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Message: 3100 - Contents - Hide Contents Date: Thu, 10 Jan 2002 19:17:02 Subject: Re: Distinct p-limit intervals and ets From: monz> From: paulerlich <paul@xxxxxxxxxxxxx.xxx> > To: <tuning-math@xxxxxxxxxxx.xxx> > Sent: Thursday, January 10, 2002 6:34 PM > Subject: [tuning-math] Re: Distinct p-limit intervals and ets > > > Huh? I'm looking at Definitions of tuning terms: unique, (c) 1998 ... * [with cont.] (Wayb.) , > and I see that the links are to > ftp://ella.mills.edu/ccm/tuning/papers/consist_limits.txt . . . You > should change that to > Consistency limits of equal temperaments * [with cont.] (Wayb.) . . .OK, that's done, and it's been uploaded. I just wasn't sure if the other link should have been in the definition. Anyway, my request still stands: can you please explain these tables in more detail? I don't quite understand what's in them. -monz _________________________________________________________ Do You Yahoo!? Get your free @yahoo.com address at Yahoo! Mail - The best web-based email! * [with cont.] (Wayb.)
Message: 3101 - Contents - Hide Contents Date: Thu, 10 Jan 2002 19:45:16 Subject: Re: Distinct p-limit intervals and ets From: paulerlich --- In tuning-math@y..., <manuel.op.de.coul@e...> wrote:>>> Monz, the links to the tables are outdated. Manuel, could you provide >> the updated links? > > Consistency limits of equal temperaments * [with cont.] (Wayb.) and > Equal temperament step size ranges for consist... * [with cont.] (Wayb.)Monz, would you update your links in the "unique" definition, please?
Message: 3102 - Contents - Hide Contents Date: Thu, 10 Jan 2002 18:11:03 Subject: Re: Distinct p-limit intervals and ets From: monz Hi Paul,> From: paulerlich <paul@xxxxxxxxxxxxx.xxx> > To: <tuning-math@xxxxxxxxxxx.xxx> > Sent: Thursday, January 10, 2002 11:45 AM > Subject: [tuning-math] Re: Distinct p-limit intervals and ets > > > --- In tuning-math@y..., <manuel.op.de.coul@e...> wrote: >>>>> Monz, the links to the tables are outdated. Manuel, could you >>> provide the updated links? >> >> Consistency limits of equal temperaments * [with cont.] (Wayb.) and >> Equal temperament step size ranges for consist... * [with cont.] (Wayb.) >> Monz, would you update your links in the "unique" definition, please?I started to do this, but I see that the original links both point to the first URL listed here. But I've never fully understood these tables, so I'm not sure how to link to them. Please clarify. Feel free to expand your "unique" definition if needed. Diagrams *always* help me. :) -monz _________________________________________________________ Do You Yahoo!? Get your free @yahoo.com address at Yahoo! Mail - The best web-based email! * [with cont.] (Wayb.)
Message: 3103 - Contents - Hide Contents Date: Thu, 10 Jan 2002 19:46:03 Subject: Re: OPTIMAL 5-LIMIT GENERATORS FOR DAVE From: paulerlich --- In tuning-math@y..., "clumma" <carl@l...> wrote:>>> As in, part or parts in the music sharing the same rhythm. >>>> So what does the sentence, >> >> "I've never heard a voice in the music that was triads, Paul." >> >> mean. You haven't heard parallel triads? Me either! >> I've never heard a voice that played triads, one after the > other. -C.Fine. But I never mentioned triads in these discussions, only intervals.
Message: 3104 - Contents - Hide Contents Date: Thu, 10 Jan 2002 19:47:43 Subject: Re: Distinct p-limit intervals and ets From: paulerlich --- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:> --- In tuning-math@y..., <manuel.op.de.coul@e...> wrote: > >> Consistency limits of equal temperaments * [with cont.] (Wayb.) and >> Equal temperament step size ranges for consist... * [with cont.] (Wayb.) >> These don't contain the same information as I was looking at; I >only considered the standard et val which rounds to the nearest >integer for each prime,I don't like considering this "the standard et val" . . . perhaps you can call this the genewardsmith val or something.
