Eikosany query

Hi folks

I'm tuning up my synths to experiment with two eikosanies, the 1, 3, 5,
7, 9, 11 and the 1, 3, 7, 9, 11, 15. When I made up the ratios for these
I took my 3 out of 6 and used the products as numerators and the nearest
power of two as a denominator, so for example 1, 3, 5 would be 15/8.

So can anyone explain the following that I found in a load of scala
files that I downloaded a while back?

! Eikosany.scl
!
3)6 1.3.5.7.9.11 Eikosany (1.3.5 tonic)
20
!
33/32
21/20
11/10
9/8
7/6
99/80
77/60
21/16
11/8
7/5
231/160
3/2
63/40
77/48
33/20
7/4
9/5
11/6
77/40
2/1

I can't get this to tally with any of my calculations and if anyone can
shed light I'd be very grateful indeed.

I've been reading a lot of Erv Wilson's articles both from Xenharmonicon
and online. Here are same observations from a not-too-mathematical
musician. Interesting though the articles are I can find nowhere where
he explains the actual process of working out the ratios, though I
figured the process out myself. There's quite a lot of his stuff that
would benefit from some clear editing and explanation. The lattices and
diamonds and tilebursts are all clear but some of the tuning layouts and
mappings and some of the diagrams are not so obvious to me, the average
reader. Before the devotees leap to Erv's defence please note that I'm
not committing the sacrilege of criticising, simply observing and
suggesting.

And furthermore! : - ) can anyone give me three (or thereabouts)
good reasons why I should tune my forthcoming new instruments to
Blackjack rather than to one of the Eikosanies? The main instruments
are: steel tube metallophone, bowed psaltery ( only 17 strings planned
), a very big mbira and a small version of the harmonic canon, ie a
zithery thing, plus a mini orchestra of slit drums. I'll be writing for
these and small choir and I intend that the music will be both modal and
harmonic.

Phew!

Thanks in anticipation

--- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
> Hi folks
>
> I'm tuning up my synths to experiment with two eikosanies, the 1,
3, 5,
> 7, 9, 11 and the 1, 3, 7, 9, 11, 15. When I made up the ratios for
these
> I took my 3 out of 6 and used the products as numerators and the
nearest
> power of two as a denominator, so for example 1, 3, 5 would be 15/8.
>
> So can anyone explain the following that I found in a load of scala
> files that I downloaded a while back?

Alison, when you take the products of three factors at a time, none
of the notes will be a 1/1. But it is customary (and probably
mandatory in Scala) to express one of the notes as 1/1. So in this
case, 1*3*5 is taken as the tonic, and all the ratios you calculated
would have to be divided by 15 to get the ratios in the Scala file.

>
> ! Eikosany.scl
> !
> 3)6 1.3.5.7.9.11 Eikosany (1.3.5 tonic)
> 20

> There's quite a lot of his stuff that
> would benefit from some clear editing and explanation.

I agree, but Kraig Grady has argued vehemently against any such
project. I do what I can here.

The lattices and
> diamonds and tilebursts are all clear but some of the tuning
layouts and
> mappings and some of the diagrams are not so obvious to me, the
average
> reader. Before the devotees leap to Erv's defence please note that
I'm
> not committing the sacrilege of criticising, simply observing and
> suggesting.

I can attempt to answer any questions you might have.
>
> And furthermore! : - ) can anyone give me three (or thereabouts)
> good reasons why I should tune my forthcoming new instruments to
> Blackjack rather than to one of the Eikosanies?

Note that Erv Wilson recommended these Eikosanies to be used as part
of 31- and 22-tone JI scales, respectively. These are CS scales, as
is Blackjack. The first Eikosany has only one 1:3:5:7 tetrad, the
second none (I think), while Blackjack has eight. Other similar
comparisons were posted back in May. But there may be other scales
even better for you than any of these options.

> The main instruments
> are: steel tube metallophone, bowed psaltery ( only 17 strings
planned
> ),

Perhaps we should limit our consideration to scales with 17 or fewer
notes? It's up to you. Remember, Blackjack was designed for Joseph
Pehrson's specific desiderata -- your mileage may vary.

What features are important to you in a scale / tuning system?

Paul Erlich wrote:

> Alison, when you take the products of three factors at a time, none
> of the notes will be a 1/1. But it is customary (and probably
> mandatory in Scala) to express one of the notes as 1/1. So in this
> case, 1*3*5 is taken as the tonic, and all the ratios you calculated
> would have to be divided by 15 to get the ratios in the Scala file.

That's a relief. I get it now.

> I can attempt to answer any questions you might have.

I'll take you up on that. I don't know if you have the Xenharmonicon back issues. I'll be
referring to some of the CPS articles that particularly confound me.

> Note that Erv Wilson recommended these Eikosanies to be used as part
> of 31- and 22-tone JI scales, respectively. These are CS scales, as
> is Blackjack. The first Eikosany has only one 1:3:5:7 tetrad, the
> second none (I think), while Blackjack has eight. Other similar
> comparisons were posted back in May. But there may be other scales
> even better for you than any of these options.
>
> Perhaps we should limit our consideration to scales with 17 or fewer
> notes? It's up to you. Remember, Blackjack was designed for Joseph
> Pehrson's specific desiderata -- your mileage may vary.
>
> What features are important to you in a scale / tuning system?

Starting with the instruments, I have planned up to 25 steel tubes. It would be nice to have an
'octave' plus some rather than 25 tones to the 'octave'. Thus I'm looking at the 15 - 22 ish notes
per 'octave'. The bowed psaltery has room for only 17 strings. I had thought of the principle of a
useful 17 tone subset of the 'master' scale or simply the best group of 17 consecutive tones. The
mbira, for bass lines mainly, has room for up to 25 tones. The zither, or more probably 3 zithers,
will have 6 tones each maximum, giving 18 tones, though I'm not sure as to how wide I can spread
the range as they will be fairly similar and using guitar strings. The tubes are fixed, the others
tunable, so I'll be looking at a very flexible and resourceful scale for the tubes as I'll be
using them for the current voice project and for pure instrumental projects.

I first intend setting various texts for voice and instruments. The vocal parts will have a
microtonal element as regards melody, though not so obscure as demanding too much of good
professional singers. There will also be harmonic part writing. The instruments will underpin and
embellish the choir and provide interludes which will modify some of the vocal melodies with more
of a microtonal twist. In a sense the instruments and choir are antiphonal at points with the
instruments bending some of the sung melodies and harmonies. Such is the general plan.

