Musical practice and discourse about music

Hello:

I've been away from the tuning list for a time, but have been told a bit about
the recent proliferation of break-away groups. This reminds me a bit of the
historical tendency among left wing political parties to split up at the
slightest provocation or perception thereof -- so diluting their strength that
powers was effectively ceded to the conservatives. I was even tempted to step in
and open a new list myself, a moderated "tuning for grown-ups", with moderation
to insure civility and seriousness.

However, it seemed to me that it might be more constructive to consider the
problems that have led to this fragmentation. My impression -- and only my
impression -- is that these problems fall into two basic categories, of which
the first category is simple miscommunication (as in: P. writes something in a
passioned but clear bit of rhetorical prose, indicating a position of
enthusiastic agreement with K.; K., however, apparently unfamiliar with the form
of language used by P, interprets P.'s expression of enthusiastic agreement as a
heated critique; result: explosive exchanges of bad feelings). Having a
moderator is one solution to this problem. Another is a more extensive use of
back channels -- before you fire off your next offensive missive, it can't hurt
to first just send a direct email and ask "Did you _really_ mean this?". Another
solution is to seriously evaluate your own skills as a reader and writer: do I
understand what has been posted? will others understand what I have written? In
all seriousness, I do believe that there are some fine musicians on the list who
are simply not writers.

I admit to having sent more than my fair share of aggressive postings, and
reading some of the intemperate exchanges in the archives is both plain
embarrassing and a sad signal to the world outside of the list, given the modest
but serious work that gets done here and should be wider known. (It is
precisely for this reason that I continue to demand the right of the individual
poster to withdraw her or his postings from the archives and from further
circulation. And this is above and beyond cosmetic issues like typos and
misspellings (after 10 years of practice I have still not mastered the use of a
writing in English on a German-layout keyboard, and such mistakes in my postings
really pain me)).

The second category of problem is more complicated, and has to do with the
relationship between practicing music and making discourse, words, about music.
Perhaps I am wrong, but it is my assumption that every reader of this list is
passionate and serious about music-making. This assumption holds whether they
themselves produce music on their own or not. Indeed, passionate and serious
people whose relationship to music is limited to listening may well value the
production of music more than those persons who are able also to produce music
(anyone with experience with the musicians' union may recognize this). It is my
further assumption that each individual's taste and style, indeed their own idea
of the nature, extent, and limits of what "music" is or might be, is not
infringeable. "Music" is such a large realm of possibilities with very few
universals, if any, that it often seems better to speak of plural, "musics" than
of a monolithic construct. Finally, I assume that the use of words to convey a
composer's, performer's, or listener's experience of music will always fall
short. For language to aspire to the "condition of music", I honestly believe
that you must turn to a parallel art form, to poetry, but even then the
vocabulary will inevitably fail, particularly in conveying the way in which
music articulates time. (Inspired by examples like those of Robert Duncan or
Nate Mackey, I have tried myself to make a kind of poetry which responds to
music, but those I trust have assured me that I should stick with music).

Given these assumptions, how could one possibly use words in a meaningful and
civil way? I don't see much promise in a list of "poetry about music": it would
most likely drown in naive sentiment and vague assertions, and I don't think
that that shows respect for music. On the other hand, there is a modest place in
the world for words dealing with the nuts and bolts of music-making: how to
notate something, or assign notes to a keyboard, how to remove frets from a
guitar or set up a synthesizer or a FFT program. And yes, there is a role for
music theory, whether speculative, analytic, or critical.

Now, most musicians haven't got the need for a music theory articulated in
public words; they simply make their music and leave the "theory" unarticulated.
However, even the most free of "free-improvisers" performs under an
unarticulated theoretical regime about what is interesting or not interesting,
about what sound to produce next, about how to articulate time. (I'm constantly
struck by how theory-bound -- and thus predictable and identifiable --
performances by "free-improvisers" turn out to be. Too, some of the most
serious critical theorists today are to be found among the free-improvising
rank-and-file).

