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Message: 4200 - Contents - Hide Contents Date: Tue, 12 Mar 2002 08:34:44 Subject: Re: 32 best 5-limit linear temperaments redux From: paulerlich --- In tuning-math@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:> --- In tuning-math@y..., "paulerlich" <paul@s...> wrote:>> --- In tuning-math@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:>>> --- In tuning-math@y..., "paulerlich" <paul@s...> wrote:>>>> ok. gene, once again, this means that in the 'gens' calculation, >> the>>>> number of generators in the 3:1 should be multiplied by log (3), >> the>>>> number of generators in the 5:3 should be multiplied by log (5), >> the>>>> number of generators in the 5:1 should be multiplied by log (5). >>>>>> And to make the result meaningful (i.e. comparable to the >> unweighted>>> values) then after you take the RMS of these weighted values you >>> should divide by sqrt(log(3)^2+log(5)^2+log(5^2)). >>>> why do you want them to be comparable to the unweighted values? >> Obviously it doesn't matter as far as choosing lists, but I like for a > human (e.g. me) to be able to look at the error values and have them > mean something. i.e. to actually be in cents. So when you see 5 you > know kinda what a 5c mistuning sounds like.but the units here are not cents, they're gens. what does 5 gens sound like? faggeddabbouddit.
Message: 4201 - Contents - Hide Contents Date: Tue, 12 Mar 2002 10:56:52 Subject: Re: Dave's 23 best 5-limit temperaments From: paulerlich --- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:> --- In tuning-math@y..., "paulerlich" <paul@s...> wrote: >>> sounds like 'bastoni' (italian bread). fits in well with 'injera' >> (ethiopian bread). actually this works well, since 225/224^49/48 >> (bastoni) is in the same 'aisle' as 81/80^50/49 (injera). >> Next time I'm stuck for a name, I'll think bread.or spiny mammal :)
Message: 4202 - Contents - Hide Contents Date: Tue, 12 Mar 2002 20:43:28 Subject: diminished temperament -- rimsky-korsakov, ravel, scriabin From: paulerlich Octatonic Scales * [with cont.] (Wayb.) V-2001 * [with cont.] (Wayb.) 404 Not Found * [with cont.] Search for http://www.azstarnet.com/~solo/sc743al.htm in Wayback Machine
Message: 4203 - Contents - Hide Contents Date: Tue, 12 Mar 2002 08:39:32 Subject: Re: heuristic... From: paulerlich --- In tuning-math@y..., Carl Lumma <carl@l...> wrote:> Paul, > > Do you have the original expository message number handy, > or any good words to search for, or do you know what list > you posted it to, or around when? > > -Carli've lost track of the original one, but last year it used to be a 'conjecture', not a 'heuristic' here's the most up-to-date exposition: Yahoo groups: /tuning-math/message/2491 * [with cont.] remember to click on 'message index' and then 'expand message' . . .
Message: 4204 - Contents - Hide Contents Date: Tue, 12 Mar 2002 11:00:01 Subject: skhismic From: paulerlich it's spelled this way sometimes. pronounce it. there's no reason one should think it might be spelled "shismic". how do you pronounce "schism"? like "shism"? naah . . .
Message: 4205 - Contents - Hide Contents Date: Tue, 12 Mar 2002 20:44:48 Subject: Re: Dave's 23 best 5-limit temperaments From: paulerlich --- In tuning-math@y..., Carl Lumma <carl@l...> wrote:>> chromatic unison vectors. >> You're suggesting this as a name for a temperament??? no!
Message: 4206 - Contents - Hide Contents Date: Tue, 12 Mar 2002 23:25:58 Subject: Re: Dave's 23 best 5-limit temperaments From: Herman Miller On Tue, 12 Mar 2002 05:30:45 -0000, "genewardsmith" <genewardsmith@xxxx.xxx> wrote:>1990656/1953125 Extends to the 1029/1024^126/125 = >[9,5,-3,-21,30,-13] system, and needs a name.) > >map [[0, 9, 5], [1, 1, 2]] > >generators 77.96498962 1200 > >keenan 12.03289099 rms 2.983295872 g 6.377042156This looks like a good candidate for the "Starling" name. Besides having 126/125 as a unison vector, its generator is a prominent melodic interval in Starling temperament.
