Topic: another place to find answers
1 scales
| File | Description | Notes | Period (ยข) | Limit |
|---|---|---|---|---|
| byzantine | Superset of several Byzantine scales by Rami Vitale, TL 29-Aug-2001 | 23 | 1200.0 | 7 |
Thread (49 messages)
From: Rami Vitale (2001-08-26) Subject: another place to find answers Hello Dears, I have read many of the messages, but I think that I have a different point of view. I'm a resercher in byzantine church music since about seven years, and I think Byzantine music has many answers we want, that because - since Byzantine music is only vocal - many real life tunings have been experienced freely for ages. Here I'm listing some scales which are already used in Byzantine church music: Diatonic: 9/8 10/9 16/15 9/8 9/8(not 10/9!) 10/9 16/15 10/9 21/20 8/7 9/8 10/9 21/20 8/7 28/27 8/7 9/8 9/8 28/27 8/7 9/8 16/15 7/6 15/14 9/8 16/15 7/6 15/14 And I would especially recommend this scale: 28/27 6/5 15/14 9/8 28/27 6/5 15/14 All these scales ( and much much more ) can be joined together in one scale of 23 key, and can be devided into two separate scales each with 16 degree, and also can be played very easily!
From: shreeswifty (2001-08-27) Subject: Re: [tuning] another place to find answers sounds like some nice intervals you got there....... Hey Dan does this count as a 28 limit scale??? hahahahaha Pat Pagano, Director South East Just Intonation Society http://www.screwmusicforever.com/SHREESWIFT/ 28/27 6/5 15/14 9/8 28/27 6/5 15/14
From: Paul Erlich (2001-08-27) Subject: Re: another place to find answers --- In tuning@y..., "Rami Vitale" <alfred1@s...> wrote: > Hello Dears, > > I have read many of the messages, but I think that I have a different point of view. > I'm a resercher in byzantine church music since about seven years, and I think Byzantine music has many answers we want, that because - since Byzantine music is only vocal - many real life tunings have been experienced freely for ages. > > Here I'm listing some scales which are already used in Byzantine church music: > > Diatonic: > 9/8 10/9 16/15 9/8 9/8(not 10/9!) 10/9 16/15 > > 10/9 21/20 8/7 9/8 10/9 21/20 8/7 > > 28/27 8/7 9/8 9/8 28/27 8/7 9/8 > > 16/15 7/6 15/14 9/8 16/15 7/6 15/14 > > And I would especially recommend this scale: > > 28/27 6/5 15/14 9/8 28/27 6/5 15/14 > > All these scales ( and much much more ) can be joined together in one scale of 23 key, > and can be devided into two separate scales each with 16 degree, and also can be played very easily! It also has been noted that 72-tET approximates all these very, very well.
From: Rami Vitale (2001-08-28) Subject: Re: [tuning] another place to find answers Sorry! My message was sent by accident and without enough information, my scale is: 15/14 21/20 28/27 15/14 36/35 49/48 64/63 15/14 21/20 15/14 21/20 28/27 15/14 36/35 49/48 64/63 another scale: 21/20 15/14 64/63 49/48 36/35 15/14 28/27 21/20 15/14 21/20 15/14 64/63 49/48 36/35 15/14 28/27 You can combine the two scales in one scale: 21/20 50/49 21/20 64/63 49/48 36/35 25/24 36/35 49/48 64/63 21/20 50/49 21/20 21/20 50/49 21/20 64/63 49/48 36/35 25/24 36/35 49/48 64/63 I will be glad to hear any comments. Rami V.
From: genewardsmith@juno.com (2001-08-27) Subject: Re: another place to find answers --- In tuning@y..., "Paul Erlich" <paul@s...> wrote: > It also has been noted that 72-tET approximates all these very, very > well. It is not alone in that, of course. The scales are all 7-limit, and the 41-et also does that very well. If that isn't good enough for some reason, there's always 99, or even 171, which does the 7-limit better than anyone probably needs.
From: jpehrson@rcn.com (2001-08-28) Subject: Re: another place to find answers --- In tuning@y..., genewardsmith@j... wrote: http://groups.yahoo.com/group/tuning/message/27481 > --- In tuning@y..., "Paul Erlich" <paul@s...> wrote: > > > It also has been noted that 72-tET approximates all these very, > very > > well. > > It is not alone in that, of course. The scales are all 7-limit, and > the 41-et also does that very well. If that isn't good enough for > some reason, there's always 99, or even 171, which does the 7-limit > better than anyone probably needs. Well, yes, but I believe that Anton Rovner was mentioning that the monks who worked with Eastern Orthodox music actually thought in terms of a 72 per octave system. Is this correct?? _____________ ______ _____ Joseph Pehrson
From: Rami Vitale (2001-08-28) Subject: [tuning] Re: another place to find answers > Well, yes, but I believe that Anton Rovner was mentioning that the > monks who worked with Eastern Orthodox music actually thought in > terms of a 72 per octave system. Is this correct?? > > _____________ ______ _____ > Joseph Pehrson No that's not right! In fact in byzantine music there are many numbers recommended per octave like: 72, 53, 68 ...etc but all these numbres are theoreticl only and are used only to simplify studying. In practical, real life tunnings are used, this is natural because byzantine music is vocal only. Yes there are some exeptions because new musicians are using instruments and theories imported from western music, but in majority real life tunnings are often used. Rami V.
From: jpehrson@rcn.com (2001-08-28) Subject: quite byzantine --- In tuning@y..., "Rami Vitale" <alfred1@s...> wrote: http://groups.yahoo.com/group/tuning/message/27507 > > Well, yes, but I believe that Anton Rovner was mentioning that the > > monks who worked with Eastern Orthodox music actually thought in > > terms of a 72 per octave system. Is this correct?? > > > > _____________ ______ _____ > > Joseph Pehrson > > No that's not right! > > In fact in byzantine music there are many numbers recommended per octave like: 72, 53, 68 ...etc > but all these numbres are theoreticl only and are used only to simplify studying. > > In practical, real life tunnings are used, this is natural because byzantine music is vocal only. > > Yes there are some exeptions because new musicians are using instruments and theories imported from western music, > but in majority real life tunnings are often used. > > Rami V. Thanks for the info! _________ __________ _____ Joseph Pehrson
From: Afmmjr@aol.com (2001-08-28) Subject: Re: [tuning] Re: another place to find answers In a message dated 8/28/01 7:49:48 AM Eastern Daylight Time, alfred1@scs-net.org writes: > > > Well, yes, but I believe that Anton Rovner was mentioning that the > > monks who worked with Eastern Orthodox music actually thought in > > terms of a 72 per octave system. Is this correct?? > > > > _____________ ______ _____ > > Joseph Pehrson > > No that's not right! > > In fact in byzantine music there are many numbers recommended per octave > like: 72, 53, 68 ...etc > but all these numbres are theoreticl only and are used only to simplify > studying. > > In practical, real life tunnings are used, this is natural because > byzantine music is vocal only. > > Yes there are some exeptions because new musicians are using instruments > and theories imported from western music, > but in majority real life tunnings are often used. > > Rami V. > > Check out www.geocities.com/romeikoweb1 to read about the Byzantine vocal ensemble that sings with the ancient tetrachords, as recommended by John Chalmers. The good news is you can hear George (Yioryos) Bilalis and his Romeiko Ensemble during the October 26th concert of MicroFest 2000 : 20 Years at St. Luke in the Fields Church in Greenwich Village. Johnny Reinhard
From: Paul Erlich (2001-08-28) Subject: Re: another place to find answers --- In tuning@y..., jpehrson@r... wrote: > --- In tuning@y..., genewardsmith@j... wrote: > > http://groups.yahoo.com/group/tuning/message/27481 > > > --- In tuning@y..., "Paul Erlich" <paul@s...> wrote: > > > > > It also has been noted that 72-tET approximates all these very, > > very > > > well. > > > > It is not alone in that, of course. The scales are all 7-limit, and > > the 41-et also does that very well. If that isn't good enough for > > some reason, there's always 99, or even 171, which does the 7- limit > > better than anyone probably needs. > > Well, yes, but I believe that Anton Rovner was mentioning that the > monks who worked with Eastern Orthodox music actually thought in > terms of a 72 per octave system. Is this correct?? > Yes, Anton did say that.