For the minority of us that like our theories in an articulate form, we have
traditions of music theory to respond to, traditions with highly -- and
sometimes not-so highly -- developed vocabularies and structures. Working as a
theorist, one has to either be able to command these traditions or to be able to
build new theory from the foundations up. Many, especially composers, like to
take that _sui generis_ path, but it is tricky, not simple, and one has to be
prepared for serious criticism, that may often leave one feeling as if one's
music or person is also being criticized.

Music theory also has a tendency to borrow from related fields: maths, physics,
psychophysics, physiology, neurology, psychology, linguistics... Many musicians
are shy or mistrustful of such borrowings. After all, one can make music just
fine without knowing any of these subjects -- why should knowing them be at all
useful?

Can we first agree to simply dismiss an anti-intellectual argument? Knowledge,
in sufficient quantity and quality, is never a bad thing. Moreover, it can be a
very practical thing. Knowing a bit about wave lengths sure helps to calculate
microphone placement or to figure out how long a resonator should be. But that's
basic stuff. One proof (or failure, as the case may be) of the effectiveness of
more sophisticated scientific borrowings or exchanges can be heard every day in
the wide variety of technology through which music is stored and reproduced.
The success of the CD -- or the tragi-comic quality of the mp3 -- recording is
due largely to an entirely practical interaction between musical,
psychophysical, and physical theories.

It is, however, maths and music that constitute the one pair of terms whose
conjunction can lead to the most bitter disputes. However, I don't think that
is a valid argument to be made against the following assertion: maths are a
most efficient way of dealing with unfathomable quantities of information. One
way to hear this is to think of the universe of possible tunings as, for all
intents and purposes, infinite, a vector space of unimaginable dimension, but
within this universe of possible tunings, the number of musically interesting
tunings is, essentially, infinitesimally small. One music theorist in
particular, Ervin Wilson, has continuously struggled with this problem of trying
to locate the infinitesimally small within the infinitely large, and his
techniques -- graphic lattices, combination sets, linear series, series with
modulations and/or permutations, scale trees, etc. -- have been astonisingly
prescient in finding musically useful material. Perhaps more sophisticated than
his techniques for deriving scales are the techniques he uses to discard
scales -- using random generators, for example, as a kind of monitor against
nonsense. Please note that I have used the qualifier "musically" here without
any definition: I intend none other than Wilson's own taste and musical
sensibility, for it is precisely here, in an interaction between a talented
musician with astonishing ears and aural imagination and a rigorous method that
the astonishing happens with unreasonable frequency.

Daniel Wolf
Composer, Budapest/Morro Bay
djwolf1@matavnet.hu
http://home.snafu.de/djwolf/

--- In tuning@y..., "Daniel Wolf" <djwolf1@m...> wrote:

/tuning/topicId_23857.html#23857

> Hello:
>
> I've been away from the tuning list for a time,

A hearty welcome back to Daniel Wolf, who has been sorely missed on
this list... particularly with respect to his historical knowledge
and his knowledge of practical notation. I would urge him to review
a few posts back, and offer his *own* comments on practical ascii
notation of 72-tET. I'm certain he would have a valuable opinion!

______ ______ ______
Joseph Pehrson

Daniel!
good to here from you.
I believe that little is lost by having different lists. Unlike left wing politics membership
in one group does not mean one cannot be members in others.
Instead of being speculative as to what or what not it means, lets look at the result.
1. more and different people are posting
2. more viewpoints are being put forth.
3. certain lists have enable certain subjects that to be discussed without interference. In
example, the Spiritual Tuning list compared to the Brian's post on my own involvement in such
subjects on the practical tuning list. It is clear that that list allows things that frankly are
best removed from these list.

All groups involve a certain conformity to the whole. When that conformity reaches a point that
alienates others , it is natural that they would go elsewhere.

Let me say as one of the great non-writers on this list, that i had very little to do with the
forming of any of these recent new lists. I am still a member here.

