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Message: 9300 - Contents - Hide Contents Date: Mon, 19 Jan 2004 01:02:42 Subject: Re: Question for Dave Keenan From: Carl Lumma>> > suppose you'd like to call it 5-limit consonance, and I would have >> no great objection to that. But what I want to know is, how can we >> tell whether it's happening or not? >>A psychological experiment concerning 'roots', perhaps? Ultimately it >will come down to perception and the reporting of perception, which >as we know, are not amenable to the exact sciences.No, you just ask people to walk over to the piano and pick out the notes they've heard. Rinse, lather, repeat. You'll find massive agreement.>> Let's assume we agree on what >> sounds consonant. How would we tell if the consonance is due to one >of>> these approximate 5-limit alignments or some other more complex but >> more accurate alignment. >>Well the perceived position of the 'root' would determine that. Exactly. -Carl
Message: 9301 - Contents - Hide Contents Date: Mon, 19 Jan 2004 01:10:27 Subject: Re: Annotated Dave Keenan file From: Carl Lumma>>> >owever, <4 -3 -17 -14 -38 -31| is closer, <4 -3 21 -14 22 57| much >>> closer yet, and <4 -3 40 -14 52 101| has the identical TOP tuning. >>>> The TOP tuning of what? > >Negri. >>>> What to do? >>>> I don't get it. Paul's temperament database doesn't list tertiathirds >> so I don't know what comma(s) tertiathirds was based on. If it's >> previously been a 5-limit linear temperament I don't see how it could >> have <-4 3] the same as negri. >>Tertiathirds is a name for the 7-limit temperament with TM comma base >{49/48, 225/224}, wedgie <<4 -3 2 -14 -8 13|| and mapping >[<1 2 2 3|, <0 -4 3 -2|]. There's been a question all along as to >whether it should be called "negri", and I suppose it should be; it's >pretty closely tied to 2/19 as a generator either way.It should; these other maps should be sent back to the cleaners. -Carl
Message: 9302 - Contents - Hide Contents Date: Mon, 19 Jan 2004 03:58:18 Subject: Re: Question for Dave Keenan From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx "Carl Lumma" <ekin@l...> wrote:>>> And can we hear a >>> sustained note around middle C. >> >> Yahoo groups: /tuning_files/files/Erlich/dave1... * [with cont.] >> Wrong file, Paul? > > -CarlTry it now.
Message: 9303 - Contents - Hide Contents Date: Mon, 19 Jan 2004 01:12:08 Subject: Re: A potentially informative property of tunings From: Carl Lumma>> >he mutation sequence for quarter-comma meantone skips over (-1, 9) and >> goes straight to (7, -10), followed by (-6, 21). >>If you want to go out this far to map 7, it probably makes more sense >to use a sharper fifth and (12, -22) for the map. This is a >temperament for meantones in the neighborhood of 67-et, and since >55-et falls in there we could be evil and call it "moztone", but given >the nature of Mozart's use of meantone that hardly makes sense. In any >case, its badness is so high because of the high complexity to get to >7s harmony it hardly makes sense to use this for an alternative to >septimal meantone. Jon might be happy with its TOP tuning, since >octaves are only a smidgen flat.I wonder if this has anything to do with the attached? -Carl [This message contained attachments]
Message: 9304 - Contents - Hide Contents Date: Mon, 19 Jan 2004 04:05:20 Subject: Re: Warping along a line From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote:> Suppose I have a piece in four-part, mostly 5-limit harmony in > porcupine, and another such piece in meantone. Suppose I take each > part in the porcupine piece, calculate the generator, and add it to > the generator of the meantone piece, then consider this to be a > generator of something in tetracot, and find a suitable octave to go > with the generator to get a note somewhere in the region of the > average of my other two notes. > > What does this give us? If the two chords are major triads and the > root, thirds and fifths correspond for the two pieces, then the result > will be a major triad with the same arrangement of root, thirds and > fifths. The same is also true if both chords are minor triads. If one > chord is major and the other is minor, then the result will be the > neutral thirds triad which is one of the features of tetracot. If the > chords are in a different inversion, then results will vary, but an > alternative approach would be to match root, third and fifth before > doing the addition. > > This is an example of what sort of warping could be done; a mutant > tetracot piece obtained by crossing a porcupine with a meantone piece. > I think it has possibilities.Maybe we should ask for volunteers to compose the two pieces in question, and get an agreement on the length of the piece and its overall structure. Presented nicely, such a request might generate interest on makemicromusic or tuning.