From: Paul Erlich (2001-08-28) Subject: Re: another place to find answers --- In tuning@y..., "Rami Vitale" <alfred1@s...> wrote: > > Well, yes, but I believe that Anton Rovner was mentioning that the > > monks who worked with Eastern Orthodox music actually thought in > > terms of a 72 per octave system. Is this correct?? > > > > _____________ ______ _____ > > Joseph Pehrson > > No that's not right! Why do you say that? You're familiar with the monks in question? > > In fact in byzantine music there are many numbers recommended per octave like: 72, 53, 68 ...etc > but all these numbres are theoreticl only and are used only to simplify studying. So it sounds like you're _agreeing_, rather than disagreeing! > > In practical, real life tunnings are used, this is natural because byzantine music is vocal only. > > Yes there are some exeptions because new musicians are using instruments and theories imported from western music, > but in majority real life tunnings are often used. > > Rami V. There is no evidence that just intonation is more of a "real life tuning" for vocalists, to within the errors of 72, 53, or 68-tone equal temperament. These are all _excellent_ ETs.
From: Alison Monteith (2001-08-28) Subject: Re: [tuning] another place to find answers Rami Vitale wrote: > I have read many of the messages, but I think that I have a different > point of view.I'm a resercher in byzantine church music since about > seven years, and I think Byzantine music has many answers we want, > that because - since Byzantine music is only vocal - many real life > tunings have been experienced freely for ages. Here I'm listing some > scales which are already used in Byzantine church music: Diatonic:9/8 > 10/9 16/15 9/8 9/8(not 10/9!) 10/9 16/15 10/9 21/20 8/7 9/8 10/9 21/20 > 8/7 28/27 8/7 9/8 9/8 28/27 8/7 9/8 16/15 7/6 15/14 9/8 16/15 7/6 > 15/14 And I would especially recommend this scale: 28/27 6/5 15/14 9/8 > 28/27 6/5 15/14 All these scales ( and much much more ) can be joined > together in one scale of 23 key,and can be devided into two separate > scales each with 16 degree, and also can be played very easily! I'd be interested in hearing how you arrived at these scales and their ratios Rami. Someone recently claimed that 'Byzantine music' was based on 72 EDO. How do you reconcile your findings with that? I am a keen student of Byzantine liturgical music and would like to see (or hear) some evidence to back up these claims. Thanks. Best Wishes
From: Paul Erlich (2001-08-28) Subject: Re: another place to find answers --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote: > I'd be interested in hearing how you arrived at these scales and their > ratios Rami. Someone recently claimed that 'Byzantine music' was based > on 72 EDO. How do you reconcile your findings with that? Easy -- they're very, very close -- 2 cents here, 3 cents there . . . no substantial difference.
From: Dave Keenan (2001-08-29) Subject: Re: another place to find answers --- In tuning@y..., "Rami Vitale" <alfred1@s...> wrote: > You can combine the two scales in one scale: > > 21/20 50/49 21/20 64/63 49/48 36/35 25/24 36/35 49/48 64/63 21/20 50/49 21/20 21/20 50/49 21/20 64/63 49/48 36/35 25/24 36/35 49/48 64/63 > > I will be glad to hear any comments. Rami, It's awesome! When the 224:225 is tempered out (to give a planar microtemperament), as may well be done by singers in practice, this may just be the most harmonically versatile superset scale of 23 notes or less, in the universe. Miracle tempering it (even all the way to 72-EDO) would probably be fine too. When this is done, it is seen to be an excellent subset of Canasta. Possibly better that Blackjack (longer chains of fifths). And so the planar temperament of it is a subset of my planar precursor to Canasta. Paul E. I believe your favourite 12 tone subset of Blackjack is also a subset of this scale. Here's the original scale in more familiar terms for those who want to examine it. ! byzantine.scl ! Superset of several Byzantine scales by Rami Vitale, TL 29-Aug-2001 23 ! 21/20 15/14 9/8 8/7 7/6 6/5 5/4 9/7 21/16 4/3 7/5 10/7 3/2 63/40 45/28 27/16 12/7 7/4 9/5 15/8 27/14 63/32 2/1 -- Dave Keenan
From: Rami Vitale (2001-08-29) Subject: Re: [tuning] another place to find answers ----- Original Message ----- From: Alison Monteith <alison.monteith3@which.net> To: <tuning@yahoogroups.com> Sent: Tuesday, August 28, 2001 5:10 PM Subject: Re: [tuning] another place to find answers > > > Rami Vitale wrote: > > > I have read many of the messages, but I think that I have a different > > point of view.I'm a resercher in byzantine church music since about > > seven years, and I think Byzantine music has many answers we want, > > that because - since Byzantine music is only vocal - many real life > > tunings have been experienced freely for ages. Here I'm listing some > > scales which are already used in Byzantine church music: Diatonic:9/8 > > 10/9 16/15 9/8 9/8(not 10/9!) 10/9 16/15 10/9 21/20 8/7 9/8 10/9 21/20 > > 8/7 28/27 8/7 9/8 9/8 28/27 8/7 9/8 16/15 7/6 15/14 9/8 16/15 7/6 > > 15/14 And I would especially recommend this scale: 28/27 6/5 15/14 9/8 > > 28/27 6/5 15/14 All these scales ( and much much more ) can be joined > > together in one scale of 23 key,and can be devided into two separate > > scales each with 16 degree, and also can be played very easily! > > I'd be interested in hearing how you arrived at these scales and their > ratios Rami. Someone recently claimed that 'Byzantine music' was based > on 72 EDO. How do you reconcile your findings with that? I am a keen > student of Byzantine liturgical music and would like to see (or hear) > some evidence to back up these claims. Thanks. > > Best Wishes Dear Alison, Did I mention that this is my personal theory? I don't know if that was clear. It was a very long way! but I think these scales reflect the practical use of Byzantine music ( reflects good performances! ). I depend on experiments, history, other musical forms like Arabic music and on old Greek and Arabic theories. Till now it is not approved by the orthodox church but I believe it will. Did you really try the 72 equal scale as mentioned in some theoretical books on an accurate device? I don't think so, because this scale may injure your ears! I think you agree that the diatonic scale used in Byzantine music is 9/8 10/9 16/15 9/8 9/8 10/9 16/15. In 72 per octave scale it will be 12.2 10.9 6.7 12.2 12.2 10.9 6.7 , accurate HEH! Believe it or not in the 72 per octave theory it is recommended as 12 10! 8! 12 12 10 8 !!!!!!!. ( mistake by 22 cent! ) it is not a sientific theory. Any way I promise that I will send you a comparison with sound as soon as possible, and more information but now I'm little busy because I have an exam on Saturday. Rami Vitale
From: Alison Monteith (2001-08-29) Subject: Re: [tuning] another place to find answers Rami Vitale wrote:Dear Alison, > > Did I mention that this is my personal theory? I don't know if that was > clear. > > It was a very long way! but I think these scales reflect the practical use > of Byzantine music ( reflects good performances! ). > > I depend on experiments, history, other musical forms like Arabic music and > on old Greek and Arabic theories. > > Till now it is not approved by the orthodox church but I believe it will. That would be a very important milestone. > Did you really try the 72 equal scale as mentioned in some theoretical books > on an accurate device? I don't think so, because this scale may injure your > ears! I haven't had time to try realising Byzantine music with anything other than 12 tet and some very simple just tetrachordal scales > > I think you agree that the diatonic scale used in Byzantine music is 9/8 > 10/9 16/15 9/8 9/8 10/9 16/15. > > In 72 per octave scale it will be 12.2 10.9 6.7 12.2 12.2 10.9 6.7 , > accurate HEH! > > Believe it or not in the 72 per octave theory it is recommended as 12 10! 8! > 12 12 10 8 !!!!!!!. > ( mistake by 22 cent! ) it is not a sientific theory. Then the 72 tet person whose name I forget needs to know this. > > Any way I promise that I will send you a comparison with sound as soon as > possible, and more information but now I'm little busy because I have an > exam on Saturday. > > Rami Vitale > Thanks Rami. I would dearly love to hear more about your theories. I'm about to embark on a postgraduate course on liturgical music. As I am writing a lot for choirs with a view to eventually introducing microtonal music into my work I've been led naturally to the Byzantine liturgy. Best of luck with the exam. Regards.
