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!

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

--- 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.

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.

--- 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.

--- In tuning@y..., genewardsmith@j... wrote:

/tuning/topicId_27464.html#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

> 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.

--- In tuning@y..., "Rami Vitale" <alfred1@s...> wrote:

/tuning/topicId_27464.html#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

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

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., genewardsmith@j... wrote:
>
> /tuning/topicId_27464.html#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.

--- 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.

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

--- 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.

--- 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

----- 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

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.

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.

--- 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 . . .

--- 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!

--- 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.

--- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:

/tuning/topicId_27464.html#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

--- 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://dkeenan.com

----- 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

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.

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

--- 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 . . .

--- 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.

--- 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.

--- 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

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

/tuning/topicId_27464.html#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

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:

/tuning/topicId_27464.html#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

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

Have you attended to all your family and work responsibilities?

* David Beardsley
* http://biink.com
* http://mp3.com/davidbeardsley

----- 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

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> /tuning/topicId_27464.html#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.

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

--- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:

/tuning/topicId_27464.html#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

--- 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.

--- 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 . . .

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

/tuning/topicId_27464.html#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

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

--- 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?

--- 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.

--- 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.

--- 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?)!

--- 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.

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!

--- 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?

--- 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.