Message: 4207 - Contents - Hide Contents Date: Tue, 12 Mar 2002 08:40:47 Subject: Re: amt From: genewardsmith --- In tuning-math@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:> How was the name amt arrived at. Is it an abbreviation for something?It's an acronym for "acute minor third", from its generator.> It could be called "fifth of eleventh".Sounds like a borg.
Message: 4208 - Contents - Hide Contents Date: Tue, 12 Mar 2002 11:24:53 Subject: Re: skhismic From: genewardsmith --- In tuning-math@y..., "paulerlich" <paul@s...> wrote:> it's spelled this way sometimes. pronounce it. there's no reason one > should think it might be spelled "shismic".I used to spell it that way, but quit because everyone seemed to spell it differently. Still use "sk" to mean 2^(1/612), though. how do you> pronounce "schism"? like "shism"? naah . . .Usage Note: The word schism, which was originally spelled scisme in English, is traditionally pronounced (szm). However, in the 16th century the word was respelled with an initial sch in order to conform to its Latin and Greek forms. From this spelling arose the pronunciation (skzm). Long regarded as incorrect, it became so common in both British and American English that it gained acceptability as a standard variant. Evidence indicates, however, that it is now the preferred pronunciation, at least in American English. In a recent survey 61 percent of the Usage Panel indicated that they use (skzm), while 31 percent said they use (szm). A smaller number, 8 percent, preferred a third pronunciation, (shzm). In the ethnic bread department, the closest I can come to "chromic" seems to be "chimichurri", an Argentine bread. Other great names abound--lavosh, focaccia, ekmek, hapanleipa, panatone and malasadas.
Message: 4209 - Contents - Hide Contents Date: Tue, 12 Mar 2002 21:20:07 Subject: the underappreciated augmented system From: paulerlich Hexatonic thirds from Schubert to Schoenberg: ... * [with cont.] (Wayb.) 404 Not Found * [with cont.] Search for http://theory.esm.rochester.edu/smt-99.abstracts/schuster-craig.html in Wayback Machine 404 Not Found * [with cont.] Search for http://www.scalamusica.com/sca/jz02.htm in Wayback Machine
Message: 4210 - Contents - Hide Contents Date: Tue, 12 Mar 2002 00:42:04 Subject: Re: A proposed list of 5-limit not-quite-Just-thingies From: Carl Lumma>neutral thirds >meantone >pelogic >augmented >porcupine >diminished >diaschismic >small diesic >quarter fourths >kleismic >twin meantone >half meantone-fourth >half meantone-fifth >minimal diesic >schismic >wuerschmidt >tiny diesic >orwell >amtWhat you're calling small diesic is magic. I wonder why 5-limit miracle didn't make Gene's original list... otherwise the short list has everything I care about. -Carl
Message: 4211 - Contents - Hide Contents Date: Tue, 12 Mar 2002 11:37:56 Subject: bread From: paulerlich --- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:> Other great names abound--ekmek,sounds like 'ekmelic' -- richter-herf's name for 72-equal.>panatone wow!
