Topic: Eikosany query
1 scales
| File | Description | Notes | Period (ยข) | Limit |
|---|---|---|---|---|
| Eikosany | 3)6 1.3.5.7.9.11 Eikosany (1.3.5 tonic) | 20 | 1200.0 | 11 |
Thread (41 messages)
From: Alison Monteith (2001-10-09) Subject: Eikosany query Hi folks I'm tuning up my synths to experiment with two eikosanies, the 1, 3, 5, 7, 9, 11 and the 1, 3, 7, 9, 11, 15. When I made up the ratios for these I took my 3 out of 6 and used the products as numerators and the nearest power of two as a denominator, so for example 1, 3, 5 would be 15/8. So can anyone explain the following that I found in a load of scala files that I downloaded a while back? ! Eikosany.scl ! 3)6 1.3.5.7.9.11 Eikosany (1.3.5 tonic) 20 ! 33/32 21/20 11/10 9/8 7/6 99/80 77/60 21/16 11/8 7/5 231/160 3/2 63/40 77/48 33/20 7/4 9/5 11/6 77/40 2/1 I can't get this to tally with any of my calculations and if anyone can shed light I'd be very grateful indeed. I've been reading a lot of Erv Wilson's articles both from Xenharmonicon and online. Here are same observations from a not-too-mathematical musician. Interesting though the articles are I can find nowhere where he explains the actual process of working out the ratios, though I figured the process out myself. There's quite a lot of his stuff that would benefit from some clear editing and explanation. The lattices and diamonds and tilebursts are all clear but some of the tuning layouts and mappings and some of the diagrams are not so obvious to me, the average reader. Before the devotees leap to Erv's defence please note that I'm not committing the sacrilege of criticising, simply observing and suggesting. And furthermore! : - ) can anyone give me three (or thereabouts) good reasons why I should tune my forthcoming new instruments to Blackjack rather than to one of the Eikosanies? The main instruments are: steel tube metallophone, bowed psaltery ( only 17 strings planned ), a very big mbira and a small version of the harmonic canon, ie a zithery thing, plus a mini orchestra of slit drums. I'll be writing for these and small choir and I intend that the music will be both modal and harmonic. Phew! Thanks in anticipation
From: Paul Erlich (2001-10-09) Subject: Re: Eikosany query --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote: > Hi folks > > I'm tuning up my synths to experiment with two eikosanies, the 1, 3, 5, > 7, 9, 11 and the 1, 3, 7, 9, 11, 15. When I made up the ratios for these > I took my 3 out of 6 and used the products as numerators and the nearest > power of two as a denominator, so for example 1, 3, 5 would be 15/8. > > So can anyone explain the following that I found in a load of scala > files that I downloaded a while back? Alison, when you take the products of three factors at a time, none of the notes will be a 1/1. But it is customary (and probably mandatory in Scala) to express one of the notes as 1/1. So in this case, 1*3*5 is taken as the tonic, and all the ratios you calculated would have to be divided by 15 to get the ratios in the Scala file. > > ! Eikosany.scl > ! > 3)6 1.3.5.7.9.11 Eikosany (1.3.5 tonic) > 20 > There's quite a lot of his stuff that > would benefit from some clear editing and explanation. I agree, but Kraig Grady has argued vehemently against any such project. I do what I can here. The lattices and > diamonds and tilebursts are all clear but some of the tuning layouts and > mappings and some of the diagrams are not so obvious to me, the average > reader. Before the devotees leap to Erv's defence please note that I'm > not committing the sacrilege of criticising, simply observing and > suggesting. I can attempt to answer any questions you might have. > > And furthermore! : - ) can anyone give me three (or thereabouts) > good reasons why I should tune my forthcoming new instruments to > Blackjack rather than to one of the Eikosanies? Note that Erv Wilson recommended these Eikosanies to be used as part of 31- and 22-tone JI scales, respectively. These are CS scales, as is Blackjack. The first Eikosany has only one 1:3:5:7 tetrad, the second none (I think), while Blackjack has eight. Other similar comparisons were posted back in May. But there may be other scales even better for you than any of these options. > The main instruments > are: steel tube metallophone, bowed psaltery ( only 17 strings planned > ), Perhaps we should limit our consideration to scales with 17 or fewer notes? It's up to you. Remember, Blackjack was designed for Joseph Pehrson's specific desiderata -- your mileage may vary. What features are important to you in a scale / tuning system?
From: Alison Monteith (2001-10-09) Subject: Re: [tuning] Re: Eikosany query Paul Erlich wrote: > Alison, when you take the products of three factors at a time, none > of the notes will be a 1/1. But it is customary (and probably > mandatory in Scala) to express one of the notes as 1/1. So in this > case, 1*3*5 is taken as the tonic, and all the ratios you calculated > would have to be divided by 15 to get the ratios in the Scala file. That's a relief. I get it now. > I can attempt to answer any questions you might have. I'll take you up on that. I don't know if you have the Xenharmonicon back issues. I'll be referring to some of the CPS articles that particularly confound me. > Note that Erv Wilson recommended these Eikosanies to be used as part > of 31- and 22-tone JI scales, respectively. These are CS scales, as > is Blackjack. The first Eikosany has only one 1:3:5:7 tetrad, the > second none (I think), while Blackjack has eight. Other similar > comparisons were posted back in May. But there may be other scales > even better for you than any of these options. > > Perhaps we should limit our consideration to scales with 17 or fewer > notes? It's up to you. Remember, Blackjack was designed for Joseph > Pehrson's specific desiderata -- your mileage may vary. > > What features are important to you in a scale / tuning system? Starting with the instruments, I have planned up to 25 steel tubes. It would be nice to have an 'octave' plus some rather than 25 tones to the 'octave'. Thus I'm looking at the 15 - 22 ish notes per 'octave'. The bowed psaltery has room for only 17 strings. I had thought of the principle of a useful 17 tone subset of the 'master' scale or simply the best group of 17 consecutive tones. The mbira, for bass lines mainly, has room for up to 25 tones. The zither, or more probably 3 zithers, will have 6 tones each maximum, giving 18 tones, though I'm not sure as to how wide I can spread the range as they will be fairly similar and using guitar strings. The tubes are fixed, the others tunable, so I'll be looking at a very flexible and resourceful scale for the tubes as I'll be using them for the current voice project and for pure instrumental projects. I first intend setting various texts for voice and instruments. The vocal parts will have a microtonal element as regards melody, though not so obscure as demanding too much of good professional singers. There will also be harmonic part writing. The instruments will underpin and embellish the choir and provide interludes which will modify some of the vocal melodies with more of a microtonal twist. In a sense the instruments and choir are antiphonal at points with the instruments bending some of the sung melodies and harmonies. Such is the general plan. But as I said I'd like the master instrument scale, which will be fixed for the tubes, to have both good harmonic and melodic resources. The jury is still out on the relevance of the inharmonicity of the tubes, and indeed the mbira, so I'm not too concerned about spectral matching and the like. 'Blackjack' to my ears, and from studying the correspondence, has exceptional harmonic resources, but I'd have to spend more time to ponder the melodic possibilities. The Eikosanies again seem to have interesting harmonic possibilities and strange melodic features. I rather like the idea of having several tetrachordal possibilities in the one scale, since I've worked a lot with modal modulation in past pieces. Finding a solution that provides good harmonic potential would be one satisfactory solution. My heart is for JI, my head often leans towards Equal Temperament so I've no party card. Naturally I don't anticipate a solution but suggestions would be welcome. After all, you got Joseph "sorted" and look where that all led! Many thanks. Best wishes
From: Paul Erlich (2001-10-10) Subject: Re: Eikosany query --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote: > I rather like the idea of having several tetrachordal possibilities in the one scale, since I've > worked a lot with modal modulation in past pieces. Finding a solution that provides good harmonic > potential would be one satisfactory solution. My heart is for JI, my head often leans towards > Equal Temperament so I've no party card. How about 19-out-of-meantone? This will be very singable, very tetrachordal, very modulatable, and rich in near-JI chords, which a choir could always adaptively and subliminally alter into true JI verticalities. It's not too hot in the 11-limit, though . . . not sure how much that matters to you. > Naturally I don't anticipate a solution but suggestions would be welcome. After all, you got > Joseph "sorted" and look where that all led! Not sure what you mean . . . Joseph wrote a very nice Blackjack piece and will likely write even nicer ones in the future (now that we've discussed melody a bit more). Did you mean to insert a smiley there?
