This is an Opt In Archive . We would like to hear from you if you want your posts included. For the contact address see About this archive. All posts are copyright (c).
- Contents - Hide Contents - Home - Section 65000 5050 5100 5150 5200 5250 5300 5350 5400 5450 5500 5550 5600 5650 5700 5750 5800 5850 5900 5950
5600 - 5625 -
Message: 5603 - Contents - Hide Contents Date: Sat, 23 Nov 2002 09:56:47 Subject: Re: Adaptive JI notated on staff From: monz i added Dave's graphic and a MIDI-file of it to my "adaptive-JI" definition: Definitions of tuning terms: adaptive JI, (c) ... * [with cont.] (Wayb.) -monz ----- Original Message ----- From: "Dave Keenan" <d.keenan@xx.xxx.xx> To: <tuning-math@xxxxxxxxxxx.xxx> Sent: Friday, November 22, 2002 8:01 PM Subject: [tuning-math] Re: Adaptive JI notated on staff> --- In tuning-math@y..., "dkeenanuqnetau" <d.keenan@u...> wrote: > > --- In tuning-math@y..., "emotionaljourney22" <paul@s...> wrote: >>>> right, but i'd like to see this actually notated, on a staff. >> Here it is. > Yahoo groups: /tuning-math/files/Dave/Adaptive... * [with cont.]
Message: 5604 - Contents - Hide Contents Date: Sat, 23 Nov 2002 00:08:14 Subject: Re: 5-limit comma names From: Gene Ward Smith --- In tuning-math@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...> wrote:> is there no n for which this would be ambiguous?Certainly there are--80 is a convergent for 9/7 and 11/10, for instance. If you go out far enough any n will be ambiguous.
Message: 5605 - Contents - Hide Contents Date: Sat, 23 Nov 2002 18:18:57 Subject: Paul's new names From: Gene Ward Smith Here are some comma/temperament names introduced on the dualzoomer series. I give the name, the comma, (weighted) complexity, rms error and badness in that order. dicot 25/24 1.597771 28.851897 117.684239 unicorn 16875/16384 4.719204 5.942563 624.568220 diaschizoid 6561/6250 5.526963 8.492497 1433.821424 schizoid 262144/253125 6.027920 5.487501 1201.924424 valentine 1990656/1953125 7.198353 2.983296 1112.745097 shibboleth 1953125/1889568 8.141716 4.245388 2291.212088 sycamore 48828125/47775744 8.794602 2.796055 1901.928533 vulture 10485760000/10460353203 13.577520 .153767 384.880223 crazy 9010162353515625/9007199254740992 17.879417 .017725 101.309796 tricot 68719476736000/68630377364883 19.249427 .057500 410.130475 "Dicot" I've been calling "neutral thirds", which might be confusing. "Unicorn" I called "negrisma"--did I get that wrong? "Crazy" seems to be a mutant form of my "quasiseptima", but where "vulture" comes from I have no idea. It's not as bad as it sounds, though!