Message: 3105 - Contents - Hide Contents Date: Thu, 10 Jan 2002 19:59:04 Subject: Re: Dictionary query From: paulerlich --- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:> --- In tuning-math@y..., graham@m... wrote: > > That's where the>> "positive"/"negative" terminology is defined, and it is relative to >> 12-equal, not Pythagorean. If you'd been paying attention, you could >> have checked it. One of Erv Wilson's early Xenharmonikon articles >> reiterates this, and another (I think "On Linear Notations ...") extends >> it for ETs other than 12. >> Now all that's left is to get it to make a particle of sense.This is a rich and deep literature we're referencing. Your arrogance has won you few fans on the other lists, and if you are to correspond with other mathematically-oriented tuning theorists, you may be well advised to try to keep it in check. So you've read all of Bosanquet and Wilson and come to the conclusion that they were total ignorami? That's the impression you're giving. Though you and I may have come up with different definitions of "positive" and "negative" had we been the first in this field, fortunately we're not, and the terms have been quite fruitful for generations of theorists who would disprove your seeming attitude that you possess 100% of the world's intelligence on these matters. Perhaps a conversation with John Chalmers would be well-advised for you at this point. All that said, please let it be known that I am greatly humbled by the depth of your vision and the quantity and quality of your efforts, especially on the subjects I am particularly interested in. Does becoming a leading contributor in this field mean that you have to take a dismissive and patronizing attitude toward all others who have touched it? If nothing else, sheer _politics_ would dictate that a different tone might be more fruitful.
Message: 3106 - Contents - Hide Contents Date: Thu, 10 Jan 2002 19:52:37 Subject: positive/skhismic systems (was: Re: Dictionary query) From: monz> From: paulerlich <paul@xxxxxxxxxxxxx.xxx> > To: <tuning-math@xxxxxxxxxxx.xxx> > Sent: Thursday, January 10, 2002 7:20 PM > Subject: [tuning-math] Re: Dictionary query > > > --- In tuning-math@y..., "monz" <joemonz@y...> wrote: >>> OK, but if they don't post anything here, please do give me >> more info. >> I have some of the original Bosanquet papers . . . I'll try to bring > them in.Hmmm ... I have a copy of Bosanquet's book ... let me know where to find the info.> Well, let me put it this way. For meantone systems, the meaning of > _which_ comma you're talking about is clear from the way meantone > works. If you're describing a non-meantone system as "x/y-comma" > whatever, then it's ambiguous. At least specify _which_ comma you're > talking about, that will at least make the specification > mathematically precise. But functionally, schismic temperaments are > best described by the fraction of the schimsa that's tempered > out . . . 1/8 schisma is Helmholtian, 1/9 schism is Sabat-Garibaldi's > Dinarra tuning . . . am I making any sense?Right, sure, I know about both of those. What has me puzzled is the large size of the "fraction of the skhisma" that's tempered out in the examples on my webpage. You and Gene already discussed 22-EDO, but what about 17- and 39-EDO, where the "5th" is +2 and nearly +3 skhismas wider, respectively, than a 3:2? And even 29-EDO's "5th" is nearly a whole skhisma wider. -monz _________________________________________________________ Do You Yahoo!? Get your free @yahoo.com address at Yahoo! Mail - The best web-based email! * [with cont.] (Wayb.)
Message: 3107 - Contents - Hide Contents Date: Thu, 10 Jan 2002 21:00:42 Subject: Re: Distinct p-limit intervals and ets From: genewardsmith --- In tuning-math@y..., "paulerlich" <paul@s...> wrote:> I don't like considering this "the standard et val" . . .Why not? I can think of other standards, but this one is easy and is the first thing anyone would think of, I should imagine.