Daniel Wolf wrote:
-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

--- In tuning@y..., "Daniel Wolf" <djwolf1@m...> wrote:

> Perhaps more sophisticated than
> his techniques for deriving scales are the techniques he uses to
discard
> scales -- using random generators, for example, as a kind of
monitor against
> nonsense.

I haven't heard of this before -- that's terrific! Has Wilson
published any of this work? Or is it "top secret"?

There's an additional factor in all of this: Time. A major benefit of having several lists is
that we can subscribe only to the lists that interest us. It's very difficult to figure out which
posts are along your lines of interest when they all appear in one all-encompassing category.

Paul!
I for one am not quite sure i am getting what he is referring to. I know of no scales he
dismisses. The scale tree show one way of mapping the continuum that i have ever heard him dismiss
as unusable. I will say though that those generators that result in ET seem to have the least
interest for him. Yet he seems to rejoice when he sees others pulling things out of them.

Paul Erlich wrote:

> --- In tuning@y..., "Daniel Wolf" <djwolf1@m...> wrote:
>
> > Perhaps more sophisticated than
> > his techniques for deriving scales are the techniques he uses to
> discard
> > scales -- using random generators, for example, as a kind of
> monitor against
> > nonsense.
>
> I haven't heard of this before -- that's terrific! Has Wilson
> published any of this work? Or is it "top secret"?

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:

> I will say though that those generators that result in ET seem to
have the least
> interest for him.

You can think of the MIRACLE generator as the golden mean between
7/72 and 11/113 on the Scale Tree if you so desire. Perhaps Erv could
propose a keyboard mapping for this generator that would extend at
least a little beyond the 41-tone MOS (if not all the way to 72), and
would facilitate the playing of 11-limit hexads? Would such a mapping
be realizable on any of the Starr Labs products currently?

The optimal meantone generator is close enough to Kornerup. Lots of
other interesting generators are coming up on the tuning-math list
and they can all be noble-ized without detrimentally affecting the
consonances.

Also, Graham claimed that Erv Wilson sometimes refers to fractions of
an octave as an Interval of Equivalence, even though they're not
necessarily the same as a Formal Octave. Do you have any references
to this? If so, it would back up Dan Stearns' claim that my
symmetrical decatonic scale could in fact be considered an MOS.

Paul!
He does not dismiss tone and did mention to him that people where working on the 7/17 MOS's.
He hasn't said anything to me about it which no one should take to me anything. I did mention to
Joseph the following mapping to to starr lab product which was one of the consideration when it
was decided how far to take out the keyboard. Hanson's layout.
http://www.anaphoria.com/images/hebdo15rank.GIF
hard to see but the 7's run in a row!
hmmm this one is the same maybe clearer
http://www.anaphoria.com/images/hebdo-key2.gif

http://www.anaphoria.com/images/hebdo.GIF
another layout of the 72 plus his notational system to boot.

Erv accepts the idea of scales repeating at other places that the 2/1. Is this what your scale
does?

Paul Erlich wrote:

>
> You can think of the MIRACLE generator as the golden mean between
> 7/72 and 11/113 on the Scale Tree if you so desire. Perhaps Erv could
> propose a keyboard mapping for this generator that would extend at
> least a little beyond the 41-tone MOS (if not all the way to 72), and
> would facilitate the playing of 11-limit hexads? Would such a mapping
> be realizable on any of the Starr Labs products currently?
>
> The optimal meantone generator is close enough to Kornerup. Lots of
> other interesting generators are coming up on the tuning-math list
> and they can all be noble-ized without detrimentally affecting the
> consonances.
>
> Also, Graham claimed that Erv Wilson sometimes refers to fractions of
> an octave as an Interval of Equivalence, even though they're not
> necessarily the same as a Formal Octave. Do you have any references
> to this? If so, it would back up Dan Stearns' claim that my
> symmetrical decatonic scale could in fact be considered an MOS.
>

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

should have read
He does not dismiss ET and did mention to him that people where
working on the 7/17 MOS's.
another short circuit

Kraig Grady wrote:

>
> He does not dismiss tone and did mention to him that people where
> working on the 7/17 MOS's.

