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Message: 5450 - Contents - Hide Contents Date: Thu, 24 Oct 2002 01:46:00 Subject: Re: NMOS From: Carl Lumma>> > don't see how the symmetrical decatonics can be MOS, since >> they don't have Myhill's property. >> They look awfully Myhill to me.Look again, or use Scala. -C.

Message: 5451 - Contents - Hide Contents Date: Thu, 24 Oct 2002 03:44:53 Subject: Re: NMOS From: Carl Lumma>scratch that -- i see now! they *are* superposed at the chromatic >unison vector -- i was thinking of the end of one being attached >to the beginning of the other via the generator, but this is >equivalent! thanks carl!So my only point/question there was why should continuing the chain be any better than superposing at some other interval. IOW, why would NMOS be special scales of this type?>the reason torsion comes in is that we are treating the chromatic >unison vector as a *step* in the NMOS, while an *integer multiple* >(or exponent, in frequency-ratio space) of the chromatic unison >vector is a 0-step interval. thus the paradox -- if you temper out >the latter, you end up tempering out the former, and you end up >with the "wrong" number of notes -- a fraction of what the >determinant of the fokker matrix would tell you.Okay, I've cut and pasted that, and look forward to when I have some pegs to hang it on. I'm afraid I also don't understand the difference between the ie (in the MOS sense) and the interval of repetition. It looks to me like the symmetrical decatonic is MOS at the half-octave. -Carl

Message: 5452 - Contents - Hide Contents Date: Thu, 24 Oct 2002 05:08:37 Subject: Fwd: [tuning] Re: Everyone Concerned From: wallyesterpaulrus --- In tuning-math@y..., <Josh@o...> wrote:> ---- Original message ---->> Date: Wed, 23 Oct 2002 21:09:08 -0000 >> From: "wallyesterpaulrus" <wallyesterpaulrus@y...> > ...>> the edges of the screen wrap around and meet one another, > hence a >> donut topology. >> That's a little misleading. > > The video signal is linear, but gets bent around so > that it appears to take on other shapes. > > Choosing to recognize only part of the process > as relevant is opportunistic. > > Not that I actually care...i have no idea what you're talking about. have you ever played Asteroids?

Message: 5453 - Contents - Hide Contents Date: Thu, 24 Oct 2002 05:11:53 Subject: Re: NMOS From: wallyesterpaulrus --- In tuning-math@y..., "Carl Lumma" <clumma@y...> wrote:>> scratch that -- i see now! they *are* superposed at the chromatic >> unison vector -- i was thinking of the end of one being attached >> to the beginning of the other via the generator, but this is >> equivalent! thanks carl! >> So my only point/question there was why should continuing the > chain be any better than superposing at some other interval. > IOW, why would NMOS be special scales of this type?in many of these cases, there really isn't much of another interval to superpose it at, and still get a somewhat even scale.>> the reason torsion comes in is that we are treating the chromatic >> unison vector as a *step* in the NMOS, while an *integer multiple* >> (or exponent, in frequency-ratio space) of the chromatic unison >> vector is a 0-step interval. thus the paradox -- if you temper out >> the latter, you end up tempering out the former, and you end up >> with the "wrong" number of notes -- a fraction of what the >> determinant of the fokker matrix would tell you. >> Okay, I've cut and pasted that, and look forward to when I have > some pegs to hang it on. > > I'm afraid I also don't understand the difference between the ie > (in the MOS sense) and the interval of repetition. It looks to > me like the symmetrical decatonic is MOS at the half-octave.sounds fine to me! the ie (in the MOS sense) *is* the interval of repetition. it's just that i prefer not to call it the ie, and reserve ie to mean the ratio by which pitches are reduced to pitch classes (usually 2 -- the octave). we had a discussion here where many names were proposed for the former thing -- i think maybe "period" actually won out.