Message: 3108 - Contents - Hide Contents Date: Thu, 10 Jan 2002 21:09:02 Subject: Re: Dictionary query From: genewardsmith --- In tuning-math@y..., "paulerlich" <paul@s...> wrote:> So you've read all of Bosanquet and Wilson and come to the conclusion > that they were total ignorami? That's the impression you're giving.To you, perhaps. I would imagine other people might come to a more correct impression, namely that 12-et-centric thinking in my estimation makes no sense in this context, since it has nothing whatever to do with the 12-et. It ain't how a mathematician would define things, let's put it that way.> Does becoming a leading contributor in this field mean that you have > to take a dismissive and patronizing attitude toward all others who > have touched it? If nothing else, sheer _politics_ would dictate that > a different tone might be more fruitful.My interest in that sort of politics is virtually nil. It seems to me you are adopting the same line as Jon Szanto recently did, which amounts to saying that thinking for yourself and expressing your opinion amounts to heresy when a revered name is in question. I don't believe in thought control, and prefer to come to my own conclusions without someone helpfully reminding me what is and is not an acceptable thing to think. Nor do I think it is arrogant to come to a different conclusion than Partch, Bosanquet, or anyone else.
Message: 3109 - Contents - Hide Contents Date: Thu, 10 Jan 2002 21:36:20 Subject: Re: Distinct p-limit intervals and ets From: paulerlich --- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:> --- In tuning-math@y..., "paulerlich" <paul@s...> wrote: >>> I don't like considering this "the standard et val" . . . >> Why not? I can think of other standards, but this one is easy and >is the first thing anyone would think of, I should imagine. I would hope not. For example, in 64-tET for the 5-limit, it's probably only the third-best mapping. You should look at Stoney's article, for example, before assuming that this should be seen as some kind of "standard".
Message: 3110 - Contents - Hide Contents Date: Thu, 10 Jan 2002 21:38:48 Subject: Re: Dictionary query From: genewardsmith --- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:> To you, perhaps. I would imagine other people might come to a more correct impression, namely that 12-et-centric thinking in my estimation makes no sense in this context, since it has nothing whatever to do with the 12-et. It ain't how a mathematician would define things, let's put it that way.One can, of course, turn this around--if Bosanquet looked at things relative to the 12-et, then he was *not* looking at them purely as temperaments, but presumably had 12-note keyboards and the like in mind. At least, I hope when he was tuning a 31-note keyboard he was not thinking in 12-et terms.
Message: 3111 - Contents - Hide Contents Date: Thu, 10 Jan 2002 21:50:20 Subject: Re: For Joe--proposed definitions From: monz Thanks, Gene! This is great. One quibble...> From: genewardsmith <genewardsmith@xxxx.xxx> > To: <tuning-math@xxxxxxxxxxx.xxx> > Sent: Thursday, January 10, 2002 8:11 PM > Subject: [tuning-math] For Joe--proposed definitions > > > Scale > > A discrete set of real numbers, containing 1, and such > that the distance between sucessive elements of the scale > is bounded both below and above by positive real numbers. > The least upper bound of the intervals between successive > elements of the scale is the maximum scale step, and the > greatest lower bound is the minimum scale step. The element > of the scale obtained by counting up n scale steps is the > nth degree, by counting down is the -nth degree; 1 is the > 0th degree.These definitions are necessary for helping a reader to understand your tuning-math posts. While the definitions for "Tone group" and "Val" and their derivitives, and "Epimorphic", seem adequate to me, the one for "Scale", however, requires more than just your mathematical lingo. The fact that the Tuning Dictionary has been online for 3 years without a definition of "scale" attests to my procrastination in coming up with a good definition of it. It's been a real gap in the Dictionary, possibly the most important tuning term of all. This definition is great for understanding your work, but is it really correct to simply *define* a scale as "a discrete set of real numbers"? I'm thinking that this is a Dictionary entry which, like many of them, will have numbered definitions to denote distinctions in meaning. The purely musical definition of "scale" would have to begin with "... a set of musical *pitches* ...", etc. Yours would be a #2 definition. Paul, since you're a mathematically-aware musician, can you help with this? -monz _________________________________________________________ Do You Yahoo!? Get your free @yahoo.com address at Yahoo! Mail - The best web-based email! * [with cont.] (Wayb.)
