Topic: Dieterich Buxtehude and the Mean-Tone Organ
1 scales
| File | Description | Notes | Period (¢) | Limit |
|---|---|---|---|---|
| septenarian53well | Sparschuh's 53 generalization of Werckmeister's septenarius | 53 | 1200.0 | 174763 |
Thread (16 messages)
From: Mike Battaglia (2008-07-09) Subject: Dieterich Buxtehude and the Mean-Tone Organ Has anyone ever listened to this? This album is beautiful. I'm just listening to it for the first time now. I understand why quarter comma meantone is so popular now - the mood of this album is very relaxed and beautiful. I do hear what George Secor meant by the just leading tone being less effective than that of 12-et, but it's not less effective - it's just a different kind of leading tone. It creates much less tension before it leads, which partially contributes to the extremely relaxed feel of the music. Do any of the baroque and early classical music specialists on this group have any other quarter-comma or other meantone recordings they could recommend? I've never paid much attention to it before, preferring to focus on 31-tet and such instead, but it just occured to me this is a pretty easy way to get a feel for part of 31-tet anyways. Or, if anyone has any recommendations for recordings of classical works done in 53-tet or other temperaments, or even perhaps JI... That would be amazing. Acoustic or electric recordings is what I'm after specifically, not too much MIDI. I'm slowly becoming one of those people that hates 12-tet. This album got me pretty good. Even the feel of the harmony is just MUCH more complex than 12-tet. Quarter comma meantone/31-tet would be very useful in all styles of music, especially shoegaze and pop and such. Quarter comma emo maybe. Maybe not jazz, which has built up a huge vocabulary of stacked-fifth chords, but we have 12-tet for that anyway - for now. -Mike
From: Charles Lucy (2008-07-09) Subject: Re: [tuning] Dieterich Buxtehude and the Mean-Tone Organ There are lotsa LucyTuned (meantone-type) tracks from lullabies to rave out there on the net. You can find some links from: http://www.lucytune.com and http://www.lullabies.co.uk http://www.harmonics.com One day soon I'll sort them out and update the sites, after they finish digging up my street, which has been disturbing me for the past week. On 9 Jul 2008, at 11:22, Mike Battaglia wrote: > Has anyone ever listened to this? This album is beautiful. I'm just > listening to it for the first time now. I understand why quarter comma > meantone is so popular now - the mood of this album is very relaxed > and beautiful. I do hear what George Secor meant by the just leading > tone being less effective than that of 12-et, but it's not less > effective - it's just a different kind of leading tone. It creates > much less tension before it leads, which partially contributes to the > extremely relaxed feel of the music. > > Do any of the baroque and early classical music specialists on this > group have any other quarter-comma or other meantone recordings they > could recommend? I've never paid much attention to it before, > preferring to focus on 31-tet and such instead, but it just occured to > me this is a pretty easy way to get a feel for part of 31-tet anyways. > > Or, if anyone has any recommendations for recordings of classical > works done in 53-tet or other temperaments, or even perhaps JI... That > would be amazing. Acoustic or electric recordings is what I'm after > specifically, not too much MIDI. > > I'm slowly becoming one of those people that hates 12-tet. This album > got me pretty good. Even the feel of the harmony is just MUCH more > complex than 12-tet. Quarter comma meantone/31-tet would be very > useful in all styles of music, especially shoegaze and pop and such. > Quarter comma emo maybe. Maybe not jazz, which has built up a huge > vocabulary of stacked-fifth chords, but we have 12-tet for that anyway > - for now. > > -Mike > > Charles Lucy lucy@... - Promoting global harmony through LucyTuning - for information on LucyTuning go to: http://www.lucytune.com For LucyTuned Lullabies go to: http://www.lullabies.co.uk