Message: 5454 - Contents - Hide Contents Date: Thu, 24 Oct 2002 07:22:22 Subject: Re: NMOS From: Carl Lumma>sounds fine to me! the ie (in the MOS sense) *is* the interval of >repetition. it's just that i prefer not to call it the ie, and >reserve ie to mean the ratio by which pitches are reduced to pitch >classes (usually 2 -- the octave). we had a discussion here where >many names were proposed for the former thing -- i think maybe >"period" actually won out.I like "period" for the MOS sense and "interval of equivalence" or "equivalence interval" for the psychoacoustic sense. -Carl

Message: 5456 - Contents - Hide Contents Date: Fri, 25 Oct 2002 12:01:36 Subject: Re: NMOS From: Gene Ward Smith --- In tuning-math@y..., "monz" <monz@a...> wrote:> Helmholtz's tuning can be viewed as the Pythagorean > chain 3^(-16...+7). but Helmholtz himself viewed it > as a skhismic temperament described by the Euler genus > 3^(-8...+7) * 5^(0...+1).I checked before posting that, and Helmholtz clearly (pg 216)describes his tuning as the 2MOS in question.

Message: 5457 - Contents - Hide Contents Date: Fri, 25 Oct 2002 05:49:14 Subject: Re: Helmholtz's schismic temperament (was: NMOS) From: monz hi Gene,> From: "monz" <monz@xxxxxxxxx.xxx> > To: <tuning-math@xxxxxxxxxxx.xxx> > Sent: Thursday, October 24, 2002 11:15 PM > Subject: Re: [tuning-math] Re: NMOS > > ... > > Helmholtz's tuning can be viewed as the Pythagorean > chain 3^(-16...+7). but Helmholtz himself viewed it > as a skhismic temperament described by the Euler genus > 3^(-8...+7) * 5^(0...+1). > > with C as n^0 (= 1/1), this gives a 12-tone Pythagorean chain > from Ab 3^-4 to C# 3^7 which has a counterpart one syntonic comma > lower at (using {3,5}-prime-vector notation) Ab [-8 1] to C# [3 1]. > this is a 24-tone torsional periodicity-block defined by > the Pythagorean and syntonic commas, [12 0] and [4 -1].re-reading this, i realized that including prime-factor 2 in the vectors would be a good idea, since you've pointed out that it's necessary in order to see the torsion. so ... Helmholtz's tuning, as {2,3,5}-prime-vectors with C=n^0, viewed as: - a Pythagorean chain, Fbb [26 -16 0] ... C# [-11 7 0] - a 5-limit Euler genus, Ab [7 -4 0] ... C# [-11 7 0] + Ab [11 -8 1] ... C# [-7 3 1] generating unision-vectors: [-19 12 0] Pythagorean comma [-4 4 -1] syntonic comma from that data, can you explain how the torsion works in this tuning? -monz

Message: 5458 - Contents - Hide Contents Date: Fri, 25 Oct 2002 13:43:05 Subject: Re: Helmholtz's schismic temperament (was: NMOS) From: Gene Ward Smith --- In tuning-math@y..., "monz" <monz@a...> wrote:> [-19 12 0] Pythagorean comma > [-4 4 -1] syntonic comma > from that data, can you explain how the torsion > works in this tuning?These aren't unison vectors. As a 5-limit tuning, which is how Helmhotz thought of it, it is defined by the schisma, [-15 8 1]; this is why the temperament is "schismic". For Pauline's purposes, we want to add the comma 225/224, giving a septimal version of schismic. This septimal schismic; it is covered by 41 and 53 equal, and from an rms error point of view done to perfection by the 94-et. If the 7 is relatively unimportant we might prefer the 53-et, and if 41 tones is not too many to handle we could even try building a 41-et organ. A page on Helmholtz's Harmonium would be a find addition.

Message: 5459 - Contents - Hide Contents Date: Fri, 25 Oct 2002 22:06:04 Subject: Re: NMOS From: wallyesterpaulrus --- In tuning-math@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:> --- In tuning-math@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...> wrote: >>> think about the Hypothesis. the Hypothesis says that if you temper >> out all but one of the unison vectors of a fokker periodicity block, >> you get an MOS. well, if the fokker periodicity block has torsion, >> you (may?) end up with an NMOS instead! cases in point: helmoltz 24 >> and groven 36. >> Helmholtz 24 is simply 23 consecutive fifths; it can be pretty well >equated with the 24 out of 53 2MOS I gave the notes for. that's right! >Torsion is >not a consideration.not if you don't want to think in periodicity block terms!