Message: 3112 - Contents - Hide Contents Date: Thu, 10 Jan 2002 21:39:37 Subject: Re: Dictionary query From: paulerlich --- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:> --- In tuning-math@y..., "paulerlich" <paul@s...> wrote:>> So you've read all of Bosanquet and Wilson and come to the conclusion >> that they were total ignorami? That's the impression you're giving. >> To you, perhaps. I would imagine other people might come to a more > correct impression, namely that 12-et-centric thinking in my >estimation makes no sense in this context, In what context??? We're talking about a _definition_ of "positive" and "negative". The only relevant context is the context in which these terms have been used in tuning theory!>since it has nothing whatever to do with the 12-et._What_ has nothing whatever to do with the 12-tET?>> Does becoming a leading contributor in this field mean that you have >> to take a dismissive and patronizing attitude toward all others who >> have touched it? If nothing else, sheer _politics_ would dictate that >> a different tone might be more fruitful. >> My interest in that sort of politics is virtually nil. > > It seems to me you are adopting the same line as Jon Szanto >recently did, which amounts to saying that thinking for yourself and >expressing your opinion amounts to heresy when a revered name is in >question.That's not what I'm saying.>I don't believe in thought control, and prefer to come to my own >conclusions without someone helpfully reminding me what is and is >not an acceptable thing to think.God bless you for that.>Nor do I think it is arrogant to come to a different conclusion than >Partch, Bosanquet, or anyone else.No. But to say that something doesn't make a "particle of sense", when it makes absolutely perfect sense in the context in which it's been used, is arrogant and insulting.
Message: 3113 - Contents - Hide Contents Date: Thu, 10 Jan 2002 21:46:22 Subject: Re: Dictionary query From: genewardsmith --- In tuning-math@y..., "paulerlich" <paul@s...> wrote:> No. But to say that something doesn't make a "particle of sense", > when it makes absolutely perfect sense in the context in which it's > been used, is arrogant and insulting.I wasn't referring to the context in which it's been used, in fact I don't know what that is; for my guesses see my previous posting. I was referring to the context in which we were using it now--namely, to refer to linear temperaments with some type of fifth as generator, without reference to the 12-et or any other et. In that context, it manifestly makes no sense to drag in the 12-et. How does it even enter the conversation, so to speak? Who invited it, and why? Why not base everything on 53 instead, for example? It seems to me you are reading a highly personal dismissal of Bosanquet and Wilson into what I wrote, instead of looking at it on its merits.
Message: 3114 - Contents - Hide Contents Date: Thu, 10 Jan 2002 21:56:44 Subject: Re: Dictionary query From: paulerlich --- In tuning-math@y..., "monz" <joemonz@y...> wrote:> > My Dictionary entries > Definitions of tuning terms: positive system, ... * [with cont.] (Wayb.) > Definitions of tuning terms: negative system, ... * [with cont.] (Wayb.) > > define positive and negative tuning systems as those > which have "5ths" larger or smaller, respectively, > than the 700-cent 12-EDO "5th". > > > Isn't that wrong? Doesn't the 3:2 ratio define the > boundary between positive and negative? Is there > more than one accepted usage? Help! Hi Monz.The accepted usage, not in some imagined "context" that Gene may wish to dream up as his ego inflates to the point where all existing tuning literature vanishes from existence, but in the actual context in which the term has been used, has the dividing line at 700 cents. Today, on these lists, we tend to call negative systems "meantone" and positive systems "schismic". The reason 700 cents was chosen as the dividing line between "negative" and "positive" is that when the fifth is below 700 cents, the "meantone" (+4 fifths) approximation to the 5/4 is better than the "schismic" (-8 fifths) approximation to the 5/4. When the fifth is above 700 cents, the "schismic" approximation to the 5/4 is better than the "meantone" approximation to the 5/4. I might differ, saying that there is a "gray area", and also factoring the 6/5 into consideration . . . but the definitions are well-established and there is no reason to favor ones which could breed potential contradictions. As for your definition pages, Monz, they definitely give the wrong idea. Positive systems should be characterized by the fraction of a _schisma_ that the fifths differ from just -- this is the relevant measure of them. Knowing what fraction of a syntonic comma a positive system's fifth might have been _increased_ by is irrelevant for understanding the functioning of the system, and is potentially misleading.