From: Alison Monteith (2001-08-29) Subject: Re: [tuning] Re: another place to find answers Paul Erlich wrote: > --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote: > > > I'd be interested in hearing how you arrived at these scales and > their > > ratios Rami. Someone recently claimed that 'Byzantine music' was > based > > on 72 EDO. How do you reconcile your findings with that? > > Easy -- they're very, very close -- 2 cents here, 3 cents there . . . > no substantial difference. Thanks, Paul, I understand that fairly clearly. What I'm not so clear about is that one Byzantine specialist claims that the music under consideration is in 72 EDO and the other gives precise ratios. One or the other must be nearer to the truth. I would have thought that the scientific bias of this list - a good thing - would have insisted on more precision. My theory which I can't back up empirically myself (yet) is that Byzantine music, as I understand it, being modal and sung, uses inflections of (probably) just diatonic major and minor scales and their modes and that it is in this sort of analysis that a clearer understanding of the totality of sung modal Byzantine music would be found. I would be most interested in being directed to any detailed research done 'in the field' as it were. Best Wishes.
From: Paul Erlich (2001-08-29)
Subject: Re: another place to find answers
--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:
> --- In tuning@y..., "Rami Vitale" <alfred1@s...> wrote:
> > You can combine the two scales in one scale:
> >
> > 21/20 50/49 21/20 64/63 49/48 36/35 25/24 36/35 49/48 64/63 21/20
> 50/49 21/20 21/20 50/49 21/20 64/63 49/48 36/35 25/24 36/35 49/48
> 64/63
> >
> > I will be glad to hear any comments.
>
> Rami, It's awesome!
>
> When the 224:225 is tempered out (to give a planar
microtemperament),
> as may well be done by singers in practice, this may just be the
most
> harmonically versatile superset scale of 23 notes or less, in the
> universe.
Really?! How do you come to that conclusion?
>
> Miracle tempering it (even all the way to 72-EDO) would probably be
> fine too. When this is done, it is seen to be an excellent subset
of
> Canasta.
Wow. Canasta contains all the wonders of Byzantine melody?! This
needs to be explored more fully.
>
> Here's the original scale in more familiar terms for those who want
to
> examine it.
>
> ! byzantine.scl
> !
> Superset of several Byzantine scales by Rami Vitale, TL 29-Aug-
2001
> 23
> !
> 21/20
> 15/14
> 9/8
> 8/7
> 7/6
> 6/5
> 5/4
> 9/7
> 21/16
> 4/3
> 7/5
> 10/7
> 3/2
> 63/40
> 45/28
> 27/16
> 12/7
> 7/4
> 9/5
> 15/8
> 27/14
> 63/32
> 2/1
Here's a lattice of Rami's scale:
5/4------15/8
,'/|\`. ,'/|\`.
10/7-/-|-\15/14/-|-\45/28
7/6-------7/4------21/16-----63/32
,' `. |/,' \`.\|/,'/ `.\| ,' `.
4/3-------1/1-----\-3/2-/-----9/8------27/16
`. ,' |\`. /,\/|\/.\ ,'/| `. ,'
8/7---|-\12/7-/\|/\-9/7-/-|--27/14
7/5------21/20-----63/40
\|/,' `.\|/,'
6/5-------9/5
It's a 7-limit Tonality Diamond (centered around 3/2 instead of 1/1)
with some very symmetrical extensions along the 3-axis. It may very
well be the set of notes within a certain radius in the triangular
lattice (when length of ratios of N is log(N) or something like that).
What's the closest match to a periodicity block? Is it a 22-tone
periodicity block with 1 note added? I'll have to investigate . . .
From: Paul Erlich (2001-08-29) Subject: Re: another place to find answers --- In tuning@y..., "Rami Vitale" <alfred1@s...> wrote: > I think you agree that the diatonic scale used in Byzantine music is 9/8 > 10/9 16/15 9/8 9/8 10/9 16/15. > > In 72 per octave scale it will be 12.2 10.9 6.7 12.2 12.2 10.9 6.7 , > accurate HEH! > > Believe it or not in the 72 per octave theory it is recommended as 12 10! 8! > 12 12 10 8 !!!!!!!. > ( mistake by 22 cent! ) Excuse me sir, but in the 72 per octave theory the "Indian/Byzantine diatonic" is represented as 12 11 7 12 12 11 7. The maximum error is about 4 cents. > it is not a sientific theory. Calling a set of ratios "a scientific theory" for a musical style is a 19th century idea. We've progressed beyond Helmholtz!
From: Paul Erlich (2001-08-29) Subject: Re: another place to find answers --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote: > > > Paul Erlich wrote: > > > --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote: > > > > > I'd be interested in hearing how you arrived at these scales and > > their > > > ratios Rami. Someone recently claimed that 'Byzantine music' was > > based > > > on 72 EDO. How do you reconcile your findings with that? > > > > Easy -- they're very, very close -- 2 cents here, 3 cents there . . . > > no substantial difference. > > Thanks, Paul, I understand that fairly clearly. What I'm not so clear about is that one Byzantine > specialist claims that the music under consideration is in 72 EDO and the other gives precise > ratios. One or the other must be nearer to the truth. Nonsense. The differences are very tiny. One will likely find variations in practice (from region to region, for example) which swamp the differences between these two reckonings.
From: jpehrson@rcn.com (2001-08-30) Subject: the Byzantine 72-tones --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote: http://groups.yahoo.com/group/tuning/message/27588 > > > Paul Erlich wrote: > > > --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote: > > > > > I'd be interested in hearing how you arrived at these scales and > > their > > > ratios Rami. Someone recently claimed that 'Byzantine music' was > > based > > > on 72 EDO. How do you reconcile your findings with that? > > > > Easy -- they're very, very close -- 2 cents here, 3 cents there . . . > > no substantial difference. > > Thanks, Paul, I understand that fairly clearly. What I'm not so clear about is that one Byzantine > specialist claims that the music under consideration is in 72 EDO and the other gives precise > ratios. One or the other must be nearer to the truth. I would have thought that the scientific > bias of this list - a good thing - would have insisted on more precision. Hello Allison! I believe it was Anton Rovner who had heard from sources in Russia that there were 72 pitches per octave in some Russian Orthodox music. However, I am not certain that he said it was an ET.. It could have been ratios, I don't know. Anton seems to be away at the moment... probably at another Contemporary Music festival or such like, but hopefully he will respond when he gets back... best, _________ _______ _______ Joseph Pehrson
From: David C Keenan (2001-08-30)
Subject: Re: another place to find answers
--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:
> > When the 224:225 is tempered out (to give a planar
> microtemperament),
> > as may well be done by singers in practice, this may just be the
> most
> > harmonically versatile superset scale of 23 notes or less, in the
> > universe.
