The Sagittal website is officially open

See http://dkeenan.com/sagittal/

A few items will not be up for another few days. But there's
definitely enough there to make a visit worthwhile, and no reason to
delay the announcement further.

Even if you aren't particularly interested in a universal microtonal
notation system, I think you will enjoy the story of its creation.
;-)

-- Dave Keenan

hi Dave,

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:

> See http://dkeenan.com/sagittal/
>
> A few items will not be up for another few days. But there's
> definitely enough there to make a visit worthwhile, and no
> reason to delay the announcement further.
>
> Even if you aren't particularly interested in a universal
> microtonal notation system, I think you will enjoy the story
> of its creation.
> ;-)
>
> -- Dave Keenan

wow, what a coincidence. i just found this site 7 hours ago
while doing a search for websites which have links to my
webpages, and was surprised to see that it looked ready for
public viewing but hadn't been announced yet. :)

looks good.

-monz

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> hi Dave,
>
>
> wow, what a coincidence. i just found this site 7 hours ago
> while doing a search for websites which have links to my
> webpages, and was surprised to see that it looked ready for
> public viewing but hadn't been announced yet. :)
>
> looks good.

Thanks Monz. Darn those search engines are good. But if you were
there 7 hours ago, you probably would have missed the most fun
feature:
http://dkeenan.com/sagittal/gift/GiftOfTheGods.htm

Regards,
-- Dave Keenan

> "Dave Keenan" <d.keenan@b...> wrote:
> See http://dkeenan.com/sagittal/
>
> A few items will not be up for another few days. But there's
> definitely enough there to make a visit worthwhile, and no
> reason to delay the announcement further.

AWESOME!!!

I can't wait to read it.

And George, I can't believe you were sitting on those
recordings since 1976!

Is the Scalatron multi-timbral? Or was baroque improv.
multi-tracked?

-Carl

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:

> Even if you aren't particularly interested in a universal microtonal
> notation system, I think you will enjoy the story of its creation.

It's nice, finally, for Hermes to come clean with the real story of
its creation, but I see he has things yet to learn about the Internet.
H links to an encyclopedia article on Didymus the Musician, familiar
to me because I wrote it. However, he links to one of those rip-off
encyclopedias which steal content in order to put a ton of ads on the
page, and then don't link back to Wikipedia.

Hermes, I think most people here are tolerant enough that you could
have come out of the Olympian closet before now. However, there are a
few people you should be wary of, so take care.

Some comments on the first part of The Gift of the Gods...

> http://www.corporeal.com/cm_main.html

I don't know Jon's particular feelings on this, but
usually it's best to link out as far as possible, IOW
to corporeal.com/ rather than to the cm_main.html page.

> Once the harmonic resources of 12-ET were exhausted (by
> around 1920),

Is this true? Where do you establish it? If not
established, does it help or hinder the article?

> the university musical establishment now generally
> considers any efforts to create music using alternate
> tunings a complete waste of time,

Again, is this true?

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <ekin@l...> wrote:
> Some comments on the first part of The Gift of the Gods...
>
> > http://www.corporeal.com/cm_main.html
>
> I don't know Jon's particular feelings on this, but
> usually it's best to link out as far as possible, IOW
> to corporeal.com/ rather than to the cm_main.html page.
>
> > Once the harmonic resources of 12-ET were exhausted (by
> > around 1920),
>
> Is this true? Where do you establish it? If not
> established, does it help or hinder the article?

Blackwood claims to have discovered an essentially new chord
progression in 12-equal:

http://www.bruceduffie.com/blackwood.html

You probably have to purchase his very expensive, self-published
treatise to find out what it is. Oh wait, you could just listen to
the piece in question!

> > the university musical establishment now generally
> > considers any efforts to create music using alternate
> > tunings a complete waste of time,
>
> Again, is this true?

Anecdotally, it's usually true, but in my case I managed to create an
independent study course with Ramon Satyendra.

BTW, Dave and George, I took a quick peek. Margo usually puts the
beginning of the meantone era at 1470 or 1480. Are you sure you want
to say "17th century"?

--- In tuning@yahoogroups.com, "Carl Lumma" <ekin@l...> wrote:
> Some comments on the first part of The Gift of the Gods...
>
> > http://www.corporeal.com/cm_main.html
>
> I don't know Jon's particular feelings on this, but
> usually it's best to link out as far as possible, IOW
> to corporeal.com/ rather than to the cm_main.html page.

Jon's feelings are thus: in this case it is perfectly fine, as
linking to the domain directly will simply get them one of the
occasionally changing 'splash' pages. cm_main *is* the main page.
What you say is true most of the time, Carl; in this instance the
link is just right.

> > the university musical establishment now generally
> > considers any efforts to create music using alternate
> > tunings a complete waste of time,
>
> Again, is this true?

It would depend on how many exceptions to this one could bear
documenting before you'd change "generally". I just have been in
contact with a fellow who has combined study in both microtonality
and ethnomusicology, and he is doing it with none other than John
Eaton and Easley Blackwood at U of Chi.

Then again, when studying microtonality this way means studying very
academic microtonal music, just when and where does one throw up
their hands? (good thing I added "their hands"...).

Cheers,
Jon

>> > the university musical establishment now generally
>> > considers any efforts to create music using alternate
>> > tunings a complete waste of time,
>>
>> Again, is this true?
>
>It would depend on how many exceptions to this one could bear
>documenting before you'd change "generally".

I've never met anyone who considered it a "complete waste
of time". A few times I've heard, "But didn't the 24-tone
experiments fail?". But most people in academia I've
discussed it with find it fascinating.

>I just have been in
>contact with a fellow who has combined study in both microtonality
>and ethnomusicology, and he is doing it with none other than John
>Eaton and Easley Blackwood at U of Chi.