Message: 5606 - Contents - Hide Contents Date: Sat, 23 Nov 2002 04:01:48 Subject: Re: Adaptive JI notated on staff From: Dave Keenan --- In tuning-math@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...> wrote:> --- In tuning-math@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:>> --- In tuning-math@y..., "emotionaljourney22" <paul@s...> wrote:>>> right, but i'd like to see this actually notated, on a staff. >>> this notation . . . personally, it doesn't do much for me -- for > example, looking at this 217-equal example, > > Yahoo groups: /tuning-math/files/Dave/Adaptive... * [with cont.] > > only a few of the pure thirds are immediately recognizable from the > notation, unless you've memorized all the symbols and the order in > which they occur in 217-equal. the symbol for a syntonic comma > alteration will quickly be learned by any user of the system, but all > the sets of symbols whose difference is a syntonic comma in a given > tuning?Hi Paul. Thanks for your belated response. I totally agree with you re the adaptive JI example. But surely you're not rejecting all possible uses of the notation on the basis of that? I gave that example, not because I thought it was a particularly good use of the notation, but in response to your request in message 3993:>> i think it would be cool if someone notated the adaptive-ji version >> of the chord progression >> >> Cmajor -> A minor -> D minor -> G major -> C major >> >> in 217-equal. then we could all look at it and see if we have any >> major problems with it.Can you tell us what you expect of a notation for 217-ET? How might it be done better so the pure thirds could all be immediately recognisable? Surely any notation for something as large as 217-ET will require a significant learning curve? Why not tell us instead how you feel about the way the notation would work in your old favourite, 22-ET. It only needs one pair of new symbols /| (for the 5-comma), and its semantics are the same as the standard Scala one I've been promoting for ages, and I think it has the same semantics as the one Alison Monteith uses. Or in 31-ET, where there is also only one new pair of symbols /|\ which are simultaneously the 7-comma and the 11-comma (a semi-sharp in this case). Or in 72-ET where its semantics are identical to the Sims notation. Only the symbols change. /| |) /|\
Message: 5607 - Contents - Hide Contents Date: Sun, 24 Nov 2002 01:29:02 Subject: Re: 5-limit comma names From: Gene Ward Smith --- In tuning-math@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:> 2109375/2097152 "Georgema" > > After George Orwell (sorry, George. :))Somehow I missed the fact that this already has two different names on the Fokker list, one being Fokker's comma (the other is semicomma.)
Message: 5608 - Contents - Hide Contents Date: Sun, 24 Nov 2002 05:29:57 Subject: Re: Adaptive JI notated on staff From: wallyesterpaulrus you mention vicentino, but don't link to your fine page about him. note that the example in question (dave's) is a perfect illustration of what makes vicentino's tuning so good. --- In tuning-math@y..., "monz" <monz@a...> wrote:> i added Dave's graphic and a MIDI-file of it to my > "adaptive-JI" definition: > > Definitions of tuning terms: adaptive JI, (c) ... * [with cont.] (Wayb.) > > > > -monz > > > ----- Original Message ----- > From: "Dave Keenan" <d.keenan@u...> > To: <tuning-math@y...> > Sent: Friday, November 22, 2002 8:01 PM > Subject: [tuning-math] Re: Adaptive JI notated on staff > > >>> --- In tuning-math@y..., "dkeenanuqnetau" <d.keenan@u...> wrote: >> >> --- In tuning-math@y..., "emotionaljourney22" <paul@s...> wrote: >>>>>> right, but i'd like to see this actually notated, on a staff. >>>> Here it is. >> Yahoo groups: /tuning- * [with cont.] math/files/Dave/AdaptiveJI.bmp
Message: 5609 - Contents - Hide Contents Date: Sun, 24 Nov 2002 05:34:28 Subject: Re: Paul's new names From: wallyesterpaulrus --- In tuning-math@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:> Here are some comma/temperament names introduced on the dualzoomerseries. I give the name, the comma, (weighted) complexity, rms error and badness in that order.> > dicot 25/24 1.597771 28.851897 117.684239 > > unicorn 16875/16384 4.719204 5.942563 624.568220 > > diaschizoid 6561/6250 5.526963 8.492497 1433.821424 > > schizoid 262144/253125 6.027920 5.487501 1201.924424 > > valentine 1990656/1953125 7.198353 2.983296 1112.745097 > > shibboleth 1953125/1889568 8.141716 4.245388 2291.212088 > > sycamore 48828125/47775744 8.794602 2.796055 1901.928533 > > vulture 10485760000/10460353203 13.577520 .153767 384.880223 > > crazy 9010162353515625/9007199254740992 17.879417 .017725 101.309796 > > tricot 68719476736000/68630377364883 19.249427 .057500 410.130475 > > "Dicot" I've been calling "neutral thirds", which might be confusing. > "Unicorn" I called "negrisma"--did I get that wrong?you can find the real negri on my graph -- it's where 9, 10, and 19 intersect.>"Crazy" seems to be a mutant form of my "quasiseptima", how?