From: Mike Battaglia (2008-07-09) Subject: Re: [tuning] Dieterich Buxtehude and the Mean-Tone Organ Ah yeah, I've heard these... Really good. There's one, I don't remember which, in which the sample clip is in F# phrygian dominant... Really liked that one. On Wed, Jul 9, 2008 at 6:45 AM, Charles Lucy <lucy@...> wrote: > There are lotsa LucyTuned (meantone-type) tracks from lullabies to rave out > there on the net. > > You can find some links from: > http://www.lucytune.com > and > http://www.lullabies.co.uk > http://www.harmonics.com > One day soon I'll sort them out and update the sites, after they finish > digging up my street, which has been disturbing me for the past week. > > > On 9 Jul 2008, at 11:22, Mike Battaglia wrote: > > Has anyone ever listened to this? This album is beautiful. I'm just > listening to it for the first time now. I understand why quarter comma > meantone is so popular now - the mood of this album is very relaxed > and beautiful. I do hear what George Secor meant by the just leading > tone being less effective than that of 12-et, but it's not less > effective - it's just a different kind of leading tone. It creates > much less tension before it leads, which partially contributes to the > extremely relaxed feel of the music. > > Do any of the baroque and early classical music specialists on this > group have any other quarter-comma or other meantone recordings they > could recommend? I've never paid much attention to it before, > preferring to focus on 31-tet and such instead, but it just occured to > me this is a pretty easy way to get a feel for part of 31-tet anyways. > > Or, if anyone has any recommendations for recordings of classical > works done in 53-tet or other temperaments, or even perhaps JI... That > would be amazing. Acoustic or electric recordings is what I'm after > specifically, not too much MIDI. > > I'm slowly becoming one of those people that hates 12-tet. This album > got me pretty good. Even the feel of the harmony is just MUCH more > complex than 12-tet. Quarter comma meantone/31-tet would be very > useful in all styles of music, especially shoegaze and pop and such. > Quarter comma emo maybe. Maybe not jazz, which has built up a huge > vocabulary of stacked-fifth chords, but we have 12-tet for that anyway > - for now. > > -Mike > > Charles Lucy > lucy@... > - Promoting global harmony through LucyTuning - > for information on LucyTuning go to: > http://www.lucytune.com > For LucyTuned Lullabies go to: > http://www.lullabies.co.uk > > >
From: rick_ballan (2008-07-11) Subject: Re: Dieterich Buxtehude and the Mean-Tone Organ --- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...> wrote: > > Ah yeah, I've heard these... Really good. There's one, I don't > remember which, in which the sample clip is in F# phrygian dominant... > Really liked that one. > > On Wed, Jul 9, 2008 at 6:45 AM, Charles Lucy <lucy@...> wrote: > > There are lotsa LucyTuned (meantone-type) tracks from lullabies to rave out > > there on the net. > > > > You can find some links from: > > http://www.lucytune.com > > and > > http://www.lullabies.co.uk > > http://www.harmonics.com > > One day soon I'll sort them out and update the sites, after they finish > > digging up my street, which has been disturbing me for the past week. > > > > > > On 9 Jul 2008, at 11:22, Mike Battaglia wrote: > > > > Has anyone ever listened to this? This album is beautiful. I'm just > > listening to it for the first time now. I understand why quarter comma > > meantone is so popular now - the mood of this album is very relaxed > > and beautiful. I do hear what George Secor meant by the just leading > > tone being less effective than that of 12-et, but it's not less > > effective - it's just a different kind of leading tone. It creates > > much less tension before it leads, which partially contributes to the > > extremely relaxed feel of the music. > > > > Do any of the baroque and early classical music specialists on this > > group have any other quarter-comma or other meantone recordings they > > could recommend? I've never paid much attention to it before, > > preferring to focus on 31-tet and such instead, but it just occured to > > me this is a pretty easy way to get a feel for part of 31-tet anyways. > > > > Or, if anyone has any recommendations for recordings of classical > > works done in 53-tet or other temperaments, or even perhaps JI... That > > would be amazing. Acoustic or electric recordings is what I'm after > > specifically, not too much MIDI. > > > > I'm slowly becoming one of those people that hates 12-tet. This album > > got me pretty good. Even the feel of the harmony is just MUCH more > > complex than 12-tet. Quarter comma meantone/31-tet would be very > > useful in all styles of music, especially