Great!

-Carl

C,

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> I've never met anyone who considered it a "complete waste
> of time".

I'm long past being in school, but I remember Adam Silverman - on
this list, I believe - talking about being ridiculed at Yale for
having interests outside of 12. Still the description seems vague
(from the Sag. site) but I haven't read it in context yet.

> >I just have been in
> >contact with a fellow who has combined study in both microtonality
> >and ethnomusicology, and he is doing it with none other than John
> >Eaton and Easley Blackwood at U of Chi.
>
> Great!

Heh, I had a different reaction, but that would be expected! :)

Cheers,
Jon

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
>
> > Even if you aren't particularly interested in a universal
microtonal
> > notation system, I think you will enjoy the story of its
creation.
>
> It's nice, finally, for Hermes to come clean with the real story of
> its creation, but I see he has things yet to learn about the
Internet.
> H links to an encyclopedia article on Didymus the Musician,
familiar
> to me because I wrote it.

Awesome!

> However, he links to one of those rip-off
> encyclopedias which steal content in order to put a ton of ads on
the
> page, and then don't link back to Wikipedia.

Woops! That was my fault, not Hermes'. The link goes to Wikipedia
now, thanks.

>> > Once the harmonic resources of 12-ET were exhausted (by
>> > around 1920),
>>
>> Is this true? Where do you establish it? If not
>> established, does it help or hinder the article?
>
>Blackwood claims to have discovered an essentially new chord
>progression in 12-equal:
>
>http://www.bruceduffie.com/blackwood.html
>
>You probably have to purchase his very expensive, self-published
>treatise to find out what it is. Oh wait, you could just listen to
>the piece in question!

Is this what you're talking about?

"I had discovered some chord progressions in 12 notes in the
process of looking at some of the other equal tunings, which,
oddly enough, were never exploited or used by composers between
1904 and 1915 when they would have been idiomatic. And I
thought, well, to write an etude to explore these, obviously,
you don't need electronic media. You can just write it for piano.
So I wrote a piano piece in that idiom and the piece came out
sounding slightly like Scriabin with a little Milhaud perhaps
thrown in. Then it occurred to me, 'Wait a moment. I can't make
do with just one etude. I need a set.' So I wrote some more
etudes in tonal idiom that sound rather like Russian music
in 1905.'"

It isn't clear what pieces these are. Piano etudes? I've
heard them more than once, but I didn't notice any particular
progressions in them. Note he does not say 'completely new',
but rather 'missing from the period in which they would have
been natural'.

From this interview, I notice that Blackwood agrees 12 is
played out, but places the critical date not in the 20's, but
in the 60's...

"At this point, I am persuaded that the tonal and harmonic
resources of the 12 note equal scale have, in fact, been
discovered and exploited. And I think that's something that
only came true in about 1965 or 1970. After that, it's been
some kind of a rehash of what's been done before. So the last
frontier to be breached is the atonal polyrhythmic idiom,
and there's a vast repertoire in that idiom that begins
somewhere around 1948, just to pick a random year..."

-Carl

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "Carl Lumma" <ekin@l...> wrote:
> > Some comments on the first part of The Gift of the Gods...
> >
> > > http://www.corporeal.com/cm_main.html
> >
> > I don't know Jon's particular feelings on this, but
> > usually it's best to link out as far as possible, IOW
> > to corporeal.com/ rather than to the cm_main.html page.

Done. Thanks Carl.

> > > Once the harmonic resources of 12-ET were exhausted (by
> > > around 1920),
> >
> > Is this true? Where do you establish it? If not
> > established, does it help or hinder the article?
>
> Blackwood claims to have discovered an essentially new chord
> progression in 12-equal:
>
> http://www.bruceduffie.com/blackwood.html

I've taken the liberty of rewording this slightly so it says what I
think Hermes meant to say, and I've included a link to the blackwood
page. Thanks Carl and Paul.

> > > the university musical establishment now generally
> > > considers any efforts to create music using alternate
> > > tunings a complete waste of time,
> >
> > Again, is this true?
>
> Anecdotally, it's usually true, but in my case I managed to create
an
> independent study course with Ramon Satyendra.

I think we can cut Hermes a little slack here. I expect his poetic
license is up to date. But since we don't want to offend anyone, for
now I've removed the word "complete" before "waste of time". We'll
have to see if Hermes approves this. But do notice that it
says "generally". It's good that there are a few cracks in the
edifice, but Hermes is just trying to explain why the gods found us
alternative tuners strategic recipients of a gift from them.

> BTW, Dave and George, I took a quick peek. Margo usually puts the
> beginning of the meantone era at 1470 or 1480. Are you sure you
want
> to say "17th century"?

Thanks Paul. I've changed it to "This practice eventually resulted
in the general adoption of the meantone temperament in most of
Europe by the 16th century." But I wonder about the "in most of
Europe" part. By 1500? or should we read that loosely as "by some
time in the 16th century".

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:

> Thanks Paul. I've changed it to "This practice eventually resulted
> in the general adoption of the meantone temperament in most of
> Europe by the 16th century." But I wonder about the "in most of
> Europe" part. By 1500? or should we read that loosely as "by some
> time in the 16th century".

The latter reading would certainly be safer. Most of Europe did not
actually make it into recorded history :)

One feature that may be less than obvious on the Sagittal home page,
is that you can click on the image that shows an example phrase
designed to show lots of Sagittal symbols, to hear it played in
various tunings.
http://dkeenan.com/sagittal/exmp/

Unfortunately we don't have room for mp3s of these at present, so
they are midis and your mileage may vary.

