the many other "n/31" temperaments. So even > a questionable name like "nonkleismic" has some use. But "myna" is > better because it links it with the starling family of temperaments. I have been looking at "myna" in Paul's table and I never once associated it with "starling". To me it was just another random assembly of syllables. And even if I had, the name starling gives me no clues as to the identity of _that_ temperament. > Along those lines, Gene's "Japanese monster" names also provide useful > hints to similarities between temperaments. Sure, it's good to indicate similarities, but it still remains just an isolated clump of related somethings, with no clue as to what they are. The point is, we can do a lot better. We can actually have names that give someone a clue, even when they have not been initaiated into the Smith-Erlich-Miller mysteries. And in a situation where the names are a priori meaningless in musical terms, and so any one is good as another, why the heck do you guys have the need to keep changing them!!!!? It's tempting to assume it's sheer arrogance or egotism, such as I was (more or less) accused of when I wanted to use descriptive names in my Microtempered Guitar article for Xenharmonikon. So I included the cryptic/meaningless names as well, and now half of them are probably obsolete. > Why does anything have a name? Why do we talk about "major thirds" when > we could call them 5/4's? In that case, I assume it's historical. But notice that in both cases the term doesn't come from outer-space, but is descriptive, using words/symbols with something like their existing meanings. > Language works by naming things; the problem > is that the study of linear and higher-dimensional temperaments is so > new that we haven't settled on the best names for things. So in the > meantime, names which may end up being changed will have to be > supplemented by numerical keys of one kind or another. I totally disagree. I don't see any point to using musically- meaningless names or eponyms that may have to be changed, except for the few most commonly discussed or used temperaments. Paul Erlich recently pointed out that we use names for colours, not wavelength numbers. And I responded that, while most people can distinguish thousands of colours, they only use simple words for about 20, and use combinations of these, and adjectives like dark light etc. > I'm leaning toward the fractional generator + period notation for > unfamiliar temperaments, with wedgies for those few that can't easily be > symbolized in this way. But I still find names easier to remember, and I > don't want to discourage the naming of temperaments that look like they > might be useful. OK. Well It seems we aren't that far apart in our thoughts on this, but based on the colours thing, I wouldn't like to see non- descriptive names for more than about the best 20. We've already got more than 50, and we've only got to the 7-limit.
Message: 11414 Date: Sat, 17 Jul 2004 03:47:07 Subject: Re: Naming temperaments From: Dave Keenan --- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote: > At 06:37 PM 7/16/2004, Dave Keenan wrote: > >> How do you choose a period/generator representation? > > > >You don't have to. You just base it directly on the map -- any map > >that's valid. i.e. the generator doesn't have to be in lowest > >(period-reduced terms). > > So there'll be multiple names for each temperament? No. The name ends up the same. > >For any of the ET/MOS/DE-based names you need to choose specific > >values of period and generator. In most cases, different kinds of > >optima do not change the period and generator enough to make much > >difference, but I just found that while minimax and RMS versions of > >5-limit Diminished can be described as 12&16-LT or 12&28-LT, the TOP > >version cannot. It could be described as 12&20-LT or 12&32-LT but 20 > >and 32 are not 5-limit consistent, so the best you can do > >is 8&12-LT. > > I think that's why Gene is proposing to use ETs that represent the > extreme ranges of the generator. Sure, I like that idea, but what you consider extreme, depends on what you consider optimal. > >The map tells you how many periods to the octave. That's all you > >need to know about the period to know whether the temperament is > >twin or triple etc. > > What about temperaments that map 2 through a combination of both > the "period" and generator? Aw c'mon Carl. Gimme a break. :-) None of the other methods mentioned in this thread (except giving the full wedgie or a full mapping) can handle that either. > Hmm... I thought one could refactor these maps is several > annoying ways. Thus, the reason for something called hermite > normal form -- whatever that is. Sure, but it makes no difference, assuming we agree to use the smallest of the equivalent generators (the one that's less than half the period) and describe that generator as a fraction of the diamond ratio that requires the fewest (absolute number of) generators (and zero periods). Just as we describe the period as a fraction of the octave. But I certainly am assuming that the map has no generators in prime- 2, as is the case for 99.9% of maps we've ever talked about.