Message: 5610 - Contents - Hide Contents Date: Sun, 24 Nov 2002 06:43:33 Subject: Re: Paul's new names From: Gene Ward Smith --- In tuning-math@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...> wrote:>> "Crazy" seems to be a mutant form of my "quasiseptima", > how?Quasi --> crazy, as in "quasi wabbit!"
Message: 5611 - Contents - Hide Contents Date: Sun, 24 Nov 2002 07:44:17 Subject: Re: Paul's new names From: Gene Ward Smith --- In tuning-math@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...> wrote:>> "Unicorn" I called "negrisma"--did I get that wrong? >> you can find the real negri on my graph -- it's where 9, 10, and 19 > intersect.Here's the real unicorn: comma 1594323/1562500 complexity 8.939708723 rms error 2.173108990 badness 1552.571517
Message: 5612 - Contents - Hide Contents Date: Sun, 24 Nov 2002 01:18:19 Subject: Re: Adaptive JI notated on staff From: monz> From: "wallyesterpaulrus" <wallyesterpaulrus@xxxxx.xxx> > To: <tuning-math@xxxxxxxxxxx.xxx> > Sent: Saturday, November 23, 2002 9:29 PM > Subject: [tuning-math] Re: Adaptive JI notated on staff > > > --- In tuning-math@y..., "monz" <monz@a...> wrote:>> i added Dave's graphic and a MIDI-file of it to my >> "adaptive-JI" definition: >> >> Definitions of tuning terms: adaptive JI, (c) ... * [with cont.] (Wayb.) > >> you mention vicentino, but don't link to your fine > page about him. note that the example in question > (dave's) is a perfect illustration of what makes > vicentino's tuning so good.thanks, paul. actually, i mentioned Vicentino twice on the adaptive-JI definition page, and provided a link to my Vicentino page at the second mention ... i had just missed the first one, and a link has been added now. hmmm ... should i include the Dave's illustration of the 217edo comma-pump progression on my Vicentino page? -monz
Message: 5613 - Contents - Hide Contents Date: Mon, 25 Nov 2002 04:18:18 Subject: Re: Paul's new names From: wallyesterpaulrus --- In tuning-math@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:> --- In tuning-math@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...> wrote: >>>> "Crazy" seems to be a mutant form of my "quasiseptima", > >> how? >> Quasi --> crazy, as in "quasi wabbit!"h yes -- ara and i say that all the time -- so i propose we spell it "kwazy"!
Message: 5614 - Contents - Hide Contents Date: Mon, 25 Nov 2002 11:42:56 Subject: Re: Paul's new names From: Gene Ward Smith --- In tuning-math@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...> wrote:> h yes -- ara and i say that all the time -- so i propose we spell > it "kwazy"!I love it; "kwazy" it is.
Message: 5615 - Contents - Hide Contents Date: Mon, 25 Nov 2002 04:20:41 Subject: Re: Paul's new names From: wallyesterpaulrus --- In tuning-math@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:> --- In tuning-math@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...> wrote:>>> "Unicorn" I called "negrisma"--did I get that wrong? >>>> you can find the real negri on my graph -- it's where 9, 10, and 19 >> intersect. >> Here's the real unicorn: > > comma 1594323/1562500 > complexity 8.939708723 > rms error 2.173108990 > badness 1552.571517the list of commas came from monz's et page (with a few ridonculous ones deleted) . . . i'd like to know what is missing, based on some log-flat badness measure.