>
> Really?! How do you come to that conclusion?
Probably the easiest way to see it is on a chain of secors. Copy and paste this into a text editor to get rid of the extraneous line-breaks and slide the otonal pattern along. In some ways, I find this method of harmonic navigation superior to lattices (in fact it is the 1D tempered lattice).
Eb<Ev F Gb^ Bb<Bv C Db^D> F< F#vG Ab^A> C< C#vD Eb^E> G#vA Bb^B>
|--|--|--|--.--.--|--|--|--|--|--.--|--|--|--|--|--.--|--|--|--|--|--.--.--|--|--|--|
5 7 1 3 9 11
Legend:
A..G, #, b same as 12-tET
> sixth-tone sharp (+33c)
^ twelfth-tone sharp (+17c)
v twelfth-tone flat (-17c)
< sixth-tone flat (-33c)
Also I figure that having longer chains of fifths than Blackjack will make it a superset of more real-world scales.
> Wow. Canasta contains all the wonders of Byzantine melody?!
Only if Rami and Xenakis are right and the Greek Orthodox Church is wrong about those tetrachords with steps of 6/72 or 8/72 octave. Otherwise it only contains _some_ of those wonders. :-)
> Here's a lattice of Rami's scale:
>
> 5/4------15/8
> ,'/|\`. ,'/|\`.
> 10/7-/-|-\15/14/-|-\45/28
> 7/6-------7/4------21/16-----63/32
> ,' `. |/,' \`.\|/,'/ `.\| ,' `.
> 4/3-------1/1-----\-3/2-/-----9/8------27/16
> `. ,' |\`. /,\/|\/.\ ,'/| `. ,'
> 8/7---|-\12/7-/\|/\-9/7-/-|--27/14
> 7/5------21/20-----63/40
> \|/,' `.\|/,'
> 6/5-------9/5
>
> It's a 7-limit Tonality Diamond (centered around 3/2 instead of 1/1)
> with some very symmetrical extensions along the 3-axis. It may very
> well be the set of notes within a certain radius in the triangular
> lattice (when length of ratios of N is log(N) or something like
that).
Thanks for that. Yes, quite spherical.
When the 224:225 septimal kleisma is tempered out (or ignored) it looks like this.
7/6-----7/4----21/16---63/32
4/3 . \ 1/1 / \ 3/2 / \ 9/8 / 27
. \ / \ / \ /
. \ / \ / \ /
5/4----15/8.....7/5----21/20---63/40
10/7 / \15/14/ \45/28. . 6/5 . 9/5
/ \ / \ . . .
7/6 / 7/4 \ /21/16\ .63/32. .
4/3-----1/1-----3/2-----9/8----27/16
. . 8/7 . \12/7 / \ 9/7 / 27/14
. . . \ / \ /
5/4 .15/8 . . 7/5 \ /21/20\ /63/40
10/7----15/14---45/28....6/5-----9/5
/ \ / \ / \ .
/ \ / \ / \ .
4/3 / 1/1 \ / 3/2 \ / 9/8 \ .27/16
8/7----12/7-----9/7----27/14
So you can see that it's absolutely begging us to temper out the 224:225 (and the 384:385, 11's not shown).
> What's the closest match to a periodicity block? Is it a 22-tone
> periodicity block with 1 note added? I'll have to investigate . . .
Good question. That's your department. I'm dying to know if you can derive it as a PB.
-- Dave Keenan
Brisbane, Australia
http://uq.net.au/~zzdkeena
From: Rami Vitale (2001-08-30) Subject: Re: [tuning] Re: another place to find answers ----- Original Message ----- From: Paul Erlich <paul@stretch-music.com> To: <tuning@yahoogroups.com> Sent: Wednesday, August 29, 2001 4:30 PM Subject: [tuning] Re: another place to find answers > --- In tuning@y..., "Rami Vitale" <alfred1@s...> wrote: > > > I think you agree that the diatonic scale used in Byzantine music > is 9/8 > > 10/9 16/15 9/8 9/8 10/9 16/15. > > > > In 72 per octave scale it will be 12.2 10.9 6.7 12.2 12.2 10.9 6.7 , > > accurate HEH! > > > > Believe it or not in the 72 per octave theory it is recommended as > 12 10! 8! > > 12 12 10 8 !!!!!!!. > > ( mistake by 22 cent! ) >Paul Erlich wrote: > Excuse me sir, but in the 72 per octave theory the "Indian/Byzantine > diatonic" is represented as 12 11 7 12 12 11 7. The maximum error is > about 4 cents. > > > it is not a scientific theory. > > Calling a set of ratios "a scientific theory" for a musical style is > a 19th century idea. We've progressed beyond Helmholtz! Yes you are right! if it is represented as 12 11 7 12 12 11 7, but in many references I found it 12 10 8 12 12 10 8 which is not accurate, ( and which I think those respected monks have mentioned ) and I was speaking about the complete theory of 72 which I know not about the number 72. The 68 per octave form is represented in byzantine music theoretical books as ( 12 9 7 12 12 9 7 ) which is not accurate? By saying not a scientific theory I meant that the (12 10 8 ...etc) is not mathematically accurate. If you want accuracy you can use 53 per octave for this scale, and for all scales I have mentioned, I think 212 ( 53 * 4 ) per octave is the best way. Rami Vitale
From: Alison Monteith (2001-08-30) Subject: Re: [tuning] Re: another place to find answers Paul Erlich wrote: > --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote: > > > > > > Paul Erlich wrote: > > > > > --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote: > > > > > > > I'd be interested in hearing how you arrived at these scales and > > > their > > > > ratios Rami. Someone recently claimed that 'Byzantine music' was > > > based > > > > on 72 EDO. How do you reconcile your findings with that? > > > > > > Easy -- they're very, very close -- 2 cents here, 3 cents > there . . . > > > no substantial difference. > > > > Thanks, Paul, I understand that fairly clearly. What I'm not so > clear about is that one Byzantine > > specialist claims that the music under consideration is in 72 EDO > and the other gives precise > > ratios. One or the other must be nearer to the truth. > > Nonsense. The differences are very tiny. One will likely find > variations in practice (from region to region, for example) which > swamp the differences between these two reckonings. Nonsense my arse if you excuse my French. Read what I wrote please. We have one person claiming that a very important body of music is based on precisely 72 EDO, another claims that it is based on precise ratios. Despite the closeness in the assumed intervals which you rightly point out, these two concepts are miles apart. Are they both right or wrong or somewhere in between, or why bother making such specific claims? If somewhere in between that doesn't tie in with the extremely tight control that the Orthodox Church exercises on all aspects of its liturgy, of which music is an important part. Best Wishes.