Message: 9305 - Contents - Hide Contents Date: Mon, 19 Jan 2004 01:15:46 Subject: Re: Question for Dave Keenan From: Carl Lumma>> > psychological experiment concerning 'roots', perhaps? Ultimately it >> will come down to perception and the reporting of perception, which >> as we know, are not amenable to the exact sciences. >>No, you just ask people to walk over to the piano and pick out the >notes they've heard. Rinse, lather, repeat. You'll find massive >agreement.I'm assuming the predicted fundamentals will be based on the beep mapping -- that the spectra are set up with the nearest beep-mapped approx. to the harmonics. That is what your test tones (Paul) are, right? -Carl
Message: 9306 - Contents - Hide Contents Date: Mon, 19 Jan 2004 04:14:28 Subject: Re: A potentially informative property of tunings From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx Herman Miller <hmiller@I...> wrote:> Take a generator of 260.76 cents and a period of 1206.55 cents. This > defines a linear tuning which belongs to a family of related linear > temperaments. The simplest mapping is the "beep" mapping, which distributes > the 27;25 interval: > > [(1, 0), (2, -2), (3, -3)] > > but after 6 iterations of the generator, there's a better 5:1 at (1, 6), > about 15 cents flat (compared with the 51 cent sharp "beep" version of the > interval).Gotcha. Yup, it was essentially this 'consistency range' deal which caused us originally to reject certain temperaments (you might search for 'funky' on this list) which, as I recall, had a consistency range of 0.> First of all, I don't like the term "consistency range", but I couldn't > think of anything better.I like it fine, and in multi-period-per-octave tunings, I would multiply by the number of periods per octave, so that the right number of tones is involved. But which intervals are you testing? You would need to know this too to determine the "maximum consistency" version of any temperament.
Message: 9307 - Contents - Hide Contents Date: Mon, 19 Jan 2004 04:18:01 Subject: Re: Question for Dave Keenan From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx "Dave Keenan" <d.keenan@b...> wrote:> But remember that the disagreement on things like "beep" and "father" > is not whether they contain consonances but whether those consonances > have anything to do with their supposed 5-limit mappings.What would you call a virtual-pitch-based phenomenon where chord tones are assigned by the brain to specific partials within a subsuming 'harmony' -- to take typical examples, 3:4:5, 4:5:6, 5:6:8, or hypothetically, 10:12:15 (or still more hypothetically -- remember George Kahrimanis? -- 1/6:1/5:1/4)?
Message: 9308 - Contents - Hide Contents Date: Mon, 19 Jan 2004 09:21:40 Subject: Re: Question for Dave Keenan From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:> I'm assuming the predicted fundamentals will be based on the beep > mapping -- that the spectra are set up with the nearest beep-mapped > approx. to the harmonics. That is what your test tones (Paul) are, > right? > > -CarlNo, those were the top pelogic rounded to 0.1 cent ones, since that's what I asked Dave about in the original message.
Message: 9309 - Contents - Hide Contents Date: Mon, 19 Jan 2004 01:26:55 Subject: Re: Question for Dave Keenan From: Carl Lumma>> >'m assuming the predicted fundamentals will be based on the beep >> mapping -- that the spectra are set up with the nearest beep-mapped >> approx. to the harmonics. That is what your test tones (Paul) are, >> right? >> >> -Carl >>No, those were the top pelogic rounded to 0.1 cent ones, since that's >what I asked Dave about in the original message.Ok, but what I meant was, you have some way to make the predicted fundamental come out differently if the 2ndary approximations are at work? -Carl
Message: 9310 - Contents - Hide Contents Date: Mon, 19 Jan 2004 04:19:34 Subject: Re: Question for Dave Keenan From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx "Dave Keenan" <d.keenan@b...> wrote:> --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote:>> --- In tuning-math@xxxxxxxxxxx.xxxx "Dave Keenan" <d.keenan@b...>>>> And can we hear a >>> sustained note around middle C. >> >> Yahoo groups: /tuning_files/files/Erlich/dave1... * [with cont.] >> I didn't find a sustained note there.Try it now.