-- Dave Keenan

hi Dave,

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:

> Thanks Monz. Darn those search engines are good. But if you were
> there 7 hours ago, you probably would have missed the most fun
> feature:
> http://dkeenan.com/sagittal/gift/GiftOfTheGods.htm
>
> Regards,
> -- Dave Keenan

this is fantastic! thanks for putting so much work into
a well-done website.

there have been a few posts now about sweeping revisions
of classifying and naming tunings. i suggest that discussions
of that topic take sagittal notation into account ...
perhaps families of tunings should be named and classified
according to the ways that sagittal works, since it's such
a broad-based notation.

-monz

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:

> perhaps families of tunings should be named and classified
> according to the ways that sagittal works, since it's such
> a broad-based notation.

For any family not based on a single chain of fifths, it works quite
awkwardly. That one reason Carl and I weren't too crazy about it --
it favors systems like pythagorean, meantone, and
helmholtz/groven/schismic, at the expense of miracle, magic, pajara,
etc....

--- In tuning@yahoogroups.com, "Carl Lumma" <ekin@l...> wrote:

> Some comments on the first part of The Gift of the Gods...
>
> > Once the harmonic resources of 12-ET were exhausted (by
> > around 1920),
>
> Is this true? Where do you establish it? If not
> established, does it help or hinder the article?

i never bought that argument. (hmm ... but i may have
even written those exact words in some of my earlier
writings ... such is the power of peer pressure, i guess ...)

plenty of my own compositions were done in strict 12edo
using MIDI, and i like them. whether or not anyone else
considers them "great art", i've found plenty of harmonic
resources in 12edo still worth playing with, and have
been having lots of fun making my 12edo music.

... but for the record, my favorite tuning is 19-limit-JI.

-monz

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
>
> > perhaps families of tunings should be named and classified
> > according to the ways that sagittal works, since it's such
> > a broad-based notation.
>
> For any family not based on a single chain of fifths, it works
quite
> awkwardly. That one reason Carl and I weren't too crazy about it --

> it favors systems like pythagorean, meantone, and
> helmholtz/groven/schismic, at the expense of miracle, magic,
pajara,
> etc....

Yes. It so far favours an evolutionary approach over a revolutionary
one. And performers particularly, will probably appreciate that.

However, I challenge you guys to take the Sagittal system of
accidentals and figure out how to best use them with alternate
staves and non-chain-of-fifth systems of naturals. But you'll want
to wait for the XH article first.

--- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:

> --- In tuning@yahoogroups.com, "Carl Lumma" <ekin@l...> wrote:

> > > the university musical establishment now generally
> > > considers any efforts to create music using alternate
> > > tunings a complete waste of time,
> >
> > Again, is this true?
>
> It would depend on how many exceptions to this one could bear
> documenting before you'd change "generally". I just have been in
> contact with a fellow who has combined study in both microtonality
> and ethnomusicology, and he is doing it with none other than John
> Eaton and Easley Blackwood at U of Chi.
>
> Then again, when studying microtonality this way means studying very
> academic microtonal music, just when and where does one throw up
> their hands? (good thing I added "their hands"...).
>
> Cheers,
> Jon

here in San Diego, at UCSD, there are a lot of
microtonal-friendly faculty in the music department
... and not only in the composition department, but
also in performance areas too. it's not so much that
there's any particular emphasis on microtonality,
but it is a (perhaps not significant, but at least
there) part of many of the presentations of the
music department at UCSD.

Chinary Ung is one of the composition teachers there,
and he often links his interest in his native
Cambodian ethnic music with his interest in
microtonality.

i just received the long-delayed Spring-Fall 2002
issue of the _Journal of Music Theory_, and am
happy to see that about half the papers in it
use some form of lattice diagram!

-monz

hi Dave,

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:

> One feature that may be less than obvious on the Sagittal home page,
> is that you can click on the image that shows an example phrase
> designed to show lots of Sagittal symbols, to hear it played in
> various tunings.
> http://dkeenan.com/sagittal/exmp/
>
> Unfortunately we don't have room for mp3s of these at present, so
> they are midis and your mileage may vary.
>
> -- Dave Keenan

using Opera as my browser, i got an error message:

>> "this page requires that you download and install a
>> plugin, but it does not specify which one",

and gives me only a "Cancel" and a "Help" button;
the "Get plugin" button is disabled. the "Help" button
leads to a FAQ on Opera plugins. help appreciated.

(my well-protected computer suffered a serious virus attack
via a back-door which entered thru Internet Explorer,
so i'm not using that now.)

-monz

hi Paul,

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
>
> > perhaps families of tunings should be named and classified
> > according to the ways that sagittal works, since it's such
> > a broad-based notation.
>
> For any family not based on a single chain of fifths, it works quite
> awkwardly. That one reason Carl and I weren't too crazy about it --
> it favors systems like pythagorean, meantone, and
> helmholtz/groven/schismic, at the expense of miracle, magic, pajara,
> etc....

but there's the beginning of a classification right there !!

pythagorean, meantone, and schismic could all be subsets of
a larger "sagittal" category, and those with multiple
chains would have other name(s).

-monz

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> using Opera as my browser, i got an error message:
>
> >> "this page requires that you download and install a
> >> plugin, but it does not specify which one",
>
> and gives me only a "Cancel" and a "Help" button;
> the "Get plugin" button is disabled. the "Help" button
> leads to a FAQ on Opera plugins. help appreciated.