Message: 3115 - Contents - Hide Contents Date: Thu, 10 Jan 2002 22:04:06 Subject: Re: Dictionary query From: paulerlich --- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:> --- In tuning-math@y..., "paulerlich" <paul@s...> wrote: >>> No. But to say that something doesn't make a "particle of sense", >> when it makes absolutely perfect sense in the context in which it's >> been used, is arrogant and insulting. >> I wasn't referring to the context in which it's been used,But look at your posts again -- YOU were the one who brought up "context". What other context is there?>in fact I don't know what that is; for my guesses see my previous >posting. I was referring to the context in which we were using it >now--namely, to refer to linear temperaments with some type of fifth >as generator, without reference to the 12-et or any other et.What do you mean, the context in which we are using it now? Who among us has used the terms "negative" and "positive" in this context? None of us have. The only relevant context is that in which the terms _have_ been used.>In that context, it manifestly makes no sense to drag in the 12-et. >How does it even enter the conversation, so to speak? Who invited >it, and why? Why not base everything on 53 instead, for example?See my last post.>It seems to me you are reading a highly personal dismissal of >Bosanquet and Wilson into what I wrote,Not highly personal.>instead of looking at it on its merits.If you look at the thread of this conversation again, perhaps you'll see that you clearly came off as saying "whoever thought of this definition was a nitwit".
Message: 3116 - Contents - Hide Contents Date: Thu, 10 Jan 2002 22:04:40 Subject: Re: Dictionary query From: genewardsmith --- In tuning-math@y..., "paulerlich" <paul@s...> wrote:> The accepted usage, not in some imagined "context" that Gene may wish > to dream up as his ego inflates to the point where all existing > tuning literature vanishes from existence, but in the actual context > in which the term has been used, has the dividing line at 700 cents.I'm not sure why you keep attacking me--in what way have I injured you? So far as this "positive" and "negative" business goes, my suggestion would be to use "sharp" and "flat" instead, so that a "sharp system" would have a sharp fifth, and a "flat system" (which would include the 12 et) would have a flat fifth.
Message: 3117 - Contents - Hide Contents Date: Thu, 10 Jan 2002 22:06:39 Subject: All in the spirit of friendship, Gene From: paulerlich Gene, I'm just trying to help you avoid a lot of acrimony that is going to result between you and others in the future if you continue using this sort of intent. Everything I said about you was said in good fun and in the spirit of helpfulness, and I hope you take it that way. Sorry if it came off as harsh, but better you hear it from a friend now than from an enemy later.
Message: 3118 - Contents - Hide Contents Date: Thu, 10 Jan 2002 22:08:36 Subject: Re: Dictionary query From: paulerlich --- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:> So far as this "positive" and "negative" business goes, my >suggestion would be to use "sharp" and "flat" instead, so that >a "sharp system" would have a sharp fifth, and a "flat system"(which would include the 12 et) would have a flat fifth. This set of definitions is independent of the "positive" and "negative" definitions. The distinctions they draw are different and the terms they use are different. So why is this a matter of "instead"?