But as I said I'd like the master instrument scale, which will be fixed for the tubes, to have
both good harmonic and melodic resources. The jury is still out on the relevance of the
inharmonicity of the tubes, and indeed the mbira, so I'm not too concerned about spectral matching
and the like.

'Blackjack' to my ears, and from studying the correspondence, has exceptional harmonic resources,
but I'd have to spend more time to ponder the melodic possibilities. The Eikosanies again seem to
have interesting harmonic possibilities and strange melodic features.

I rather like the idea of having several tetrachordal possibilities in the one scale, since I've
worked a lot with modal modulation in past pieces. Finding a solution that provides good harmonic
potential would be one satisfactory solution. My heart is for JI, my head often leans towards
Equal Temperament so I've no party card.

Naturally I don't anticipate a solution but suggestions would be welcome. After all, you got
Joseph "sorted" and look where that all led! Many thanks.

Best wishes

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

> I rather like the idea of having several tetrachordal possibilities
in the one scale, since I've
> worked a lot with modal modulation in past pieces. Finding a
solution that provides good harmonic
> potential would be one satisfactory solution. My heart is for JI,
my head often leans towards
> Equal Temperament so I've no party card.

How about 19-out-of-meantone? This will be very singable, very
tetrachordal, very modulatable, and rich in near-JI chords, which a
choir could always adaptively and subliminally alter into true JI
verticalities. It's not too hot in the 11-limit, though . . . not
sure how much that matters to you.

> Naturally I don't anticipate a solution but suggestions would be
welcome. After all, you got
> Joseph "sorted" and look where that all led!

Not sure what you mean . . . Joseph wrote a very nice Blackjack piece
and will likely write even nicer ones in the future (now that we've
discussed melody a bit more). Did you mean to insert a smiley there?

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

/tuning/topicId_28987.html#28996

> Naturally I don't anticipate a solution but suggestions would be
welcome. After all, you got
> Joseph "sorted" and look where that all led! Many thanks.
>

Gee, Alison! I don't know *myself* where it all led, but that sounds
like a compliment! I guess one piece, for the time being, for
trombone and electronics...

I was also concerned about the melodic features of blackjack, but
Paul has convinced me that it really can be quite melodically varied
by using subsets of the scale. Just using every *other* note leads
to a scale not too far removed from traditional chromatic 12-tET,
although somewhat wider at 116 cents (a "Secors").

So, actually, I would advocate trying to work in blackjack, since
there is exceptional potential there... particularly with your
interest in JI...

best,

_______ ________ ________
Joseph Pehrson

Paul Erlich wrote:

> --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
>
> > I rather like the idea of having several tetrachordal possibilities
> in the one scale, since I've
> > worked a lot with modal modulation in past pieces. Finding a
> solution that provides good harmonic
> > potential would be one satisfactory solution. My heart is for JI,
> my head often leans towards
> > Equal Temperament so I've no party card.
>
> How about 19-out-of-meantone? This will be very singable, very
> tetrachordal, very modulatable, and rich in near-JI chords, which a
> choir could always adaptively and subliminally alter into true JI
> verticalities. It's not too hot in the 11-limit, though . . . not
> sure how much that matters to you.

That's a good idea, though I haven't worked much with meantone. Just today I decided I have enough
good timber to build two psalteries so I'm no longer restricted to 17 tones on one of the main
instruments. As they are tunable,I could have up to 34 tones shared between the two psalteries.

To answer the 11-limit question, harmonies of 11 are quite important to me as over the last year
or so, I've worked with them and have managed to really hear them in both melody and harmony. I've
just replied to Joseph on his Blackjack recommendation that I should spend quality time with the
scale, on a decent synth patch, singing against some of the harmonies. This might indeed be a good
practical way to evaluate suitable scales for the choral pieces. It might sound a bit strange but
the singing doesn't have to be exactly in the same scale as the instruments, neither is it
polymicrotonal. They just have to fit together. Where there is close imitation, or
voice/instrument simultaneity I would as you say want to choose structures and melodies from the
master scale that singers could get close to.

> Naturally I don't anticipate a solution but suggestions would be

> welcome. After all, you got
> > Joseph "sorted" and look where that all led!
>
> Not sure what you mean . . . Joseph wrote a very nice Blackjack piece
> and will likely write even nicer ones in the future (now that we've
> discussed melody a bit more). Did you mean to insert a smiley there?

I meant in the best possible way that a query from Joseph sent the list's finest into a frenzy of
creativity, discovery, and, eventually, to beautiful music by Joseph and others. Nice to think
that might happen to me - who knows?

Many thanks

jpehrson@rcn.com wrote:

> --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
>
> /tuning/topicId_28987.html#28996
>
> > Naturally I don't anticipate a solution but suggestions would be
> welcome. After all, you got
> > Joseph "sorted" and look where that all led! Many thanks.
> >
>
> Gee, Alison! I don't know *myself* where it all led, but that sounds
> like a compliment! I guess one piece, for the time being, for
> trombone and electronics...

It was indeed a compliment.

> I was also concerned about the melodic features of blackjack, but
> Paul has convinced me that it really can be quite melodically varied
> by using subsets of the scale. Just using every *other* note leads
> to a scale not too far removed from traditional chromatic 12-tET,
> although somewhat wider at 116 cents (a "Secors").
>
> So, actually, I would advocate trying to work in blackjack, since
> there is exceptional potential there... particularly with your
> interest in JI...
>
> best,
>
> _______ ________ ________
> Joseph Pehrson

I like what I've heard of Blackjack by others and from my own meanderings. It can be made to sound
very JI, if you know what I mean. It would probably be most beneficial in my case to spend time
singing against some structures to see how the scale feels as an accompaniment for choir.

Regards

--- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
>
>
> Paul Erlich wrote:
>
> > --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
> >
> > > I rather like the idea of having several tetrachordal
possibilities
> > in the one scale, since I've
> > > worked a lot with modal modulation in past pieces. Finding a
> > solution that provides good harmonic
> > > potential would be one satisfactory solution. My heart is for
JI,
> > my head often leans towards
> > > Equal Temperament so I've no party card.
> >
> > How about 19-out-of-meantone? This will be very singable, very
> > tetrachordal, very modulatable, and rich in near-JI chords, which
a
> > choir could always adaptively and subliminally alter into true JI
> > verticalities. It's not too hot in the 11-limit, though . . . not
> > sure how much that matters to you.
>
> That's a good idea, though I haven't worked much with meantone.
Just today I decided I have enough
> good timber to build two psalteries so I'm no longer restricted to
17 tones on one of the main
> instruments. As they are tunable,I could have up to 34 tones shared
between the two psalteries.
>
> To answer the 11-limit question, harmonies of 11 are quite
important to me as over the last year
> or so, I've worked with them and have managed to really hear them
in both melody and harmony. I've
> just replied to Joseph on his Blackjack recommendation that I
should spend quality time with the
> scale, on a decent synth patch, singing against some of the
harmonies. This might indeed be a good
> practical way to evaluate suitable scales for the choral pieces. It
might sound a bit strange but
> the singing doesn't have to be exactly in the same scale as the
instruments, neither is it
> polymicrotonal. They just have to fit together. Where there is
close imitation, or
> voice/instrument simultaneity I would as you say want to choose
structures and melodies from the
> master scale that singers could get close to.