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:

> Paul!
> He does not dismiss tone

You mean he puts some importance on the concept of a whole-tone? Not
sure what you're saying.

> and did mention to him that people where working on the 7/17 MOS's.

I haven't seen much discussion of those . . . perhaps you mean 7/72?

> He hasn't said anything to me about it which no one should take to
me anything. I did mention to
> Joseph the following mapping to to starr lab product which was one
of the consideration when it
> was decided how far to take out the keyboard. Hanson's layout.
> http://www.anaphoria.com/images/hebdo15rank.GIF
> hard to see but the 7's run in a row!
> hmmm this one is the same maybe clearer
> http://www.anaphoria.com/images/hebdo-key2.gif

Interesting . . . I'll have to look at these when my eyes are less
tired.
>
> http://www.anaphoria.com/images/hebdo.GIF
> another layout of the 72 plus his notational system to boot.

Uh-oh . . . Joseph's going to have a fit when he sees how this
notation directly conflicts with the Sims/Maneri notation as well as
with the Monzo.
>
> Erv accepts the idea of scales repeating at other places that the
2/1. Is this what your scale
> does?

My symmetrical decatonic scale repeats at the half-octave. Within
each half-octave, there are four small steps and one large step. But
the 2/1 is still the acoustical equivalence interval . . . lots of 7-
limit tetrads are approximated. Would Erv consider this an MOS?

yes -an MOS indeed!

Paul Erlich wrote:

> My symmetrical decatonic scale repeats at the half-octave. Within
> each half-octave, there are four small steps and one large step. But
> the 2/1 is still the acoustical equivalence interval . . . lots of 7-
> limit tetrads are approximated. Would Erv consider this an MOS?

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:

> yes -an MOS indeed!
>
Well then I have to take back much that I've written on this list
about it not being an MOS!

Did Erv every specifically mention any MOS scales that repeat at the
half-octave?

The notation is determined by the keyboard design. if you will notice that the 19 ranks at the
bottom contain your naturals, sharps and flats. (in order to place the hebdomekontany on the
keyboard you have to add to alternates like you do with 41 to have Partch's scale out to 43).

Paul Erlich wrote:

> > http://www.anaphoria.com/images/hebdo.GIF
> > another layout of the 72 plus his notational system to boot.
>
> Uh-oh . . . Joseph's going to have a fit when he sees how this
> notation directly conflicts with the Sims/Maneri notation as well as
> with the Monzo.

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:

> The notation is determined by the keyboard design.

Hmm . . . I don't see how the keyboard design will determine whether
a symbol that looks like this:

/|
/ |
/ |
/ |
/ |
|
|
|
|
|
|
|

is going to raise a 12-tET pitch by a twelfth-tone, as is does in
Wilson's notation; or a sixth-tone, as it does in Sims/Maneri
notation.

Paul Erlich wrote:

> Did Erv every specifically mention any MOS scales that repeat at the
> half-octave?

not in print for sure, from what i know of.

Although an MOS by definition, i think he would be troubled by the fact that this tritone is
not one of your basic harmonic intervals in something that is harmonically conceived. He might be
though be intrigued by an MOS that repeated at the 7/5 or 10/7. This is just to illustrate where
you each might take a different path. He might consider this also a more conservative approach,
which can be debated. I speculate tremendously here

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:
>
> > I will say though that those generators that result in ET seem to
> have the least
> > interest for him.
>
> You can think of the MIRACLE generator as the golden mean between
> 7/72 and 11/113 on the Scale Tree if you so desire.

You mean the "noble mediant" of 7/72 and 11/113. Yes. I believe Dan
Stearns posted that very early in the Miracle discussion. In lowest
terms it is the noble mediant of 1/10 and 3/31 which is

1 + 3*phi
----------- octave
10 + 31*phi

or about 116.7725 cents.