Message: 5460 - Contents - Hide Contents Date: Fri, 25 Oct 2002 22:07:29 Subject: Re: NMOS From: wallyesterpaulrus --- In tuning-math@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:> --- In tuning-math@y..., "monz" <monz@a...> wrote: >>> Helmholtz's tuning can be viewed as the Pythagorean >> chain 3^(-16...+7). but Helmholtz himself viewed it >> as a skhismic temperament described by the Euler genus >> 3^(-8...+7) * 5^(0...+1). >> I checked before posting that, and Helmholtz clearly (pg 216) >describes his tuning as the 2MOS in question.so you both agree!

Message: 5461 - Contents - Hide Contents Date: Fri, 25 Oct 2002 22:11:42 Subject: Re: Helmholtz's schismic temperament (was: NMOS) From: wallyesterpaulrus --- In tuning-math@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:> --- In tuning-math@y..., "monz" <monz@a...> wrote: >>> [-19 12 0] Pythagorean comma >> [-4 4 -1] syntonic comma > >> from that data, can you explain how the torsion >> works in this tuning? >> These aren't unison vectors.if monz changed this to schisma and diesis (not a major change), why not?>As a 5-limit tuning, which is how Helmhotz thought of it, it is >defined by the schisma, [-15 8 1]; this is why the temperament >is "schismic".that's right -- the schisma is the unison vector that is tempered out. you can use the diesis as the unison vector that *isn't* tempered out. then you clearly have a 24-tone periodicity block, a torsional one.