From: Alison Monteith (2001-08-30) Subject: Re: [tuning] the Byzantine 72-tones jpehrson@rcn.com wrote: > > Hello Allison! > > I believe it was Anton Rovner who had heard from sources in Russia > that there were 72 pitches per octave in some Russian Orthodox > music. However, I am not certain that he said it was an ET.. It > could have been ratios, I don't know. > > Anton seems to be away at the moment... probably at another > Contemporary Music festival or such like, but hopefully he will > respond when he gets back... > > best, > > _________ _______ _______ > Joseph Pehrson I'm sure that there was someone studying Byzantine music at an American College recently who talked of 72 EDO, but I don't think it was Anton. Regards
From: Paul Erlich (2001-08-30) Subject: Rami Vitale's scale (was: Re: another place to find answers) --- In tuning@y..., David C Keenan <D.KEENAN@U...> wrote: > --- In tuning@y..., "Paul Erlich" <paul@s...> wrote: > > Here's a lattice of Rami's scale: > > > > 5/4------15/8 > > ,'/|\`. ,'/|\`. > > 10/7-/-|-\15/14/-|-\45/28 > > 7/6-------7/4------21/16-----63/32 > > ,' `. |/,' \`.\|/,'/ `.\| ,' `. > > 4/3-------1/1-----\-3/2-/-----9/8------27/16 > > `. ,' |\`. /,\/|\/.\ ,'/| `. ,' > > 8/7---|-\12/7-/\|/\-9/7-/-|--27/14 > > 7/5------21/20-----63/40 > > \|/,' `.\|/,' > > 6/5-------9/5 > > > > It's a 7-limit Tonality Diamond (centered around 3/2 instead of 1/1) > > with some very symmetrical extensions along the 3-axis. It may very > > well be the set of notes within a certain radius in the triangular > > lattice (when length of ratios of N is log(N) or something like > that). > > Thanks for that. Yes, quite spherical. > > When the 224:225 septimal kleisma is tempered out (or ignored) it looks like this. [snip] > So you can see that it's absolutely begging us to temper out the 224:225 Absolutely. It's hard to get away from this UV! >(and the 384:385, 11's not shown). Rami didn't bring 11 into this, so maybe we shouldn't either. > > What's the closest match to a periodicity block? Is it a 22-tone > > periodicity block with 1 note added? I'll have to investigate . . . > > Good question. That's your department. I'm dying to know if you can derive it as a PB. Actually, I don't think it can be a 22-tone PB with 1 added note, since we have three 50:49 pairs, and 50:49 is a UV of the 22-tone group (Gene, perhaps you can make this precise). Since the scale is pretty uneven, I'm pretty comfortable guessing that the best we can do is call it a subset of a 31-tone PB . . .
From: Paul Erlich (2001-08-30) Subject: Re: another place to find answers --- In tuning@y..., "Rami Vitale" <alfred1@s...> wrote: > > ----- Original Message ----- > From: Paul Erlich <paul@s...> > To: <tuning@y...> > Sent: Wednesday, August 29, 2001 4:30 PM > Subject: [tuning] Re: another place to find answers > > > > --- In tuning@y..., "Rami Vitale" <alfred1@s...> wrote: > > > > > I think you agree that the diatonic scale used in Byzantine music > > is 9/8 > > > 10/9 16/15 9/8 9/8 10/9 16/15. > > > > > > In 72 per octave scale it will be 12.2 10.9 6.7 12.2 12.2 10.9 6.7 , > > > accurate HEH! > > > > > > Believe it or not in the 72 per octave theory it is recommended as > > 12 10! 8! > > > 12 12 10 8 !!!!!!!. > > > ( mistake by 22 cent! ) > > > >Paul Erlich wrote: > > > Excuse me sir, but in the 72 per octave theory the "Indian/Byzantine > > diatonic" is represented as 12 11 7 12 12 11 7. The maximum error is > > about 4 cents. > > > > > it is not a scientific theory. > > > > Calling a set of ratios "a scientific theory" for a musical style is > > a 19th century idea. We've progressed beyond Helmholtz! > > > Yes you are right! if it is represented as 12 11 7 12 12 11 7, but in many > references I found it 12 10 8 12 12 10 8 which is not accurate, ( and which > I think those respected monks have mentioned ) and I was > speaking about the complete theory of 72 which I know not about the number > 72. > > The 68 per octave form is represented in byzantine music theoretical books > as ( 12 9 7 12 12 9 7 ) which is not accurate? > By saying not a scientific theory I meant that the (12 10 8 ...etc) is not > mathematically accurate. Rami, I suspect, especially given John Chalmers's comments, and Manuel's mode lists, that there is a Byzantine scale, unfamiliar to yourself due to historical and/or geographical distance, that is being represented with the 12 10 8 tetrachord in 72 and the 12 9 7 tetrachord in 68. > If you want accuracy you can use 53 per octave for this scale, 53 is more accurate for the 9/8 10/9 16/15 tetrachord but once you include 7-limit ratios (of which there are many in your "master scale") then 68 and 72 are preferable. However, Dave Keenan has shown that even if one doesn't adopt an ET, tempering out 225:224 (as in a linear or planar microtemperament) can add greatly to the harmonic, and even melodic, resources of this scale. > and for all > scales I have mentioned, I think 212 ( 53 * 4 ) per octave is the > best way. Actually 171 would do much better than 212 for your "master scale". But 225:224 is not eliminated in 171, so 68 or 72 may really be better.
From: Paul Erlich (2001-08-30) Subject: Re: another place to find answers --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote: > > > Paul Erlich wrote: > > > --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote: > > > > > > > > > Paul Erlich wrote: > > > > > > > --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote: > > > > > > > > > I'd be interested in hearing how you arrived at these scales and > > > > their > > > > > ratios Rami. Someone recently claimed that 'Byzantine music' was > > > > based > > > > > on 72 EDO. How do you reconcile your findings with that? > > > > > > > > Easy -- they're very, very close -- 2 cents here, 3 cents > > there . . . > > > > no substantial difference. > > > > > > Thanks, Paul, I understand that fairly clearly. What I'm not so > > clear about is that one Byzantine > > > specialist claims that the music under consideration is in 72 EDO > > and the other gives precise > > > ratios. One or the other must be nearer to the truth. > > > > Nonsense. The differences are very tiny. One will likely find > > variations in practice (from region to region, for example) which > > swamp the differences between these two reckonings. > > Nonsense my arse if you excuse my French. Read what I wrote please. We have one person claiming > that a very important body of music is based on precisely 72 EDO, Who said _precisely_, and if so, how precisely did they mean? I'm sure they did not mean so precise as to exclude the ratios 3 or 4 cents away . . . > another claims that it is based > on precise ratios. Despite the closeness in the assumed intervals which you rightly point out, > these two concepts are miles apart. Can you _hear_ the difference, melodically? Can you _sing_ the difference, melodically? I can come up with 10 different tuning systems based on 100 different concepts within these parameters . . . no amount of measurement is going to determine which of the concepts is right. Maybe they all are. > Are they both right or wrong or somewhere in between, or why > bother making such specific claims? Because they allow you to _learn_ and _describe_ the intonation precisely (by which I mean to within 5 cents) through different _conceptual_ means. > If somewhere in between that doesn't tie in with the extremely > tight control that the Orthodox Church exercises on all aspects of its liturgy, of which music is > an important part. Aren't you the same Alison who doubted that one could even sing the difference between adjacent degrees in 72-tET? We're talking about far smaller differences here! My view is that neither the ET view nor the JI view capture much of what is aesthetically relevant about these scales. They're simply a matter of tradition, experience, learning, practice, and expression. One sees identical tetrachords of various constructions, and subtle inflections. One can attempt to quantify them in various ways, but there's no reason to assume that this quantification captures much of what is aesthetically relevant in the experience of this music itself. The music doesn't employ 7-limit tetradic harmonies, nor does it modulate to 72 tonal centers. Thus neither the 7LJI nor the 72-tET paradigms is very close, conceptually, to what goes on "behind" the music. Just my opinion.