The original MIRACLE scale of course has 31 notes per octave, and the
extension to 41 is appealing as well. This is the best system for 11-
limit harmony, according to George Secor's, Dave Keenan's, and Graham
Breed's independent evaluations. With a chain of 45 notes, you'll
essentially have Partch's 43-tone scale, as well as many of his
earlier published scales. So what would make sense to me would be to
tune all your instruments to as large a contiguous (in terms of
generators) segment of MIRACLE, which would mean Blackjack on some of
your instruments, and perhaps 45 or more written notes for your
singers. Are you planning to notate using 72-tET notation?

In-Reply-To: <9q561e+10cqq@eGroups.com>
Paul wrote:

> The original MIRACLE scale of course has 31 notes per octave, and the
> extension to 41 is appealing as well. This is the best system for 11-
> limit harmony, according to George Secor's, Dave Keenan's, and Graham
> Breed's independent evaluations. With a chain of 45 notes, you'll
> essentially have Partch's 43-tone scale, as well as many of his
> earlier published scales. So what would make sense to me would be to
> tune all your instruments to as large a contiguous (in terms of
> generators) segment of MIRACLE, which would mean Blackjack on some of
> your instruments, and perhaps 45 or more written notes for your
> singers. Are you planning to notate using 72-tET notation?

While I share your enthusiasm for Miracle temperament, I think you're
over-egging the pudding a bit there. Secor's paper at
<http://www.anaphoria.com/secor.PDF> or XH3 doesn't claim it to be the
best system for anything, or mention 11-limit harmony. It does say the
system works well with Partch's scale (note he didn't know about the
earlier 43 note scale that really does approximate to 45 Miracle notes).
My work can hardly be considered independent from Dave's. The
quantitative results were tweaked to ensure Miracle did well in the 7 and
11 limits anyway.

The 24 note Miracle (Blackjack+3) keyboard mapping has firmly established
itself as my favourite extended mapping. I can testify to its melodic
resources, and will keep working at music demonstrating this. I'm not
sure why you'd need to go beyond the 31 notes. It may be better to
squeeze in more octaves beyond that point. But yes, there's no need to
stop with an MOS. If you don't have as many as 21 notes, tune to your
favourite 11-limit JI scale.

>From <http://x31eq.com/decimal_lattice.htm>, it looks like the
d'Alessandro scale almost fits the 41 note MOS. I think it has something
to do with Eikosanies. So you could tune to a Miracle-tempered Eikosany,
and I think you'd get some extra consonances.

45 or more notes for the singers does look complex. The problem isn't so
much the inherent complexity of Miracle temperament, but the inability of
traditional notation to express it with fewer than 72 notes. You'll have
to get the message over as best you can.

Graham

--- In tuning@y..., graham@m... wrote:

> I'm not
> sure why you'd need to go beyond the 31 notes.

Alison may want to harmonize a I-IV-V-I progression with hexads, for
example.

> It may be better to
> squeeze in more octaves beyond that point.

Agreed!
>
> 45 or more notes for the singers does look complex.

Hmm . . . I'm not sure the singers would care how many notes you use,
once the 72-tET notation is understood.

> The problem isn't so
> much the inherent complexity of Miracle temperament, but the
inability of
> traditional notation to express it with fewer than 72 notes.

Right . . . (?)

Paul Erlich wrote:

>
> The original MIRACLE scale of course has 31 notes per octave, and the
> extension to 41 is appealing as well. This is the best system for 11-
> limit harmony, according to George Secor's, Dave Keenan's, and Graham
> Breed's independent evaluations.

So far so good

> With a chain of 45 notes, you'll
> essentially have Partch's 43-tone scale, as well as many of his
> earlier published scales.

How does the chain of 45 notes work? Is this just the Miracle generator extended to 45 tones.

> So what would make sense to me would be to
> tune all your instruments to as large a contiguous (in terms of
> generators) segment of MIRACLE, which would mean Blackjack on some of
> your instruments, and perhaps 45 or more written notes for your
> singers. Are you planning to notate using 72-tET notation?

I need to think this through aloud. You're saying that I should consider Miracle as the master
scale, Blackjack being a subset. I would like to understand more about what you mean by 'as large
a contiguous (in terms of generators) segment of Miracle.'

An additional consideration is that I'm going to have to be careful that I don't end up with only
one octave. Until I finish the bass mbira and tune it I won't know if I can get a complete octave
below the other instruments. I think I should wait till I know the range of the instruments and
then I can map these out graphically to see what the overall range of the "chamber ensemble" will
be.

I would certainly consider using 72 tet notation but I'd have to go through all the previous
postings and other stuff which fortunately I've downloaded and saved. Has everyone agreed on the
final notation? I seem to recall several variations.

An additional bonus is that the counter-tenor in my Early Music trio suggested using the bowed
psaltery instead of the lute for some of the 15th Century music that we play. We are talking about
the likes of Ockeghem and Dufay as well as slightly later French chanson by Claudin de Sermisy for
example. I'd imagine that meantone would be good for this period but which meantone? Or something
with Pythagorean thirds to stretch the soprano and counter-tenor? The psaltery has 17 tones in
all.

Thanks for being so patient and for the helpful suggestions.

Best Wishes

graham@microtonal.co.uk wrote:

>
> >From <http://x31eq.com/decimal_lattice.htm>, it looks like the
> d'Alessandro scale almost fits the 41 note MOS. I think it has something
> to do with Eikosanies. So you could tune to a Miracle-tempered Eikosany,
> and I think you'd get some extra consonances.

Does "a Miracle-tempered Eikosany"mean that you substitute the Eikosany tone with the nearest (in
cents) Miracle tone?

Regards.

>
>

graham@microtonal.co.uk wrote:

>
> >From <http://x31eq.com/decimal_lattice.htm>, it looks like the
> d'Alessandro scale almost fits the 41 note MOS. I think it has something
> to do with Eikosanies. So you could tune to a Miracle-tempered Eikosany,
> and I think you'd get some extra consonances.