Message: 5462 - Contents - Hide Contents Date: Sun, 27 Oct 2002 02:26:51 Subject: Re: A common notation for JI and ETs From: gdsecor --- In tuning-math@y..., "dkeenanuqnetau" <d.keenan@u...> wrote [#4662]:> --- In tuning-math@y..., "gdsecor" <gdsecor@y...> wrote:>> --- In tuning-math@y..., David C Keenan <d.keenan@u...> wrote:>>> --- In tuning-math@y..., "gdsecor" <gdsecor@y...> wrote: >>>>>>>> 159a: |( ~|( /| |\ ~|\ /|) /|\ (|) (|\ ~||( /||||\ ~||\ /||) /||\>>> >>> I prefer >>> 159b: ~| ~|( /| |\ (|( /|) /|\ (|) (|\ ~||( /||||\ (||( /||) /||\ (RC & MS)>> >> The (| flag is not the same number of degrees in (|( and (|\, so (|( is >> not valid. >> >> I prefer |( because it is valid as the 5:7, 11:13, and 17'-17 commas, >> hence is more desirable for its lower-prime applications than a >> 17-comma symbol. In addition, it is consistent as the rational >> complement of /||). Neither of our options has rational >> complementation throughout.> OK. I'll go with yours. 159a.I've been reviewing a lot of these divisions over the past few days, and I now think that ~|\ is not a very good choice for 5deg159. If we used the 7 comma instead of the 11-5 comma for 4deg (thereby foregoing matching symbols, as you proposed for 125) and the 5+5 comma instead of the 13 diesis for 6deg, then a combination of our two proposals would work very nicely: 159c: |( ~|( /| |) (|( //| /|\ (|) ~|| ~||( ||) ||\ (|| ( /||) /||\ (RC) This has the advantage of having the lowest prime-number choices for all of the single-shaft symbols, which are (in addition) valid in all of their roles. Besides, 7 is slightly more accurate than 13 in 159. I would not have thought of doing anything like this before your proposal for replacing |\ with |) for 125, which I agreed to in message #4664 (and with which I now agree even more strongly): 125b: |( /| |) //| /|\ (|) ~|| ||) ||\ /||) /||\ (RC) --- In tuning-math@y..., "gdsecor" <gdsecor@y...> wrote [#4656]:> --- In tuning-math@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:>> --- In tuning-math@y..., "gdsecor" <gdsecor@y...> wrote: >>>>>> 171: |( ~|( /| |) |\ ~|\ /|) /|\ (|\ ~||( /|| ||)||\ ~||\ /||) /||\>> >> I think I prefer >> 171b: |( ~|( /| |) |\ //| /|) /|\ (|\ ~||( /|| ||)||\ //|| /||) /||\> > Okay!After reviewing 171, I am totally in agreement with your choice of single-shaft symbols, but I would like to see meaningful double-shaft symbols. May we use their rational complements? 171c: |( ~|( /| |) |\ //| /|) /|\ (|\ ~|| /|| ||) ||\ (||( /||) /||\ (RC) Since abandonment of matching sequences in 125 and 159 would require that rational complementation be the determining principle for the double-shaft symbols, and since it is RC rather than MS that are the usual determining principle for the smaller divisions, I believe that RC will be as least as important as MS as an organizing principle for aiding in the memorization of symbols in ETs. If a division has both, then that's great, but if it can have just one, shouldn't it be RC, especially if there are no unusual single-shaft symbols? After all, the more a principle is used, the better it is remembered. Change of subject: Regarding 152, our discussion about this has been extensive, but I will quote only the end of my last message (#4682) about this: [GS:]> You followed up that thought in a subsequent message (#4673), which I will > include here: [DK:]>> Now that I've looked at this myself, I definitely agree that 2deg152 should >> be ~|(. There's more of an argument for 3deg217 being |~. I can accept >> either /|~ or (|( for 5deg152. I also realised that we should not be using >> 13-comma symbols in 152. It has inconsistent 13s. The symbol //| is quite >> valid (in all its roles) for 6deg152. >> >> 152j: )| ~|( /| |\ (|( //| /|\ (|) )|| ~||( /|| ||\(||( //|| /||\ (MS)>> 152k: )| ~|( /| |\ /|~ //| /|\ (|) )|| ~||( /||||\ /||~ //|| /||\ (MS)> You have a couple of good points there. Using ~|( agrees with itsuse in 494> as 2/3 of the 5 comma. > If those who attach harmonic meaning to the symbols recognize that ratios of > 13 are compromised in 152, then they would readily accept the factthat (|( is> not valid as the 7:13 comma. So I have no objections to using the single-shaft > symbols of 152j. I have some reservations about the meaningof //|| being> misleading, since it's not valid as the complement of the 17 comma,but at this> point I can provide neither a good alternative proposal nor a good rationale for > using something else, so I can't disagree with what you have. > I will have to see if there are any other divisions for which //|might be more> appropriate than /|) and if there is any advantage in changingthose from what> we already have.Relevant to my last remark is my proposal for 159, above. After doing the above divisions and making my latest comments, I would now like to use your single-shaft symbols from 152j and have rational complements instead of matching symbols: 152m: )| ~|( /| |\ (|( //| /|\ (|) ~|| ~||( /|| ||\ (|| ( (||~ /||\ (RC) This for the same reasons I gave for 171, above. --George