Message: 4212 - Contents - Hide Contents Date: Tue, 12 Mar 2002 21:45:53 Subject: A common notation for JI and ETs From: gdsecor This subject began on the main tuning list and is in reply to Dave Keenan's message #35580 of 11 March 2002. --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:> --- In tuning@y..., "gdsecor" <gdsecor@y...> wrote: >> Dave, >>>> This is just to let you know that I have taken some time off from the >> Tuning List to work on the sagittal notation per our last >> conversation. I've eliminated a number of possibilities that didn't >> work to my satisfaction and am now much closer to a final solution. >> Thanks for letting me know. I'm glad someone's still working on it. > Johny Reinhard took the wind right out of my sails.I followed that conversation and, although I have strong convictions about what was discussed, I just didn't have the time to get involved in it. My thoughts on this are: 1) Johnny is already very familiar with cents, so that is what works for him. For the rest of us it would take a bit of training to be able to do the same, and then might we need a calculator to determine the intervals? When you are writing chords, where do all the cents numbers go, and how can you read something like that with any fluency? (But that is for instruments of fixed pitch, which do not require cents, which brings us to the next point.) 2) Tablatures were mentioned in connection with instruments of fixed pitch, where cents would be inappropriate. I hate tablatures with a vengeance! Each instrument might have a different notation, and this makes analysis of a score very difficult. We need a notation that enables us to understand the pitches and intervals, regardless of what sort of instrument is used. 3) Gene mentioned that we are most comfortable with whatever is the most familiar, but a multi-EDO/JI notation such as we are trying to achieve is going to have something new to learn, no matter what. It's best to make it as simple and logical as possible, and in my opinion this is best accomplished by symbols that correspond simply and directly to tones in each system, maintaining commonality across those systems as much as possible. Whether the maximum symbols per note should be one or two is something that still needs to be resolved, but I think that we should develop both approaches and see what results. Once that is done, then we can evaluate each, pro and con. As long as microtonality is such a niche market, I think that this is one extravagance that we can afford.>>> It depends on the context. [whether 8:13 is more of a major or minor 6th] >> True. So what is it in the most common contexts? >>> I hear 8:11 primarily as an augmented fourth (rather than a perfect fourth), >> Me too, although I call it a super fourth, leaving "augmented" for > 5:7. >>> and when the 8:11:13 is >> sounded, the 13 will sound more like an A than an A-flat. (I noticed >> that Paul Erlich said something to this effect in his reply.) > > Yes. >>> Anyway, this is beside the point, in light of what I have to say >> below. > > OK. >>> As it turns out, neither variation of the approach that I am now >> taking pairs the 7 and 13 factors together, and the one that looks >> most promising at the moment requires all defining commas to be no >> more than half of an apotome, >> This seems like a sensible criterion to me too, perhaps for other > reasons. >>> so it *must* use 1024:1053 instead of >> 26:27. > > OK. >>>> If you're still planning to assume that certain very small commas >>> vanish (so certain combinations of the prime-commas never occur) then >>> they had better be very small (like 1 cent or less) to keep theJI folks happy.>> >> I was wondering whether you had a particular comma in mind when you >> said this, because a very useful one that I found is around 0.4 cents. >> No I didn't. So what are the smallest ETs in which this comma > consistently fails to vanish?The comma is 4095:4096 (~0.423 cents). (Has anyone previously found it and given it a name?) Multiplying 81/80 by 64/63 gives 36/35 (~48.770 cents), which comes very close to 1053/1024 (~48.348 cents), the ratio which is to define the 13 factor. This very small comma vanishes in ET's 12, 17, 22, 24, 31, 34, 36, 39, 41, 43, 46, 53, 94, 96, 130, 140, 152, 171, 181, 183, 193, 207, 217, 224, 270, 311, 364, 388, 400, 494, 525, 581, 612, and 742. It does not vanish in 19, 27, 50, 58, 72, 149, 159, or 198, and this seems to be due to inconsistencies in those ET's. For those systems under 100 in which it does not vanish, I don't think that ratios of 13 will be used to define their notation, so this should not be a problem.