shoegaze and pop and such. > > Quarter comma emo maybe. Maybe not jazz, which has built up a huge > > vocabulary of stacked-fifth chords, but we have 12-tet for that anyway > > - for now. > > > > -Mike > > > > Charles Lucy > > lucy@... > > - Promoting global harmony through LucyTuning - > > for information on LucyTuning go to: > > http://www.lucytune.com > > For LucyTuned Lullabies go to: > > http://www.lullabies.co.uk > > > >Digging up the street hah. Very annoying. Probably the local council creating another unnecessary speed hump? Yes, those lullabies are very interesting and beautiful indeed. Just to play devils advocate, wouldn't you say that the advantage of Bach over Buxtehude is all of those wonderful modulations and counterpoint so characteristic of Bach and the 12-tet tuning system? I'm just wondering, is this possible in the meantone system? For eg, given maj 3 as 5/4 and min as 19/16, then the fifth is the product of the two giving 95/64. Since multiplication is commutative (A x B = B x A) then the maj3 from the min3 = the min3 from the maj3 and both = the fifth. But then applying this 12 times does not reach the octave (giving around 114). A better approx. is min3 = 609/512 and maj3 = 645/512. Their product (the fifth) gives 392805/262144 which is very close to the tempered fifth and applying this 12 times gives 128.128...which is very close to 128, the 7'th octave. Yet it is still harmonic. Of course, we are here dealing with just a few notes and it becomes much more complicated when we extend this problem from all points of view. It still seems to me that for all its faults the 'democratic' 12-tet system resolves this issue so nicely. But as Mike said, we still have it anyway. > > >PS. Charles, I don't need new glasses. Ends up I'm allergic to wattle, which being one of our natural faunas is so un-Australian of me. Rick
From: Mike Battaglia (2008-07-11) Subject: Re: [tuning] Re: Dieterich Buxtehude and the Mean-Tone Organ > Just to play devils advocate, wouldn't you say that the advantage of > Bach over Buxtehude is all of those wonderful modulations and > counterpoint so characteristic of Bach and the 12-tet tuning system? > I'm just wondering, is this possible in the meantone system? For eg, > given maj 3 as 5/4 and min as 19/16, then the fifth is the product of > the two giving 95/64. Since multiplication is commutative (A x B = B x > A) then the maj3 from the min3 = the min3 from the maj3 and both = the > fifth. But then applying this 12 times does not reach the octave > (giving around 114). Bach didn't compose in 12-tet. From what I know, he started off in meantone like everyone else, and then switched to one or more forms of well temperament later on. But he never messed around with 12-equal, as far as I know. > A better approx. is min3 = 609/512 and maj3 = 645/512. Their product > (the fifth) gives 392805/262144 which is very close to the tempered > fifth and applying this 12 times gives 128.128...which is very close > to 128, the 7'th octave. Yet it is still harmonic. Of course, we are > here dealing with just a few notes and it becomes much more > complicated when we extend this problem from all points of view. It > still seems to me that for all its faults the 'democratic' 12-tet > system resolves this issue so nicely. But as Mike said, we still have > it anyway. That's a decently rational intonation version of 12-tet. -Mike
From: rick_ballan (2008-07-12) Subject: Re: Dieterich Buxtehude and the Mean-Tone Organ --- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...> wrote: > > > Just to play devils advocate, wouldn't you say that the advantage of > > Bach over Buxtehude is all of those wonderful modulations and > > counterpoint so characteristic of Bach and the 12-tet tuning system? > > I'm just wondering, is this possible in the meantone system? For eg, > > given maj 3 as 5/4 and min as 19/16, then the fifth is the product of > > the two giving 95/64. Since multiplication is commutative (A x B = B x > > A) then the maj3 from the min3 = the min3 from the maj3 and both = the > > fifth. But then applying this 12 times does not reach the octave > > (giving around 114). > > Bach didn't compose in 12-tet. From what I know, he started off in > meantone like everyone else, and then switched to one or more forms of > well temperament later on. But he never messed around with 12-equal, > as far as I know. > > > A better approx. is min3 = 609/512 and maj3 = 