From: Dave Keenan (2001-08-31) Subject: Rami Vitale's scale (was: Re: another place to find answers) --- In tuning@y..., "Paul Erlich" <paul@s...> wrote: > Actually, I don't think it can be a 22-tone PB with 1 added note, > since we have three 50:49 pairs, and 50:49 is a UV of the 22-tone > group (Gene, perhaps you can make this precise). > > Since the scale is pretty uneven, I'm pretty comfortable guessing > that the best we can do is call it a subset of a 31-tone PB . . . I suspect we can do slightly better. A 19 note PB with 4 extra notes. I think, but I haven't time to check, that it is a chain of 23 notes in a "second-order linear temperament" (A 2nd order MOS carried on past its otherwise 19 tones by 4 notes). The first MOS is 31-of-miracle (Canasta), then the generator within that is 13 steps (which generates 3:4's most of the time). I think this answers Joseph's original question about the best 19 notes from 72-tET. It's the 19 note 2nd order "meantone" MOS from Canasta. I think it corresponds to Rami's scale without 21/16, 63/32, 8/7, 12/7, which I think is more even. And Paul, I think your 12-of-blackjack is such a "meantone of miracle" 2nd order MOS too. Is Partch's final 43 even better described as some kind of 2nd order thing involving miracle, than it is in straight miracle? "miracle of schismic"? But if you're interested, you're gonna have to confirm these yourself, because I gotta leave the list for a few months, and severely cut down my list activity permanently. Rami, whether or not your master scale covers all things Byzantine or not, it is a wonderful scale (particularly when the 224:225 is tempered or ignored). And it has shown the way to what I suspect is an important new family of scales. -- Dave Keenan
From: jpehrson@rcn.com (2001-08-31) Subject: Re: another place to find answers --- In tuning@y..., "Paul Erlich" <paul@s...> wrote: http://groups.yahoo.com/group/tuning/message/27666 > > My view is that neither the ET view nor the JI view capture much of > what is aesthetically relevant about these scales. They're simply a > matter of tradition, experience, learning, practice, and expression. One sees identical tetrachords of various constructions, and subtle inflections. One can attempt to quantify them in various ways, but there's no reason to assume that this quantification captures much of what is aesthetically relevant in the experience of this music itself. The music doesn't employ 7-limit tetradic harmonies, nor does it modulate to 72 tonal centers. Thus neither the 7LJI nor the 72-tET paradigms is very close, conceptually, to what goes on "behind" the music. Just my opinion. Paul! Do you know who you sound like here?? His last name begins with an "m" and then there's a "c" and then there's a "liar-en" or some such.... _______ _______ _______ ____ Joseph Pehrson
From: jpehrson@rcn.com (2001-08-31) Subject: subsets of 72-tET --- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote: http://groups.yahoo.com/group/tuning/message/27676 > > I think this answers Joseph's original question about the best 19 > notes from 72-tET. It's the 19 note 2nd order "meantone" MOS from > Canasta. I think it corresponds to Rami's scale without 21/16, 63/32, 8/7, 12/7, which I think is more even. > > And Paul, I think your 12-of-blackjack is such a "meantone of miracle" 2nd order MOS too. > Now... these are interesting... At some point, I may be asking you gentlemen for suggestions as to other interesting subsets of 72- tET...since I'm pretty convinced I want to stay in 72 subsets for awhile... It would be great to have a catalogued and illustrated list of some of these... But, for now, "blackjack" has me preoccupied... > But if you're interested, you're gonna have to confirm these yourself, because I gotta leave the list for a few months, and severely cut down my list activity permanently. > Now, this is really bad news. I can't imagine what you could be doing that would be more important than participating on this list! I sure hope it doesn't involve *money.* That would be just terrible! :) _________ _______ ______ Joseph Pehrson
From: Dave Keenan (2001-08-31)
Subject: Rami Vitale's scale (was: Re: another place to find answers)
Wait a minute!
Rami,
If we temper out the 224:225s, which is essentially the same as
mapping your scale to 72-tET (but not 53 or 68),
*---------------------------------*
| you only need 19 notes, not 23, |
*---------------------------------*
to contain all 5 of those Byzantine 7-note scales you gave, and much,
much more.
In steps of 72-tET it is
5 2 5 4 3 4 3 4 5 2 5 2 2 5 4 3 4 3 4
This is exactly the same 19 note subset of 72-tET that answered Joseph
Pehrsons question.
I going now, really :-)
-- Dave Keenan
From: David Beardsley (2001-08-31) Subject: Re: [tuning] Rami Vitale's scale (was: Re: another place to find answers) Have you attended to all your family and work responsibilities? * David Beardsley * http://biink.com * http://mp3.com/davidbeardsley
From: Rami Vitale (2001-08-31) Subject: Re: [tuning] Rami Vitale's scale (was: Re: another place to find answers) ----- Original Message ----- From: Dave Keenan <D.KEENAN@UQ.NET.AU> To: <tuning@yahoogroups.com> Sent: Friday, August 31, 2001 2:19 AM Subject: [tuning] Rami Vitale's scale (was: Re: another place to find answers) > Wait a minute! > > Rami, > > If we temper out the 224:225s, which is essentially the same as > mapping your scale to 72-tET (but not 53 or 68), > > *---------------------------------* > | you only need 19 notes, not 23, | > *---------------------------------* > > to contain all 5 of those Byzantine 7-note scales you gave, and much, > much more. > > In steps of 72-tET it is > 5 2 5 4 3 4 3 4 5 2 5 2 2 5 4 3 4 3 4 > > This is exactly the same 19 note subset of 72-tET that answered Joseph > Pehrsons question. > > I going now, really :-) > -- Dave Keenan I don't like ro ignore the 225/224, I can assure you that I can feel the difference between 15/14 and 16/15 which is 225/224, and the difference between 28/27 and 25/24 which is 225/224. Rami Vitale
From: Paul Erlich (2001-08-31) Subject: Re: another place to find answers --- In tuning@y..., jpehrson@r... wrote: > --- In tuning@y..., "Paul Erlich" <paul@s...> wrote: > > http://groups.yahoo.com/group/tuning/message/27666 > > > > > My view is that neither the ET view nor the JI view capture much of > > what is aesthetically relevant about these scales. They're simply a > > matter of tradition, experience, learning, practice, and > expression. One sees identical tetrachords of various constructions, > and subtle inflections. One can attempt to quantify them in various > ways, but there's no reason to assume that this quantification > captures much of what is aesthetically relevant in the experience of > this music itself. The music doesn't employ 7-limit tetradic > harmonies, nor does it modulate to 72 tonal centers. Thus neither > the 7LJI nor the 72-tET paradigms is very close, conceptually, to > what goes on "behind" the music. Just my opinion. > > > Paul! Do you know who you sound like here?? His last name begins > with an "m" and then there's a "c" and then there's a "liar-en" or > some such.... As you know, I happen to agree with a lot of what he says . . . but then again, he spews out such a vast river of self-contradictory diatribe, that _anyone_ is likely to find something in there that they agree with, in some particular context.