But I must say that I am more interested in optimising the
Miracle generator for consonance (even by ear) than I am in having a
generator that is noble and will therefore go on generating more notes
indefinitely. 41 notes per octave is already too many.

I too am interested in Kraig's answers to Paul's questions.

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:
>
> Although an MOS by definition, i think he would be troubled by
the fact that this tritone is
> not one of your basic harmonic intervals in something that is
harmonically conceived.
> He might be
> though be intrigued by an MOS that repeated at the 7/5 or 10/7.

But Kraig, the half-octave _is_ conceived as the 7:5 (the largest
error, comparable with the 6:5's error in 12-tET). I think I may go
with Carl Lumma's suggestion and send Erv a copy of _The Forms of
Tonality_. He deserves a free copy, for his contributions to my
thought and presentation.

The symbol means also "up keyboard". His notation is not based on 12 ET but on the 19 tone subset.
From the hansonian POV 72 is reached through the series of 19,34,53,72. We let go of 12.
If you look at where the like symbols fall, they are consistent on the keyboard.
bottom row: sharps, flats, naturals
second row: add the arrow below
third row: add +
fourth row: add + and arrow

Paul Erlich wrote:

> --- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:
>
> > The notation is determined by the keyboard design.
>
> Hmm . . . I don't see how the keyboard design will determine whether
> a symbol that looks like this:
>
> /|
> / |
> / |
> / |
> / |
> |
> |
> |
> |
> |
> |
> |
>

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

Stand Corrected. it might be a stretch for him to think of an interval the same as the 12 ET
tritone as the 7/5 of 10/7. But it might be best not to second guess him too much.

Paul Erlich wrote:

> But Kraig, the half-octave _is_ conceived as the 7:5 (the largest
> error, comparable with the 6:5's error in 12-tET). I think I may go
> with Carl Lumma's suggestion and send Erv a copy of _The Forms of
> Tonality_. He deserves a free copy, for his contributions to my
> thought and presentation.

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

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

> But I must say that I am more interested in optimising the
> Miracle generator for consonance (even by ear) than I am in having
a
> generator that is noble and will therefore go on generating more
notes
> indefinitely.

Me too. Anyway, Joseph Pehrson and I were listening to Joe Monzo's
arrangement of Graham Breed's 7-limit chord progression in 72-tET,
and I would say, Dave, that all the beating is near or _below_ the
range that you would want it, to avoid the unpleasant "phase-locked"
effect. When you go to live performers on physical instruments, all
these distinctions are within a fly's anomalous saturated suspension.

> 41 notes per octave is already too many.

Yeah -- too bad it's just short of a diamond's worth (45).

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:

> We let go of 12.

Good! Similarly, Graham Breed notates based on the MIRACLE generator
itself, based on the first proper MOS, at 10. Too bad few performers
are likely to follow.

Paul Erlich wrote:
> Did Erv every specifically mention any MOS scales that repeat at
> the half-octave?

Kraig grady replied:
...
> Although an MOS by definition, i think he would be troubled by
the fact that this tritone is
> not one of your basic harmonic intervals in something that is
harmonically conceived. He might be
> though be intrigued by an MOS that repeated at the 7/5 or 10/7. This
is just to illustrate where
> you each might take a different path. He might consider this also a
more conservative approach,
> which can be debated. I speculate tremendously here

Paul,

MOS is fundamentally a melodic property. A scale can be a MOS and
contain no good approximations to any consonance. If the generator
doesn't need to have any particular relationship to consonance, why
should the period. Kraig Grady, Graham Breed, Dan Stearns and I all
now agree that your symmetric decatonic is MOS. If you want to be more
specific you can say it is MOS at the half-octave.

So Graham's bizarre new 58 tone per octave 15-limit scale is MOS at
the 1/29th of an octave with a 16.4 cent generator! There is only one
instance of the generator in each 1/29th of an octave period (41.4
cents).