I'm only guessing it wants something to let it play .mid files.
Try some of these URLs directly and see if the same thing happens.

http://dkeenan.com/sagittal/exmp/ExmpJI.mid
http://dkeenan.com/sagittal/exmp/Exmp12.mid
http://dkeenan.com/sagittal/exmp/Exmp19.mid
http://dkeenan.com/sagittal/exmp/Exmp22.mid
http://dkeenan.com/sagittal/exmp/Exmp31.mid
http://dkeenan.com/sagittal/exmp/Exmp41.mid
http://dkeenan.com/sagittal/exmp/Exmp46.mid
http://dkeenan.com/sagittal/exmp/Exmp53.mid
http://dkeenan.com/sagittal/exmp/Exmp58.mid
http://dkeenan.com/sagittal/exmp/Exmp72.mid

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> hi Paul,
>
>
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
>
> > --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> >
> > > perhaps families of tunings should be named and classified
> > > according to the ways that sagittal works, since it's such
> > > a broad-based notation.
> >
> > For any family not based on a single chain of fifths, it works
quite
> > awkwardly. That one reason Carl and I weren't too crazy about
it --
> > it favors systems like pythagorean, meantone, and
> > helmholtz/groven/schismic, at the expense of miracle, magic,
pajara,
> > etc....
>
>
> but there's the beginning of a classification right there !!
>
> pythagorean, meantone, and schismic could all be subsets of
> a larger "sagittal" category, and those with multiple
> chains would have other name(s).

Monz,

I have to say I think you're barking up the wrong tree here. What
makes for relationships between regular temperaments is the
_vanishing_ commas that they have in common, not the _notational_
commas. If a comma vanishes in some temperament then it can't be
used as chromatic accidental in that temperament, and that says very
little about what commas _can_ or _should_ be used as chromatic
accidentals in that temperament.

And calling temperaments generated by fifths "sagittal" would
certainly be a misnomer. Sagittal is primarily a system that
provides symbols for commas as pitch alterations. At this stage I
don't see any reason why it can't be used with systems of nominals
that are not in a chain of fifths.

But there are unsolved problems that relate to how to name these
nominals so that confusion between different temperaments is
minimised. Erv Wilson made one run at this fence but, perhaps
ironically, only considered temperaments generated by fourths/fifths.

In an investigation I did some months back, I came to the conclusion
that a set of 72 nominals to the octave would do the trick (or maybe
36 would do at a pinch). But what symbols to use for these in text
and speech (given that 7 widely spaced ones are already called
ABCDEFG), and how to represent them on staves (or otherwise)?

Regards,
-- Dave Keenan

hi Dave,

thanks, these links worked.
wonder why the links on the website don't?

-monz

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:

> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> > using Opera as my browser, i got an error message:
> >
> > >> "this page requires that you download and install a
> > >> plugin, but it does not specify which one",
> >
> > and gives me only a "Cancel" and a "Help" button;
> > the "Get plugin" button is disabled. the "Help" button
> > leads to a FAQ on Opera plugins. help appreciated.
>
> I'm only guessing it wants something to let it play .mid files.
> Try some of these URLs directly and see if the same thing happens.
>
> http://dkeenan.com/sagittal/exmp/ExmpJI.mid
> http://dkeenan.com/sagittal/exmp/Exmp12.mid
> http://dkeenan.com/sagittal/exmp/Exmp19.mid
> http://dkeenan.com/sagittal/exmp/Exmp22.mid
> http://dkeenan.com/sagittal/exmp/Exmp31.mid
> http://dkeenan.com/sagittal/exmp/Exmp41.mid
> http://dkeenan.com/sagittal/exmp/Exmp46.mid
> http://dkeenan.com/sagittal/exmp/Exmp53.mid
> http://dkeenan.com/sagittal/exmp/Exmp58.mid
> http://dkeenan.com/sagittal/exmp/Exmp72.mid

hi Dave,

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:

> I have to say I think you're barking up the wrong tree
> here. What makes for relationships between regular temperaments
> is the _vanishing_ commas that they have in common, not the
> _notational_ commas. If a comma vanishes in some temperament
> then it can't be used as chromatic accidental in that
> temperament, and that says very little about what commas _can_
> or _should_ be used as chromatic accidentals in that temperament.
>
> And calling temperaments generated by fifths "sagittal" would
> certainly be a misnomer. Sagittal is primarily a system that
> provides symbols for commas as pitch alterations. At this stage
> I don't see any reason why it can't be used with systems of
> nominals that are not in a chain of fifths.

my comment about grouping tunings into a "sagittal"
family was just a quick knee-jerk kind of response to
what Paul said ... i really didn't put much thought
into it. just trying to provoke other minds out there
(like yours!) into contributing some thoughtful answers
to the idea of reclassifying and renaming.

honestly, i've been real busy with my own work for a
few months now and haven't really been following developements
here very much. i went on a real binge last night and
read and responded to a bunch of stuff. thanks for
jumping in here and clarifying things a bit.

i think (as i just posted on tuning-math) that with
the great increase of new tuning tools recently --
namely, Gene's enormous contributions from the past few
years, and the imminent arrival of both sagittal notation
and the Tonalsoft software -- the time may be right for
a serious re-thinking of our naming procedures.

> But there are unsolved problems that relate to how to
> name these nominals so that confusion between different
> temperaments is minimised. Erv Wilson made one run at this
> fence but, perhaps ironically, only considered temperaments
> generated by fourths/fifths.
>
> In an investigation I did some months back, I came to the
> conclusion that a set of 72 nominals to the octave would do
> the trick (or maybe 36 would do at a pinch). But what symbols
> to use for these in text and speech (given that 7 widely spaced
> ones are already called ABCDEFG), and how to represent them on
> staves (or otherwise)?

i've already taken a shot at a simplified notation
for 72edo here, using my "quarter-tone staff" idea:

http://tonalsoft.com/enc/72edo.htm#qtstaff

-monz

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:

> I have to say I think you're barking up the wrong tree here. What
> makes for relationships between regular temperaments is the
> _vanishing_ commas that they have in common, not the _notational_
> commas.