Does "a Miracle-tempered Eikosany"mean that you substitute the Eikosany tone with the nearest (in
cents) Miracle tone?

Regards.

>

Alison wrote:

> Does "a Miracle-tempered Eikosany"mean that you substitute the Eikosany
> tone with the nearest (in
> cents) Miracle tone?

Every 11-limit interval has a unique mapping to Miracle temperament.
That's what temperaments do. It'll always be the best approximation to
both 31- and 72-equal. That should get it to around 40 cents of just, but
you don't need to worry about cents to work it out.

Graham

--- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
>
>
> Paul Erlich wrote:
>
> >
> > The original MIRACLE scale of course has 31 notes per octave, and
the
> > extension to 41 is appealing as well. This is the best system for
11-
> > limit harmony, according to George Secor's, Dave Keenan's, and
Graham
> > Breed's independent evaluations.
>
> So far so good
>
> > With a chain of 45 notes, you'll
> > essentially have Partch's 43-tone scale, as well as many of his
> > earlier published scales.
>
> How does the chain of 45 notes work? Is this just the Miracle
generator extended to 45 tones.

Yes.

>
> > So what would make sense to me would be to
> > tune all your instruments to as large a contiguous (in terms of
> > generators) segment of MIRACLE, which would mean Blackjack on
some of
> > your instruments, and perhaps 45 or more written notes for your
> > singers. Are you planning to notate using 72-tET notation?
>
> I need to think this through aloud. You're saying that I should
consider Miracle as the master
> scale, Blackjack being a subset.

Right.

> I would like to understand more about what you mean by 'as large
> a contiguous (in terms of generators) segment of Miracle.'

That was a typo -- I left out the continuation of that
sentence: ". . . as possible for each instrument". But I wouldn't
sacrifice the instrument's natural pitch range and tune all the
pitches within one octave!
>
> I would certainly consider using 72 tet notation but I'd have to go
through all the previous
> postings and other stuff which fortunately I've downloaded and
saved. Has everyone agreed on the
> final notation? I seem to recall several variations.

Well, we had some disagreement on ASCII notations, but for written
scores, there are two notations which have some currency: the Boston
Sims-Maneri notation (which you can find on Ted Mook's page) and
Richter-Herf's notation. Pick one or invent your own -- the idea
being a 12-tET basis with some new accidentals.
>
> An additional bonus is that the counter-tenor in my Early Music
trio suggested using the bowed
> psaltery instead of the lute for some of the 15th Century music
that we play. We are talking about
> the likes of Ockeghem and Dufay as well as slightly later French
chanson by Claudin de Sermisy for
> example. I'd imagine that meantone would be good

I'd ask Margo . . .

> for this period but which meantone?

In the early 16th century, no one tuned "perfect" meantones . . .
most likely, there was some variation in the fifths, perhaps ranging
most typically from 2/7-comma to 1/4-comma in flatness.

> Or something
> with Pythagorean thirds to stretch the soprano and counter-tenor?

Don't quite understand what kind of "stretch" you mean.

--- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
>
>
> graham@m... wrote:
>
> >
> > >From <http://x31eq.com/decimal_lattice.htm>, it looks
like the
> > d'Alessandro scale almost fits the 41 note MOS. I think it has
something
> > to do with Eikosanies. So you could tune to a Miracle-tempered
Eikosany,
> > and I think you'd get some extra consonances.
>
> Does "a Miracle-tempered Eikosany"mean that you substitute the
Eikosany tone with the nearest (in
> cents) Miracle tone?

In principle, it wouldn't necessarily be the nearest tone -- instead,
one would make sure each consonant interval was represented by its
Miracle equivalent. In practice, this might turn out to be equivalent
to using the nearest tone. But I find it unlikely that the Eikosany
is going to meet your compositional goals . . . for one thing, it's
conceived as an "atonal" tuning system.

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

/tuning/topicId_28987.html#29063

> I meant in the best possible way that a query from Joseph sent the
list's finest into a frenzy of creativity, discovery, and,
eventually, to beautiful music by Joseph and others. Nice to think
> that might happen to me - who knows?
>

Hello Allison...

Well, I guess it was true that I was rather a "catalyst" in this, so
much so that Graham Breed called me the conceivable "inventor" of
Blackjack.

I have to cough... (fortunately it's not anthrax...)

Just asking some dumb questions... but people did get busy it is
true... In fact, they got so busy that it forced all the lists to
split off... if people recall, that was the instigator of the split-
ups...

But, of course, there is so much more to do. I only did *one* piece,
and Paul and Dave have been very helpful in showing me all the
potentialities of the intriguing scale they invented.

That's why it probably is a good idea for more of us to explore it.
There is a lot there, and every person brings a different insight and
capability.

I'm sure you will make a major contribution when you work with it!

best,

_______ _________ _______
Joseph Pehrson

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

/tuning/topicId_28987.html#29065

> The original MIRACLE scale of course has 31 notes per octave, and
the extension to 41 is appealing as well. This is the best system
for 11- limit harmony, according to George Secor's, Dave Keenan's,
and Graham Breed's independent evaluations. With a chain of 45
notes, you'll essentially have Partch's 43-tone scale, as well as
many of his earlier published scales. So what would make sense to me
would be to tune all your instruments to as large a contiguous (in
terms of generators) segment of MIRACLE, which would mean Blackjack
on some of your instruments, and perhaps 45 or more written notes
for your singers. Are you planning to notate using 72-tET notation?

This is, of course, an excellent suggestion for Allison, but unless
it is done properly it could, conceivably lead to a rehearsal
nightmare... It seems the singers probably need some kind
of "crutch" and if they are playing *more* notes of Miracle than the
instruments this might get quite confusing for them.

That is, of course, unless you're suggesting that the instruments are
also *supplementing* Blackjack with the additional choral pitches...

Or, perhaps something could be done like Toby Twining... a very
talented microtonal composer who posted at least *once* to this list.

I heard a piece done by Bang on a Can which was controlled with a
laptop computer and headphones for all the singers for pitch
reference...

Now it seems the chances for accuracy would be greatly enhanced with
such a system. Of course, it means more equipment... but not really
all that much. Adequate headphones wouldn't be *that* expensive...