Message: 5616 - Contents - Hide Contents Date: Mon, 25 Nov 2002 11:54:10 Subject: Re: Paul's new names From: Gene Ward Smith --- In tuning-math@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...> wrote:> the list of commas came from monz's et page (with a few ridonculous > ones deleted) . . . i'd like to know what is missing, based on some > log-flat badness measure.Here's my personal 5-limit comma list, which I've been using for some time; unweighted rms badness is less than 500, and complexity less than 50. 17763568394002504646778106689453125/ 17763086495282268024161967871623168 381520424476945831628649898809/381469726562500000000000000000 22300745198530623141535718272648361505980416/ 22297583945629639856633730232715606689453125 162285243890121480027996826171875/162259276829213363391578010288128 450359962737049600/450283905890997363 444089209850062616169452667236328125/ 444002166576103304796646509039845376 116450459770592056836096/ 116415321826934814453125 9010162353515625/9007199254740992 2475880078570760549798248448/2474715001881122589111328125 7629394531250/7625597484987 50031545098999707/50000000000000000 274877906944/274658203125 582076609134674072265625/581595589965365114830848 32805/32768, 19073486328125/19042491875328, 6115295232/6103515625, 1224440064/1220703125, 1600000/1594323, 15625/15552, 2109375/2097152, 393216/390625, 78732/78125, 2048/2025, 81/80, 3125/3072, 128/125, 250/243, 648/625, 25/24, 135/128, 16/15, 27/25
Message: 5617 - Contents - Hide Contents Date: Mon, 25 Nov 2002 04:22:10 Subject: Re: Adaptive JI notated on staff From: wallyesterpaulrus --- In tuning-math@y..., "monz" <monz@a...> wrote:>> From: "wallyesterpaulrus" <wallyesterpaulrus@y...> >> To: <tuning-math@y...> >> Sent: Saturday, November 23, 2002 9:29 PM >> Subject: [tuning-math] Re: Adaptive JI notated on staff >> >> >> --- In tuning-math@y..., "monz" <monz@a...> wrote:>>> i added Dave's graphic and a MIDI-file of it to my >>> "adaptive-JI" definition: >>> >>> Definitions of tuning terms: adaptive JI, (c) ... * [with cont.] (Wayb.) >> >>>> you mention vicentino, but don't link to your fine >> page about him. note that the example in question >> (dave's) is a perfect illustration of what makes >> vicentino's tuning so good. > >> thanks, paul. actually, i mentioned Vicentino twice > on the adaptive-JI definition page, and provided a link > to my Vicentino page at the second mention ... i had > just missed the first one, and a link has been added now. > > > hmmm ... should i include the Dave's illustration of the > 217edo comma-pump progression on my Vicentino page?yes, since this is how dave and george propose to notate it when played in vicentino's original tuning.
Message: 5618 - Contents - Hide Contents Date: Mon, 25 Nov 2002 14:25:46 Subject: TM reduced bases for 5-limit ets From: Gene Ward Smith Here is everything with a log-flat badness less than 1 up to 100000, along with the TM basis: 1, <(5)/(3), (2)^2/(3)> 2, <(2)*(3)/(5), (3)^2/(2)^3> 3, <(2)*(5)/(3)^2, (2)^4/(3)/(5)> 4, <(3)^2/(2)^3, (5)^2/(2)^3/(3)> 5, <(3)^3/(5)^2, (2)^4/(3)/(5)> 7, <(5)^2/(2)^3/(3), (3)^4/(2)^4/(5)> 12, <(2)^7/(5)^3, (3)^4/(2)^4/(5)> 15, <(2)*(5)^3/(3)^5, (2)^7/(5)^3> 19, <(5)^5/(2)^10/(3), (3)^4/(2)^4/(5)> 31, <(3)^4/(2)^4/(5), (2)^17*(3)/(5)^8> 34, <(2)^11/(3)^4/(5)^2, (5)^6/(2)^6/(3)^5> 53, <(5)^6/(2)^6/(3)^5, (3)^8*(5)/(2)^15> 65, <(2)^2*(3)^9/(5)^7, (3)^8*(5)/(2)^15> 118, <(2)^8*(3)^14/(5)^13, (3)^8*(5)/(2)^15> 171, <(3)^8*(5)/(2)^15, (2)*(5)^18/(3)^27> 289, <(2)^7*(3)^41/(5)^31, (3)^8*(5)/(2)^15> 441, <(2)^38/(3)^2/(5)^15, (2)*(5)^18/(3)^27> 559, <(2)^38/(3)^2/(5)^15, (3)^35/(2)^16/(5)^17> 612, <(2)*(5)^18/(3)^27, (3)^10*(5)^16/(2)^53> 