As I pointed out a while back, you could use commas for a naming
scheme. You could try to make this possible to actually name things
with by using monosyllables for the commas. If 81/80 is "me".
3125/3072 is "mag", 2109375/2097152 is "or", "126/125" is "star" and
"225/224" is "mar", then some 7-limit temperaments are "mestar" for
meantone (not "memar", since 126/125 has a lower Tenney height than
any alternative), "magstar" for muggles, and "orstar" for an orwell
variant of small interest. Also we have "ormar" for orwell and
"magmar" for magic.

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> hi Paul,
>
>
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
>
> > --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> >
> > > perhaps families of tunings should be named and classified
> > > according to the ways that sagittal works, since it's such
> > > a broad-based notation.
> >
> > For any family not based on a single chain of fifths, it works
quite
> > awkwardly. That one reason Carl and I weren't too crazy about it -
-
> > it favors systems like pythagorean, meantone, and
> > helmholtz/groven/schismic, at the expense of miracle, magic,
pajara,
> > etc....
>
>
> but there's the beginning of a classification right there !!
>
> pythagorean, meantone, and schismic could all be subsets of
> a larger "sagittal" category, and those with multiple
> chains would have other name(s).

Miracle only has one chain.

Some time ago I decided to follow up on the desire of Paul Erlich,
Carl Lumma and others, to have notations for linear temperaments
where the nominals (i.e. the notes representable without
accidentals) are contiguous on a short chain of the generators of
that temperament. The nominals would form a Moment of Symmetry (MOS)
or Distributionally Even (DE) scale in that temperament, having a
cardinality (number of notes) that was preferably between about 5
and 10. An example is Graham Breeds decimal notation for the Miracle
temperament.

In the cases where the generator is a fifth, or equivalently a
fourth (it's conventional to use the smallest of the equivalent
generators) this is easy. We simply use the standard 7 nominals in
the chain B E A D G C F. This works for generators in the range of
480 c to 514 c (2/5 to 3/7 of an octave) and maybe even out to 533 c
(4/9 oct).

But what's needed is a system that covers all generators in the
range 0 to 600 c, and does it in such a way that the meaning of a
natural symbol (or staff position) and the pitch relationships
between them do not change wildly from one temperament to another.

In 1975, in Xenharmonikon 3, Erv Wilson considered this question for
linear temperaments whose generators are in the range from 400 c to
600 c (1/3 to 1/2 oct).

See, in particular, the chart "A System of Fluctuating Nominals" on
page 5, in which he uses lowercase greek letters (and "H") for new
nominals, interspersed between the standard uppercase latin A thru G.

Thanks to Kraig Grady you can view this article online at:
http://www.anaphoria.com/xen3a.PDF

I took this as my starting point and decided to try extending this
chart downwards to cover the remaining 2/3 of the range. At the same
time I wanted to remove the asymmetry and apparent arbitrariness
that beset Ervs version.

Unfortunately the only graph paper I had at the time was already
used and so the resulting palimpsest (some would say ratsnest) is
unfortunately unsuitable for anyone but me to follow. And even I am
having trouble a few months down the track. In any case, I'd like to
see what others come up with when they try this (without being
influenced by my version).

But I will try to influence you about a few aspects. Firstly, to
remove the asymmetry I put D (not C) at the vertical edges of the
diagram and ensured that any lines drawn were reflected about the
vertical centerline (halfway between G and A).

Secondly, while I agree with Erv that "If we are going to adapt
existing notation to new systems, obviously _something_ is going to
have to give." And I also agree that we should "allow the melodic
values to vary." However I think it is going too far to allow them
to vary so much that "sometimes ... B can be higher than C". I could
not bring myself to allow crossovers like this. The question then is
how few unique nominal symbols can we get away with to cover all
possible (at this stage octave-equivalent) linear temperaments,
without allowing such pitch crossovers in any temperament.

Notice that this doesn't mean that a B in one temperament cannot be
higher than a C in another temperament. But there should be
reasonable limits to how far B's or C's can range from their
standard Pythagorean/12-equal/meantone pitches.

I came up with the number of 72 nominals, not because of the good
properties of 72-ET as a temperament. It has nothing to do with
that. But simply because it is an "almost-LCM (LCM = least common
multiple) for the integers from 5 to 10, the intended cardinalities
of the various nominal systems. Or rather because it is the larger
of two numbers, namely 70 and 72, which are very close together, and
between them are evenly divisible by all these integers.

With 72 we also get divisibility by 12 for free, but unfortunately
there are no multiples of 11 or 13 nearby. In fact they are as far
away as they can be (66, 77 and 65, 78). And there are some small
ranges of generator size where one would be tempted to use such
large sets of nominals. Erv certainly thought so.

But 72 is just too many nominals to find symbols for. There must be
a better way.

And note that we have so far only considered linear temperaments
where the period is a full octave (or approximation thereof). We
also need to consider the cases where the period is a half-octave or
a third of an octave, etc.

We need some ideas. How about a bit of brainstorming. Just blurt it
out. No idea is too stupid at this stage. Also remind us about ideas
you may have already put forward on this.

Should this discussion be conducted on tuning-math?

Regards,
-- Dave Keenan

>But what's needed is a system that covers all generators in the
>range 0 to 600 c, and does it in such a way that the meaning of a
>natural symbol (or staff position) and the pitch relationships
>between them do not change wildly from one temperament to another.

This sounds worth looking into.

>But I will try to influence you about a few aspects. Firstly, to
>remove the asymmetry I put D (not C) at the vertical edges of the
>diagram and ensured that any lines drawn were reflected about the
>vertical centerline (halfway between G and A).

This sounds like a nice thing to have. Fixing it with
enharmonics is sometimes possible. I wonder when this is so.

Which reminds me, in that big angry thread we had (Dave) some
neat questions were nonetheless raised. I vaguely remember
looking at things like number of accidentals per Cartesian
cross set, while you were looking at something else....