>>>> Except that as Manuel pointed out, it's considered bad form to combine >>> an up accidental with a down. In that case you'd need a binary >>> sequence like 1, 2, 4, 8. At least we do have that with the larger >>> commas (and hence lower numbered ETs). >>>> That's something that I don't like about the Sims notation -- down >> arrows used in conjunction with sharps, and up arrows with flats. >> I think Manuel exempts sharps and flats from this criticism. > > If you had a ruler with only inch marks, what could you find quicker > (a) two and a half, less an eighth, or > (b) two and three eights?Or given these choices, (a) one and a half, less an eighth, or (b) one and three eighths, or (c) three, less one-fourth? The particular intervals that were mentioned (farther above) in connection with this issue are ratios of 11 and 13 that I like to think of as semi- and sesqui-sharps/flats. Making these the large units of notation (according to the number of stems in the symbol) rather than full sharps and flats makes the reading of these ratios much simpler and solves the problem of having to decide whether to notate a half-sharp/flat or a sharp/flat less a half. In effect, by halving the units I have turned the halves into wholes, which makes available choice (c) above, which, in addition to being at least as simple as choice (a), does not combine an up with a down. (As to how I make the distinction between ratios such as 11/9, 39/32, and 16/13, you will have to wait a while to see; at present I have two different methods.) Anyway, when in doubt I think it will come down to trying it both ways in order to see what looks better. I mentioned that my latest approach has two variations, and if I can't determine a clear choice of one over the other, then I will be presenting both so that we can decide which is better. --George
Message: 4213 - Contents - Hide Contents Date: Tue, 12 Mar 2002 08:44:49 Subject: Re: A proposed list of 5-limit not-quite-Just-thingies From: genewardsmith --- In tuning-math@y..., Carl Lumma <carl@l...> wrote:> What you're calling small diesic is magic.Sorry, my mistake.
Message: 4214 - Contents - Hide Contents Date: Tue, 12 Mar 2002 14:37 +0 Subject: Re: 32 best 5-limit linear temperaments redux From: graham@xxxxxxxxxx.xx.xx In-Reply-To: <a6jdeq+58k4@xxxxxxx.xxx> paulerlich wrote:> ok. gene, once again, this means that in the 'gens' calculation, the > number of generators in the 3:1 should be multiplied by log(3), the > number of generators in the 5:3 should be multiplied by log(5), the > number of generators in the 5:1 should be multiplied by log(5). this > will cause temperaments generated by the fifth to look better than > they currently do, relative to those that aren't. this is important > since augmented (especially) and diminished (a little less so) are > far harder for the ear to understand than meantone, even when all are > *tuned* in 12-equal, and the badness values would no longer put > meantone as the 'best'.When was it decided these temperaments were "far harder for the ear to understand"? Even if so, augmented is more complex than meantone if you measure by the simplest MOS to contain a consonant chord (8 compared to 5 notes). Still, for whatever reason you want to privilege fifths. The rule you give, generalized to higher limits, will favour simpler ratios in general. That'll give the usual bias towards temperaments that work with the limit lower than the one you asked for. And it'll miss temperaments where a simple interval is close enough to use in modulations, but isn't the defined approximation to 3:2. Graham
Message: 4215 - Contents - Hide Contents Date: Tue, 12 Mar 2002 23:20:31 Subject: Re: A proposed list of 5-limit not-quite-Just-thingies From: dkeenanuqnetau --- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:> --- In tuning-math@y..., "dkeenanuqnetau" <d.keenan@u...> wrote: >>> Oh I think I realise why you ask, since you wouldn't want it by your >> own badness measure. You think I'm violating my own badness measure. >> Nope. My 5-limit badness is 774, not something to set the world onfire, but it did pass your measure, as you say.>That was before I went back to using Paul's weighted complexity. Now it comes out badder than pelogic and semisuper (and with my new parameters 5.5c and 0.43 power, badder than seventh of major third [-9,7] and parakleismic).> I want a name for it because my 7-limit badness score is 173, so we > have a decent 5-limit temperament which heats up in the 7-limit.Being good at 7-limit is a good reason to have a name for it, but obviously should have no bearing on whether or not it's included in the 5-limit list. If you modify your badness to use log-of-odd-limit weighted complexity you will see that its requirement of 9 generators to the fifth combined with its so-so 3 cent rms error, gives it a badness of 1113 that pushes it way down the list. The worst on my proposed list so far is only 625 by this badness (quadrafourths). But I don't mind including it so long as it doesn't require you to include anything else. By your badness with weighted complexity, there may well be some others in between quadrafourths and "chrome" that I will find objectionable. There are certainly some that _you_ will find objectionable: the half and twin neutral thirds and kleismics (that I'm happy to omit).