Message: 11415 Date: Sat, 17 Jul 2004 03:49:53 Subject: Re: Extreme precison (Olympian) Sagittal From: Dave Keenan --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote: > I was just hoping for a statement of the problem which did not require > me to read things I have to squint at and still can't make out. What > are the barbs, arcs, scrolls, boathooks and accent marks supposed to > do, in numerical terms? I'll get that for you eventually Gene. Sorry for the delay.
Message: 11416 Date: Sat, 17 Jul 2004 03:58:51 Subject: Re: Naming temperaments From: Dave Keenan --- In tuning-math@xxxxxxxxxxx.xxxx Herman Miller <hmiller@I...> wrote: > Dave Keenan wrote: > > e.g. Miracle is "semi 7:8's" or "semi supermajor seconds". > > This could be potentially useful up to a point; certainly there's a > mnemonic value in names like "semisixths". But I don't see how this can > be generalized to the 7-limit and higher without being arbitrary. > Which > LT gets to be called "fourths" -- dominant (5&12), meantone (12&19), > superpyth[agorean] (5&22), flattone (19&26), or schismic (12&29)? You > could make good arguments at least for dominant, meantone, and schismic; > then you need to figure out how to name the others. "Major thirds" could > be either muggles (16&19) or magic (19&22), and so on. Right. This is where we use adjectives like wide and narrow applied to the generator (but only where these don't imply a different n- limit ratio entirely). And the fallback method is to rank them by some badness measure (probably most reasonable badness measures will agree on the ranking of temperaments having the same ratio approximated by their generator), and then the best one gets to have no adjective and the others are called "complex", "supercomplex" or "inaccurate", "super- inaccurate", as the case may be. Is their a shorter word for "inaccurate"? > > This is used up to some point where the LT is so complex you just > > describe the generator in cents. e.g. What used to be called > > Aritoxenean is the 12-fold 15 cent LT. > > > > This at least works up to 11-limit. > > But giving the generator in cents doesn't determine a unique mapping; > you can derive one from a rational generator/period ratio if you make > some assumptions, but an arbitrary value in cents could represent more > than one temperament. An LT with a 316.5 cent generator can be mapped as > [<1, 0, 1, 2|, <0, 6, 5, 3|] or [<1, 0, 1, -3|, <0, 6, 5, 22|]. With > rational generators and the naming conventions I've described, you can > unambiguously describe the first mapping as 5/19 and the second as 19/72. I only proposed using cents when the temp is so complex that the diamond ratio with the fewest generators has say 5 or more generators in it. That's getting pretty complex. How many 12-fold 15- cent temperaments do you know of?