>Notice that this doesn't mean that a B in one temperament cannot
>be higher than a C in another temperament. But there should be
>reasonable limits to how far B's or C's can range from their
>standard Pythagorean/12-equal/meantone pitches.

I would think of it as: the master list of nominals is ordered,
and taking any ordered subset, you want the nominals in that
subset to remain ordered with the fewest number of symbols while
doing things like transposing it to different members of itself.

>I came up with the number of 72 nominals, not because of the good
>properties of 72-ET as a temperament. It has nothing to do with
>that. But simply because it is an "almost-LCM (LCM = least common
>multiple) for the integers from 5 to 10, the intended cardinalities
>of the various nominal systems. Or rather because it is the larger
>of two numbers, namely 70 and 72, which are very close together, and
>between them are evenly divisible by all these integers.

I like 84 and 42 for this. Or 70. But 72 has too many 6's in it.
I'm assuming 6-9 are the most important numbers for cognitive-
psychological reasons; another idea might be to take a survey of
good MOSs in good (low badness (whatever that means!)) temperaments.

Were you being facetious about 72 being a good division not having
anything to do with this? 'Cause I don't believe you. :)

>With 72 we also get divisibility by 12 for free, but unfortunately
>there are no multiples of 11 or 13 nearby.

I can live without them. Though for some of the higher-limit
temperaments, as Herman points out, it might be nice to support
some larger divisions, cognitive psychology bedamned.

The problem with all of this, of course, is that we are going
to end of with too many nominals. One can imaging a master
list with smoothly-changing font morphology, so that likely
(properish) subsets will wind up with maximum differentiation...

>But 72 is just too many nominals to find symbols for. There must be
>a better way.

Aha!

>And note that we have so far only considered linear temperaments
>where the period is a full octave (or approximation thereof). We
>also need to consider the cases where the period is a half-octave or
>a third of an octave, etc.

Why? The temperament maps 2, or it wouldn't have low badness.
Isn't this all that matters?

-Carl

I've been working on a system of 28 nominals (not evenly spaced but
symmetric about D) using ABCDEFG in their usual 12-equal positions
and using lowercase greek letters with the same or similar sounds,
for nominals slightly below these, as Erv Wilson did. I'm using the
Greek to Roman/Latin transliteration implied by the popular "Symbol"
font. i.e. ABCDEFG goes to alpha beta chi epsilon phi gamma. "Chi"
looks like an "x" and the "ch" in its name is pronounced as
in "Bach". If you have trouble making that hissy sound with the spit
in the back of your throat, just pronounce it as a "k" (never as
the "ch" in "chair"). The phi is the straight one, not the curly one.

See http://www.ibiblio.org/koine/greek/lessons/alphabet.html
http://www.mathacademy.com/pr/prime/articles/greek/index.asp

Then for those nominals slightly lower again in pitch, I use the
corresponding uppercase greek letter, except where these look the
same as a Roman/Latin letter in the set ABCDEFGH. Instead of capital
BETA (which is "B") I use capital THETA, and instead of capital
EPSILON (which is "E") I use capital UPSILON (which is "Y").
Fortunately I don't need to use capital ALPHA (which is "A").

To keep the name short I propose calling the uppercase Greek letters
neither "uppercase" nor "capital", but "prote" (one syllable), as
in "GAMMA prote. "Prote" resembles a greek word for "capital",
although I'm not sure if it's the correct meaning. It seems right
because it implies "earlier in time", as in "protean". The capital
letters came first historically. Are there any Greek speakers out
there who can tell me the greek word for "capital" as in "capital
letters"?

For nominals slightly higher in pitch than the standard ABCDEFG I'm
using Hebrew characters with the same or similar sounds. Alef, bet,
chaf, dalet, hey, fey, gimmel. (Again the "ch" in "chaf" is
pronounced as in the German "Bach").

See http://www.njop.org/jsAlephbet/sound_main.html
http://www.jewfaq.org/alephbet.htm
http://www.akhlah.com/Aleph_Bet/aleph-bet.asp

Hebrew only has one case (no upper and lower), but it does
have "sofit" or final versions of certain characters. i.e. special
forms used only on the ends of words, called e.g. "chaf sofit"
and "fey sofit".

This use of "sofit" is another reason I want to use "prote" or
something like it, as a suffix to indicate uppercase Greek letters.

There is no final form of aleph, and so I use the letter ayin
instead. Fortunately I don't need final forms of bet, dalet, hey or
gimmel, because there aren't any.

The nominal which is halfway between G and A, could be called
either "ALPHA prote" or "gimmel sofit" except that the first would
be another "A" and the second doesn't exist. So I thought it could
be called "O". That's a Roman/Latin uppercase letter "O", but it can
also be thought of as a zero. It is a point of symmetry for the
notation and corresponds to the zero of decimal notation a la Graham
Breed.

Hebrew fonts are not that common on the computers of English
speakers, but "Symbol" is very common, so it is rather convenient
that "Symbol" not only has the upper and lowercase Greek letters and
the Hebrew letter alef, but provides enough mathematical and other
symbols that we can find passable approximations of the remaining
Hebrew characters that we need.

For Hebrew Use Symbol font character
---------------------------------------------------------
Bet superset-or-equal sign
Chaf superset sign
Chaf sofit right square bracket fragment, top
Dalet logical not sign
Hey greater-or-equal sign
Fey backwards epsilon (backwards element-of sign)
Fey sofit florin (lowercase "f" will long hooked descender)
Gimmel right square bracket

We would also need a way to represent all 28 nominals in ASCII.
Given 26 letters and 8 digits (excluding 0 and 1 since they look
like uppercase o and i) this should be doable.

Does this sound like it could work?