730, <(3)^35/(2)^16/(5)^17, (3)^10*(5)^16/(2)^53> 1171, <(2)^37*(3)^25/(5)^33, (2)^54*(5)^2/(3)^37> 1783, <(2)^54*(5)^2/(3)^37, (5)^49/(2)^90/(3)^15> 2513, <(3)^47*(5)^14/(2)^107, (3)^62/(2)^17/(5)^35> 4296, <(2)^71*(5)^37/(3)^99, (5)^49/(2)^90/(3)^15> 6809, <(3)^146/(2)^178/(5)^23, (5)^49/(2)^90/(3)^15> 16572, <(2)^92*(3)^191/(5)^170, (2)^161/(3)^84/(5)^12> 20868, <(2)^161/(3)^84/(5)^12, (2)^21*(3)^290/(5)^207> 25164, <(5)^256/(2)^111/(3)^305, (2)^161/(3)^84/(5)^12> 52841, <(3)^153*(5)^73/(2)^412, (2)^21*(3)^290/(5)^207> 73709, <(2)^21*(3)^290/(5)^207, (3)^237*(5)^85/(2)^573> 78005, <(2)^140*(5)^195/(3)^374, (3)^237*(5)^85/(2)^573>
Message: 5619 - Contents - Hide Contents Date: Mon, 25 Nov 2002 14:48:30 Subject: Even more ridiculous 5-comma list From: Gene Ward Smith I merged the list I gave previously with everything which came up as a TM basis element in the previous posting, and looked at the resulting list. The numbers are unweighted complexity and badness, followed by weighted complexity and badness. My attempt to name 2^(-90) 3^(-15) 5^49 was not well received before, but it remains a remarkable comma; so also is 2^161 3^(-84) 5^(-12). 5/3 .816497 340.389827 .871098 413.347156 4/3 .816497 191.697610 .694533 117.986270 6/5 .816497 121.490388 .871098 147.529986 9/8 1.632993 313.939984 1.389065 193.224150 10/9 1.414214 210.621665 1.312845 168.499608 27/25 2.160247 358.982164 2.117162 337.928683 16/15 1.414214 129.016176 1.312845 103.214335 135/128 2.943920 461.234866 2.558773 302.858095 25/24 1.414214 81.605488 1.597771 117.684239 648/625 3.265986 385.301392 3.484393 467.884825 250/243 3.559026 359.557053 3.413659 317.274064 128/125 2.449490 142.232058 2.613295 172.717315 3125/3072 3.741657 239.363598 4.128051 321.440927 81/80 2.943920 107.611082 2.558773 70.660069 2048/2025 4.320494 210.722021 3.822599 145.943888 78732/78125 6.683313 345.537861 6.772338 359.530849 393216/390625 6.164414 251.101816 6.722154 325.611578 2109375/2097152 7.257180 305.925879 7.187007 297.136920 15625/15552 4.546061 96.735253 4.990527 127.973025 1600000/1594323 9.273618 305.537220 8.314888 220.234641 (2)^8*(3)^14/(5)^13 11.045361 372.731488 11.618628 433.831341 (2)^7*(3)^41/(5)^31 30.232433 2337.628278 30.446552 2387.649135 (2)^23*(3)^6/(5)^14 9.933110 190.150656 11.205944 273.015594 (5)^19/(2)^14/(3)^19 15.513435 391.217013 16.550868 475.068368 (3)^8*(5)/(2)^15 6.976150 54.895845 5.957336 34.186002 (5)^34/(2)^52/(3)^17 24.041631 477.611283 27.162114 688.768879 (2)^38/(3)^2/(5)^15 13.140269 137.999227 13.679676 155.700958 (3)^35/(2)^16/(5)^17 24.752104 386.194094 22.873419 304.763201 (2)*(5)^18/(3)^27 19.442222 188.083834 19.054459 177.053149 (2)^91/(3)^12/(5)^31 31.379399 463.252410 31.274979 458.643165 (3)^10*(5)^16/(2)^53 18.547237 113.091251 17.879417 101.309796 (2)^37*(3)^25/(5)^33 24.344746 178.739193 27.016133 244.271942 (5)^51/(2)^36/(3)^52 42.055519 346.619485 44.707429 416.411830 (2)^54*(5)^2/(3)^37 29.427878 146.241253 25.054172 90.247095 (3)^47*(5)^14/(2)^107 45.188494 326.880658 39.136911 212.356350 (2)^144/(3)^22/(5)^47 49.846431 352.012120 49.076087 335.942685 (3)^62/(2)^17/(5)^35 43.962105 256.793793 41.677831 218.808617 (3)^146/(2)^178/(5)^23 111.016515 1530.538820 95.204576 965.283848 (2)^92*(3)^191/(5)^170 148.123822 943.596569 154.481332 1070.384081 (2)^71*(5)^37/(3)^99 70.743669 181.089163 63.242667 129.377945 (5)^49/(2)^90/(3)^15 35.505868 34.075240 39.697565 47.624467 (5)^256/(2)^111/(3)^305 231.633331 1286.017248 238.618149 1405.898784 (3)^153*(5)^73/(2)^412 163.109370 226.729751 143.955865 155.869043 (2)^161/(3)^84/(5)^12 73.972968 48.546279 63.238794 30.331058 (2)^21*(3)^290/(5)^207 211.217108 235.136329 210.059812 231.292406 (2)^140*(5)^195/(3)^374 264.538592 419.006551 247.279087 342.228257 (3)^237*(5)^85/(2)^573 235.992938 74.673031 205.656081 49.418713