By the way, it contains 29 complete otonal 15-limit octads (e.g
4:5:6:7:9:11:13:15) with a maximum error of 4.7 cents.

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:

> Stand Corrected. it might be a stretch for him to think of an
interval the same as the 12 ET
> tritone as the 7/5 of 10/7. But it might be best not to second
guess him too much.

Since the 7/6 is so good and the 7/4 acceptable, the 7/5, though off,
works well in complete tetrads.

The decatonic scale can be used with pure 7-limit harmony by allowing
each of the 10 notes to have essentially two variants, 17 cents
apart. Then you get six to eight pure 7-limit tetrads.

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

> If the generator
> doesn't need to have any particular relationship to consonance, why
> should the period.

I was thinking of the Pelog scale, etc., where Wilson seems to be
sticking to the octave as the periodicity despite no particular
relationship to any other

> Kraig Grady, Graham Breed, Dan Stearns and I all
> now agree that your symmetric decatonic is MOS.

Awesome! So my favorite non-MOS scale is the pentachordal decatonic.
>
> So Graham's bizarre new 58 tone per octave 15-limit scale is MOS at
> the 1/29th of an octave with a 16.4 cent generator!

Graham suggests two keyboards, each tuned to 29-tET.

> There is only one
> instance of the generator in each 1/29th of an octave period (41.4
> cents).

Yup -- much like my proposal of two 12-tET keyboards, 15 cents apart,
for 5-limit harmony . . . or two decatonic scales a twelfth-tone
apart in 72-tET.
>
> By the way, it contains 29 complete otonal 15-limit octads (e.g
> 4:5:6:7:9:11:13:15) with a maximum error of 4.7 cents.

The Jon Szanto prize goes to the best 58-tone composition exploiting
all 29 complete otonal ogdoads.

Dave!
BTW Congrads on having your piece done up north!
I hope you don't mind me adding my 17.4878074 cents here.
It seems that when one constructs a scale one would be somewhat consistent. If one uses a harmonic
construct and then find the smallest scale that contains it, one would want to fill it out with
similar material. It would be aesthetically inconsistent to lets say start with a JI Partch
diamond, and fill it the missing 41 tone MOS with ET intervals. Although stranger things to me
have been proposed.

Dave Keenan wrote:

> Paul,
>
> MOS is fundamentally a melodic property. A scale can be a MOS and
> contain no good approximations to any consonance. If the generator
> doesn't need to have any particular relationship to consonance, why
> should the period.

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:
> The symbol means also "up keyboard". His notation is not based on 12
ET but on the 19 tone subset.
> From the hansonian POV 72 is reached through the series of
19,34,53,72. We let go of 12.

Ok. These are the kleismic tunings.

The generator is a 5:6 minor third widened by some fraction of a
kleisma. The noble version is

5 + 14*phi
----------- ~= 316.765 cents
19 + 53*phi

For more info see
http://dkeenan.com/Music/ChainOfMinor3rds.htm

So the generator is approximated by 19/72 oct, not the Miracle 7/72
oct, so that keyboard layout and notation will not be appropriate for
Miracle.

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:
>
> > We let go of 12.
>
> Good! Similarly, Graham Breed notates based on the MIRACLE generator
> itself, based on the first proper MOS, at 10. Too bad few performers
> are likely to follow.

To pick up on a point that Julie (BMS) made:
Who cares if the _performers_ don't follow, but it might be wise if
the _composers_ learnt decimal and then had it automatically
translated to 6*12 notation for the performers. Of course if BlackJack
or Canasta instruments were built specifically (or Miracle keyboard
layouts used on generalised keyboards) then there might be some
advantage in the performers learning decimal.