Message: 9311 - Contents - Hide Contents Date: Mon, 19 Jan 2004 05:01:42 Subject: Re: TOP on the web From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote:> Here's some data on superpelog. You can see the top tunings for it > correspond in the 5, 7 and 11 limits, so would you object to simply > calling this "pelog", and saying "11-limit pelog" or "7-limit pelog" > if you want to be more specific? They have the same generators. > > TOP 5: [1206.548265, 1891.576247, 2771.109113] > TOP 7: [1206.548264, 1891.576247, 2771.109113, 3358.884653] > TOP 11: [1206.548264, 1891.576247, 2771.109113, 3358.884653, 4141.165078] > > Wedgies > pelog7: <<2 -6 1 -14, -4 19|| > pelog11: <<2 -6 1 -2 -14 -4 -10 19 16 -9}|| > > TM comma basis > 5 limit: {135/128} > 7 limit: {135/128, 49/48} > 11 limit: {33/32, 45/44, 49/48, 33/32}33/32 twice? ;)
Message: 9312 - Contents - Hide Contents Date: Mon, 19 Jan 2004 09:28:10 Subject: Re: Question for Dave Keenan From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:>>> I'm assuming the predicted fundamentals will be based on the beep >>> mapping -- that the spectra are set up with the nearest beep- mapped >>> approx. to the harmonics. That is what your test tones (Paul) are, >>> right? >>> >>> -Carl >>>> No, those were the top pelogic rounded to 0.1 cent ones, since that's >> what I asked Dave about in the original message. >> Ok, but what I meant was, you have some way to make the predicted > fundamental come out differently if the 2ndary approximations are > at work?You lost me.
Message: 9313 - Contents - Hide Contents Date: Mon, 19 Jan 2004 05:01:43 Subject: Re: Strange9 From: Dave Keenan --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote:> On Dave's web page is a discussion of "Strange9" > > KeenanTuning * [with cont.] (Wayb.) > > This is either Pajara, Pajara[10], or both.How can it be Pajara. It is planar. Pajara is linear. How can it be any [10]? It has 12 notes.> Dave wanted to beat Paul's > Pajara[10] tuned to 22-equal, and ended up detempering it, though not > on purpose. Paul came up with "Pajara" as a name for the temperament; > I'm wondering if Dave was proposing "Strange" or "Strange9" for it.I used "Strange9" for the article, but had no thoughts of any wider context, such as catalogs of temperaments, at the time.
Message: 9314 - Contents - Hide Contents Date: Mon, 19 Jan 2004 09:31:08 Subject: Re: A potentially informative property of tunings From: Carl Lumma> I wonder if this has anything to do with the attached?Which got repeated to me via e-mail, but I'm glad I checked the web site, which sucks. Here is the file... http://lumma.org/tuning/01.gif - Type Ok * [with cont.] (Wayb.) -Carl
Message: 9315 - Contents - Hide Contents Date: Mon, 19 Jan 2004 05:14:53 Subject: Re: Strange9 From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Dave Keenan" <d.keenan@b...> wrote:> --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> > wrote:>> On Dave's web page is a discussion of "Strange9" >> >> KeenanTuning * [with cont.] (Wayb.) >> >> This is either Pajara, Pajara[10], or both. >> How can it be Pajara. It is planar.What you describe on your website is not planar, since you show it as equating things 50/49, 64/63 and 225/224 apart. Pajara is linear. How can it be> any [10]? It has 12 notes. Sorry, Pajara[12].
Message: 9316 - Contents - Hide Contents Date: Mon, 19 Jan 2004 09:33:25 Subject: Re: A potentially informative property of tunings From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx "Carl Lumma" <ekin@l...> wrote:>> I wonder if this has anything to do with the attached? >> Which got repeated to me via e-mail, but I'm glad I checked > the web site, which sucks. > > Here is the file... > > http://lumma.org/tuning/01.gif - Type Ok * [with cont.] (Wayb.) > > -CarlI see two searchlights, nothing else.