-- Dave Keenan

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> >And note that we have so far only considered linear temperaments
> >where the period is a full octave (or approximation thereof). We
> >also need to consider the cases where the period is a half-octave
or
> >a third of an octave, etc.
>
> Why? The temperament maps 2, or it wouldn't have low badness.
> Isn't this all that matters?

No, Carl -- all of Dave's message previous to this point had assumed
MOS (in the traditional sense:) rather than DE.

Dave Keenan wrote:
> having trouble a few months down the track. In any case, I'd like to > see what others come up with when they try this (without being > influenced by my version).
> > But I will try to influence you about a few aspects. Firstly, to > remove the asymmetry I put D (not C) at the vertical edges of the > diagram and ensured that any lines drawn were reflected about the > vertical centerline (halfway between G and A). I've mentioned some of my notation systems (or rather, note-labeling systems, since I don't know how to notate them on paper but I use them to label the keys on the keyboard and the notes of the Cakewalk piano roll) that are based on the generators of a linear temperament, like the "superpelog" notation (http://www.io.com/~hmiller/music/superpelog.html)

generators 0 5 10 1 6 11 2 7 12 3 8 13 4 9 0
note name A F K B G L C H M D I N E J A
degree of 23-ET 0 2 4 5 7 9 10 12 14 15 17 19 20 22 23

This can easily be extended by adding more letters, but runs into trouble with fractional-octave temperaments (like lemba!).

So another idea I've been trying to work out is a system of "symmetrical alphabetic" notation: label the notes of an MOS scale in alphabetical order. This means that you'd never have a scale where F comes before E (as in Erv Wilson's system). The middle note in the sequence (D in the case of a 7-note MOS) is set to the center of symmetry of the MOS, if it has an odd number of notes, or the middle two notes if it has an even number of notes. If there's more than one period in the octave, just continue in alphabetical order for the rest of the notes in the octave. So taking lemba temperament as an example:

0 3 6 1 4 7 2 5 0 3 6 1 4 7 2 5 0 (generators)
A Ax B B# C CxDb D#Dx E ExF Fx G G# AbA (26-ET notation)
(Bbb)(Cbb) (Ebb) (Fb) (Gbb)

Lemba has a 5-note half-octave MOS (A Ax B# C Db / Dx E F Fx G#). It's symmetrical around Db or G#, so this becomes the center of the 5-note scale, which is repeated with the next five letters of the alphabet in the next half octave.

A B C D E F G H I J
0 3 6 1 4 7 2 5 0 3 6 1 4 7 2 5 0 3
A Ax B B# C CxDb D#Dx E ExF Fx G G# AbA Ax

Then accidentals are added to fill in the remaining notes.

AbA B CbC DbD E FbF G HbH IbI J
0 3 6 1 4 7 2 5 0 3 6 1 4 7 2 5 0 3
A Ax B B# C CxDb D#Dx E ExF Fx G G# AbA Ax

Actually, any of these notes could have been identified with C, since it's arbitrary how many generators above and below the center you can use, and what pitch the central note is tuned to. Here's an alternative.

A B B# C DbD E E# F G G# H IbI J J#
0 3 6 1 4 7 2 5 0 3 6 1 4 7 2 5 0 3
A Ax B B# C CxDb D#Dx E ExF Fx G G# AbA Ax

You'll run into trouble if the tuning you're using can't be approximated by an MOS/DE scale with 26 notes per octave or less, but I don't think there are many practical scales like that. JI can be notated with the standard diatonic scale and accidentals for the commas, if miracle notation is inadequate for a particular use. For ennealimmal, just notate the 9 periods per octave and use accidentals for the generators.

There are also some cases where the scale is too symmetrical to apply the standard labeling: take the octatonic scale for instance. Do you label starting with A-B as a semitone or a whole tone? To resolve this case, choose the labeling that maximizes the distance between successive copies of the MOS:

C C# EbE F#G A Bb C (12-ET notation)
A B C D E F G H A (Symmetrical alphabetic notation)

For a generic "standard", I've considered setting the central pitch to one of the following: A=440, C=256, or D=290. But I don't have any particular preference for one over any of the others.

> Secondly, while I agree with Erv that "If we are going to adapt > existing notation to new systems, obviously _something_ is going to > have to give." And I also agree that we should "allow the melodic > values to vary." However I think it is going too far to allow them > to vary so much that "sometimes ... B can be higher than C". I could > not bring myself to allow crossovers like this. The question then is > how few unique nominal symbols can we get away with to cover all > possible (at this stage octave-equivalent) linear temperaments, > without allowing such pitch crossovers in any temperament.

Valentine (77.8 cent generator, wedgie <<9, 5, -3, -13, -30, -21||, map [<1, 1, 2, 3|, <0, 9, 5, -3|]) is going to need at least 15.

Nominals are one thing. Notating music is another.

--- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:
> I've mentioned some of my notation systems (or rather, note-
labeling
> systems, since I don't know how to notate them on paper but I use
them
> to label the keys on the keyboard and the notes of the Cakewalk
piano
> roll) that are based on the generators of a linear temperament,
like the
> "superpelog" notation
(http://www.io.com/~hmiller/music/superpelog.html)
>
> generators 0 5 10 1 6 11 2 7 12 3 8 13 4 9 0
> note name A F K B G L C H M D I N E J A
> degree of 23-ET 0 2 4 5 7 9 10 12 14 15 17 19 20 22 23
>
> This can easily be extended by adding more letters, but runs into
> trouble with fractional-octave temperaments (like lemba!).

So the above method just makes ABC... correspond to the chain of
generators no matter their size, and would result in no fixed pitch
ordering of the superset and no correspondence whatsoever between
the same letter in different linear temperaments (LTs)?