________ ______ _______
Joseph Pehrson

jpehrson@rcn.com wrote:

> --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
>
> /tuning/topicId_28987.html#29063
>
> > I meant in the best possible way that a query from Joseph sent the
> list's finest into a frenzy of creativity, discovery, and,
> eventually, to beautiful music by Joseph and others. Nice to think
> > that might happen to me - who knows?
> >
>
> Hello Allison...
>
> Well, I guess it was true that I was rather a "catalyst" in this, so
> much so that Graham Breed called me the conceivable "inventor" of
> Blackjack.
>
> I have to cough... (fortunately it's not anthrax...)
>
> Just asking some dumb questions... but people did get busy it is
> true... In fact, they got so busy that it forced all the lists to
> split off... if people recall, that was the instigator of the split-
> ups...
>
> But, of course, there is so much more to do. I only did *one* piece,
> and Paul and Dave have been very helpful in showing me all the
> potentialities of the intriguing scale they invented.
>
> That's why it probably is a good idea for more of us to explore it.
> There is a lot there, and every person brings a different insight and
> capability.
>
> I'm sure you will make a major contribution when you work with it!
>
> best,

Hope so. Can't wait to get down to the actual writing. One question, which frequency did you
centre everything on, A440 or on C? I'm having a bit of a struggle deciding how to start tuning
my fixed pitch metal tubes. Because the scale isn't Just I have to be careful where I start.

Regards

Paul Erlich wrote:>

> Well, we had some disagreement on ASCII notations, but for written
> scores, there are two notations which have some currency: the Boston
> Sims-Maneri notation (which you can find on Ted Mook's page) and
> Richter-Herf's notation. Pick one or invent your own -- the idea
> being a 12-tET basis with some new accidentals.
> >
> > An additional bonus is that the counter-tenor in my Early Music
> trio suggested using the bowed
> > psaltery instead of the lute for some of the 15th Century music
> that we play. We are talking about
> > the likes of Ockeghem and Dufay as well as slightly later French
> chanson by Claudin de Sermisy for
> > example. I'd imagine that meantone would be good
>
> I'd ask Margo . . .
>
> > for this period but which meantone?
>
> In the early 16th century, no one tuned "perfect" meantones . . .
> most likely, there was some variation in the fifths, perhaps ranging
> most typically from 2/7-comma to 1/4-comma in flatness.
>
> > Or something
> > with Pythagorean thirds to stretch the soprano and counter-tenor?
>
> Don't quite understand what kind of "stretch" you mean.

Thank you for this information. I mean stretch in the sense of "challenge". Despite the fact that
we are a very close trio I still get the "are you an alien" look when I talk about Pythagorean
thirds. But with the chance to use other than 12 tunings on an 'early' instrument I have a foot in
the door as it were.

Regards

Paul Erlich wrote:

> --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
> >
> >
> > graham@m... wrote:
> >
> > >
> > > >From <http://x31eq.com/decimal_lattice.htm>, it looks
> like the
> > > d'Alessandro scale almost fits the 41 note MOS. I think it has
> something
> > > to do with Eikosanies. So you could tune to a Miracle-tempered
> Eikosany,
> > > and I think you'd get some extra consonances.
> >
> > Does "a Miracle-tempered Eikosany"mean that you substitute the
> Eikosany tone with the nearest (in
> > cents) Miracle tone?
>
> In principle, it wouldn't necessarily be the nearest tone -- instead,
> one would make sure each consonant interval was represented by its
> Miracle equivalent. In practice, this might turn out to be equivalent
> to using the nearest tone. But I find it unlikely that the Eikosany
> is going to meet your compositional goals . . . for one thing, it's
> conceived as an "atonal" tuning system.

Yes, I've decided to tune the current metallophone to Blackjack and my only problem is which
frequency to start with. Probably A440 then I'll have to work out the rest. Anybody got a quick
spreadsheet?

Regards.

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

> Hope so. Can't wait to get down to the actual writing. One
question, which frequency did you
> centre everything on, A440 or on C?

Joseph centered everthing on C, but certainly D would be more
symmetrical.

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

> Yes, I've decided to tune the current metallophone to Blackjack and
my only problem is which
> frequency to start with. Probably A440

Not a bad choice -- I'm planning to center my MIRACLE guitar on A.
The most likely tonal centers then are C quatertone-sharp and F
quartertone-sharp.

> then I'll have to work out the rest. Anybody got a quick
> spreadsheet?

here's one octave:

440.0000
448.5539
470.6732
479.8234
503.4847
513.2728
538.5836
549.0540
576.1292
587.3295
616.2922
628.2734
659.2551
672.0715
705.2130
718.9228
754.3747
769.0402
806.9636
822.6514
863.2185
880.0000

Hi Alison,

I'm sure Kraig would be the one to answer the Eikosany part of
your query, but since he isn't posting at the moment as far
as I can see:

The idea of the Eikosany is it has many pure triad, tetrad
etc. subsets.

They aren't that easy to find though, if you are presented
with the scale notes.

So, I expect one would want to do something with the layout
of the instruments to make them easier to find them if
building one.

(In FTS I'm experimenting with ways of using the midi keyboard to select
subsets of the Eikosany by devoting some of the octaves
to the task of selecting subsets, rather than playing notes).

If in the way of building musical instruments, I'd love to
make, say, a hexany as six pointed star.

I.e. six pointed star as two interlaced triangles; each
triangle plays a triad; and each adjacent group of three
points round the edge of the star also plays a triad, making
eight triads in all, easy to find.

One could make the 1 3 5 7, 1 3 5 11, 1 3 5 9, 1 3 7 11
or even 1 5 7 11 hexanies. All these can be found as subsets
of the 1 3 5 7 9 11 Eikosany, so this is also introducing
one gradually to the Eikosany subsets.

Then I'd perhaps want to make a dekany next. If the instruments
were ones that one could mount in a light framework, maybe
one could actually mount the ten notes in the Octahedron + tetrahedron
arrangement in the projection Paul used in his dekany
animations (and I use on my dekany web page).

Excuse me if this has already been said. I could easily have
missed a post. However seemed the discussion has been
focussed on 72-tet scales rather than the Eikosany itself
as such. I think with Eikosany as based on the idea of
really pure triads etc, would be nice if one could do them
pure, and perhaps this would help hone ones perception of
pure intervals.

I wonder a little if retuning _everything_ to an approximation
to j.i. might in the end run somewhat dull ones perception
of j.i.?? Or at least, not stretch it in the direction
of hearing j.i. intervals more and more finely.

72-tet is also just one of many n-tets. E.g. I've recently
been exploring 55-tet, which is fascinating. If building
instruments, one is hard-coding to a particular n-tet
- okay if it is easy to make them or retune them,
but quite a commitment to that n-tet if it is a matter
of, say, many weeks or months of work...