645/512. Their product > > (the fifth) gives 392805/262144 which is very close to the tempered > > fifth and applying this 12 times gives 128.128...which is very close > > to 128, the 7'th octave. Yet it is still harmonic. Of course, we are > > here dealing with just a few notes and it becomes much more > > complicated when we extend this problem from all points of view. It > > still seems to me that for all its faults the 'democratic' 12-tet > > system resolves this issue so nicely. But as Mike said, we still have > > it anyway. > > That's a decently rational intonation version of 12-tet. > > -Mike >I suppose that he was just the first to compose on it with the well tempered clavier. But I am no expert. In fact, all of the intervals from 640 to 648 over 512 seem to correspond to different versions of our major 3rd. Can someone please remind me of the just noticeable difference. (I've re-ordered Helmholtz' sensation of tone but it takes months to get here to Australia). I'm just thinking that entire 'chunks' of the harmonic series can be assigned to each interval within each respective octave and that there is a limit to the number of octaves we can perceive. The same might apply to any other tuning system. Rick
From: Andreas Sparschuh (2008-07-14) Subject: gneralizing Werckmeister's septenarius Newton's 53, was: Re:Buxtehude --- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...> wrote: > > Or, if anyone has any recommendations for recordings of classical > works done in 53-tet or other temperaments, or even perhaps JI... Dear Mike & all others, for Newton's "horogramm" in 53: http://mto.societymusictheory.org/issues/mto.93.0.3/mto.93.0.3.lindley7.gif in the http://www.rzuser.uni-heidelberg.de/~tdent/septenarius.html style, i do reccomend the epimoric stepwise cycle of 5ths modulo octaves in Bosanquet's notation in terms of the corresponding absolute pitches: 0; c-_-4 = 1 ... c-_4=256Hz unison as general reference to the unit 1; g-_-2 = 3 ! 5th 2; d-_-1 = 9 ! major-tone 3; a-_0 = 27 ! Pythagorean 6th 4; e-_2 = 81 ! ditone 5; b-_3 = 243 ! octave:limma 6; gB_6 = 729 ! tritone 7; dB_7 = 2,187 ! apotome 4,374 [< 4,375 = 5*a\_5] the 'ragisma' 8; aB_3 = 205 410 820 1,640 3,280 6,560 (<6,561 = 3^8) 9; eB_5 = 615 10; bB_5 = 1,845 11; f\_7 = 2,767 5,534 (<5,535) 12; c\_7 = 2,075 4,150 8,300 (<8,301) 13; g\_4 = 389 778 1,556 3,112 6.224 (<6,225) 14; d\_6 = 1,167 15; a\_5 = 875=5*f._3 ; 1,750 3,500 (<3,501) JI 3rds: F. -> A\ 16; e\_7 = (41 82 164 328 656 1,312 2,624<) 2625 = 5*c._3 17; b\_8 = (123 ... 7.872<) 7875 = 5*g._6 18; gb_10 = (369 ... 23,616<) 23,625 = 5*d._8 last JI 3rd among 4 19; db_6 = 1107 20; ab_4 = 415 830 1,660 3,320 (<3321) neoBaroque tuning-forks 21; eb_6 = 1,245 22; bb_6 = 1,867 3,734 (<3,735) 23; f._3 = 175 350 700 1,400 2,800 5,600(<5601) instead W's "176" 24; c._5 = 525 tenor_C5 ; middle_C4 = 262.5 Hz 25; g._6 = 1,575 26; d._8 = 4,725 27; a._9 = 14,175 28; e._11 = 42,525 29; b._12 = 127,575 30; f#_12 = (1,495 ... 95,680<) 95,681 ... 382,724 (<382,725) 31; c#_8 = 4,485 32; g#_9 = 13,455 33; d#_11 = 40,365 34; a#_12 = 121,095 35; f/_12 = 90,821 181,642 363,284 (<363,285) 36; c/_13 = 136,231 272,462 (<272,463) 37; g/_12 = 102,173 204,346 408,692 (<408,693) 38; d/_13 = 153,259 306,518 (<306,519) 39; a/_4 = 449 ... 459,776 (<459,777) 40; e/_6 = 1,347 41; b/_7 = 4,041 42; f&_9 = 12,123 := f#/ with '&'='#'*'/' about 6 commata sharper 43; c&_11 = 36,369 44; g&_12 = 109,107 45; d&_11 = 40,915 ... 327,320 (<327,321) 46; a&_9 = 15,343 ... 122,744 (<122,745) 47; f+_11 = 46,029 := f//_11 with '+':= '//' double comma elevation 48; c+_12 = 69,043 138,086 (<138,087) 49; g+_10 = 25,891 ... 207,128 (<207,129) 50; d+_12 = 77,673 51; a+_12 = 116,509 233,018 (<233,019) 52; ( e+ = f- )_13 = 177,763 349,526 (<349,527) enharmoic change 53=0'; b+_3 = c-_4 = 256Hz=2^8 ... 2^19=524,288 (<524,299) back home that cycle matches almost http://en.wikipedia.org/wiki/53_equal_temperament it also subdivides the "Mercator's Comma. Mercator's Comma is of such small value to begin with (~3.615 cents)" into the above 23 epimoric subfactors instead of 53 equal ones. Attend within that the schisma 32805:32768 inbetween: ...Gb 2624:2625 Db 3320:3321 Ab Eb 3734:3735 Bb 5600:5601 F... gaining JI heptatonics for C-major in 1. major and minor 3rds: [F.] 5:4 [A\] 6:5 [C.] 5:4 [E\] 6:5 [G.] 5:4 [B\] 6:5 [D.] 2. as scale of whole&semi-tones: [C.] 9:8 [D.] 10:9 [E\]16:15[F.] 9:8 [G.] 10:9 [A\] 9:8 [B\]16:15[c.] or in commatic ascending order, as in Newton's 1664 drawing: !septenarian53well.scl Sparschuh's 53 generalization of Werckmeister's septenarius 53 2075/2048 ! 