Message: 5620 - Contents - Hide Contents Date: Mon, 25 Nov 2002 17:24:59 Subject: Re: Adaptive JI notated on staff From: gdsecor --- In tuning-math@y..., "monz" <monz@a...> wrote:> i added Dave's graphic and a MIDI-file of it to my > "adaptive-JI" definition: > > Definitions of tuning terms: adaptive JI, (c) ... * [with cont.] (Wayb.) > > -monz Monz,We appreciate your doing this. Just one problem: the graphic is out of date. We've changed three of the symbols in the 217-ET standard set since that it was made. This includes adoption of the alternate 8deg symbol as the standard one. You should use this graphic instead: Yahoo groups: /tuning- * [with cont.] math/files/secor/notation/AdaptJI.gif --George
Message: 5621 - Contents - Hide Contents Date: Mon, 25 Nov 2002 18:25:52 Subject: Re: Adaptive JI notated on staff From: gdsecor --- In tuning-math@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...> wrote:> --- In tuning-math@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:>> --- In tuning-math@y..., "emotionaljourney22" <paul@s...> wrote:>>> right, but i'd like to see this actually notated, on a staff. >>> this notation . . . personally, it doesn't do much for me -- for > example, looking at this 217-equal example, > > Yahoo groups: /tuning-math/files/Dave/Adaptive... * [with cont.]Per my previous message, this should now be replaced with: Yahoo groups: /tuning- * [with cont.] math/files/secor/notation/AdaptJI.gif I think that the 3-degree symbol is now easier to remember, since it is simply a combination of the 1deg and 2deg flags. Also, lateral confusability with the 2deg symbol has been eliminated.> only a few of the pure thirds are immediately recognizable from the > notation, unless you've memorized all the symbols and the order in > which they occur in 217-equal. the symbol for a syntonic comma > alteration will quickly be learned by any user of the system, but all > the sets of symbols whose difference is a syntonic comma in a given > tuning?Yes, as Dave also said, this is a rather complicated application of the notation and not the best way to get started with it. But I should also point out that the same 217-ET symbols are also used for strict JI (independent of any ET mapping) -- only that the 6- degree symbol |\ is replaced by (| -- both symbols are valid for 6 degrees. This modified 217 set can then be used for JI that modulates beyond the strict JI definition of the symbols (and must therefore be 217-mapped. Here the harmonic meanings of the symbols would be similarly obscured unless you've memorized the 217 set. I also discuss a 494-ET JI mapping in my paper, but recent private correspondence with Dave Keenan has turned up a problem with using 494 for JI notation (apart from its complexity, which makes 217 look like a walk in the park). So I am having serious thoughts about scratching that idea. (I'll be moving that discussion onto this list so we have it documented here.) However, I do have an alterative idea that addresses the difficulty that you observed. It would be possible to draw a large n/4-comma-up (or down) symbol to the left of a triad that would modify all of the notes in the triad, and then add the appropriate 5-comma symbol to put the third of the chord into JI. So the A minor triad in the adaptive JI example could be changed by a 3/4-comma-down symbol: from: to: ~!( A large A ~!( E ~!( E |( C symbol /| C And the large symbol would be canceled by a large natural sign or replaced by aother large symbol for the following chord. There are all sorts of other possibilities for this sort of idea, including incorporating one of these symbols into a key signature. This would only be done, of course, if it made reading a manuscript simpler. --George