From: jpehrson@rcn.com (2001-10-11) Subject: Re: Eikosany query --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote: http://groups.yahoo.com/group/tuning/message/28996 > Naturally I don't anticipate a solution but suggestions would be welcome. After all, you got > Joseph "sorted" and look where that all led! Many thanks. > Gee, Alison! I don't know *myself* where it all led, but that sounds like a compliment! I guess one piece, for the time being, for trombone and electronics... I was also concerned about the melodic features of blackjack, but Paul has convinced me that it really can be quite melodically varied by using subsets of the scale. Just using every *other* note leads to a scale not too far removed from traditional chromatic 12-tET, although somewhat wider at 116 cents (a "Secors"). So, actually, I would advocate trying to work in blackjack, since there is exceptional potential there... particularly with your interest in JI... best, _______ ________ ________ Joseph Pehrson
From: Alison Monteith (2001-10-11) Subject: Re: [tuning] Re: Eikosany query Paul Erlich wrote: > --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote: > > > I rather like the idea of having several tetrachordal possibilities > in the one scale, since I've > > worked a lot with modal modulation in past pieces. Finding a > solution that provides good harmonic > > potential would be one satisfactory solution. My heart is for JI, > my head often leans towards > > Equal Temperament so I've no party card. > > How about 19-out-of-meantone? This will be very singable, very > tetrachordal, very modulatable, and rich in near-JI chords, which a > choir could always adaptively and subliminally alter into true JI > verticalities. It's not too hot in the 11-limit, though . . . not > sure how much that matters to you. That's a good idea, though I haven't worked much with meantone. Just today I decided I have enough good timber to build two psalteries so I'm no longer restricted to 17 tones on one of the main instruments. As they are tunable,I could have up to 34 tones shared between the two psalteries. To answer the 11-limit question, harmonies of 11 are quite important to me as over the last year or so, I've worked with them and have managed to really hear them in both melody and harmony. I've just replied to Joseph on his Blackjack recommendation that I should spend quality time with the scale, on a decent synth patch, singing against some of the harmonies. This might indeed be a good practical way to evaluate suitable scales for the choral pieces. It might sound a bit strange but the singing doesn't have to be exactly in the same scale as the instruments, neither is it polymicrotonal. They just have to fit together. Where there is close imitation, or voice/instrument simultaneity I would as you say want to choose structures and melodies from the master scale that singers could get close to. > Naturally I don't anticipate a solution but suggestions would be > welcome. After all, you got > > Joseph "sorted" and look where that all led! > > Not sure what you mean . . . Joseph wrote a very nice Blackjack piece > and will likely write even nicer ones in the future (now that we've > discussed melody a bit more). Did you mean to insert a smiley there? I meant in the best possible way that a query from Joseph sent the list's finest into a frenzy of creativity, discovery, and, eventually, to beautiful music by Joseph and others. Nice to think that might happen to me - who knows? Many thanks
From: Alison Monteith (2001-10-11) Subject: Re: [tuning] Re: Eikosany query jpehrson@rcn.com wrote: > --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote: > > http://groups.yahoo.com/group/tuning/message/28996 > > > Naturally I don't anticipate a solution but suggestions would be > welcome. After all, you got > > Joseph "sorted" and look where that all led! Many thanks. > > > > Gee, Alison! I don't know *myself* where it all led, but that sounds > like a compliment! I guess one piece, for the time being, for > trombone and electronics... It was indeed a compliment. > I was also concerned about the melodic features of blackjack, but > Paul has convinced me that it really can be quite melodically varied > by using subsets of the scale. Just using every *other* note leads > to a scale not too far removed from traditional chromatic 12-tET, > although somewhat wider at 116 cents (a "Secors"). > > So, actually, I would advocate trying to work in blackjack, since > there is exceptional potential there... particularly with your > interest in JI... > > best, > > _______ ________ ________ > Joseph Pehrson I like what I've heard of Blackjack by others and from my own meanderings. It can be made to sound very JI, if you know what I mean. It would probably be most beneficial in my case to spend time singing against some structures to see how the scale feels as an accompaniment for choir. Regards
From: Paul Erlich (2001-10-11) Subject: Re: Eikosany query --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote: > > > Paul Erlich wrote: > > > --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote: > > > > > I rather like the idea of having several tetrachordal possibilities > > in the one scale, since I've > > > worked a lot with modal modulation in past pieces. Finding a > > solution that provides good harmonic > > > potential would be one satisfactory solution. My heart is for JI, > > my head often leans towards > > > Equal Temperament so I've no party card. > > > > How about 19-out-of-meantone? This will be very singable, very > > tetrachordal, very modulatable, and rich in near-JI chords, which a > > choir could always adaptively and subliminally alter into true JI > > verticalities. It's not too hot in the 11-limit, though . . . not > > sure how much that matters to you. > > That's a good idea, though I haven't worked much with meantone. Just today I decided I have enough > good timber to build two psalteries so I'm no longer restricted to 17 tones on one of the main > instruments. As they are tunable,I could have up to 34 tones shared between the two psalteries. > > To answer the 11-limit question, harmonies of 11 are quite important to me as over the last year > or so, I've worked with them and have managed to really hear them in both melody and harmony. I've > just replied to Joseph on his Blackjack recommendation that I should spend quality time with the > scale, on a decent synth patch, singing against some of the harmonies. This might indeed be a good > practical way to evaluate suitable scales for the choral pieces. It might sound a bit strange but > the singing doesn't have to be exactly in the same scale as the instruments, neither is it > polymicrotonal. They just have to fit together. Where there is close imitation, or > voice/instrument simultaneity I would as you say want to choose structures and melodies from the > master scale that singers could get close to. The original MIRACLE scale of course has 31 notes per octave, and the extension to 41 is appealing as well. This is the best system for 11- limit harmony, according to George Secor's, Dave Keenan's, and Graham Breed's independent evaluations. With a chain of 45 notes, you'll essentially have Partch's 43-tone scale, as well as many of his earlier published scales. So what would make sense to me would be to tune all your instruments to as large a contiguous (in terms of generators) segment of MIRACLE, which would mean Blackjack on some of your instruments, and perhaps 45 or more written notes for your singers. Are you planning to notate using 72-tET notation?