Message: 4216 - Contents - Hide Contents Date: Tue, 12 Mar 2002 08:48:30 Subject: Re: Dave's 23 best 5-limit temperaments From: genewardsmith --- In tuning-math@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:> --- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:>> 1990656/1953125 Extends to the 1029/1024^126/125 = >> [9,5,-3,-21,30,-13] system, and needs a name.) >> >> map [[0, 9, 5], [1, 1, 2]] >> >> generators 77.96498962 1200 >> >> keenan 12.03289099 rms 2.983295872 g 6.377042156 >> How about "quarter major thirds"?Not accurate; I think "chromic" would be a good name, since the generator is 21/20~25/24, the chromatic semitone or chroma.>> 16875/16384 (Extends to the 225/224^49/48 = [4,-3,2,13,-8,-14]> system, and needs a name.) >>>> map [[0, -4, 3], [1, 2, 2]] >> >> generators 126.2382718 1200 >> >> keenan 12.16857021 rms 5.942562596 g 4.966554810 >> I've called it "quarter fourths" in the past, but it could also be > "third of major thirds".I think quadrafourths would be fine.
Message: 4217 - Contents - Hide Contents Date: Tue, 12 Mar 2002 14:37 +0 Subject: Re: 32 best 5-limit linear temperaments redux From: graham@xxxxxxxxxx.xx.xx In-Reply-To: <a6iupi+ksb1@xxxxxxx.xxx> Dave K:>> One of the reasons given for using rms was that if there was > an>> outlier the LT still got credit for the intervals it did well. But if >> we're looking at say {1,3,5,7} then if _any_ {1,3,5,7} interval is >> very wide, I don't think it is a good {1,3,5,7} temperament. Let it > be>> found to be a good {2,5,7} temperament or whatever. Paul:> it might not -- again, what if it's really a good {2, 3, 7/5} > temperament?There shouldn't be anything special about 1.3.5 and 1.3.7 compared to 1.3.7:5 as defining chords. So far my script only works with the former, but don't make any plans assuming that will always be the case. It should even be possible to automatically find and evaluate the simplest subset if that's all you want. Graham
Message: 4218 - Contents - Hide Contents Date: Tue, 12 Mar 2002 23:46:46 Subject: Weighting complexity (was: 32 best 5-limit linear temperaments) From: dkeenanuqnetau --- In tuning-math@y..., "paulerlich" <paul@s...> wrote:>>> ok. gene, once again, this means that in the 'gens' calculation, > the>>> number of generators in the 3:1 should be multiplied by log(3), > the>>> number of generators in the 5:3 should be multiplied by log(5), > the>>> number of generators in the 5:1 should be multiplied by log(5). > this>>> will cause temperaments generated by the fifth to look better > than>>> they currently do, relative to those that aren't.Paul, don't you mean "divided by". log(3) is smaller than log(5) so if you want to favour fifths ... Here's the formula I'm using: SQRT(((gens(1:3)/LN(3))^2+(gens(1:5)/LN(5))^2+(gens(3:5)/LN(5))^2)/(1/ LN(3)^2+1/LN(5)^2+1/LN(5)^2))*1200/period_in_cents
Message: 4219 - Contents - Hide Contents Date: Tue, 12 Mar 2002 00:37:03 Subject: Re: 32 best 5-limit linear temperaments redux From: paulerlich --- In tuning-math@y..., Carl Lumma <carl@l...> wrote:>> Going by my map: >> >> max int width card(map) me g >> 5-limit 10 2 5 7.257 >> 11-limit 11 4 2.75 ?? >> >> I have no idea how Gene got 7.257, so I can't fill >> g in for the 11-limit. >> Dave's getting 7.3 too, with this: > > SQRT((E13^2+F13^2+(E13-F13)^2)/3)*1200/L13 > > Anybody care to explain why this isn't total rubbish? Putting > both the individual gens per idenitity (E13 and F13) and the > total width of the chain (E13-F13) together into the rms calc???carl, if 'identity' is defined as 'consonant interval', then the *only* thing going in here is the individual gens per identity. that's all. E13-F13 is the major sixth or minor third.