Message: 5622 - Contents - Hide Contents Date: Mon, 25 Nov 2002 18:36:45 Subject: Re: A common notation for JI and ETs From: gdsecor [This discussion with Dave Keenan was begun off-list.] [DK:]>>>>> I note that there's a rather huge schisma involved betweenthe 5:13 and the>>>>> 7:17 interpretations of //|, and 7:17 could almost be ~|\.But I expect I>>>>> agreed to accept this schisma at some time and I've just forgotten. >>>> [GS:]>>>> I proposed that in message #4580, but you didn't say anything about it, >>>> so it was allowed to stand. I couldn't see introducing another symbol >>>> for a ratio of 17 on account of a schisma that's just a hair over a >>>> cent (relative to the principal comma). >>> [DK:]>>> I agree we shouldn't introduce a new flag just for that, andsince it would>>> otherwise be the only ratio in the 17-limit diamond that is not notated, >>> and assuming it vanishes in 217 and 494 ETs, then I agree it should >>> stand. >> [GS:]>> Oops! It vanishes in 217 but not 494. Now what do we do? >> >> As long as we're talking about commas involved with //|, I remember >> that you mentioned notating the diaschisma a short while back. I just >> noticed that I used it in Table 2 for notating 25/16 as Ab)!~. This >> isn't valid in 217, but it is in 494. I added a footnote to this >> effect that says: >> >> << There is one schisma not implied in Table 1 that occurs in the >> alternate notation for 25/16 and 32/25 in Table 2, where the 19+23 >> comma symbol )|~, 432:437, ~19.922c, is used for the diaschisma >> (2025:2048, ~19.553c). This schisma, 32768:32775 (~0.370c) vanishes in >> 494-ET, but not in 217-ET. >> >> >> I had to say "19+3 comma symbol" rather than "19' comma symbol", >> because that one isn't valid in 494, which I explained in the following >> footnote (where I'm also going to have to add the 7:17 comma as invalid >> in 494 if we leave it as is. (And if so, at least we can still claim a >> rational notation that is independent of any octave division.) > [DK:]> Hmm. This all sounds a bit too "up in the air". Perhaps you shouldcut it back to the 15-limit> diamond for the XH18 article. Or simply omit 7:17 and the alternatenotation for 25/16 and> 32/25 until we've had more time to think about them.I don't think the deadline for the article is that close, so I took some time to look at the 7:17 comma problem. I thought the problem might be a matter of requiring the //| symbol to represent all of the roles ranging from ~42.0c (for the 7:17 comma) to ~43.8c (for the 5:13 comma), but I see that there are a number of divisions above 217 in which //| is valid for all of these: 224, 270, 282, 342, 388, and 612. Those in which //| is not valid for all of these are 306, 311, 364, and 400, and curiously, in most of these the 7:17 comma is the same number of degrees as the 7:17 comma, but different for the 5+5 comma. So I think that we just ran out of luck with 494. The symbol with which we would have no problem is the one that represents the 7:17 comma exactly (a zero schisma, so it would be valid everywhere that both the 17' and 7 commas are valid): the 17'+7 comma, or ~|(). It's three flags, but I tried making the symbol, and it looks nice enough (i.e., it's easy enough to identify all the flags). In looking for a rational complement I find that ~)|| is very close, but it's already the rational complement of ~|\, although it could serve for both. But it could