From: graham@microtonal.co.uk (2001-10-12)
Subject: Re: Eikosany query
In-Reply-To: <9q561e+10cqq@eGroups.com>
Paul wrote:
> The original MIRACLE scale of course has 31 notes per octave, and the
> extension to 41 is appealing as well. This is the best system for 11-
> limit harmony, according to George Secor's, Dave Keenan's, and Graham
> Breed's independent evaluations. With a chain of 45 notes, you'll
> essentially have Partch's 43-tone scale, as well as many of his
> earlier published scales. So what would make sense to me would be to
> tune all your instruments to as large a contiguous (in terms of
> generators) segment of MIRACLE, which would mean Blackjack on some of
> your instruments, and perhaps 45 or more written notes for your
> singers. Are you planning to notate using 72-tET notation?
While I share your enthusiasm for Miracle temperament, I think you're
over-egging the pudding a bit there. Secor's paper at
<http://www.anaphoria.com/secor.PDF> or XH3 doesn't claim it to be the
best system for anything, or mention 11-limit harmony. It does say the
system works well with Partch's scale (note he didn't know about the
earlier 43 note scale that really does approximate to 45 Miracle notes).
My work can hardly be considered independent from Dave's. The
quantitative results were tweaked to ensure Miracle did well in the 7 and
11 limits anyway.
The 24 note Miracle (Blackjack+3) keyboard mapping has firmly established
itself as my favourite extended mapping. I can testify to its melodic
resources, and will keep working at music demonstrating this. I'm not
sure why you'd need to go beyond the 31 notes. It may be better to
squeeze in more octaves beyond that point. But yes, there's no need to
stop with an MOS. If you don't have as many as 21 notes, tune to your
favourite 11-limit JI scale.
>From <http://www.microtonal.co.uk/decimal_lattice.htm>, it looks like the
d'Alessandro scale almost fits the 41 note MOS. I think it has something
to do with Eikosanies. So you could tune to a Miracle-tempered Eikosany,
and I think you'd get some extra consonances.
45 or more notes for the singers does look complex. The problem isn't so
much the inherent complexity of Miracle temperament, but the inability of
traditional notation to express it with fewer than 72 notes. You'll have
to get the message over as best you can.
Graham
From: Paul Erlich (2001-10-12) Subject: Re: Eikosany query --- In tuning@y..., graham@m... wrote: > I'm not > sure why you'd need to go beyond the 31 notes. Alison may want to harmonize a I-IV-V-I progression with hexads, for example. > It may be better to > squeeze in more octaves beyond that point. Agreed! > > 45 or more notes for the singers does look complex. Hmm . . . I'm not sure the singers would care how many notes you use, once the 72-tET notation is understood. > The problem isn't so > much the inherent complexity of Miracle temperament, but the inability of > traditional notation to express it with fewer than 72 notes. Right . . . (?)
From: Alison Monteith (2001-10-14) Subject: Re: [tuning] Re: Eikosany query Paul Erlich wrote: > > The original MIRACLE scale of course has 31 notes per octave, and the > extension to 41 is appealing as well. This is the best system for 11- > limit harmony, according to George Secor's, Dave Keenan's, and Graham > Breed's independent evaluations. So far so good > With a chain of 45 notes, you'll > essentially have Partch's 43-tone scale, as well as many of his > earlier published scales. How does the chain of 45 notes work? Is this just the Miracle generator extended to 45 tones. > So what would make sense to me would be to > tune all your instruments to as large a contiguous (in terms of > generators) segment of MIRACLE, which would mean Blackjack on some of > your instruments, and perhaps 45 or more written notes for your > singers. Are you planning to notate using 72-tET notation? I need to think this through aloud. You're saying that I should consider Miracle as the master scale, Blackjack being a subset. I would like to understand more about what you mean by 'as large a contiguous (in terms of generators) segment of Miracle.' An additional consideration is that I'm going to have to be careful that I don't end up with only one octave. Until I finish the bass mbira and tune it I won't know if I can get a complete octave below the other instruments. I think I should wait till I know the range of the instruments and then I can map these out graphically to see what the overall range of the "chamber ensemble" will be. I would certainly consider using 72 tet notation but I'd have to go through all the previous postings and other stuff which fortunately I've downloaded and saved. Has everyone agreed on the final notation? I seem to recall several variations. An additional bonus is that the counter-tenor in my Early Music trio suggested using the bowed psaltery instead of the lute for some of the 15th Century music that we play. We are talking about the likes of Ockeghem and Dufay as well as slightly later French chanson by Claudin de Sermisy for example. I'd imagine that meantone would be good for this period but which meantone? Or something with Pythagorean thirds to stretch the soprano and counter-tenor? The psaltery has 17 tones in all. Thanks for being so patient and for the helpful suggestions. Best Wishes
From: Alison Monteith (2001-10-14) Subject: Re: [tuning] Re: Eikosany query graham@microtonal.co.uk wrote: > > >From <http://www.microtonal.co.uk/decimal_lattice.htm>, it looks like the > d'Alessandro scale almost fits the 41 note MOS. I think it has something > to do with Eikosanies. So you could tune to a Miracle-tempered Eikosany, > and I think you'd get some extra consonances. Does "a Miracle-tempered Eikosany"mean that you substitute the Eikosany tone with the nearest (in cents) Miracle tone? Regards. > >
From: Alison Monteith (2001-10-14) Subject: Re: [tuning] Re: Eikosany query graham@microtonal.co.uk wrote: > > >From <http://www.microtonal.co.uk/decimal_lattice.htm>, it looks like the > d'Alessandro scale almost fits the 41 note MOS. I think it has something > to do with Eikosanies. So you could tune to a Miracle-tempered Eikosany, > and I think you'd get some extra consonances. Does "a Miracle-tempered Eikosany"mean that you substitute the Eikosany tone with the nearest (in cents) Miracle tone? Regards. >
From: graham@microtonal.co.uk (2001-10-14)
Subject: Re: Eikosany query
Alison wrote:
> Does "a Miracle-tempered Eikosany"mean that you substitute the Eikosany
> tone with the nearest (in
> cents) Miracle tone?