Message: 4220 - Contents - Hide Contents Date: Tue, 12 Mar 2002 08:52:57 Subject: Re: Dave's 23 best 5-limit temperaments From: paulerlich --- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:> --- In tuning-math@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:>> --- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote: >>>> 1990656/1953125 Extends to the 1029/1024^126/125 = >>> [9,5,-3,-21,30,-13] system, and needs a name.) >>> >>> map [[0, 9, 5], [1, 1, 2]] >>> >>> generators 77.96498962 1200 >>> >>> keenan 12.03289099 rms 2.983295872 g 6.377042156 >>>> How about "quarter major thirds"? >> Not accurate; I think "chromic" would be a good name, since thegenerator is 21/20~25/24, the chromatic semitone or chroma. what about chromatic unison vectors?
Message: 4221 - Contents - Hide Contents Date: Tue, 12 Mar 2002 08:55:40 Subject: Re: A proposed list of 5-limit not-quite-Just-thingies From: genewardsmith --- In tuning-math@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:> I propose we go with either these 19 (in weighted-complexity order) > neutral thirds > meantone > pelogic > augmented > porcupine > diminished > diaschismic > small diesic = magic > quarter fourths = quadrafourths > kleismic > twin meantone = garbage > half meantone-fourth = ditto > half meantone-fifth = ditto > minimal diesic > schismic > wuerschmidt > tiny diesic > orwell > amtWhat happened to chromic?
Message: 4222 - Contents - Hide Contents Date: Tue, 12 Mar 2002 00:40:41 Subject: Re: Dave's 18 best 5-limit temperaments From: dkeenanuqnetau --- In tuning-math@y..., "paulerlich" <paul@s...> wrote:> --- In tuning-math@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:>> Comma Name Mapping Gen Period >> ------------------------------------------------------------- >> 6561/6400 twin meantone [0,-1,-4] [2,4,8] 503.8 600 >> isn't this just meantone itself? isn't this an instance of torsion?I have no idea what torsion is, but of course this is not simply meantone. It has a half-octave period. And thanks to Graham's list I've corrected its (lowest-terms) generator now to 96.2 cents.>> 81/80 half meantone-fifth [0,2,8] [1,2,4] 348.1 1200 >> 81/80 half meantone-fourth [0,-2,-8] [1,2,4] 251.9 1200 >> these are the valid instances of contortion i was talking about. they > are not temperaments, but they are quite interesting. since > their 'badness' should simply be 4 or 8 times that of meantone, such > cases can be handled with an introductory passage and never mentioned > again -- it would be easy enough for the reader to supply them for > any given badness cutoff.This assumes the reader is a mathematician. Are we planning to publish this in a math journal or a music journal? I don't see a problem with listing them in the appropriate place in the list, based on their complexity. I don't see how you can disqualify them as 5-limit temperaments simply because all the 5-limit intervals are approximated by an even number of generators. What kind of a definition of temperament would disallow that? Isn't a (octave-equivanlent) 5-limit temperament simply any scale or tuning system that approximates ratios of 1,3 and 5 and their octave equivalents? There can be no argument that they are not _linear_. They have a single generator operating withing a whole-number fraction of an octave. I think, Paul, that maybe you're being blinded by your "hypothesis", since here we have the same comma involved in different temperaments with different complexities. How about you modify your hypothesis to take care of that, rather than try to deny that these are temperaments. And lest you are tempted to now claim as Gene has, that these are simply meantone, I claim that a temperament is fundamentally defined by its mapping of generators and periods to primes (with generator and period in lowest terms), not by the commas that vanish. different mapping = different temperament. Seems obvious enough to me. If your algorithm fails to find certain kinds of temperament that other algorithms do find, you shouldn't try to deny their existence, you should fix your algorithm.