1; c\_7 : 2^11 525/512 ! 2; c._5 : 2^9 ~tenor_C in ET in reference to a4=440Hz 136231/131072! 3; c\_13 : 2^17 69043/65536 ! 4; c+_12 : 2^16 2187/2048 ! 5; dB_7 : 2^11 apotome 1107/1024 ! 6; db_6 : 2^10 4485/4096 ! 7; c#_8 : 2^12 36369/32768 ! 8; c&_11 : 2^15 9/8 ! 9; d-_3 : 2^3 Pythaogorean major-tone 1167/1024 !10; d\_6 : 2^10 4725/4096 !11; d._8 : 2^12 153259/131072!12; d\_6 : 2^10 77673/65536 !13; d+_12 : 2^16 615/512 !14; eB_5 : 2^9 (5:4)*(123:128) 1245/1024 !15; eb_6 : 2^10 (5:4)*(249:256) 40365/32768 !16; d#_11 : 2^15 (5:4)*(8073:8192) 40915/32768 !17; d&_11 : 2^15 (5:4)*(8183:8192) 81/64 !18; e-_2 : 2^6 Pythagorean ditone 2625/2048 !19; e\_7 : 2^11 = C.*(5:4) JI 3rds in [C.]->[E\] 42525/32768 !20; e._11 : 2^15 1347/1024 !21; e/_6 : 2^10 174763/131072!22;(e+=f-)_13:2^17 = (4:3)*(524,289:524,288) enharm.ch. 2767/2048 !23; f\_7 : 2^11 175/128 !24; f._3 : 2^7 instead of Werckmeister's "176" choice 90821/65536 !25; f/_12 : 2^16 46029/32768 !26; f+_11 : 2^15 729/512 !27; gB_6 : 2^9 tritone 23625/16384 !28; gb_10 : 2^14 = D.*(5:4) JI 3rds in [D]->[F#\] 95681/65536 !29; f#_12 : 2^16 12123/8192 !30; f&_12 : 2^16 3/2 !31; g-_-2 : 2 the initial 5th step at begin 389/256 !32; g\_4 : 2^8 1575/1024 !33; g-_5 : 2^10 102173/65536 !34; g/_12 : 2^16 25891/16384 !35; g+_10 : 2^14 205/128 !36; aB_3 : 2^7 415/256 !37; ab_4 : 2^8 neoBaroque tuning-fork in 415Hz 13455/8192 !38; g#_9 : 2^13 109107/65536 !39; g&_12 : 2^16 27/16 !40; a-_0 : 2^4 Pythagorean 6th 875/512 !41; a\_5 : 2^9 = F.*(5:4) JI 3rds [F.]->[A\] 14175/8192 !42; a._9 : 2^13 449/256 !43; a/_4 : 2^8 116509/65536 !44; a+-12 : 2^16 1845/1024 !45; bB_6 : 2^10 1867/1024 !46; bb-6 : 2^10 121095/65536 !47; a#_12 : 2^16 15343/8192 !48; c&_9 : 2^13 243/128 !49; b-_3 : 2^7 Pythagorean 7th or octave:limma 7875/4096 !50; b\-8 : 2^12 127575/65536 !51; b._12 : 2^16 4041/2048 !52; b/_7 : 2^11 2/1 ! 53==0 ; ( b+ = 2*c+ )_3 Helmholtz's enharmonics: B// = C\\ ! ! that yiedls -compared against 53EDO- an intersting 53-comma key-charcteristics http://www.wmich.edu/mus-theo/courses/keys.html because all the 3rds range in fine graduation inbetween 8192:6561 ~384Cents (schimatic 3rd) <<<???<<< and 5:4 ~386Cents Attend for instance the 3rd [A\] -> [DB] that becomes about an http://en.wikipedia.org/wiki/Ragisma flattend. That small interval was also historically also used for coin-making: http://de.wikipedia.org/wiki/Karlspfund "Bei historischen LängenmaÃen liegt der Variationskoeffizient im allgemeinen unter 1/500, was eine Genauigkeit von ± 0,2 % bedeutet. So gelten bei den LängenmaÃen z.B. 1/2400 oder 1/4374, also die 7-glatten Ratios 2401 : 2400 und 4375 : 4374, sowie ihre Reziprokwerte nicht als eigentliche Ratios, sondern nur als Kommata." Yours Sincerely A.S.
From: threesixesinarow (2008-07-14) Subject: Wikipedia Newton's 53, was: Re:Buxtehude --- In tuning@yahoogroups.com, "Andreas Sparschuh" <a_sparschuh@...> wrote: > Newton's "horogramm" in 53: > >http://mto.societymusictheory.org/issues/mto.93.0.3/ mto.93.0.3.lindley7.gif Can someone help these lazy people? http://en.wikipedia.org/wiki/ Talk:53_equal_temperament#Newton.27s_unpublished_manuscripts.3F
From: Carl Lumma (2008-07-15) Subject: Wikipedia Newton's 53, was: Re:Buxtehude Clark wrote: > > Newton's "horogramm" in 53: > > > >http://mto.societymusictheory.org/issues/mto.93.0.3/ > >mto.93.0.3.lindley7.gif > > Can someone help these lazy people? > > http://en.wikipedia.org/wiki/ > Talk:53_equal_temperament#Newton.27s_unpublished_manuscripts.3F Why do you call them that? The above is already linked in their discussion. -Carl
From: threesixesinarow (2008-07-15) Subject: Wikipedia Newton's 53, was: Re:Buxtehude --- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote: > > Clark wrote: > > > > Newton's "horogramm" in 53: > > > > > >http://mto.societymusictheory.org/issues/mto.93.0.3/ > > >mto.93.0.3.lindley7.gif > > > > Can someone help these lazy people? > > > > http://en.wikipedia.org/wiki/ > > Talk:53_equal_temperament#Newton.27s_unpublished_manuscripts.3F > > Why do you call them that? The above is already > linked in their discussion. > > -Carl > I know some howlers where historians just relied on a picture or worse instead of reading the accompanying text and at least one of those editors didn't bother to look it up in Lindley's book.