Message: 9317 - Contents - Hide Contents Date: Mon, 19 Jan 2004 01:34:37 Subject: Re: Question for Dave Keenan From: Carl Lumma>>>> >'m assuming the predicted fundamentals will be based on the beep >>>> mapping -- that the spectra are set up with the nearest beep- >>>> mapped approx. to the harmonics. That is what your test >>>> tones (Paul) are, right? >>>> >>>> -Carl >>>>>> No, those were the top pelogic rounded to 0.1 cent ones, since >>> that's what I asked Dave about in the original message. >>>> Ok, but what I meant was, you have some way to make the predicted >> fundamental come out differently if the 2ndary approximations are >> at work? >>You lost me.If the partials are individually at their nearest pelogic-mapped values and people consistently identify the 'fundamental' as being the pitch of the tone, could it be claimed that the extra-map consonances Dave is pointing out were at work? -Carl
Message: 9318 - Contents - Hide Contents Date: Mon, 19 Jan 2004 05:16:28 Subject: Re: TOP on the web From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote:>> 11 limit: {33/32, 45/44, 49/48, 33/32} >> 33/32 twice? ;)It's a set, Paul. I can list 33/32 as many times as I feel like, and it doesn't change anything. :)
Message: 9319 - Contents - Hide Contents Date: Mon, 19 Jan 2004 01:42:03 Subject: Re: A potentially informative property of tunings From: Carl Lumma>> >he mutation sequence for quarter-comma meantone skips over (-1, 9) and >> goes straight to (7, -10), followed by (-6, 21). //>>> I wonder if this has anything to do with the attached? >>>> Which got repeated to me via e-mail, but I'm glad I checked >> the web site, which sucks. >> >> Here is the file... >> >> http://lumma.org/tuning/01.gif - Type Ok * [with cont.] (Wayb.) >> >> -Carl >>I see two searchlights, nothing else.Oh, bother. This would have been much better: http://lumma.org/tuning/05.gif - Type Ok * [with cont.] (Wayb.) -Ca.
Message: 9320 - Contents - Hide Contents Date: Mon, 19 Jan 2004 05:32:14 Subject: Re: Question for Dave Keenan From: Dave Keenan --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote:> --- In tuning-math@xxxxxxxxxxx.xxxx "Dave Keenan" <d.keenan@b...> > wrote: >>> But remember that the disagreement on things like "beep" > and "father">> is not whether they contain consonances but whether those > consonances>> have anything to do with their supposed 5-limit mappings. >> What would you call a virtual-pitch-based phenomenon where chord > tones are assigned by the brain to specific partials within a > subsuming 'harmony' -- to take typical examples, 3:4:5, 4:5:6, 5:6:8, > or hypothetically, 10:12:15 (or still more hypothetically -- remember > George Kahrimanis? -- 1/6:1/5:1/4)?I suppose you'd like to call it 5-limit consonance, and I would have no great objection to that. But what I want to know is, how can we tell whether it's happening or not? Let's assume we agree on what sounds consonant. How would we tell if the consonance is due to one of these approximate 5-limit alignments or some other more complex but more accurate alignment. e.g. with TOP Beep, you were asking us to believe that the 260 c generator could be "experienced as" an approximate 5:6 even though it is only 7 cents away from 6:7, and 55 cents away from 5:6.
Message: 9321 - Contents - Hide Contents Date: Mon, 19 Jan 2004 05:36:14 Subject: Attn: Gene From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote:> --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> > wrote:>> --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> > wrote: >>>>> Now what if we apply 'odd-limit-weighting' to each of the > intervals,>>> including 9:3 which is treated as having an odd-limit of 9? Try >>> using 'odd-limit' plus-or-minus 1 or 1/2 too. >>>> Is the weighting by multiplying or dividing by the log of the odd >> limit? Presumably mutliplying will make more sense. >> Divide. As in TOP, errors of more complex intervals are divided by > larger numbers. >>> Do we square and >> then multiply, since we will be taking square roots? >> No, we want to apply the weighting directly to the errors, before > deciding how overall error is calculated from the individual weighted > errors. >>>>> I think my idea of using >>>> the dual norm to my "geometric" norm makes more sense. >>>>>> Why is that? >>>> It's more or less reasonable to start with. We have >> >> ||3/2|| = log2(3), ||9/8|| = 2log2(3), ||5/4|| = log2(5), >> ||6/5|| = log2(5), ||7/6|| = ||7/5|| = ||7/4|| = log2(7), >> ||11/6|| = ||11/7|| = ||11/8|| = ||11/10|| = log2(11), >> ||9/5|| = sqrt(2log2(3)^2 + log2(5)^2) >> ||9/7|| = sqrt(2log2(3)^2 + log2(7)^2) >> ||11/9|| = sqrt(2log2(3)^2 + log2(11)^2) >> >> which isn't too bad. >> OK, but I think my proposal above will make even more sense than > this. The two should agree for 7-odd-limit and below.