Dave!
You are probably correct but wish to say something about layouts.
For my 22 tone eikosany vibraphone i have mounted it 3 different ways, all using a generalized
keyboard. The one i settled on is farthest from how the scale is actually constructed.
The reason i did this is that it makes the diatonic the hardest to play and pelog like (7/6
chains) easiest, this way when people improvise on it the layout forces the into a different
melodic terrain. It is really impossible to explain in this media, but in the long run, the least
related turned out to be the best.
One could map 3 different "instruments" over this 72 in the gaps in the pattern.
Just a quick thought.

Dave Keenan wrote:

> So the generator is approximated by 19/72 oct, not the Miracle 7/72
> oct, so that keyboard layout and notation will not be appropriate for
> Miracle.

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

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

/tuning/topicId_23857.html#23966

> > http://www.anaphoria.com/images/hebdo.GIF
> > another layout of the 72 plus his notational system to boot.
>
> Uh-oh . . . Joseph's going to have a fit when he sees how this
> notation directly conflicts with the Sims/Maneri notation as well
as with the Monzo.
> >

This is pretty funny... well, we're all, obviously "individualists..."
Kraig has shown me this keyboard before, but I fear I might have
trouble navigating with it.... Too stuck in the "traditional..."
perhaps... alas.

______ ______ _____
Joseph Pehrson

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> . . . or two decatonic scales a twelfth-tone
> apart in 72-tET.

It's not clear what you are calling a _single_ decatonic in 72-EDO.
You can't really have one can you? The 109 cents (or equivalently 709
cent) generator is smack in between 6/72 oct (100 c) and 7/72 oct (117
c). I suppose you could alternate it between these two values. Such a
decatonic, with a 5:7 replacing the half-octave, might even fit in
Blackjack, but it would have some 15c wolf fifths.

I see that putting two of something together might give you an
"adaptive Erlich-symmetrical-decatonic" but I'm not convinced that
what you end up with is a MOS (in the same way that Grahams 15-limit
58 and your 5-limit 24 are). Not that it really matters.

----- Original Message -----
From: Paul Erlich <paul@stretch-music.com>
To: <tuning@yahoogroups.com>
Sent: Tuesday, May 29, 2001 3:40 PM
Subject: [tuning] Re: Musical practice and discourse about music

> You can think of the MIRACLE generator as the
> golden mean between 7/72 and 11/113 on the
> Scale Tree if you so desire.

This is really cool.

> Perhaps Erv could propose a keyboard mapping for
> this generator that would extend at least a little
> beyond the 41-tone MOS (if not all the way to 72),
> and would facilitate the playing of 11-limit hexads?
> Would such a mapping be realizable on any of the
> Starr Labs products currently?

Paul, the Starr Labs Ztar and Zboard have keys laid
out in an array of 24 x 6 and 12, respectively.
A mapping to 72 steps fits very comfortably on them.

One Ztar mapping I devised even looks like the
"6 bike gears of 12-EDO" concept of 72-EDO:
http://tonalsoft.com/enc/number/72edo.aspx#ztar

(Hmmm... I just realized that the bike metaphor
is even more apt for this particular arrangement.
The "regular" 12-EDO scale "gears" appear just above
the middle, which is exactly where most bike riding
is done, the higher and lower gears being reserved
for extreme conditions.)

-monz
http://www.monz.org
"All roads lead to n^0"

_________________________________________________________
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Get your free @yahoo.com address at http://mail.yahoo.com

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:
> It would be aesthetically inconsistent to lets say start with a JI
Partch
> diamond, and fill it the missing 41 tone MOS with ET intervals.

Why? Do you not accept the 72-tET approximations of the Partch
diamond? Because that _is_ what we're talking about -- not the Partch
diamond in strict JI form. When Partch compares various ETs to his
diamond, he finds 24 has good 11s, 36 has good 7s . . . but didn't
think to look at 72. If he did, I think even he might have accepted
that it represents his diamond rather well. In practice, it would be
very difficult for mere mortals to hear the difference in most
musical circumstances. Hence Ted Mook using 72-tET notation for
Partch, etc.