From: threesixesinarow (2008-07-15) Subject: Sensations of Tone (was Re: Dieterich Buxtehude and the Mean-Tone Organ) --- In tuning@yahoogroups.com, "rick_ballan" <rick_ballan@...> wrote: >(I've re-ordered Helmholtz' sensation of tone but it takes > months to get here to Australia). http://books.google.com/books?id=x_A5AAAAIAAJ http://www.archive.org/details/onsensationsofto00helmrich
From: Carl Lumma (2008-07-15) Subject: Sensations of Tone (was Re: Dieterich Buxtehude and the Mean-Tone Organ) > >(I've re-ordered Helmholtz' sensation of tone but it takes > > months to get here to Australia). > > http://books.google.com/books?id=x_A5AAAAIAAJ > http://www.archive.org/details/onsensationsofto00helmrich We've discovered that certain Google books that are available in the U.S. are not available down under. However, the second link, to the internet archive, looks like a winner! -Carl
From: Andreas Sparschuh (2008-07-16) Subject: Some historically information additional to: RE: Wikipedia Newton's 53, --- In tuning@yahoogroups.com, "threesixesinarow" <CACCOLA@...> wrote: > > Newton's "horogramm" in 53: > > > >http://mto.societymusictheory.org/issues/mto.93.0.3/ > mto.93.0.3.lindley7.gif > > Can someone help these lazy people? > > http://en.wikipedia.org/wiki/ > Talk:53_equal_temperament#Newton.27s_unpublished_manuscripts.3F > Dear CACCOLA & all others that want to understand N's draft sketch, here comes some more work for "lazy people" beyond my earlier interpretations of Newton's layout: http://launch.groups.yahoo.com/group/tuning/message/72161 http://launch.groups.yahoo.com/group/tuning/message/73536 Provenace: " Newton's autograph drawing is dated November 1665: Literature reference: The original manuscript is located at: Cambridge Univ.Lib. Signature: Ms.Add.4000,fol.105v " Has anybody in that group access to that original or an copy of that, and could please offer an reprint to us group-members here in that forum? All i know about N's diagramm bases barely on the views of my old colleauge and friend and expert in that field: http://en.wikipedia.org/wiki/Mark_Lindley He refers to N's delineation in his encyclopecic ripely in depth article 'tuning & temperature' standard reference article: "Stimmung und Temperatur" within the book: (F. Zaminer, Editor, Geschichte der Musiktheorie, Vol. 6: Hören, Messen und Rechnen in der Frühen Neuzeit (Wissenschaftliche Buchgesellschaft, 1987) pp.205-210 Sadly -sorry i'm afraid- in print that's available solely in German :-( How unfortunately! Lindley's scholar article reproduces also an similar even earlier "horogramm" -appearently an forerunning predecessor- made by http://en.wikipedia.org/wiki/Ren%C3%A9_Descartes that appeared in his famous: "1618. Compendium Musicae. A treatise on music theory and the aesthetics of music written for Descartes's early collaborator Isaac Beeckman." http://en.wikipedia.org/wiki/Isaac_Beeckman R. Descartes reports about that encounter when meeting Beekman personally: http://www.3villagecsd.k12.ny.us/wmhs/Departments/Math/OBrien/descartes.html " Around 1618 I believe, I began to study mathematics once again under the Dutch scientist Isaac Beekman, who I had met one day walking through the streets when he translated a Dutch placard for me that turned out to be a math problem." Probably D. refers in his advanced blueprint -written already at age of 22 years- to the questionable treatment of the subject by an precursor: http://en.wikipedia.org/wiki/Robert_Fludd 's outlines: http://www.celestialmonochord.org/log/images/celestial_monochord.jpg or if you prefer the same pic in somewhat higher resolution: http://www.imaginatorium.org/books/monochd.gif Attend God's divine hand out of the clouds that tunes the string. http://www.bach1722.com/ 'Il temperamento di Dio' == ???"God's temperament"??? including an Italian foro di propagare: http://www.edumus.com/forum/read.php?21,54338,page=1 Parlare a vuoto di un agrumento putativo inprofessionale: Che palle! ....... ...... ..... .... ... .. . But better let's retrun back at that point of no return -away from that nonsensial layman's flubdub- toggeling reverse to our's historically real serious D&N: Beyond Fludd's heptatonics Descartes explains there in his compedium en detail -alike in Newton's later refinement too- how to obtain the 53-commata scale from shifting hexachords by 4ths(4:3) from hard(durum) to soft(molle) modes by changeing the keys: G-C-F in refernce to the incomlete C-major scale, because in coeval hexachords the pitch-class of 'B' is left out there. http://en.wikipedia.org/wiki/Hexachord In order to understand N's conceptual design read the 5 concentric circles from inside to outside as scales over: outest = 44Bb(ut,) > 21F(ut) > 53=0C(Ut) > 