Every 11-limit interval has a unique mapping to Miracle temperament.
That's what temperaments do. It'll always be the best approximation to
both 31- and 72-equal. That should get it to around 40 cents of just, but
you don't need to worry about cents to work it out.
Graham
From: Paul Erlich (2001-10-14) Subject: Re: Eikosany query --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote: > > > Paul Erlich wrote: > > > > > The original MIRACLE scale of course has 31 notes per octave, and the > > extension to 41 is appealing as well. This is the best system for 11- > > limit harmony, according to George Secor's, Dave Keenan's, and Graham > > Breed's independent evaluations. > > So far so good > > > With a chain of 45 notes, you'll > > essentially have Partch's 43-tone scale, as well as many of his > > earlier published scales. > > How does the chain of 45 notes work? Is this just the Miracle generator extended to 45 tones. Yes. > > > So what would make sense to me would be to > > tune all your instruments to as large a contiguous (in terms of > > generators) segment of MIRACLE, which would mean Blackjack on some of > > your instruments, and perhaps 45 or more written notes for your > > singers. Are you planning to notate using 72-tET notation? > > I need to think this through aloud. You're saying that I should consider Miracle as the master > scale, Blackjack being a subset. Right. > I would like to understand more about what you mean by 'as large > a contiguous (in terms of generators) segment of Miracle.' That was a typo -- I left out the continuation of that sentence: ". . . as possible for each instrument". But I wouldn't sacrifice the instrument's natural pitch range and tune all the pitches within one octave! > > I would certainly consider using 72 tet notation but I'd have to go through all the previous > postings and other stuff which fortunately I've downloaded and saved. Has everyone agreed on the > final notation? I seem to recall several variations. Well, we had some disagreement on ASCII notations, but for written scores, there are two notations which have some currency: the Boston Sims-Maneri notation (which you can find on Ted Mook's page) and Richter-Herf's notation. Pick one or invent your own -- the idea being a 12-tET basis with some new accidentals. > > An additional bonus is that the counter-tenor in my Early Music trio suggested using the bowed > psaltery instead of the lute for some of the 15th Century music that we play. We are talking about > the likes of Ockeghem and Dufay as well as slightly later French chanson by Claudin de Sermisy for > example. I'd imagine that meantone would be good I'd ask Margo . . . > for this period but which meantone? In the early 16th century, no one tuned "perfect" meantones . . . most likely, there was some variation in the fifths, perhaps ranging most typically from 2/7-comma to 1/4-comma in flatness. > Or something > with Pythagorean thirds to stretch the soprano and counter-tenor? Don't quite understand what kind of "stretch" you mean.
From: Paul Erlich (2001-10-14) Subject: Re: Eikosany query --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote: > > > graham@m... wrote: > > > > > >From <http://www.microtonal.co.uk/decimal_lattice.htm>, it looks like the > > d'Alessandro scale almost fits the 41 note MOS. I think it has something > > to do with Eikosanies. So you could tune to a Miracle-tempered Eikosany, > > and I think you'd get some extra consonances. > > Does "a Miracle-tempered Eikosany"mean that you substitute the Eikosany tone with the nearest (in > cents) Miracle tone? In principle, it wouldn't necessarily be the nearest tone -- instead, one would make sure each consonant interval was represented by its Miracle equivalent. In practice, this might turn out to be equivalent to using the nearest tone. But I find it unlikely that the Eikosany is going to meet your compositional goals . . . for one thing, it's conceived as an "atonal" tuning system.
From: jpehrson@rcn.com (2001-10-15) Subject: blackjack miracles --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote: http://groups.yahoo.com/group/tuning/message/29063 > I meant in the best possible way that a query from Joseph sent the list's finest into a frenzy of creativity, discovery, and, eventually, to beautiful music by Joseph and others. Nice to think > that might happen to me - who knows? > Hello Allison... Well, I guess it was true that I was rather a "catalyst" in this, so much so that Graham Breed called me the conceivable "inventor" of Blackjack. I have to cough... (fortunately it's not anthrax...) Just asking some dumb questions... but people did get busy it is true... In fact, they got so busy that it forced all the lists to split off... if people recall, that was the instigator of the split- ups... But, of course, there is so much more to do. I only did *one* piece, and Paul and Dave have been very helpful in showing me all the potentialities of the intriguing scale they invented. That's why it probably is a good idea for more of us to explore it. There is a lot there, and every person brings a different insight and capability. I'm sure you will make a major contribution when you work with it! best, _______ _________ _______ Joseph Pehrson
From: jpehrson@rcn.com (2001-10-15) Subject: Re: Eikosany query --- In tuning@y..., "Paul Erlich" <paul@s...> wrote: http://groups.yahoo.com/group/tuning/message/29065 > The original MIRACLE scale of course has 31 notes per octave, and the extension to 41 is appealing as well. This is the best system for 11- limit harmony, according to George Secor's, Dave Keenan's, and Graham Breed's independent evaluations. With a chain of 45 notes, you'll essentially have Partch's 43-tone scale, as well as many of his earlier published scales. So what would make sense to me would be to tune all your instruments to as large a contiguous (in terms of generators) segment of MIRACLE, which would mean Blackjack on some of your instruments, and perhaps 45 or more written notes for your singers. Are you planning to notate using 72-tET notation? This is, of course, an excellent suggestion for Allison, but unless it is done properly it could, conceivably lead to a rehearsal nightmare... It seems the singers probably need some kind of "crutch" and if they are playing *more* notes of Miracle than the instruments this might get quite confusing for them. That is, of course, unless you're suggesting that the instruments are also *supplementing* Blackjack with the additional choral pitches... Or, perhaps something could be done like Toby Twining... a very talented microtonal composer who posted at least *once* to this list. I heard a piece done by Bang on a Can which was controlled with a laptop computer and headphones for all the singers for pitch reference... Now it seems the chances for accuracy would be greatly enhanced with such a system. Of course, it means more equipment... but not really all that much. Adequate headphones wouldn't be *that* expensive... ________ ______ _______ Joseph Pehrson