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> > . . . or two decatonic scales a twelfth-tone
> > apart in 72-tET.
>
> It's not clear what you are calling a _single_ decatonic in 72-EDO.
> You can't really have one can you?

This is what I meant:

] = 1/4 tone up
> = 1/6 tone up
^ = 1/12 tone up
v = 1/12 tone down
< = 1/6 tone down
[ = 1/4 tone down

The "two decatonic scales a twelfth-tone apart in 72-tET", for the
dynamic symmetrical case, would be (with the number of tetrads each
pitch is involved in in parentheses):

C (3) C^ (1)
C# (2) C#^ (1)
Eb< (1) Ebv (2)
E< (1) Ev (3)
Fv (1) F (1)
F# (3) F#^ (1)
G (2) G^ (1)
A< (1) Av (2)
Bb< (1) Bbv (3)
Bv (1) B (1)

> The 109 cents (or equivalently 709
> cent) generator is smack in between 6/72 oct (100 c) and 7/72 oct
(117
> c).

That's why it works so well!
>
> I see that putting two of something together might give you an
> "adaptive Erlich-symmetrical-decatonic" but I'm not convinced that
> what you end up with is a MOS (in the same way that Grahams 15-
limit
> 58 and your 5-limit 24 are). Not that it really matters.

I don't know, but it's a very different concept. Each of the pairs of
pitches above are "inflections" of one basic "pitch class". I look
forward to your mathematical ruminations (perhaps better posted on
the tuning-math list).

--- In tuning@y..., "Joe Monzo" <joemonz@y...> wrote:
>
> Paul, the Starr Labs Ztar and Zboard have keys laid
> out in an array of 24 x 6 and 12, respectively.
> A mapping to 72 steps fits very comfortably on them.

Yes, but Erv has made keyboard designs that _especially_ suit various
generators, including the 19/72 generator . . . so one that suits the
7/72 generator would be nice.
>>
> (Hmmm... I just realized that the bike metaphor
> is even more apt for this particular arrangement.
> The "regular" 12-EDO scale "gears" appear just above
> the middle, which is exactly where most bike riding
> is done, the higher and lower gears being reserved
> for extreme conditions.)
>
Funny, I always ride my bike at the extreme (hardest, fastest) gear,
switching only when going uphill. Is that a bicycling no-no (please
reply to the tuning-bike list . . . :))?

On 5/30/01 4:37 PM, "Paul Erlich" <paul@stretch-music.com> wrote:

> ] = 1/4 tone up
>> = 1/6 tone up
> ^ = 1/12 tone up
> v = 1/12 tone down
> < = 1/6 tone down
> [ = 1/4 tone down

Nope.
Gotta use something different than ">" for a 1/6 up.
It turns the wrong color in internet style quoting.

(I'm kidding, I'm kidding, I'm kidding, I'm kidding...)

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

/tuning/topicId_23857.html#24035

> --- In tuning@y..., "Joe Monzo" <joemonz@y...> wrote:
> >
> > Paul, the Starr Labs Ztar and Zboard have keys laid
> > out in an array of 24 x 6 and 12, respectively.
> > A mapping to 72 steps fits very comfortably on them.
>
> Yes, but Erv has made keyboard designs that _especially_ suit
various
> generators, including the 19/72 generator . . . so one that suits
the
> 7/72 generator would be nice.
> >>
> > (Hmmm... I just realized that the bike metaphor
> > is even more apt for this particular arrangement.
> > The "regular" 12-EDO scale "gears" appear just above
> > the middle, which is exactly where most bike riding
> > is done, the higher and lower gears being reserved
> > for extreme conditions.)
> >
> Funny, I always ride my bike at the extreme (hardest, fastest)
gear,
> switching only when going uphill. Is that a bicycling no-no (please
> reply to the tuning-bike list . . . :))?

Good one, Paul... but of course it should be on the "Tuning-Joke"
list...

_______ _____ _______
Joseph Pehrson