From: Alison Monteith (2001-08-31) Subject: Re: [tuning] Re: another place to find answers Paul Erlich wrote: > > > Aren't you the same Alison who doubted that one could even sing the > difference between adjacent degrees in 72-tET? We're talking about > far smaller differences here! True, but I'm coming round to a willingness to at least make an attempt at singing and at coaching others to sing finer and finer divisions. Maybe I need to get a hold of the Boston 72 school's materials as I find it very time consuming to devise my own exercises. > My view is that neither the ET view nor the JI view capture much of > what is aesthetically relevant about these scales. They're simply a > matter of tradition, experience, learning, practice, and expression. > One sees identical tetrachords of various constructions, and subtle > inflections. One can attempt to quantify them in various ways, but > there's no reason to assume that this quantification captures much of > what is aesthetically relevant in the experience of this music > itself. The music doesn't employ 7-limit tetradic harmonies, nor does > it modulate to 72 tonal centers. Thus neither the 7LJI nor the 72-tET > paradigms is very close, conceptually, to what goes on "behind" the > music. Just my opinion. I agree with that excellent conclusion. It struck me though that despite what I said about the conservatism and control structure of the Orthodox Church, perhaps they don't really know of the finer details musically speaking. I think that some of the points that have been raised in this discussion by yourself and others should be of great interest to the upper echelons of the church's hierarchy in view of the fact that they (the Church) are greatly concerned with the "correct" tones - to quote John Tavener during a BBC interview. Best Wishes
From: jpehrson@rcn.com (2001-09-01) Subject: Re: another place to find answers --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote: http://groups.yahoo.com/group/tuning/message/27713 > > > Paul Erlich wrote: > > > > > > > Aren't you the same Alison who doubted that one could even sing the > > difference between adjacent degrees in 72-tET? We're talking about > > far smaller differences here! > > True, but I'm coming round to a willingness to at least make an attempt at singing and at coaching > others to sing finer and finer divisions. Maybe I need to get a hold of the Boston 72 school's > materials as I find it very time consuming to devise my own exercises. > Hi Allison! You need, of course, Joe Maneri's _Preliminary Studies in the Virtual Pitch Continuum_ rather than re-inventing the wheel! I'm fortunate to have a copy here. I thought that Joe Maneri's address was in the book, but it's not. I'm sure somebody else has it... Dan Stearns, or Joe Monzo.... best, _________ _______ ________ Joseph Pehrson
From: Paul Erlich (2001-09-01) Subject: Rami Vitale's scale (was: Re: another place to find answers) --- In tuning@y..., "Rami Vitale" <alfred1@s...> wrote: > > ----- Original Message ----- > From: Dave Keenan <D.KEENAN@U...> > To: <tuning@y...> > Sent: Friday, August 31, 2001 2:19 AM > Subject: [tuning] Rami Vitale's scale (was: Re: another place to find > answers) > > > > Wait a minute! > > > > Rami, > > > > If we temper out the 224:225s, which is essentially the same as > > mapping your scale to 72-tET (but not 53 or 68), > > > > *---------------------------------* > > | you only need 19 notes, not 23, | > > *---------------------------------* > > > > to contain all 5 of those Byzantine 7-note scales you gave, and much, > > much more. > > > > In steps of 72-tET it is > > 5 2 5 4 3 4 3 4 5 2 5 2 2 5 4 3 4 3 4 > > > > This is exactly the same 19 note subset of 72-tET that answered Joseph > > Pehrsons question. > > > > I going now, really :-) > > -- Dave Keenan > > I don't like ro ignore the 225/224, > > I can assure you that I can feel the difference between 15/14 and 16/15 > which is 225/224, > and the difference between 28/27 and 25/24 which is 225/224. > > Rami Vitale Hi Rami, This may be true, but there is a difference between _tempering out_ the 225:224, and _ignoring_ the 225:224. For a similar example, look at the Western European diatonic scale in meantone temperament (used 1500-1800), where the 81:80 is tempered out. Although 81:80 is 22 cents, in meantone temperament, no consonant interval is off JI by more than 6 cents.
From: Paul Erlich (2001-09-01) Subject: Re: subsets of 72-tET --- In tuning@y..., jpehrson@r... wrote: > > Now... these are interesting... At some point, I may be asking you > gentlemen for suggestions as to other interesting subsets of 72- > tET...since I'm pretty convinced I want to stay in 72 subsets for > awhile... How about trying out a subset that has nothing to do with JI premises? Certainly this would seem to be a "balanced" approach considering the Brian McLaren and Boston Microtonal Society anti-JI philosophies, which you appeared to give some consideration . . . Perhaps the Balzano scale in 72-tET, which I believe would be 17 notes of a 17/72 oct. generator, would be one anti-JI idea to try . . . If you do want to stick with approximating large numbers of JI chords, then we need Graham to tell us if any of the linear temperaments he catalogued work in 72-tET. What about kleismic -- perhaps 19 of kleismic? And I suspect that a good number of those that have an interval of repetition that is a fraction of an octave will work . . . since 72-tET contains a 1/2 octave, 1/3 octave, 1/4 octave, 1/6 octave, 1/8 octave, 1/9 octave . . .
From: jpehrson@rcn.com (2001-09-01) Subject: Re: subsets of 72-tET --- In tuning@y..., "Paul Erlich" <paul@s...> wrote: http://groups.yahoo.com/group/tuning/message/27778 > --- In tuning@y..., jpehrson@r... wrote: > > > > Now... these are interesting... At some point, I may be asking you > > gentlemen for suggestions as to other interesting subsets of 72- > > tET...since I'm pretty convinced I want to stay in 72 subsets for > > awhile... > > How about trying out a subset that has nothing to do with JI premises? Certainly this would > seem to be a "balanced" approach considering the Brian McLaren and Boston Microtonal > Society anti-JI philosophies, which you appeared to give some consideration . . . Perhaps the > Balzano scale in 72-tET, which I believe would be 17 notes of a 17/72 oct. generator, would be > one anti-JI idea to try . . . > > If you do want to stick with approximating large numbers of JI chords, then we need Graham to > tell us if any of the linear temperaments he catalogued work in 72- tET. What about kleismic -- > perhaps 19 of kleismic? And I suspect that a good number of those that have an interval of > repetition that is a fraction of an octave will work . . . since 72- tET contains a 1/2 octave, 1/3 > octave, 1/4 octave, 1/6 octave, 1/8 octave, 1/9 octave . . . These are *really* good suggestions, Paul... and I will keep in touch about all of this. Probably the best thing would be to try, as you suggest, and "anti just" 72-tET approach as a contrast. I'm not ready for this, though... I want to write *several* extensive "Miracle" pieces before I go in this direction... Then, of course, I will appreciate the "anti's" more... I think it's what's called "upping the ante..." :) __________ ______ ______ Joseph Pehrson
From: graham@microtonal.co.uk (2001-09-01)
Subject: Re: subsets of 72-tET
Paul wrote:
> If you do want to stick with approximating large numbers of JI chords,
> then we need Graham to tell us if any of the linear temperaments he
> catalogued work in 72-tET. What about kleismic -- perhaps 19 of
> kleismic? And I suspect that a good number of those that have an
> interval of repetition that is a fraction of an octave will work . . .
> since 72-tET contains a 1/2 octave, 1/3 octave, 1/4 octave, 1/6 octave,
> 1/8 octave, 1/9 octave . . .
Hello!
If you look at the "mapping by steps" the first pair of numbers are
ETs/subsets. You'll see 72 comes up quite a lot. If you can be bothered
to download a Python interpreter, you can choose an ET to combine with 72,
and see what temperament pops out.
Graham
From: Paul Erlich (2001-09-01) Subject: Re: subsets of 72-tET --- In tuning@y..., graham@m... wrote: > If you look at the "mapping by steps" the first pair of numbers are > ETs/subsets. You'll see 72 comes up quite a lot. Would you mind posting these here, to this list?