From: Alison Monteith (2001-10-15) Subject: Re: [tuning] blackjack miracles jpehrson@rcn.com wrote: > --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote: > > http://groups.yahoo.com/group/tuning/message/29063 > > > I meant in the best possible way that a query from Joseph sent the > list's finest into a frenzy of creativity, discovery, and, > eventually, to beautiful music by Joseph and others. Nice to think > > that might happen to me - who knows? > > > > Hello Allison... > > Well, I guess it was true that I was rather a "catalyst" in this, so > much so that Graham Breed called me the conceivable "inventor" of > Blackjack. > > I have to cough... (fortunately it's not anthrax...) > > Just asking some dumb questions... but people did get busy it is > true... In fact, they got so busy that it forced all the lists to > split off... if people recall, that was the instigator of the split- > ups... > > But, of course, there is so much more to do. I only did *one* piece, > and Paul and Dave have been very helpful in showing me all the > potentialities of the intriguing scale they invented. > > That's why it probably is a good idea for more of us to explore it. > There is a lot there, and every person brings a different insight and > capability. > > I'm sure you will make a major contribution when you work with it! > > best, Hope so. Can't wait to get down to the actual writing. One question, which frequency did you centre everything on, A440 or on C? I'm having a bit of a struggle deciding how to start tuning my fixed pitch metal tubes. Because the scale isn't Just I have to be careful where I start. Regards
From: Alison Monteith (2001-10-15) Subject: Re: [tuning] Re: Eikosany query Paul Erlich wrote:> > Well, we had some disagreement on ASCII notations, but for written > scores, there are two notations which have some currency: the Boston > Sims-Maneri notation (which you can find on Ted Mook's page) and > Richter-Herf's notation. Pick one or invent your own -- the idea > being a 12-tET basis with some new accidentals. > > > > An additional bonus is that the counter-tenor in my Early Music > trio suggested using the bowed > > psaltery instead of the lute for some of the 15th Century music > that we play. We are talking about > > the likes of Ockeghem and Dufay as well as slightly later French > chanson by Claudin de Sermisy for > > example. I'd imagine that meantone would be good > > I'd ask Margo . . . > > > for this period but which meantone? > > In the early 16th century, no one tuned "perfect" meantones . . . > most likely, there was some variation in the fifths, perhaps ranging > most typically from 2/7-comma to 1/4-comma in flatness. > > > Or something > > with Pythagorean thirds to stretch the soprano and counter-tenor? > > Don't quite understand what kind of "stretch" you mean. Thank you for this information. I mean stretch in the sense of "challenge". Despite the fact that we are a very close trio I still get the "are you an alien" look when I talk about Pythagorean thirds. But with the chance to use other than 12 tunings on an 'early' instrument I have a foot in the door as it were. Regards
From: Alison Monteith (2001-10-15) Subject: Re: [tuning] Re: Eikosany query Paul Erlich wrote: > --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote: > > > > > > graham@m... wrote: > > > > > > > > >From <http://www.microtonal.co.uk/decimal_lattice.htm>, it looks > like the > > > d'Alessandro scale almost fits the 41 note MOS. I think it has > something > > > to do with Eikosanies. So you could tune to a Miracle-tempered > Eikosany, > > > and I think you'd get some extra consonances. > > > > Does "a Miracle-tempered Eikosany"mean that you substitute the > Eikosany tone with the nearest (in > > cents) Miracle tone? > > In principle, it wouldn't necessarily be the nearest tone -- instead, > one would make sure each consonant interval was represented by its > Miracle equivalent. In practice, this might turn out to be equivalent > to using the nearest tone. But I find it unlikely that the Eikosany > is going to meet your compositional goals . . . for one thing, it's > conceived as an "atonal" tuning system. Yes, I've decided to tune the current metallophone to Blackjack and my only problem is which frequency to start with. Probably A440 then I'll have to work out the rest. Anybody got a quick spreadsheet? Regards.
From: Paul Erlich (2001-10-15) Subject: Re: blackjack miracles --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote: > Hope so. Can't wait to get down to the actual writing. One question, which frequency did you > centre everything on, A440 or on C? Joseph centered everthing on C, but certainly D would be more symmetrical.
From: Paul Erlich (2001-10-15) Subject: Re: Eikosany query --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote: > Yes, I've decided to tune the current metallophone to Blackjack and my only problem is which > frequency to start with. Probably A440 Not a bad choice -- I'm planning to center my MIRACLE guitar on A. The most likely tonal centers then are C quatertone-sharp and F quartertone-sharp. > then I'll have to work out the rest. Anybody got a quick > spreadsheet? here's one octave: 440.0000 448.5539 470.6732 479.8234 503.4847 513.2728 538.5836 549.0540 576.1292 587.3295 616.2922 628.2734 659.2551 672.0715 705.2130 718.9228 754.3747 769.0402 806.9636 822.6514 863.2185 880.0000
From: Robert Walker (2001-10-16) Subject: Re: Eikosany query Hi Alison, I'm sure Kraig would be the one to answer the Eikosany part of your query, but since he isn't posting at the moment as far as I can see: The idea of the Eikosany is it has many pure triad, tetrad etc. subsets. They aren't that easy to find though, if you are presented with the scale notes. So, I expect one would want to do something with the layout of the instruments to make them easier to find them if building one. (In FTS I'm experimenting with ways of using the midi keyboard to select subsets of the Eikosany by devoting some of the octaves to the task of selecting subsets, rather than playing notes). If in the way of building musical instruments, I'd love to make, say, a hexany as six pointed star. I.e. six pointed star as two interlaced triangles; each triangle plays a triad; and each adjacent group of three points round the edge of the star also plays a triad, making eight triads in all, easy to find. One could make the 1 3 5 7, 1 3 5 11, 1 3 5 9, 1 3 7 11 or even 1 5 7 11 hexanies. All these can be found as subsets of the 1 3 5 7 9 11 Eikosany, so this is also introducing one gradually to the Eikosany subsets. Then I'd perhaps want to make a dekany next. If the instruments were ones that one could mount in a light framework, maybe one could actually mount the ten notes in the Octahedron + tetrahedron arrangement in the projection Paul used in his dekany animations (and I use on my dekany web page). Excuse me if this has already been said. I could easily have missed a post. However seemed the discussion has been focussed on 72-tet scales rather than the Eikosany itself as such. I think with Eikosany as based on the idea of really pure triads etc, would be nice if one could do them pure, and perhaps this would help hone ones perception of pure intervals. I wonder a little if retuning _everything_ to an approximation to j.i. might in the end run somewhat dull ones perception of j.i.?? Or at least, not stretch it in the direction of hearing j.i. intervals more and more finely. 