Message: 5463 - Contents - Hide Contents Date: Mon, 28 Oct 2002 10:36:04 Subject: Re: A common notation for JI and ETs From: David C Keenan At 07:35 PM 26/10/2002 -0700, you wrote:>From: George Secor, 10/26/2002 (#4897) >Subject: A common notation for JI and ETs > >--- In tuning-math@y..., "dkeenanuqnetau" <d.keenan@u...> wrote >[#4662]:>> --- In tuning-math@y..., "gdsecor" <gdsecor@y...> wrote:>>> --- In tuning-math@y..., David C Keenan <d.keenan@u...> wrote:>>>> --- In tuning-math@y..., "gdsecor" <gdsecor@y...> wrote: >>>>>>>>>> 159a: |( ~|( /| |\ ~|\ /|) /|\ (|) (|\ ~||( /|| ||\>~||\ /||) /||\ >>>> >>>> I prefer>>>> 159b: ~| ~|( /| |\ (|( /|) /|\ (|) (|\ ~||( /|| ||\>(||( /||) /||\ (RC & MS) >>>>>> The (| flag is not the same number of degrees in (|( and (|\, so >(|( is >>> not valid. >>> >>> I prefer |( because it is valid as the 5:7, 11:13, and 17'-17 >commas,>>> hence is more desirable for its lower-prime applications than a >>> 17-comma symbol. In addition, it is consistent as the rational >>> complement of /||). Neither of our options has rational >>> complementation throughout. >>> OK. I'll go with yours. 159a. >>I've been reviewing a lot of these divisions over the past few days, >and I now think that ~|\ is not a very good choice for 5deg159. If we >used the 7 comma instead of the 11-5 comma for 4deg (thereby foregoing >matching symbols, as you proposed for 125) and the 5+5 comma instead of >the 13 diesis for 6deg, then a combination of our two proposals would >work very nicely: > >159c: |( ~|( /| |) (|( //| /|\ (|) ~|| ~||( ||) ||\ (||( >/||) /||\ (RC) > >This has the advantage of having the lowest prime-number choices for >all of the single-shaft symbols, which are (in addition) valid in all >of their roles. Besides, 7 is slightly more accurate than 13 in 159.OK. Yes. This looks fine.>--- In tuning-math@y..., "gdsecor" <gdsecor@y...> wrote [#4656]:>> --- In tuning-math@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:>>> --- In tuning-math@y..., "gdsecor" <gdsecor@y...> wrote: >>>>>>>> 171: |( ~|( /| |) |\ ~|\ /|) /|\ (|\ ~||( /|| ||)>||\ ~||\ /||) /||\ >>>>>> I think I prefer >>> 171b: |( ~|( /| |) |\ //| /|) /|\ (|\ ~||( /|| ||) ||\> //|| /||) /||\ >> >> Okay! >>After reviewing 171, I am totally in agreement with your choice of >single-shaft symbols, but I would like to see meaningful double-shaft >symbols. May we use their rational complements? > >171c: |( ~|( /| |) |\ //| /|) /|\ (|\ ~|| /|| ||) ||\ >(||( /||) /||\ (RC) > >Since abandonment of matching sequences in 125 and 159 would require >that rational complementation be the determining principle for the >double-shaft symbols, and since it is RC rather than MS that are the >usual determining principle for the smaller divisions, I believe that >RC will be as least as important as MS as an organizing principle for >aiding in the memorization of symbols in ETs. If a division has both, >then that's great, but if it can have just one, shouldn't it be RC, >especially if there are no unusual single-shaft symbols? After all, >the more a principle is used, the better it is remembered.OK. I'll go along with this.>Change of subject: Regarding 152, our discussion about this has been >extensive, but I will quote only the end of my last message (#4682) >about this: > >[GS:]>> You followed up that thought in a subsequent message (#4673), which I >will >> include here: > >[DK:]>>> Now that I've looked at this myself, I definitely agree that >2deg152 should>>> be ~|(. There's more of an argument for 3deg217 being |~. I can >accept>>> either /|~ or (|( for 5deg152. I also realised that we should not >be using>>> 13-comma symbols in 152. It has inconsistent 13s. The symbol //| is >quite>>> valid (in all its roles) for 6deg152. >>> >>> 152j: )| ~|( /| |\ (|( //| /|\ (|) )|| ~||( /|| ||\>(||( //|| /||\ (MS)>>> 152k: )| ~|( /| |\ /|~ //| /|\ (|) )|| ~||( /|| ||\>/||~ //|| /||\ (MS) >>> You have a couple of good points there. Using ~|( agrees with its>use in 494>> as 2/3 of the 5 comma. > >> If those who attach harmonic meaning to the symbols recognize that >ratios of>> 13 are compromised in 152, then they would readily accept the fact>that (|( is>> not valid as the 7:13 comma. So I have no objections to using the >single-shaft>> symbols of 152j. I have some reservations about the meaning of //|| >being>> misleading, since it's not valid as the complement of the 17 comma,>but at this>> point I can provide neither a good alternative proposal nor a good >rationale for>> using something else, so I can't disagree with what you have. > >> I will have to see if there are any other divisions for which //|>might be more>> appropriate than /|) and if there is any advantage in changing those >from what>> we already have. >>Relevant to my last remark is my proposal for 159, above. > >After doing the above divisions and making my latest comments, I would >now like to use your single-shaft symbols from 152j and have rational >complements instead of matching symbols: > >152m: )| ~|( /| |\ (|( //| /|\ (|) ~|| ~||( /|| ||\ (||( >(||~ /||\ (RC) > >This for the same reasons I gave for 171, above.Yes. This makes sense. -- Dave Keenan Brisbane, Australia Dave Keenan's Home Page * [with cont.] (Wayb.)