Message: 3119 - Contents - Hide Contents Date: Thu, 10 Jan 2002 22:13:57 Subject: Re: All in the spirit of friendship, Gene From: genewardsmith --- In tuning-math@y..., "paulerlich" <paul@s...> wrote:> Gene, I'm just trying to help you avoid a lot of acrimony that is > going to result between you and others in the future if you continue > using this sort of intent. Everything I said about you was said in > good fun and in the spirit of helpfulness, and I hope you take it > that way.For future reference, that sort of harsh personal attack is not normally going to be taken in a spirit of fun, and should be avoided unless you mean to get into serious eye-gouging. Sorry if it came off as harsh, but better you hear it from> a friend now than from an enemy later.Hmmm...well, I suppose you know people say exactly the same sort of things about you. In fact, I think I've heard more about PE's arrogance than of GWS's.
Message: 3120 - Contents - Hide Contents Date: Thu, 10 Jan 2002 22:21:03 Subject: Re: Dictionary query From: genewardsmith --- In tuning-math@y..., "paulerlich" <paul@s...> wrote:> This set of definitions is independent of the "positive" > and "negative" definitions. The distinctions they draw are different > and the terms they use are different. So why is this a matter > of "instead"?Your proposal is that 700 cents is the border between meantone and schismic, if I understand correctly, since the third you get by going round each way on a 12-et will of course be the same. I could object that a 701 cent tuning is more likely to be used in a meantone manner anyway, but more to the point, why not simply say "schismic" or "meantone" if that is what you mean? After all, a 22 or 46 et isn't either one but can also be using a generator of a fifth, and even discounting that kind of possibility, there are in theory at least an infinite number of other possible 5-limit temperaments using a fifth+octave scheme. What is the point of saying "schismic is a positive system" and "meantone is a negative system" on your view--or does one say that sort of thing?
Message: 3121 - Contents - Hide Contents Date: Thu, 10 Jan 2002 22:31:52 Subject: Re: All in the spirit of friendship, Gene From: paulerlich --- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:> --- In tuning-math@y..., "paulerlich" <paul@s...> wrote: >>> Gene, I'm just trying to help you avoid a lot of acrimony that is >> going to result between you and others in the future if you continue >> using this sort of intent. Everything I said about you was said in >> good fun and in the spirit of helpfulness, and I hope you take it >> that way. >> For future reference, that sort of harsh personal attack is not >normally going to be taken in a spirit of fun, and should be avoided >unless you mean to get into serious eye-gouging.Correct, my apologies, and promises never to repeat . . .> Sorry if it came off as harsh, but better you hear it from>> a friend now than from an enemy later. >> Hmmm...well, I suppose you know people say exactly the same sort of >things about you. In fact, I think I've heard more about PE's >arrogance than of GWS's.Fair enough -- see my private e-mail to you. I'm working on it, and by investing a lot of time and effort, I've been able to defuse most of the more violent misunderstandings I've been involved in, and keep them defused. Let me propose the following agreement: rather than questioning whether a certain item (which inevitably has one or more authors) makes negligible sense, infinitesimal sense, or somewhere in between, and leaving it at that, we will, in the future, (a) state that we disagree, perhaps "disagree strongly" with said item; (b) explain clearly what we perceive as the problem with said item; (c) if possible, propose an improvement. Such a procedure, in my experience, will be far more powerful as a rebuttal or reaction, than a trite dismissal. The trite dismissal exudes a very strong smell of arrogance, because it implies that the explanation for the dismissal need not be given, all of sufficient/worthy intelligence will immediately see it or already know it. Moreover, if trite, the angle at which the dismissal is being made can leave much ambiguity and uncertainty as to what aspect of the item is being objected to. I hope you will consider this agreement. My hand is outstretched toward you in cyberspace, and I hope you will shake it. In friendship, Paul