Also, like Dan, I wonder if consistency though interesting as a
concept, might possibly be overrated as regards musicality.

Does it matter how the intervals add up?? At least, I'd
want to see from actual musical examples and compositions
why it is important to have consistency; rather than just formulae.
Or, see what effect it has compositionally, and decide for myself
if I like that kind of an effect.

Irregularity is interesting and composers often are doing things
to throw rhythms etc. out from perfect symmetry, so
maybe "inconsistent" scales could be desirable too?
Perhaps dep. on the composer and the style of the piece.

A few thoughts anyway. Not trying to dissuade you at all
if you are keen on building 72-tet subsets; especially
if this is because you like the sound of 72-tet.

Robert

[Alison wrote:]
>>Yes, I've decided to tune the current metallophone to Blackjack and
>>my only problem is which frequency to start with. Probably A440.

[Paul E:]
>Not a bad choice -- I'm planning to center my MIRACLE guitar on A.
>The most likely tonal centers then are C quatertone-sharp and F
>quartertone-sharp.

Wouldn't that be 1/12 tone sharp in each case?

JdL

--- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote:
> [Alison wrote:]
> >>Yes, I've decided to tune the current metallophone to Blackjack
and
> >>my only problem is which frequency to start with. Probably A440.
>
> [Paul E:]
> >Not a bad choice -- I'm planning to center my MIRACLE guitar on A.
> >The most likely tonal centers then are C quatertone-sharp and F
> >quartertone-sharp.
>
> Wouldn't that be 1/12 tone sharp in each case?

No, sir . . . I'm not sure why you'd think that. If you go to

/tuning/files/perlich/scales/

download bjlatt.zip, and look at blackjack0.bmp, you'll see that, for
a blackjack scale centered on C, the notes that participate in the
most consonances are A quartertone-flat and E quartertone-flat.
Transposing the center to A, these become F quartertone-sharp and C
quartertone-sharp.

--- In tuning@y..., "Robert Walker" <robertwalker@n...> wrote:

> Also, like Dan, I wonder if consistency though interesting as a
> concept, might possibly be overrated as regards musicality.
>
> Does it matter how the intervals add up?? At least, I'd
> want to see from actual musical examples and compositions
> why it is important to have consistency; rather than just formulae.
> Or, see what effect it has compositionally, and decide for myself
> if I like that kind of an effect.

Forgetting about consistency has led many researchers to overrate the
ability of 24-tET to support 7-limit harmony. That's why it's
important. I'm not sure why you bring it up here, under this
topic . . .

As for the rest of your message, Robert, 72-tET is exceedingly
accurate in the 7- and 11-limits (much more accurate than mere
consistency would imply, BTW) . . . the harmonies sound
unmistakably "just" should you care to try them out . . . and the
temperament allows for a larger number of consonant chords than any
similar JI system would. Kraig Grady himself said that 72 was OK by
him and that one could spend a lifetime exploring MIRACLE (for
example, the dekanies alone could occupy one for decades). A
religious attachment to pure JI is all well and good until you
actually sit down and play with these things on an instrument. On my
keyboard, the 72-tET harmonies _are_ just . . . end of story. Plus,
the natural fluctuations in tuning of string or metal instruments or
human voices will render such distinctions meaningless anyway . . .

Just my opinion!

P.S. The only definite thing you actually said about the Eikosany is
that it contains a lot of consonant chords . . . but Blackjack
contains far more of almost all varieties . . . this comparison was
done, I think, in May . . .

--- In tuning@y..., "Robert Walker" <robertwalker@n...> wrote:
>
> If in the way of building musical instruments, I'd love to
> make, say, a hexany as six pointed star.
>
> I.e. six pointed star as two interlaced triangles; each
> triangle plays a triad; and each adjacent group of three
> points round the edge of the star also plays a triad, making
> eight triads in all, easy to find.

Hi Robert!

As someone deeply interested in the Wilson CPS I find this idea of a
star-shaped instrument very interesting. What if you wanted more than
one octave in your instrument? Would it have many six pointed stars
side by side or some other configuration?

Kalle

[Alison wrote:]
>>>>Yes, I've decided to tune the current metallophone to Blackjack and
>>>>my only problem is which frequency to start with. Probably A440.

[Paul E:]
>>>Not a bad choice -- I'm planning to center my MIRACLE guitar on A.
>>>The most likely tonal centers then are C quatertone-sharp and F
>>>quartertone-sharp.

[I wrote:]
>>Wouldn't that be 1/12 tone sharp in each case?

[Paul:]
>No, sir . . . I'm not sure why you'd think that. If you go to

>/tuning/files/perlich/scales/

>download bjlatt.zip, and look at blackjack0.bmp, you'll see that, for
>a blackjack scale centered on C, the notes that participate in the
>most consonances are A quartertone-flat and E quartertone-flat.
>Transposing the center to A, these become F quartertone-sharp and C
>quartertone-sharp.

Went there, did that. Nice colors! And all those symbols that have so
many definitions that were argued about endlessly. My eyes pretty much
glaze over in the absence of a legend.

I was thinking that A was neither flat nor sharp, and that it formed a
good minor third with C. Must've made a false assumption there!

JdL

--- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote:

> Went there, did that. Nice colors! And all those symbols that have so
> many definitions that were argued about endlessly. My eyes pretty much
> glaze over in the absence of a legend.

Sorry John -- here it is:

] = 1/4 tone sharp
> = 1/6 tone sharp
^ = 1/12 tone sharp
v = 1/12 tone flat
< = 1/6 tone flat
[ = 1/4 tone flat
>
> I was thinking that A was neither flat nor sharp,

Right . . .

> and that it formed a
> good minor third with C.

It forms a better minor third with Cv.

--- In tuning@y..., "Robert Walker" <robertwalker@n...> wrote:

> Also, like Dan, I wonder if consistency though interesting as a
> concept, might possibly be overrated as regards musicality.
>
> Does it matter how the intervals add up?? At least, I'd
> want to see from actual musical examples and compositions
> why it is important to have consistency; rather than just formulae.
> Or, see what effect it has compositionally, and decide for myself
> if I like that kind of an effect.

Hi Robert.

In case you don't understand why it matters _compositionally_ how the
intervals add up, I'll attempt to illustrate with an example.