From: genewardsmith@juno.com (2001-09-02) Subject: Re: subsets of 72-tET --- In tuning@y..., "Paul Erlich" <paul@s...> wrote: > --- In tuning@y..., jpehrson@r... wrote: > > Now... these are interesting... At some point, I may be asking you > > gentlemen for suggestions as to other interesting subsets of 72- > > tET...since I'm pretty convinced I want to stay in 72 subsets for > > awhile... > How about trying out a subset that has nothing to do with JI premises? Certainly this would > seem to be a "balanced" approach considering the Brian McLaren and Boston Microtonal > Society anti-JI philosophies, which you appeared to give some consideration . . . Perhaps the > Balzano scale in 72-tET, which I believe would be 17 notes of a 17/72 oct. generator, would be > one anti-JI idea to try . . . Theorem EZ concurs with 17 mod 72 as a generator, and I tested out EZ for some other scales around the same size as 21 out of 72, finding: 7 mod 18, repeated four times for a 20 out of 72 scale, with pattern 34344 * 4. 13 mod 36, repeated two times for a 22 out of 72 scale, with pattern 33343334334 * 2, and 19 mod 72 for a 19 out of 72 scale, with pattern 4444344443444434443. Since the 17-et is more distantly related to 72 than any of the above, it is more "anti-JI", but it will approximate a lot of intervals. > If you do want to stick with approximating large numbers of JI chords, then we need Graham to > tell us if any of the linear temperaments he catalogued work in 72- tET. All of my choices ought to work from a JI point of view; one could always find the corresponding PBs and see what they look like if we wanted to proceed in the other direction.
From: genewardsmith@juno.com (2001-09-02) Subject: Re: subsets of 72-tET --- Paul wrote: > > How about trying out a subset that has nothing to do with JI > premises? Certainly this would > > seem to be a "balanced" approach considering the Brian McLaren and > Boston Microtonal > > Society anti-JI philosophies, which you appeared to give some > consideration . . . Perhaps the > > Balzano scale in 72-tET, which I believe would be 17 notes of a > 17/72 oct. generator, would be > > one anti-JI idea to try . . . Let's see how anti-JI it is, by getting it from a block. If we take as commas 12005/11979, 243/242, 385/384 and 15488/15435, we get a block with 17 notes to the octave, which we may regard as the thing we want to approximate. I could calculate a scale for this mess if anyone really cared; the point being we can see it as JI if we want. Of course this is a highly non-unique proceedure.
From: Paul Erlich (2001-09-02) Subject: Re: subsets of 72-tET --- In tuning@y..., genewardsmith@j... wrote: > --- In tuning@y..., "Paul Erlich" <paul@s...> wrote: > > --- In tuning@y..., jpehrson@r... wrote: > > > > Now... these are interesting... At some point, I may be asking > you > > > gentlemen for suggestions as to other interesting subsets of 72- > > > tET...since I'm pretty convinced I want to stay in 72 subsets for > > > awhile... > > > How about trying out a subset that has nothing to do with JI > premises? Certainly this would > > seem to be a "balanced" approach considering the Brian McLaren and > Boston Microtonal > > Society anti-JI philosophies, which you appeared to give some > consideration . . . Perhaps the > > Balzano scale in 72-tET, which I believe would be 17 notes of a > 17/72 oct. generator, would be > > one anti-JI idea to try . . . > > Theorem EZ concurs with 17 mod 72 as a generator, Is it true in general that if A*B=C, then in C-tET, a generator of A+B will lead to an MOS with A+B notes? You can reply at the tuning- math group: tuning-math@yahoogroups.com > and I tested out EZ > for some other scales around the same size as 21 out of 72, finding: > > 7 mod 18, repeated four times for a 20 out of 72 scale, with pattern > 34344 * 4. > > 13 mod 36, repeated two times for a 22 out of 72 scale, with pattern > 33343334334 * 2, > > and 19 mod 72 for a 19 out of 72 scale, with pattern > 4444344443444434443. This will be the kleismic scale I was referring to. The kleismic temperament is generated by the minor third 6:5. Dave Keenan has a wonderful webpage on it, and specifically an important 11-tone MOS in it: http://www.uq.net.au/~zzdkeena/Music/ChainOfMinor3rds.htm The 19 mod 72 for a 19 out of 72 scale was discussed back in February. > Since the 17-et is more distantly related to 72 than any of the > above, it is more "anti-JI", but it will approximate a lot of > [consonant] intervals. Yup, accidentally. Hard to avoid. Any non-MOSs do the job better? > > If you do want to stick with approximating large numbers of JI > chords, then we need Graham to > > tell us if any of the linear temperaments he catalogued work in 72- > tET. > > All of my choices ought to work from a JI point of view; Well they're certainly not created equal in the number of consonant chords they produce; having a large number of them is what I refer to (in a scale) as coming from the "JI point of view" when I say "anti- JI". > one could > always find the corresponding PBs and see what they look like if we > wanted to proceed in the other direction. But we wouldn't find anything else, you're saying . . . we're done. Awesome, Gene, you've saved us a lot of work (you're assuming my Hypothesis is true in this context, I take it from what you've done?)!
From: Paul Erlich (2001-09-02) Subject: Re: subsets of 72-tET --- In tuning@y..., genewardsmith@j... wrote: > --- Paul wrote: > > > > How about trying out a subset that has nothing to do with JI > > premises? Certainly this would > > > seem to be a "balanced" approach considering the Brian McLaren > and > > Boston Microtonal > > > Society anti-JI philosophies, which you appeared to give some > > consideration . . . Perhaps the > > > Balzano scale in 72-tET, which I believe would be 17 notes of a > > 17/72 oct. generator, would be > > > one anti-JI idea to try . . . > > Let's see how anti-JI it is, by getting it from a block. If we take > as commas 12005/11979, 243/242, 385/384 and 15488/15435, we get a > block with 17 notes to the octave, which we may regard as the thing > we want to approximate. I could calculate a scale for this mess if > anyone really cared; the point being we can see it as JI if we want. > Of course this is a highly non-unique proceedure. Deep stuff, Gene. I'm guessing some of these unison vectors are at small angles to others, or that the 2-D subspace spanned by two of the unison vectors is at a small angle to the 2-D subspace spanned by the other two. Thus there won't be a lot of complete, consonant chords within the hyperparallelepiped. And since 17-tET doesn't share any elements of its kernel with those of the kernel-generators above (does it?), you don't get any "extra" consonant chords forming across the borders between hyperparallepiped periods. Reply to the tuning-math list tuning-math@yahoogroups.com as usual.
From: Paul Erlich (2001-09-02) Subject: Re: subsets of 72-tET I wrote, > And since 17-tET doesn't share > any elements of its kernel with those of the kernel-generators above > (does it?), OOPS -- it has to have three, otherwise an MOS wouldn't result (right)? So what I suspect is, that the "period boundaries" spanned by these three unison vectors, and separated by the fourth unison vector, are very close to one another, leaving little or no room for complete chords, and the room is cramped for getting many consonant intervals at all!
From: Paul Erlich (2001-09-03) Subject: Re: subsets of 72-tET --- In tuning@y..., genewardsmith@j... wrote: >I tested out EZ > for some other scales around the same size as 21 out of 72, finding: > > 7 mod 18, repeated four times for a 20 out of 72 scale, with pattern > 34344 * 4. how about 62622 * 4? > > 13 mod 36, repeated two times for a 22 out of 72 scale, with pattern > 33343334334 * 2, > > and 19 mod 72 for a 19 out of 72 scale, with pattern > 4444344443444434443. With 21 notes, you not only have the blackjack scale, but also 3434343 * 4, for example. With 18 notes, you have 53 * 9 62 * 9 71 * 9 . . . Did EZ miss these, or were you not attempting to be complete?
From: genewardsmith@juno.com (2001-09-03) Subject: Re: subsets of 72-tET --- In tuning@y..., "Paul Erlich" <paul@s...> wrote: > Did EZ miss these, or were you not attempting to be complete? I made no attempt to be complete, so it wasn't much of a test. I was just finding the smoothest version among available possibilities.