31G(UT) > 9(UT') = innerst so that Descartes's C-major 'scala-naturalis' is located in the middle at the center of N's 5 concentric circles: That old gamut (GAMMA-UT) is labeld in today's modern concept as: 1. extended tonic durum-hexachord C-major-Mixolydian 7-tone scale: consisting of 2 http://en.wikipedia.org/wiki/Tetrachord s and an major-tone 9:8 intbetween both of them: Yilding an C-major http://en.wikipedia.org/wiki/Tonic_%28music%29 scale with legenda: C=0Ut=1:1 +8 8Re=10:9 +9 17Mi=5:4 +5 22Fa=4:3 first-tetrachord22Fa4:3 22Fa=4:3 +9 31Sol=3:2 major-tone9commata inbetween both tetrachords 31Sol=3:2 +8 39La +5 44--16:9 +9 (53=0)Ut'=2:1 second-tetrachord On the one hand: Step from that one cirle nearer to the main focal point, that corresponds to an transition an 5th upwards into the: http://en.wikipedia.org/wiki/Dominant_%28music%29 2. dominant hard(sharp)-hexachord G-major-Mixolydian 7-tone scale with legenda: G=31UT=3:2 +8 39RE=5:3 +9 48MI=15:8 +5 53=0FA=1:1 first-tetrachord 53=0FA=1:1 +9 9SOL=9:8 major-tone 9:8 consists of 9 commata steps 9SOL=9:8 +8 17LA=5:4 +5 22--=4:3 +9 31UT second-tetrachord On the other hand: By stepping in reverse direction by one 4th (4:3) from the middle-C-major cicle into outwards direction we yield an change of key into the: http://en.wikipedia.org/wiki/Subdominant 3. subdominant moll(soft)-hexachord F-major-Mixolydian 7-tone scale: Legenda: F=22ut=4:3 +8 30re40:27 +9 39mi=5:3 +5 44fa=16:9 first-tetrachord 44fa=16:9 +9 53=0sol=1:1 major-tone 9:8 of 9 commatas 0sol1:1 +8 8la=10:9 +5 13--=50:27 +9 22ut4:3 So far N's scribble agrees in the 3 innerst circles fully with Descartes's elaborated original scheme. But beyond D's hexachords in barely the kernel keys F > C > G N. delivers additional Bb > (F > C > G) > D in extending D's range from the double-subdomiant=Bb>(subdom.=F > tonic=C > dom.=G)>double-dom.=D by 2 additional outer scales. N. also extends by the note '--' the classial Hexachords into to the mixolydian scale, with distances in commatas: C +8 D\ +9 E\ +5 F +9 G +8 A\ +5 Bb +9 C' instead of the todays common usual 'Ionian'-C-major scale: C +9 D +8 E\ +5 F +9 G +8 A\ +9 B\ +5 C' N's outest circle exterior corresponds analogous to the double-subdominant-flattend Bb-major mixolydian heptatonic scale: Legenda: Bb=44ut, 52re, 8mi, 13fa, 22sol, 30=la, 35--, 44ut,=Bb And finally: respectively inside the interiorst cycle represents double-dominant-sharpend D-major mixolydian hepatonics: Legenda: D=9UT' 17RE' 26MI' 31FA' 40SOL' 48LA' 53=0--' 9UT'=D in comleting all 5 cases. hope that helps to illustrate and understand N's division of the octave into 53. when transferred into modern terminology. from traditionally medivial hexachordian terminology over N's personal Bb-F-C-G-D "Mixolydian" concept over of Rameau's "Ionian" major 'triad' F-C-G Rameau's terms for an change of the actual key: C=tonique 1:1 with its 2 transpositons: F=sous-dominant by an 4th 4:3, labeled by an b-sign(molle)in the score C=super-dominant by an 5th 3:2, corresponds an #-sign(durum)in score resulting finally in the point of: http://en.wikipedia.org/wiki/Hugo_Riemann 's http://en.wikipedia.org/wiki/Tonnetz when applied to the good-old song, http://en.wikipedia.org/wiki/Ut_queant_laxis then N's drawing represents simply the transpositions of that chant through the pentard of keys: outside = Bb > F > C > G > D = inside For HIP experts: Attend N. starts in his original considerations at GAMMA-UT = 0 == 53 http://tede.ibict.br/tde_busca/processaArquivo.php?codArquivo=354 http://jrma.oxfordjournals.org/cgi/reprint/115/2/145.pdf (Warning: That both do deliver exhausting depletive informations!) That can be easier expressed in todays modern terms by the simplifications over the last few centuries: http://en.wikipedia.org/wiki/Solf%C3%A8ge Here ends my historically excursus, into the conservative N's old mediaevel world, his Baroque coevals considered his way of treating the subject as an antediluvian-reactionar-fossil relict of the middle-age, but still worth to read for the purpose of inspiration of 53 refinements... ...just let me conclude in quoteing an prince of poets laureats: J.W.Goethe http://www.zitate-online.de/literaturzitate/allgemein/16754/was-du-ererbt-von-deinen-vaetern-hast-erwirb.html Was du ererbt von Deinen Vätern hast, erwirb es, um es zu besitzen." Translation: "What you have (once) inherit from Yours (late) fathers, retrieve it (yourself again anew), in order to possess it (henceforward as yours own personal belongings)." Quest: Which native english speaker in that group here can offer for us an more appropriate and accurate translation, that is more apt, than my humble attempt? With sorry for beeing so much verbose Yours Sincerely A.S.