Message: 5464 - Contents - Hide Contents Date: Mon, 28 Oct 2002 22:37:48 Subject: Re: A common notation for JI and ETs From: gdsecor --- In tuning-math@y..., "gdsecor" <gdsecor@y...> wrote [#4664]:> --- In tuning-math@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:>> --- In tuning-math@y..., "gdsecor" <gdsecor@y...> wrote:>>> --- In tuning-math@y..., David C Keenan <d.keenan@u...> wrote:>>>> --- In tuning-math@y..., "gdsecor" <gdsecor@y...> wrote: >>>>>>>>>> 176a: |( |~ /| |) |\ ~|) /|) /|\ (|) (|\||~ /|| ||) ||\ ~||) /||) /||\ (RC & MS)>>>>> 176b: |( ~| /| |) |\ ~|) /|) /|\ (|) (|\~|| /|| ||) ||\ ~||) /||) /||\ (MS & MM)>>>> >>>> Of those two, I prefer 176a, but I like these single-shafters better >>>> 176c: |( |~ /| |) |\ //| /|) /|\ (|) (|\ >>>> 176d: |( ~| /| |) |\ //| /|) /|\ (|) (|\ >>>>>> This is another of the half-dozen larger divisions in which it is >>> possible to have both matching symbols and complete rational >>> complementation (version 176a), but it is at the price of using a >>> couple of relatively unimportant symbols. Evidently you didn't care >>> too much for them. >>> >>> Your versions differ only in using //| for 6deg. This time for //| >>> it's only 1 out of 3: as the 5+5 comma, but not as the 25 or 5:13 >>> commas. For the more nondescript symbol ~|) it's 1 out of 2: as the >>> 7+17 comma, but not as the 5:17 comma; but this is of little >>> significance -- it's just a symbol to match ~||), the rational >>> complement of |~. >>> >>> For (|(, a symbol that neither of us chose, it's 3 out of 3: as 5:11, >>> 7:13, and 11:17 commas, but its unidecimal-diesis complement ~|( does >>> not have the same number of degrees for the |( flag, so ~|( can't be >>> used. With this many degrees in the apotome I thought it advisable to >>> use matching symbols, so if I were to pick the best single-shaft >>> symbols and duplicate the flags in the double-shaft symbols, I would >>> have this: >>> >>> 176e: |( ~| /| |) |\ (|( /|) /|\ (|) (|\ ~|| /||||) ||\ (||( /||) /||\ (MS)>>> >>> On the other hand, using the same single-shaft symbols along with their >>> rational complements would give this: >>> >>> 176f: |( ~| /| |) |\ (|( /|) /|\ (|) (|\ ~||( /||||) ||\ //|| /||) /||\ (RC)>>> >>> I'm beginning to wonder whether it would be more meaningful to have >>> rational complements (instead of matching flags) for the double- shaft >>> symbols whenever there is a good set of single-shaft symbols. (I'll >>> have to try experimenting with the second half-apotome of some of these >>> larger divisions to see how often that will work without the symbol >>> arithmetic going to pieces.) >>> >>> Anyway, what do you think of the single-shaft symbols in those last >>> two? >>>> I like em. >> I thought so. I think I'll defer a decision on the double-shaftsymbols for a> little while, because I don't know which ones I prefer.I'm glad that I waited on this, because with the passage of time comes a better perspective. I now have a new proposal for this one that changes one of your single-shaft symbols, replacing the 17 comma with the 17' comma: 176g: |( ~|( /| |) |\ (|( /|) /|\ (|) (|\ ~||( /|| ||) ||\ (||( /||) /||\ (RC & MS) With this we get both rational complements and matching symbols as in my initial (176a) proposal, but with better single-shaft symbols. I think that the reason why I didn't try this before is that I found that |( is technically not the same number of degrees in the first two symbols. But since ~| is not found in any other single-shaft symbol, it doesn't matter, because the symbol arithmetic is still consistent. In addition, ~|( is correct as the 17' comma for 2deg176, while |( is correct as 1deg for both the 5:7 and 11:13 commas, and all the other symbols are valid in all of their roles. So I would say this one's a winner! --George