Message: 3122 - Contents - Hide Contents Date: Thu, 10 Jan 2002 22:46:37 Subject: Re: Dictionary query From: paulerlich --- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:> --- In tuning-math@y..., "paulerlich" <paul@s...> wrote: >>> This set of definitions is independent of the "positive" >> and "negative" definitions. The distinctions they draw are different >> and the terms they use are different. So why is this a matter >> of "instead"? >> Your proposal is that 700 cents is the border between meantone and >schismic, if I understand correctly, since the third you get by >going round each way on a 12-et will of course be the same.This is not "my proposal", Gene, this is the _established definition_. Monz is not producing a dictionary of Gene-and-Paul- tuning-terms -- it's a Dictionary of tuning terms, which means it accounts, as well as possible, for the intended meanings of words as they have been used in the tuning literature. Take a look at the Microtonal Bibliography on the Huygens-Fokker page to get an idea of how vast this literature is.>I could object that a 701 cent tuning is more likely to be used in a >meantone manner anyway,I would agree, and objection was in my mind when I wrote, 'I might differ, saying that there is a "gray area", . . . '>but more to the point, why not simply say "schismic" or "meantone" >if that is what you mean? After all, a 22 or 46 et isn't either oneActually, I simplified my explanation slightly. There are other possible subcategories of "negative" besides "meantone", and of "positive" besides "schismic". You might want to look at Bosanquet's discussion of 22, for example. He was very well aware of this fact, as was Wilson, and did not leave it unaccounted for. In fact, Bosanquet presents some rigorous mathematical formulae, which may not be very interesting to you and I currently, and we are certainly in agreement about the 12-centricity of them (which Paul Rapaport, for example, would disagree with us), but they are nonetheless mathematically correct and form part of the literature.>What is the point of saying "schismic is a positive system" >and "meantone is a negative system" on your view--or does one say >that sort of thing?The terms, as far as I've seen them used, have mainly been applied to ETs.
Message: 3123 - Contents - Hide Contents Date: Thu, 10 Jan 2002 22:52:10 Subject: Re: All in the spirit of friendship, Gene From: genewardsmith --- In tuning-math@y..., "paulerlich" <paul@s...> wrote:> (a) state that we disagree, perhaps "disagree strongly" with said > item; > > (b) explain clearly what we perceive as the problem with said item; > > (c) if possible, propose an improvement.I can't promise to always know what someone will take umbrage at, but I'll try to work more like this. In that spirit, can you explain if the 27-et hyperpythagorean system is positive, or something else? Before I thought I understood the definition, but didn't like it, but now I don't know if it is talking about anything other than meantone vs schismic.
Message: 3124 - Contents - Hide Contents Date: Fri, 11 Jan 2002 02:34:20 Subject: Re: Distinct p-limit intervals and ets From: paulerlich --- In tuning-math@y..., "monz" <joemonz@y...> wrote:> Hi Paul, >>> From: paulerlich <paul@s...> >> To: <tuning-math@y...> >> Sent: Thursday, January 10, 2002 11:45 AM >> Subject: [tuning-math] Re: Distinct p-limit intervals and ets >> >> >> --- In tuning-math@y..., <manuel.op.de.coul@e...> wrote: >>>>>>> Monz, the links to the tables are outdated. Manuel, could you >>>> provide the updated links? >>> >>> Consistency limits of equal temperaments * [with cont.] (Wayb.) and >>> Equal temperament step size ranges for consist... * [with cont.] (Wayb.) >>>> Monz, would you update your links in the "unique" definition, please? > >> I started to do this, but I see that the original links both > point to the first URL listed here.Huh? I'm looking at Definitions of tuning terms: unique, (c) 1998 ... * [with cont.] (Wayb.) , and I see that the links are to ftp://ella.mills.edu/ccm/tuning/papers/consist_limits.txt . . . You should change that to Consistency limits of equal temperaments * [with cont.] (Wayb.) . . .
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