Many researchers (Meyer, Yunik and Swift come to mind) observe 12-tET's
best approximations to the 5-limit interval classes (aside from the unison):

ratio 12-tET steps error (cents)
2:3 7 2
4:5 4 14
5:6 3 16

Then they observe 24-tET's best approximations to the 7-limit interval classes
(aside from the unison):

ratio 24-tET steps error (cents)
2:3 14 2
4:5 8 14
4:7 19 19
5:6 6 16
5:7 12 17
6:7 5 17

Noticing that the errors are about the same size in both tables, they conclude
that 24-tET is about as good in the 7-limit as 12-tET is in the 5-limit. Meyer
even went to the trouble of constructing a 24-tET keyboard.

Now let's say we want to compose something using these ideas. Let's start with
a nice big consonant chord, that has all the 7-limit interval classes in it (just
as the major triad has all the 5-limit interval classes in it). The most likely
choice is of course a 4:5:6:7 chord (a "harmonic seventh" chord).

I'll leave the rest of this argument as an exercise for the reader. Construct the
chord, using the intervals in the above table. Can it be done? If not, might it
have something to do with the fact that the intervals don't "add up"?

[I wrote:]
>>Went there, did that. Nice colors! And all those symbols that have
>>so many definitions that were argued about endlessly. My eyes pretty
>>much glaze over in the absence of a legend.

[Paul wrote:]
>Sorry John -- here it is:
>
> ] = 1/4 tone sharp
> > = 1/6 tone sharp
> ^ = 1/12 tone sharp
> v = 1/12 tone flat
> < = 1/6 tone flat
> [ = 1/4 tone flat

[JdL:]
>>I was thinking that A was neither flat nor sharp,

[Paul:]
>Right . . .

[JdL:]
>>and that it formed a good minor third with C.

[Paul:]
>It forms a better minor third with Cv.

OK, I figured out the lines:

red: 3/2 (right) even
dark blue: 5/4 (up, right) -1/72
purple: 6/5 (down, right) +1/72
green: 7/4 (up, right) -2/72
yellow: 7/6 (up, left) -2/72
lite blue: 7/5 (up, left) -1/72

Relationships:

red = dark blue + purple
green = dark blue + lite blue
green = red + yellow
lite blue = purple + yellow

So, no purple extends from C (which is transposed to A).

It'll come as no surprise to you that my [mind, heart, some part] rebels
against any lattice that is missing so many connections. It seems so
unnecessary (when adaptive tuning is available, which is not always).
But I understand better my error in guessing what you were saying to
Alison.

JdL

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

/tuning/topicId_28987.html#29190

> Hope so. Can't wait to get down to the actual writing. One
question, which frequency did you
> centre everything on, A440 or on C? I'm having a bit of a struggle
deciding how to start tuning
> my fixed pitch metal tubes. Because the scale isn't Just I have to
be careful where I start.
>
> Regards

Hi Alison...

I see Paul beat me to answering this question, but I used "Middle C"
261 hz... since I wanted it the same on my "changable" piano keyboard
as on my acoustic one...

Dave Keenan is keen-on using D as the basis, as Paul mentions. I
guess it makes more sense mathematically... but there is still
something dear to my heart about "Middle C..."

________ ________ _______
Joseph Pehrson

Hi Paul,

Thanks, a nice clear example. I have a much better idea of how consistency / inconsistency works
compositionally as a result.

E.g. could use
C G A+ E+ G+ A# E# C#

to modulate from C to C# via C using the 24-tet approximations to 1/1 5/4 3/2 7/4.

(+ = quarter tone sharp).

I've done a short melody that does exactly this (with extra notes to elaborate it)
on my improvisations page, as a musical ex. for consistency / inconsistency.

http://members.tripod.com/~robertinventor/tunes/improvisations.htm#24-tet

N.B. as logician by training at one point, would like to point out, consistency is a
reasonable name for this, but that it is consistency of a particular set of axioms
/ assumptions that is involved. Here the assumption that if you multiply two
intervals, you can add their approximations in n-tet and get the same result.

Adding that axiom in for n-limit ratios is consistent if (in current terminology)
the scale is consistent up to the n-limit.

So it is possibly something of a misnomer to call the scale itself inconsistent - it is
a particular set of assumptions about the way that one wants to work with it that
is inconsistent instead.

Robert

Hi Kalle,

> As someone deeply interested in the Wilson CPS I find this idea of a
> star-shaped instrument very interesting. What if you wanted more than
> one octave in your instrument? Would it have many six pointed stars
> side by side or some other configuration?

That sounds like a possibility doesn't it. Six six pointed stars
surrounding the player in a circle to make six octaves perhaps...

I've no experience at all of building instruments (unless you count
virtual VRML models, and I somehow don't think they give much
experience for building real world ones :-) ).

Kraig Grady has built and played CPS set instruments for many years.
However he doesn't seem to be posting to the TL at the moment.

Robert

--- In tuning@y..., "Robert Walker" <robertwalker@n...> wrote:
> Hi Kalle,
>
> > As someone deeply interested in the Wilson CPS I find this idea
of a
> > star-shaped instrument very interesting. What if you wanted more
than
> > one octave in your instrument? Would it have many six pointed
stars
> > side by side or some other configuration?
>
> That sounds like a possibility doesn't it. Six six pointed stars
> surrounding the player in a circle to make six octaves perhaps...
>

Yes, it is a possibility but I am very skeptical about the ergonomics
side. Hexanies are quite easy to learn when mapped to a standard
keyboard. After all, there are "only" 8 different chords in a hexany.
So for them six keys or blocks side by side and octave-repeating is
just as good a design as this star-shaped instrument. But it would be
nice if there were some such intuitive design for the eikosany.

> I've no experience at all of building instruments (unless you count
> virtual VRML models, and I somehow don't think they give much
> experience for building real world ones :-) ).
>

Me neither.

> Kraig Grady has built and played CPS set instruments for many years.
> However he doesn't seem to be posting to the TL at the moment.
>
> Robert

He has used scales which are basically CPS but with added notes to
make them Constant Structures and this is reflected in the designs of
the instruments. This is Wilson's recommendation. They don't think
that plain eikosanies or dekanies are scales at all. Scales or not, I
think they are musically useful as tunings.

Kalle

Hi Kalle,

> Yes, it is a possibility but I am very skeptical about the ergonomics
> side. Hexanies are quite easy to learn when mapped to a standard
> keyboard. After all, there are "only" 8 different chords in a hexany.
> So for them six keys or blocks side by side and octave-repeating is
> just as good a design as this star-shaped instrument. But it would be
> nice if there were some such intuitive design for the eikosany.

Maybe a skyscraper type design? Or concentric stars maybe for the
octaves?...