72-tet is also just one of many n-tets. E.g. I've recently been exploring 55-tet, which is fascinating. If building instruments, one is hard-coding to a particular n-tet - okay if it is easy to make them or retune them, but quite a commitment to that n-tet if it is a matter of, say, many weeks or months of work... Also, like Dan, I wonder if consistency though interesting as a concept, might possibly be overrated as regards musicality. Does it matter how the intervals add up?? At least, I'd want to see from actual musical examples and compositions why it is important to have consistency; rather than just formulae. Or, see what effect it has compositionally, and decide for myself if I like that kind of an effect. Irregularity is interesting and composers often are doing things to throw rhythms etc. out from perfect symmetry, so maybe "inconsistent" scales could be desirable too? Perhaps dep. on the composer and the style of the piece. A few thoughts anyway. Not trying to dissuade you at all if you are keen on building 72-tet subsets; especially if this is because you like the sound of 72-tet. Robert
From: John A. deLaubenfels (2001-10-16) Subject: Re: Eikosany query [Alison wrote:] >>Yes, I've decided to tune the current metallophone to Blackjack and >>my only problem is which frequency to start with. Probably A440. [Paul E:] >Not a bad choice -- I'm planning to center my MIRACLE guitar on A. >The most likely tonal centers then are C quatertone-sharp and F >quartertone-sharp. Wouldn't that be 1/12 tone sharp in each case? JdL
From: Paul Erlich (2001-10-16) Subject: Re: Eikosany query --- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote: > [Alison wrote:] > >>Yes, I've decided to tune the current metallophone to Blackjack and > >>my only problem is which frequency to start with. Probably A440. > > [Paul E:] > >Not a bad choice -- I'm planning to center my MIRACLE guitar on A. > >The most likely tonal centers then are C quatertone-sharp and F > >quartertone-sharp. > > Wouldn't that be 1/12 tone sharp in each case? No, sir . . . I'm not sure why you'd think that. If you go to http://groups.yahoo.com/group/tuning/files/perlich/scales/ download bjlatt.zip, and look at blackjack0.bmp, you'll see that, for a blackjack scale centered on C, the notes that participate in the most consonances are A quartertone-flat and E quartertone-flat. Transposing the center to A, these become F quartertone-sharp and C quartertone-sharp.
From: Paul Erlich (2001-10-16) Subject: Re: Eikosany query --- In tuning@y..., "Robert Walker" <robertwalker@n...> wrote: > Also, like Dan, I wonder if consistency though interesting as a > concept, might possibly be overrated as regards musicality. > > Does it matter how the intervals add up?? At least, I'd > want to see from actual musical examples and compositions > why it is important to have consistency; rather than just formulae. > Or, see what effect it has compositionally, and decide for myself > if I like that kind of an effect. Forgetting about consistency has led many researchers to overrate the ability of 24-tET to support 7-limit harmony. That's why it's important. I'm not sure why you bring it up here, under this topic . . . As for the rest of your message, Robert, 72-tET is exceedingly accurate in the 7- and 11-limits (much more accurate than mere consistency would imply, BTW) . . . the harmonies sound unmistakably "just" should you care to try them out . . . and the temperament allows for a larger number of consonant chords than any similar JI system would. Kraig Grady himself said that 72 was OK by him and that one could spend a lifetime exploring MIRACLE (for example, the dekanies alone could occupy one for decades). A religious attachment to pure JI is all well and good until you actually sit down and play with these things on an instrument. On my keyboard, the 72-tET harmonies _are_ just . . . end of story. Plus, the natural fluctuations in tuning of string or metal instruments or human voices will render such distinctions meaningless anyway . . . Just my opinion! P.S. The only definite thing you actually said about the Eikosany is that it contains a lot of consonant chords . . . but Blackjack contains far more of almost all varieties . . . this comparison was done, I think, in May . . .
From: kalleaho@mappi.helsinki.fi (2001-10-16) Subject: Re: Eikosany query --- In tuning@y..., "Robert Walker" <robertwalker@n...> wrote: > > If in the way of building musical instruments, I'd love to > make, say, a hexany as six pointed star. > > I.e. six pointed star as two interlaced triangles; each > triangle plays a triad; and each adjacent group of three > points round the edge of the star also plays a triad, making > eight triads in all, easy to find. Hi Robert! As someone deeply interested in the Wilson CPS I find this idea of a star-shaped instrument very interesting. What if you wanted more than one octave in your instrument? Would it have many six pointed stars side by side or some other configuration? Kalle
From: John A. deLaubenfels (2001-10-16) Subject: Re: Eikosany query [Alison wrote:] >>>>Yes, I've decided to tune the current metallophone to Blackjack and >>>>my only problem is which frequency to start with. Probably A440. [Paul E:] >>>Not a bad choice -- I'm planning to center my MIRACLE guitar on A. >>>The most likely tonal centers then are C quatertone-sharp and F >>>quartertone-sharp. [I wrote:] >>Wouldn't that be 1/12 tone sharp in each case? [Paul:] >No, sir . . . I'm not sure why you'd think that. If you go to >http://groups.yahoo.com/group/tuning/files/perlich/scales/ >download bjlatt.zip, and look at blackjack0.bmp, you'll see that, for >a blackjack scale centered on C, the notes that participate in the >most consonances are A quartertone-flat and E quartertone-flat. >Transposing the center to A, these become F quartertone-sharp and C >quartertone-sharp. Went there, did that. Nice colors! And all those symbols that have so many definitions that were argued about endlessly. My eyes pretty much glaze over in the absence of a legend. I was thinking that A was neither flat nor sharp, and that it formed a good minor third with C. Must've made a false assumption there! JdL
From: Paul Erlich (2001-10-16) Subject: Re: Eikosany query --- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote: > Went there, did that. Nice colors! And all those symbols that have so > many definitions that were argued about endlessly. My eyes pretty much > glaze over in the absence of a legend. Sorry John -- here it is: ] = 1/4 tone sharp > = 1/6 tone sharp ^ = 1/12 tone sharp v = 1/12 tone flat < = 1/6 tone flat [ = 1/4 tone flat > > I was thinking that A was neither flat nor sharp, Right . . . > and that it formed a > good minor third with C. It forms a better minor third with Cv.