Message: 11418 Date: Sat, 17 Jul 2004 05:13:37 Subject: Re: Naming temperaments From: monz hi Dave and Herman (and everyone else), --- In tuning-math@xxxxxxxxxxx.xxxx "Dave Keenan" <d.keenan@b...> wrote: > --- In tuning-math@xxxxxxxxxxx.xxxx Herman Miller <hmiller@I...> > wrote: > As I've said elsewhere, in the two-ET/MOS/DE method > (the two-cardinalities method?) of naming, I'd like the > two numbers to give the denominators of two convergents > (or semi-convergents) of the generator as an octave fraction, > such that one is near the minimum useful generator size > and the other is near the maximum. > > <snip most of a long and interesting post> > > > I'm leaning toward the fractional generator + period > > notation for unfamiliar temperaments, with wedgies for > > those few that can't easily be symbolized in this way. > > But I still find names easier to remember, and I > > don't want to discourage the naming of temperaments > > that look like they might be useful. > > OK. Well It seems we aren't that far apart in our > thoughts on this, but based on the colours thing, > I wouldn't like to see non-descriptive names for more > than about the best 20. We've already got more than 50, > and we've only got to the 7-limit. i'm convinced that those of you who are putting forth the argument against the cute verbal names are just frustrated at the inability to keep up with the pace of developments in tuning theory recently. verbal names are really easy to remember, and short concise numerical descriptions convey a lot of data, so why not just use both? i've always been a huge fan of redundant coding. it makes life easy. so what if there is already one name for something? natural linguistic processes are always coining new names for old things. i pursue the goal of including individual entries for all these different temperaments and numerical descriptions in the Encyclopaedia. that way a reader can simply look up any name that's unfamiliar. i'm just buried with work and haven't kept up with the lists for a long time until recently, and would have to study a bit to be able to write those pages. if anyone else would like to contribute to this project, please just post your efforts here and i'll make the posts into webpages. i'll start the project by sending a bunch of posts with the temperament names in the subject lines. if no-one objects to this, then by all means please feel free to contribute more names as individual threads. doing this will also coalesce a lot of related data together for the archives of this list. -monz
Message: 11420 Date: Sat, 17 Jul 2004 05:28:41 Subject: names and definitions: meantone From: monz let's start the whole project with perhaps the most familiar family of tunings. i already have a page about meantone at http://tonalsoft.com/enc * i realize that some of the categories below require data for specific flavors of meantone, and not the whole family itself. but if there is a way to put in a range of data that does cover the whole family, it think that is good. please keep in mind that this is an extremely rough draft that's coming right off the top of my head. i'm real busy with other things but while i'm in the thick of working on the Encyclopaedia, i might as well use the opportunity to create a whole slew of webpages covering the names that everyone is complaining about. so that at least then familiarity can breed contempt ... ;-) fill in the blanks, and adjust, correct, argue etc. as much as possible ... family name: meantone period: 2:1 ratio generator: wedge product: wedgie: unison-vectors: monzos, multimonzos: vals, multivals: badness: MOS: DE: propriety: consistency: characteristic interval(s): x-chordal interval structure (tetrachord, pentachord, etc.): -monz
Message: 11421 Date: Sat, 17 Jul 2004 05:29:56 Subject: names and definitions: aristoxenean From: monz i already have a page about aristoxenean at http://tonalsoft.com/enc * fill in the blanks, and adjust, correct, argue etc. as much as possible. feel free to add new categories and descriptive text commentary as needed. family name: meantone period: 2:1 ratio generator: wedge product: wedgie: unison-vectors: monzos, multimonzos: vals, multivals: badness: MOS: DE: propriety: consistency: characteristic interval(s): x-chordal interval structure (tetrachord, pentachord, etc.): -monz
Message: 11422 Date: Sat, 17 Jul 2004 05:31:08 Subject: names and definitions: schismic From: monz NOTE: i propose that we drop "schismatic" as a synonymous term, or at least always mention that it is a synonym. (it is, right?) i already have a page about schismic at http://tonalsoft.com/enc * fill in the blanks, and adjust, correct, argue etc. as much as possible. feel free to add new categories and descriptive text commentary as needed. family name: meantone period: 2:1 ratio generator: wedge product: wedgie: unison-vectors: monzos, multimonzos: vals, multivals: badness: MOS: DE: propriety: consistency: characteristic interval(s): x-chordal interval structure (tetrachord, pentachord, etc.): -monz
Message: 11423 Date: Sat, 17 Jul 2004 05:32:37 Subject: names and definitions: orwell From: monz i already have a page about orwell at http://tonalsoft.com/enc * but it's very much in need of amending. fill in the blanks, and adjust, correct, argue etc. as much as possible. feel free to add new categories and descriptive text commentary as needed. family name: meantone period: 2:1 ratio generator: wedge product: wedgie: unison-vectors: monzos, multimonzos: vals, multivals: badness: MOS: DE: propriety: consistency: characteristic interval(s): x-chordal interval structure (tetrachord, pentachord, etc.): -monz
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