It's fairly easy to find the hexany chords on keyboard, but a little
unintuitive improvising on hexany in keyboard layout. You can't so easily see the
geometry; the way the chords relate to each other. I feel that a six pointed star
would be more intuitive. Or indeed, a 3D octahedron.

You could prob. get nice symmetrical arrangements for the eikosany.
I think symmetry would make it easier to learn where the chords
are as one has only a few patterns to learn.

Ditto for the dekany. There I think the 3D shape would be really great if it was
possible in terms of ergonomics to play the notes. (You just need the ten vertices
and the framework to hold them).

I'd like to make one some day, actually...

I'm not really set up for making instruments at present though, in terms of space,
equipment etc, (and so much I want to do in way of software), so it's something
for further into the future.

Robert

Paul Erlich wrote:

> --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
>
> > Yes, I've decided to tune the current metallophone to Blackjack and
> my only problem is which
> > frequency to start with. Probably A440
>
> Not a bad choice -- I'm planning to center my MIRACLE guitar on A.
> The most likely tonal centers then are C quatertone-sharp and F
> quartertone-sharp.
>
> > then I'll have to work out the rest. Anybody got a quick
> > spreadsheet?
>
> here's one octave:
>
> 440.0000
> 448.5539
> 470.6732
> 479.8234
> 503.4847
> 513.2728
> 538.5836
> 549.0540
> 576.1292
> 587.3295
> 616.2922
> 628.2734
> 659.2551
> 672.0715
> 705.2130
> 718.9228
> 754.3747
> 769.0402
> 806.9636
> 822.6514
> 863.2185
> 880.0000

That's most helpful. Thank you.

Best Wishes.

Robert Walker wrote:

> Hi Alison,
>
> I'm sure Kraig would be the one to answer the Eikosany part of
> your query, but since he isn't posting at the moment as far
> as I can see:
>
> The idea of the Eikosany is it has many pure triad, tetrad
> etc. subsets.
>
> They aren't that easy to find though, if you are presented
> with the scale notes.
>
> So, I expect one would want to do something with the layout
> of the instruments to make them easier to find them if
> building one.
>
> (In FTS I'm experimenting with ways of using the midi keyboard to select
> subsets of the Eikosany by devoting some of the octaves
> to the task of selecting subsets, rather than playing notes).
>
> If in the way of building musical instruments, I'd love to
> make, say, a hexany as six pointed star.
>
> I.e. six pointed star as two interlaced triangles; each
> triangle plays a triad; and each adjacent group of three
> points round the edge of the star also plays a triad, making
> eight triads in all, easy to find.

Some sort of metallophone or marimba would fit this layout. Have you read the back issues of
Xenharmonicon? There are some incredibly detailed articles on layouts for instruments, mainly by
Erv Wilson. I'm sure you'd get the details on the anaphoria website.

> One could make the 1 3 5 7, 1 3 5 11, 1 3 5 9, 1 3 7 11
> or even 1 5 7 11 hexanies. All these can be found as subsets
> of the 1 3 5 7 9 11 Eikosany, so this is also introducing
> one gradually to the Eikosany subsets.
>
> Then I'd perhaps want to make a dekany next. If the instruments
> were ones that one could mount in a light framework, maybe
> one could actually mount the ten notes in the Octahedron + tetrahedron
> arrangement in the projection Paul used in his dekany
> animations (and I use on my dekany web page).
>
> Excuse me if this has already been said. I could easily have
> missed a post. However seemed the discussion has been
> focussed on 72-tet scales rather than the Eikosany itself
> as such. I think with Eikosany as based on the idea of
> really pure triads etc, would be nice if one could do them
> pure, and perhaps this would help hone ones perception of
> pure intervals.
>
> I wonder a little if retuning _everything_ to an approximation
> to j.i. might in the end run somewhat dull ones perception
> of j.i.?? Or at least, not stretch it in the direction
> of hearing j.i. intervals more and more finely.

I'm still not sure about this. I'm coming round to the opinion, through listening and comparing,
that 2 - 3 cents of Just is pretty much Just, given the inharmonicity of strings in particular. I
intend to try a small group of instruments, including metal tubes, tuned to 'Blackjack'. As with
22 tet I like to work with one tuning for a reasonable length of time. Then I'll make a set of
Eikosany tubes and work with that. After all that I might be qualified to comment on the effects
of tempering.

> 72-tet is also just one of many n-tets. E.g. I've recently
> been exploring 55-tet, which is fascinating. If building
> instruments, one is hard-coding to a particular n-tet
> - okay if it is easy to make them or retune them,
> but quite a commitment to that n-tet if it is a matter
> of, say, many weeks or months of work...
>
> Also, like Dan, I wonder if consistency though interesting as a
> concept, might possibly be overrated as regards musicality.
>
> Does it matter how the intervals add up?? At least, I'd
> want to see from actual musical examples and compositions
> why it is important to have consistency; rather than just formulae.
> Or, see what effect it has compositionally, and decide for myself
> if I like that kind of an effect.
>
> Irregularity is interesting and composers often are doing things
> to throw rhythms etc. out from perfect symmetry, so
> maybe "inconsistent" scales could be desirable too?
> Perhaps dep. on the composer and the style of the piece.
>
> A few thoughts anyway. Not trying to dissuade you at all
> if you are keen on building 72-tet subsets; especially
> if this is because you like the sound of 72-tet.

Well, I suppose the sound comes first and I have to say that I liked Joseph's piece and I have a
batch of ideas from tinkering with 'Blackjack' on my synth. It all depends on whether I can get
the sounds into my head and start thinking and creating with that scale. Same old problem.

Regards

>
>
>

--- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote:

> So, no purple extends from C (which is transposed to A).
>
> It'll come as no surprise to you that my [mind, heart, some part]
rebels
> against any lattice that is missing so many connections.

Missing? Well, if you used the 31-tET version of blackjack, there
would be a good minor third here . . . but then many of the
consonances shown with connections (as well as many ratios of 9 and
of 11) would be noticeably less just. And remember, intervals that
are not consonances can be useful in their own right.

> It seems so
> unnecessary (when adaptive tuning is available, which is not >
always).

Here it clearly isn't -- Alison will be using many fixed-pitch
instruments.

--- In tuning@y..., "Robert Walker" <robertwalker@n...> wrote:

> Kraig Grady has built and played CPS set instruments for many years.
> However he doesn't seem to be posting to the TL at the moment.
>
> Robert

One can examine the layouts of Kraig's instruments at anaphoria.com.
The Eikosanies are embedded into 22-tone and 31-tone Constant
Structures, and these are laid out roughly in order of pitch, with
different vertical positions being used in a smart way.