Message: 9322 - Contents - Hide Contents Date: Mon, 19 Jan 2004 09:43:10 Subject: Re: Question for Dave Keenan From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:>>>>> I'm assuming the predicted fundamentals will be based on the beep >>>>> mapping -- that the spectra are set up with the nearest beep- >>>>> mapped approx. to the harmonics. That is what your test >>>>> tones (Paul) are, right? >>>>> >>>>> -Carl >>>>>>>> No, those were the top pelogic rounded to 0.1 cent ones, since >>>> that's what I asked Dave about in the original message. >>>>>> Ok, but what I meant was, you have some way to make the predicted >>> fundamental come out differently if the 2ndary approximations are >>> at work? >>>> You lost me. >> If the partials are individually at their nearest pelogic-mapped > values and people consistently identify the 'fundamental' as > being the pitch of the tone, could it be claimed that the extra-map > consonances Dave is pointing out were at work?How could they possibly come into play? The map (from primes -- clearly generators are irrelevant here) is only carried out as far as a single big major triad, no further. The melodic intervals, should it matter, were not pelogic ones.
Message: 9323 - Contents - Hide Contents Date: Mon, 19 Jan 2004 02:07:00 Subject: Re: Question for Dave Keenan From: Carl Lumma>>>>>> >'m assuming the predicted fundamentals will be based on the >>>>>> beep mapping -- that the spectra are set up with the nearest >>>>>> beep-mapped approx. to the harmonics. That is what your test >>>>>> tones (Paul) are, right? >>>>>> >>>>>> -Carl >>>>>>>>>> No, those were the top pelogic rounded to 0.1 cent ones, since >>>>> that's what I asked Dave about in the original message. >>>>>>>> Ok, but what I meant was, you have some way to make the predicted >>>> fundamental come out differently if the 2ndary approximations are >>>> at work? >>>>>> You lost me. >>>> If the partials are individually at their nearest pelogic-mapped >> values and people consistently identify the 'fundamental' as >> being the pitch of the tone, could it be claimed that the extra-map >> consonances Dave is pointing out were at work? >>How could they possibly come into play? The map (from primes -- >clearly generators are irrelevant here) is only carried out as far as >a single big major triad, no further.Just clarifying. So one could conduct this experiment and if the results are as I suggest it would allow one to reasonably claim that the 5-limit (if one didn't use any other partials in the synthesis) approximations of pelogic are indeed 5-limit approximations. -Carl
Message: 9324 - Contents - Hide Contents Date: Mon, 19 Jan 2004 05:42:03 Subject: Re: Strange9 From: Dave Keenan --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote:> --- In tuning-math@xxxxxxxxxxx.xxxx "Dave Keenan" <d.keenan@b...> > wrote:>> --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> >> wrote:>>> On Dave's web page is a discussion of "Strange9" >>> >>> KeenanTuning * [with cont.] (Wayb.) >>> >>> This is either Pajara, Pajara[10], or both. >>>> How can it be Pajara. It is planar. >> What you describe on your website is not planar, since you show it as > equating things 50/49, 64/63 and 225/224 apart.Hmm. Then I'd like to understand what's going on. Because it relies on having two different sizes of fifth. i.e. it has two generators in addition to the half-octave period. You can see its error minimum on the charts, in a valley going off at right angles to the Pajara line (where both fifth sizes are the same). Did I make a mistake with the rationalisations, or am I using an inconsistent mapping?
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