Message: 4223 - Contents - Hide Contents Date: Tue, 12 Mar 2002 09:52:22 Subject: Re: 32 best 5-limit linear temperaments redux From: dkeenanuqnetau --- In tuning-math@y..., "paulerlich" <paul@s...> wrote:> but the units here are not cents, they're gens. what does 5 gens > sound like? faggeddabbouddit.Oh dear I keep doing that don't I. Must be the Alzheimer's. :-)
Message: 4224 - Contents - Hide Contents Date: Tue, 12 Mar 2002 20:30:33 Subject: Re: Systematic naming of new temperaments (was: amt) From: Carl Lumma>Well yeah, but if possible, they should give you some clue as to what >the temperament is. This can beWell, crazy names won't tell you as much, but are more memorable, and might make up for it. See also my complaint about using diatonic intervals for temperaments where the diatonic scale may not even be supported.>hemithirds >quadrafourths/bestonic >chromeI still don't know the generators for these.>augmented (indirectly) >diminished (indirectly) >pelogic (indirectly)Where historical names exist, I think they should be used.>orwell (obscurely)But you'll never forget it once you've heard it.>and possibly semisuper if "semi" is meant to indicate the half-octave >period and "super" is short for super fourth. However I don't think >most people distinguish between semi and hemi,I'm not sure I do. I'd guess semi is partial, while hemi is exactly half. Super is short for super fourth?>(b)The comma that vanishes: >schismic >kleismic >diaschismic >wuerschmidt >tiny diesic >minimal diesic >limmal >meantone (indirectly)These are my favs -- I consider unison vectors far more informative than generator size. Except for stuff like "tiny" diesic vs. "minimal" diesic, which I still don't know as I write this.>or is "meantone" indicating the generator size indirectly?Meantone is just historical. It doesn't have to make sense.>Unfortunately this method doesn't generalise well to higher limits >since more than one comma vanishes.I was just going to mention that.>We could stick to using the single comma that vanishes in its >5-limit subset, but that won't work for temperaments that don't >_have_ a 5-limit subset.Indeed. That's when we resort to shamelessly locking in all of our surnames! :)>starlingWhen was this ratified?>There's nothing particularly magical or miraculuos about Magic and >Miracle at the 5-limit.That's okay. These names are historical now, too.>> 1. Three words. Temperaments should have cool, single-word >> names. >>I can't see any reason to stop calling neutral thirds by a two word >three syllable name.I don't think any established (as in, more than a month or two) names should be changed at all.>I think number of syllable is more relevant than number of words.I don't care if it's hard to say, I just want people to want to say it. Compare "Acute minor thirds" to "kleismic" here. Characters from novels, breads, etc., are also good.>> 2. I find it perverse to name temperaments by their relation to >> diatonic intervals. I guess this counts against Amt too. >>I know what you mean, but it's not too perverse for 5-limit since the >JI diatonic is 5-limit. But hey, that's simply how we name intervals, >of any limit. I think we're stuck with it.I'm willing to accept this, but I don't have to like it. I try to avoid it, at any rate.>Tiny diesic becomes hemisixths. >Minimal diesic becomes quadrafifths. >4294967296/4271484375 becomes septathirds. > >Any valid generator could be used, not just the smallest one. >So semisuper becomes twin tritenths or double tritenths. > >But it's no use calling pajara/twintone/paultone "twin fourths" or >"twin fifths", since that could apply to twin meantone as well. > >And Magic and Wuerschmidt would both be "major thirds" so they had >better stay as they are.There's not enough variety in this naming scheme for my taste. In effect, I'm going to have to think about the name each time I hear the temperament, whereas "orwell" lives in my mind as its own entity. -Carl
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