From: Paul Erlich (2001-10-16) Subject: Consistency again (for Robert Walker) --- In tuning@y..., "Robert Walker" <robertwalker@n...> wrote: > Also, like Dan, I wonder if consistency though interesting as a > concept, might possibly be overrated as regards musicality. > > Does it matter how the intervals add up?? At least, I'd > want to see from actual musical examples and compositions > why it is important to have consistency; rather than just formulae. > Or, see what effect it has compositionally, and decide for myself > if I like that kind of an effect. Hi Robert. In case you don't understand why it matters _compositionally_ how the intervals add up, I'll attempt to illustrate with an example. Many researchers (Meyer, Yunik and Swift come to mind) observe 12-tET's best approximations to the 5-limit interval classes (aside from the unison): ratio 12-tET steps error (cents) 2:3 7 2 4:5 4 14 5:6 3 16 Then they observe 24-tET's best approximations to the 7-limit interval classes (aside from the unison): ratio 24-tET steps error (cents) 2:3 14 2 4:5 8 14 4:7 19 19 5:6 6 16 5:7 12 17 6:7 5 17 Noticing that the errors are about the same size in both tables, they conclude that 24-tET is about as good in the 7-limit as 12-tET is in the 5-limit. Meyer even went to the trouble of constructing a 24-tET keyboard. Now let's say we want to compose something using these ideas. Let's start with a nice big consonant chord, that has all the 7-limit interval classes in it (just as the major triad has all the 5-limit interval classes in it). The most likely choice is of course a 4:5:6:7 chord (a "harmonic seventh" chord). I'll leave the rest of this argument as an exercise for the reader. Construct the chord, using the intervals in the above table. Can it be done? If not, might it have something to do with the fact that the intervals don't "add up"?
From: John A. deLaubenfels (2001-10-17) Subject: Re: Eikosany query [I wrote:] >>Went there, did that. Nice colors! And all those symbols that have >>so many definitions that were argued about endlessly. My eyes pretty >>much glaze over in the absence of a legend. [Paul wrote:] >Sorry John -- here it is: > > ] = 1/4 tone sharp > > = 1/6 tone sharp > ^ = 1/12 tone sharp > v = 1/12 tone flat > < = 1/6 tone flat > [ = 1/4 tone flat [JdL:] >>I was thinking that A was neither flat nor sharp, [Paul:] >Right . . . [JdL:] >>and that it formed a good minor third with C. [Paul:] >It forms a better minor third with Cv. OK, I figured out the lines: red: 3/2 (right) even dark blue: 5/4 (up, right) -1/72 purple: 6/5 (down, right) +1/72 green: 7/4 (up, right) -2/72 yellow: 7/6 (up, left) -2/72 lite blue: 7/5 (up, left) -1/72 Relationships: red = dark blue + purple green = dark blue + lite blue green = red + yellow lite blue = purple + yellow So, no purple extends from C (which is transposed to A). It'll come as no surprise to you that my [mind, heart, some part] rebels against any lattice that is missing so many connections. It seems so unnecessary (when adaptive tuning is available, which is not always). But I understand better my error in guessing what you were saying to Alison. JdL
From: jpehrson@rcn.com (2001-10-17) Subject: say, can you C?? --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote: http://groups.yahoo.com/group/tuning/message/29190 > Hope so. Can't wait to get down to the actual writing. One question, which frequency did you > centre everything on, A440 or on C? I'm having a bit of a struggle deciding how to start tuning > my fixed pitch metal tubes. Because the scale isn't Just I have to be careful where I start. > > Regards Hi Alison... I see Paul beat me to answering this question, but I used "Middle C" 261 hz... since I wanted it the same on my "changable" piano keyboard as on my acoustic one... Dave Keenan is keen-on using D as the basis, as Paul mentions. I guess it makes more sense mathematically... but there is still something dear to my heart about "Middle C..." ________ ________ _______ Joseph Pehrson
From: Robert Walker (2001-10-17) Subject: Re: Consistency again (for Robert Walker) Hi Paul, Thanks, a nice clear example. I have a much better idea of how consistency / inconsistency works compositionally as a result. E.g. could use C G A+ E+ G+ A# E# C# to modulate from C to C# via C using the 24-tet approximations to 1/1 5/4 3/2 7/4. (+ = quarter tone sharp). I've done a short melody that does exactly this (with extra notes to elaborate it) on my improvisations page, as a musical ex. for consistency / inconsistency. http://members.tripod.com/~robertinventor/tunes/improvisations.htm#24-tet N.B. as logician by training at one point, would like to point out, consistency is a reasonable name for this, but that it is consistency of a particular set of axioms / assumptions that is involved. Here the assumption that if you multiply two intervals, you can add their approximations in n-tet and get the same result. Adding that axiom in for n-limit ratios is consistent if (in current terminology) the scale is consistent up to the n-limit. So it is possibly something of a misnomer to call the scale itself inconsistent - it is a particular set of assumptions about the way that one wants to work with it that is inconsistent instead. Robert
From: Robert Walker (2001-10-17) Subject: Re: Eikosany query Hi Kalle, > As someone deeply interested in the Wilson CPS I find this idea of a > star-shaped instrument very interesting. What if you wanted more than > one octave in your instrument? Would it have many six pointed stars > side by side or some other configuration? That sounds like a possibility doesn't it. Six six pointed stars surrounding the player in a circle to make six octaves perhaps... I've no experience at all of building instruments (unless you count virtual VRML models, and I somehow don't think they give much experience for building real world ones :-) ). Kraig Grady has built and played CPS set instruments for many years. However he doesn't seem to be posting to the TL at the moment. Robert
From: kalleaho@mappi.helsinki.fi (2001-10-17) Subject: Re: Eikosany query --- In tuning@y..., "Robert Walker" <robertwalker@n...> wrote: > Hi Kalle, > > > As someone deeply interested in the Wilson CPS I find this idea of a > > star-shaped instrument very interesting. What if you wanted more than > > one octave in your instrument? Would it have many six pointed stars > > side by side or some other configuration? > > That sounds like a possibility doesn't it. Six six pointed stars > surrounding the player in a circle to make six octaves perhaps... > Yes, it is a possibility but I am very skeptical about the ergonomics side. Hexanies are quite easy to learn when mapped to a standard keyboard. After all, there are "only" 8 different chords in a hexany. So for them six keys or blocks side by side and octave-repeating is just as good a design as this star-shaped instrument. But it would be nice if there were some such intuitive design for the eikosany. > I've no experience at all of building instruments (unless you count > virtual VRML models, and I somehow don't think they give much > experience for building real world ones :-) ). > Me neither. > Kraig Grady has built and played CPS set instruments for many years. > However he doesn't seem to be posting to the TL at the moment. > > Robert He has used scales which are basically CPS but with added notes to make them Constant Structures and this is reflected in the designs of the instruments. This is Wilson's recommendation. They don't think that plain eikosanies or dekanies are scales at all. Scales or not, I think they are musically useful as tunings. Kalle
From: Robert Walker (2001-10-17) Subject: Re: Eikosany query Hi Kalle, > Yes, it is a possibility but I am very skeptical about the ergonomics > side. Hexanies are quite easy to learn when mapped to a standard > keyboard. After all, there are "only" 8 different chords in a hexany. > So for them six keys or blocks side by side and octave-repeating is > just as good a design as this star-shaped instrument. But it would be > nice if there were some such intuitive design for the eikosany. Maybe a skyscraper type design? Or concentric stars maybe for the octaves?... It's fairly easy to find the hexany chords on keyboard, but a little unintuitive improvising on hexany in keyboard layout. You can't so easily see the geometry; the way the chords relate to each other. I feel that a six pointed star would be more intuitive. Or indeed, a 3D octahedron. You could prob. get nice symmetrical arrangements for the eikosany. I think symmetry would make it easier to learn where the chords are as one has only a few patterns to learn. Ditto for the dekany. There I think the 3D shape would be really great if it was possible in terms of ergonomics to play the notes. (You just need the ten vertices and the framework to hold them). I'd like to make one some day, actually... I'm not really set up for making instruments at present though, in terms of space, equipment etc, (and so much I want to do in way of software), so it's something for further into the future. Robert
From: Alison Monteith (2001-10-17) Subject: Re: [tuning] Re: Eikosany query Paul Erlich wrote: > --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote: > > > Yes, I've decided to tune the current metallophone to Blackjack and > my only problem is which > > frequency to start with. Probably A440 > > Not a bad choice -- I'm planning to center my MIRACLE guitar on A. > The most likely tonal centers then are C quatertone-sharp and F > quartertone-sharp. > > > then I'll have to work out the rest. Anybody got a quick > > spreadsheet? > > here's one octave: > > 440.0000 > 448.5539 > 470.6732 > 479.8234 > 503.4847 > 513.2728 > 538.5836 > 549.0540 > 576.1292 > 587.3295 > 616.2922 > 628.2734 > 659.2551 > 672.0715 > 705.2130 > 718.9228 > 754.3747 > 769.0402 > 806.9636 > 822.6514 > 863.2185 > 880.0000 That's most helpful. Thank you. Best Wishes.