be argued that this adds too many complications in trying to solve a problem that seems to be of concern only insofar as it applies to 494 (and which we wouldn't be facing if you weren't attaching so much importance to 494). But I will briefly consider the other alternative. I see that ~|\, which is already the (11-5)+17 comma (4352:4455, ~40.496c) and 23' comma (16384:16767, ~40.004c) is valid for both of these plus the 7:17 comma (448:459, ~41.995c) in quite a few of the better divisions: 94, 111, 118, 140, 171, 183, 193, 200, 217, 282, 311, and 494. So it's valid in *both* 217 and 494, the divisions for which we wanted a free-modulation JI option to be available. The only hitch is that the schisma for ~|\ is 1155:1156, ~1.498c, compared to the schisma for //|, 1700:1701, (~1.018c, the difference between the 5+5 comma and the 7:17 comma). This one's a tough call, because, although ~|\ works as the 7:17 comma in both 217 and 494, the schisma is larger than for //|. Also, this would require two different symbols for 8 degrees of 217 when it's used for freely modulating JI, which would unncessarily complicate the 217-JI-17 notation, which does just fine with //|. (I really wonder how many composers would consider using the 494 notation for JI, when it requires so many more single-shaft symbols, 26 vs. 12 for 217, so I am beginning to think that a 494-JI option isn't really practical. This is in addition to the potentially confusing symbol-size reversal between 3 and 4deg494.) If you feel that it's necessary to have the notation validated by a high-precision division like 494, then I would suggest using ~|() for the exact 7:17 comma for theoretical purposes and electronic music (with ~)|| as rational complement, if needed), and replacing ~|() with //| for 217-based JI. I would view this as a compromise that would keep the notation simple for the simpler 217-JI mapping. I believe that others are going to find that 217 is complicated enough for them, and 494 would be unthinkable. --George
Message: 5624 - Contents - Hide Contents Date: Mon, 25 Nov 2002 14:07:53 Subject: Re: Even more ridiculous 5-comma list From: Pierre Lamothe How the harmonic entropy approach could be conciliate with this approach? Goethe said: (excuse for that bad translation from French) "Do you want to penetrate the infinity? Go always away and in all directions in the finity." In that sense I understand well the necessity to go away and far in all directions at same time, but it could be already useful to confront, relatively to our capacity to perceive a kind of harmonic order, the over optimism implied by the fanciest commas, with the slight pessimism, in my opinion, of the harmonic entropy. ( It's not there an attack against the harmonic entropy. I believe only the approach appears slightly pessimistic for the level is the sensation one, so neglecting contextual reinforcement arising at perception level. ) Once the word ridiculous has been used, as to suggest one have to think at the limit, one have to elaborate on the sense of a such limit. There is not only one valid perspective, but I believe we have to distinguish minimally the perceptual one concerning the music and the technical one concerning the luthery. Where abondant decimals of cents may have sense in the technical perspective, it becomes rather ridiculous (indeed) in the musical perspective. So, I invite to reflexion in view to precise sense and perspective of these few notions illustrated with so much buch of numbers. Pierre [This message contained attachments]
5000 5050 5100 5150 5200 5250 5300 5350 5400 5450 5500 5550 5600 5650 5700 5750 5800 5850 5900 5950
5600 - 5625 -