From: threesixesinarow (2008-07-17) Subject: RE: Wikipedia Newton's 53, --- In tuning@yahoogroups.com, "Andreas Sparschuh" <a_sparschuh@...> wrote: http://mto.societymusictheory.org/issues/mto.93.0.3/ mto.93.0.3.lindley7.gif http://en.wikipedia.org/wiki/ Talk:53_equal_temperament#Newton.27s_unpublished_manuscripts.3F > > [Lindley] refers to N's delineation > in his encyclopecic ripely in depth article > 'tuning & temperature' standard reference article: > "Stimmung und Temperatur" > within the book: > (F. Zaminer, Editor, Geschichte der > Musiktheorie, Vol. 6: Hören, Messen und Rechnen in der > Frühen Neuzeit (Wissenschaftliche Buchgesellschaft, > 1987) pp.205-210 Do you think you can amend the statement on Wikipedia so it more accurately reflects how he refers to Newton's treatment of 53 equal in this article? > Lindley's scholar article reproduces also an similar > even earlier "horogramm" > -appearently an forerunning predecessor- > made by [René Descartes] > that appeared in his famous: > "1618. Compendium Musicae. Neat, and there's more than one diagram. Musicae compendium / Renati Des Cartes (1695) http://gallica.bnf.fr/notice?N=FRBNF37240052 Excellent compendium of musick with necessary and judicious animadversions there upon : by a person of honour / Renatus Descartes (1653) http://gallica.bnf.fr/notice?N=FRBNF37240054 Clark
From: Andreas Sparschuh (2008-07-17) Subject: lacking information for amending: was, Re: Wikipedia Newton's 53, --- In tuning@yahoogroups.com, "threesixesinarow" <CACCOLA@...> wrote: > > Do you think you can amend the statement on Wikipedia > so it more accurately reflects how he refers to Newton's > treatment of 53 equal in this article? > Dear Clark and all others that seek a deeper understanding of Newton, sorry, i'm afraid, all i know about N's53 stems barely from one source alone: Mark Lindley critizises Newton for an supposed neglect of the schismatic 5*3^8:2^15 subdivision, which consequently would result in an double allocation for the 3rd at step 17 out of 53 into: http://en.wikipedia.org/wiki/Interval_(music) "A schismic major third is a schisma different from a just major third, eight fifths down and five octaves up, Fâ in C." L. assumes that N. had no idea of discerning properly inbetween: 1.) 2^13:3^8 = 8192:6561 ~384Cents an Pythagoren diminshed 4th 2.) 5:4 ~386Cents JI 3rd in presuming that N. wasn't clear aware of the schismatic concept: http://en.wikipedia.org/wiki/Schismatic_temperament "Mark Lindley and Ronald Turner-Smith argue that schismatic tuning was briefly in use during the late medieval period." Fully agreed. For reassessing the uncertainty about N's view, i simply need more historically checkable facts for verification, that i do suspect in N's unpublished autograph. For an apt review i would have to study N's own concrete ratios myself: How do they fit to N's drawing? In order to stay honest and fair against N. Without such an verification in reference to N's original i do hesitate to repeat again L's complains of finding fault in N's considerations, that i want accept preliminary only tentative with reservation, barely with a tiny grain of salt. But unfortunately L. presents there no concrete numerical-values in his (supposeable overly hypercritically?) evaluation: At the moment my situation consists still in a gap in my knowledge about N's real data: Simply i know to less about it. All i can say about it hitherto is precious few: From L. discussion arises the question, if N. actually refers to 53-EDO at all, or if he had something complete rational in his mind, when he penned down his 5 intersecting mixolydian hexachords? There remain some open questions: Weather meant N. really Holder's 53-EDO?: The schisma of ~2Cents refers to an finer resolution than the more coarse 2^(1:53) ~22.6415...Cents http://en.wikipedia.org/wiki/Holdrian_comma I really don't know if N. overtook the 2^(1:53) concept from http://en.wikipedia.org/wiki/William_Holder or vice versa just or was it just the other way around? Whom of that invented 53-EDO? Hence, please understand my caution about careless overhasty jumps into premature rash half-cocked conclusions: Without having read N's original myself, i'm not able to decide whether M. Lindley's objections against N's representation is justified or not? But if Mark says so, his review has to be taken serious. My conclusion: All i can report at the moment: My lacking personal insight into N's autograph and my respcet for his genius forbids me to invent disputable hypothesises about his work: http://en.wikipedia.org/wiki/Hypotheses_non_fingo > > > Ren� Descartes, 1618. Compendium Musicae. > > Neat, and there's more than one diagram. > Musicae compendium / Renati Des Cartes (1695) > http://gallica.bnf.fr/notice?N=FRBNF37240052 > http://gallica.bnf.fr/notice?N=FRBNF37240054 Lindley's copy originates exactly from the horogramm there in that. > But http://en.wikipedia.org/wiki/Edmond_de_Coussemaker 's "Scriptores de musica medii aevi (4 delen) (1864-1876)" contains appearently an other one even older more archaic-looking "horogramm" forerunner model of D's & N's. in staying tuned what N. really wrote or may-be even not time will show that Yours Sincerely A.S.
From: Andreas Sparschuh (2008-07-17) Subject: Goethe device about Descartes & Newton again, was : 53, - --- In tuning@yahoogroups.com, "threesixesinarow" <CACCOLA@> wrote: Hi all lovers of old slogans, probably > J.W.Goethe referred to D's & N's http://en.wikipedia.org/wiki/Theory_of_Colours in reference to n's quote: http://en.wikipedia.org/wiki/Standing_on_the_shoulders_of_giants "Pigmaei gigantum humeris impositi plusquam ipsi gigantes vident" 'If I have seen a little further it is by standing on the shoulders of Giants.' http://www.aerospaceweb.org/question/history/q0162b.shtml That sounds in G's version: http://www.zitate-online.de/literaturzitate/allgemein/16754/was-du-ererbt-von-deinen-vaetern-hast-erwirb.html "Was du ererbt von Deinen Vaetern hast, erwirb es, um es zu besitzen." 'Retrieve yours fahters inheritance, for possessing that as internalized own property' G's dictum can i.m.h.o. also be referred well to D's & N's tunings A.S.