Message: 5466 - Contents - Hide Contents Date: Wed, 30 Oct 2002 15:20:24 Subject: Re: NMOS From: monz hey guys, i missed something at the beginning of this thread. what the heck is "NMOS" and "2MOS"? (sheesh ... i had a hard enough time understanding "MOS" at first ...) -monz

Message: 5467 - Contents - Hide Contents Date: Wed, 30 Oct 2002 22:05:01 Subject: Re: NMOS From: monz> From: "Gene Ward Smith" <genewardsmith@xxxx.xxx> > To: <tuning-math@xxxxxxxxxxx.xxx> > Sent: Wednesday, October 30, 2002 5:35 PM > Subject: [tuning-math] Re: NMOS > > > --- In tuning-math@y..., "monz" <monz@a...> wrote: >> hey guys, >> >>>> i missed something at the beginning of this thread. >> what the heck is "NMOS" and "2MOS"? >> A 2MOS would be a scale of 2M notes to each period (eg, octaves) withgenerator g, where M notes to a period with generator g is a MOS. thanks, Gene, but ... hmmm -- i think i'd understand this a whole lot better with an example. and i still don't have any idea what "NMOS" is. -monz

Message: 5469 - Contents - Hide Contents Date: Thu, 31 Oct 2002 01:35:19 Subject: Re: NMOS From: Gene Ward Smith --- In tuning-math@y..., "monz" <monz@a...> wrote:> hey guys, > > > i missed something at the beginning of this thread. > what the heck is "NMOS" and "2MOS"?A 2MOS would be a scale of 2M notes to each period (eg, octaves) with generator g, where M notes to a period with generator g is a MOS.

Message: 5470 - Contents - Hide Contents Date: Thu, 31 Oct 2002 19:06:08 Subject: Re: New file uploaded to tuning-math From: Carl Lumma This .gif is golden. But I forget the coloring scheme... -Carl

Message: 5472 - Contents - Hide Contents Date: Thu, 31 Oct 2002 06:59:15 Subject: Re: NMOS From: wallyesterpaulrus --- In tuning-math@y..., "monz" <monz@a...> wrote:>>> From: "Gene Ward Smith" <genewardsmith@j...> >> To: <tuning-math@y...> >> Sent: Wednesday, October 30, 2002 5:35 PM >> Subject: [tuning-math] Re: NMOS >> >> >> --- In tuning-math@y..., "monz" <monz@a...> wrote: >>> hey guys, >>> >>>>>> i missed something at the beginning of this thread. >>> what the heck is "NMOS" and "2MOS"? >>>> A 2MOS would be a scale of 2M notes to each period (eg, octaves) with> generator g, where M notes to a period with generator g is a MOS. > > > thanks, Gene, but ... hmmm -- i think i'd understand this > a whole lot better with an example.helmholtz 24 is an example, as is groven 36. the MOS is the 12-note scale in schismic temperament, and these tunings are 2MOS and 3MOS, repectively.

Message: 5473 - Contents - Hide Contents Date: Thu, 31 Oct 2002 11:33:57 Subject: Dictionary of Tuning Terms URL (was: NMOS) From: monz ----- Original Message ----- From: <paul.hjelmstad@xx.xxx.xxx> To: <tuning-math@xxxxxxxxxxx.xxx> Sent: Thursday, October 31, 2002 11:28 AM Subject: Re: [tuning-math] Re: NMOS> > Message for Joe Monzo: > > I can no longer get to your Definition of Tuning Terms > page. Please provide a new link. THANKS! Definitions of tuning terms: index, (c) 1998 b... * [with cont.] (Wayb.) -monz

Message: 5474 - Contents - Hide Contents Date: Thu, 31 Oct 2002 21:31:55 Subject: Re: New file uploaded to tuning-math From: wallyesterpaulrus --- In tuning-math@y..., "Carl Lumma" <clumma@y...> wrote:> This .gif is golden. > > But I forget the coloring scheme... > > -Carlbluish = consistent reddish = inconsistent is that what you meant?

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