From: Alison Monteith (2001-10-17) Subject: Re: [tuning] Re: Eikosany query Robert Walker wrote: > Hi Alison, > > I'm sure Kraig would be the one to answer the Eikosany part of > your query, but since he isn't posting at the moment as far > as I can see: > > The idea of the Eikosany is it has many pure triad, tetrad > etc. subsets. > > They aren't that easy to find though, if you are presented > with the scale notes. > > So, I expect one would want to do something with the layout > of the instruments to make them easier to find them if > building one. > > (In FTS I'm experimenting with ways of using the midi keyboard to select > subsets of the Eikosany by devoting some of the octaves > to the task of selecting subsets, rather than playing notes). > > If in the way of building musical instruments, I'd love to > make, say, a hexany as six pointed star. > > I.e. six pointed star as two interlaced triangles; each > triangle plays a triad; and each adjacent group of three > points round the edge of the star also plays a triad, making > eight triads in all, easy to find. Some sort of metallophone or marimba would fit this layout. Have you read the back issues of Xenharmonicon? There are some incredibly detailed articles on layouts for instruments, mainly by Erv Wilson. I'm sure you'd get the details on the anaphoria website. > One could make the 1 3 5 7, 1 3 5 11, 1 3 5 9, 1 3 7 11 > or even 1 5 7 11 hexanies. All these can be found as subsets > of the 1 3 5 7 9 11 Eikosany, so this is also introducing > one gradually to the Eikosany subsets. > > Then I'd perhaps want to make a dekany next. If the instruments > were ones that one could mount in a light framework, maybe > one could actually mount the ten notes in the Octahedron + tetrahedron > arrangement in the projection Paul used in his dekany > animations (and I use on my dekany web page). > > Excuse me if this has already been said. I could easily have > missed a post. However seemed the discussion has been > focussed on 72-tet scales rather than the Eikosany itself > as such. I think with Eikosany as based on the idea of > really pure triads etc, would be nice if one could do them > pure, and perhaps this would help hone ones perception of > pure intervals. > > I wonder a little if retuning _everything_ to an approximation > to j.i. might in the end run somewhat dull ones perception > of j.i.?? Or at least, not stretch it in the direction > of hearing j.i. intervals more and more finely. I'm still not sure about this. I'm coming round to the opinion, through listening and comparing, that 2 - 3 cents of Just is pretty much Just, given the inharmonicity of strings in particular. I intend to try a small group of instruments, including metal tubes, tuned to 'Blackjack'. As with 22 tet I like to work with one tuning for a reasonable length of time. Then I'll make a set of Eikosany tubes and work with that. After all that I might be qualified to comment on the effects of tempering. > 72-tet is also just one of many n-tets. E.g. I've recently > been exploring 55-tet, which is fascinating. If building > instruments, one is hard-coding to a particular n-tet > - okay if it is easy to make them or retune them, > but quite a commitment to that n-tet if it is a matter > of, say, many weeks or months of work... > > Also, like Dan, I wonder if consistency though interesting as a > concept, might possibly be overrated as regards musicality. > > Does it matter how the intervals add up?? At least, I'd > want to see from actual musical examples and compositions > why it is important to have consistency; rather than just formulae. > Or, see what effect it has compositionally, and decide for myself > if I like that kind of an effect. > > Irregularity is interesting and composers often are doing things > to throw rhythms etc. out from perfect symmetry, so > maybe "inconsistent" scales could be desirable too? > Perhaps dep. on the composer and the style of the piece. > > A few thoughts anyway. Not trying to dissuade you at all > if you are keen on building 72-tet subsets; especially > if this is because you like the sound of 72-tet. Well, I suppose the sound comes first and I have to say that I liked Joseph's piece and I have a batch of ideas from tinkering with 'Blackjack' on my synth. It all depends on whether I can get the sounds into my head and start thinking and creating with that scale. Same old problem. Regards > > >
From: Paul Erlich (2001-10-17) Subject: Re: Eikosany query --- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote: > So, no purple extends from C (which is transposed to A). > > It'll come as no surprise to you that my [mind, heart, some part] rebels > against any lattice that is missing so many connections. Missing? Well, if you used the 31-tET version of blackjack, there would be a good minor third here . . . but then many of the consonances shown with connections (as well as many ratios of 9 and of 11) would be noticeably less just. And remember, intervals that are not consonances can be useful in their own right. > It seems so > unnecessary (when adaptive tuning is available, which is not > always). Here it clearly isn't -- Alison will be using many fixed-pitch instruments.
From: Paul Erlich (2001-10-17) Subject: Re: Eikosany query --- In tuning@y..., "Robert Walker" <robertwalker@n...> wrote: > Kraig Grady has built and played CPS set instruments for many years. > However he doesn't seem to be posting to the TL at the moment. > > Robert One can examine the layouts of Kraig's instruments at anaphoria.com. The Eikosanies are embedded into 22-tone and 31-tone Constant Structures, and these are laid out roughly in order of pitch, with different vertical positions being used in a smart way.