> So another idea I've been trying to work out is a system
of "symmetrical
> alphabetic" notation: label the notes of an MOS scale in
alphabetical
> order. This means that you'd never have a scale where F comes
before E
> (as in Erv Wilson's system).
> The middle note in the sequence (D in the
> case of a 7-note MOS) is set to the center of symmetry of the MOS,
if it
> has an odd number of notes, or the middle two notes if it has an
even
> number of notes. If there's more than one period in the octave,
just
> continue in alphabetical order for the rest of the notes in the
octave.

I see this as a major advance. But still we don't have much
agreement between LTs, do we? If you were to plot the nominals for
each LT on a pitch line from left to right and then line them all up
vertically, how well would the letters line up?

You could do this in ASCII by using 72 positions per line of text
and rounding each nominal's pitch to the nearest degree of 72-ET.

> So taking lemba temperament as an example:
...

I'm not familiar with most of these LT names. They seem to keep
changing. It would be useful if you could give an approximate
generator and period of each one you mention whose name is less than
a decade old.

> You'll run into trouble if the tuning you're using can't be
approximated
> by an MOS/DE scale with 26 notes per octave or less, but I don't
think
> there are many practical scales like that.

No. I'm currently working on the assumption that no LT will require
more than 16 nominals, but these must be chosen from a larger set of
28, or maybe 32. This is so that any given nominal will not vary too
widely in pitch between LTs.

> JI can be notated with the
> standard diatonic scale and accidentals for the commas, if miracle
> notation is inadequate for a particular use. For ennealimmal, just
> notate the 9 periods per octave and use accidentals for the
generators.
>
> There are also some cases where the scale is too symmetrical to
apply
> the standard labeling: take the octatonic scale for instance. Do
you
> label starting with A-B as a semitone or a whole tone?

So octatonic has a generator near 150 cents?

The 28 nominal superset thingy I'm looking into would notate this
with Roman, Hebrew and Greek characters as follows:
O AYIN bet chaf D epsilon phi GAMMA O

> To resolve this
> case, choose the labeling that maximizes the distance between
successive
> copies of the MOS:
>
> C C# EbE F#G A Bb C (12-ET notation)
> A B C D E F G H A (Symmetrical alphabetic notation)
>
> For a generic "standard", I've considered setting the central
pitch to
> one of the following: A=440, C=256, or D=290. But I don't have any
> particular preference for one over any of the others.

Not having absolute pitch, this doesn't bother me too much either,
but I'd lean towards D (the only note guaranteed to be in every LT
notation in my system) having its usual 12-equal pitch of 292.66 Hz,
and because of the way the system works this would put any A or C
close to their usual 12-equal pitches as well.

> Valentine (77.8 cent generator, wedgie <<9, 5, -3, -13, -30, -
21||, map
> [<1, 1, 2, 3|, <0, 9, 5, -3|]) is going to need at least 15.

OK. So we're in agreement (and Carl too) that we won't want to go
beyond 16 nominals for any given LT (although the superset may be
larger).

-- Dave Keenan

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:

> > There are also some cases where the scale is too symmetrical to
> apply
> > the standard labeling: take the octatonic scale for instance. Do
> you
> > label starting with A-B as a semitone or a whole tone?
>
> So octatonic has a generator near 150 cents?

No, it's the 12-equal C C# Eb E F# G A Bb (C).

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> Nominals are one thing. Notating music is another.

I think we're all well aware of that. But we've got the accidentals
licked, and finding new positions to put lines on a page seems a
_lot_ easier than assigning new symbols to them for text, and names
for them in speech, in such a way that the melodic relationships are
easy to remember.

So I thought I tackle the hard stuff first. :-)

At the moment I'm really fond of extending Erv Wilsons lowercase
greek so around each Roman letter from A to G we have the following
transliteral characters in pitch order.

uppercase Greek
lowercase Greek
uppercase Roman
standard Hebrew
final Hebrew

or some approximation thereof.

In the XH3 article Erv Wilson gives one logical way of designing
staves for specific LTs. I like the general principle of making the
line spacing proportional to pitch. This seems an obvious thing to
do. Then the bare staff tells you what temperament you're looking
at. But whether to do like Erv and force all octaves to be the same
by having wide spaces where a note can be at the top or bottom of
the space, is another question.

I look forward to a positive contribution from you on this Paul,
when you have more time.

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
>
> > > There are also some cases where the scale is too symmetrical
to
> > apply
> > > the standard labeling: take the octatonic scale for instance.
Do
> > you
> > > label starting with A-B as a semitone or a whole tone?
> >
> > So octatonic has a generator near 150 cents?
>
> No, it's the 12-equal C C# Eb E F# G A Bb (C).

So what are the generator and period?

Just for some background-I do believe Erv was trying to build on Yasser
notation here, thinking at that time that music might evolve to 31 (as
opposed to yasser's 19)

Dave Keenan wrote:

> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> > Nominals are one thing. Notating music is another.
>
> I think we're all well aware of that. But we've got the accidentals
> licked, and finding new positions to put lines on a page seems a
> _lot_ easier than assigning new symbols to them for text, and names
> for them in speech, in such a way that the melodic relationships are
> easy to remember.
>
> So I thought I tackle the hard stuff first. :-)
>
> At the moment I'm really fond of extending Erv Wilsons lowercase
> greek so around each Roman letter from A to G we have the following
> transliteral characters in pitch order.
>
> uppercase Greek
> lowercase Greek
> uppercase Roman
> standard Hebrew
> final Hebrew
>
> or some approximation thereof.
>
> In the XH3 article Erv Wilson gives one logical way of designing
> staves for specific LTs. I like the general principle of making the
> line spacing proportional to pitch. This seems an obvious thing to
> do. Then the bare staff tells you what temperament you're looking
> at. But whether to do like Erv and force all octaves to be the same
> by having wide spaces where a note can be at the top or bottom of
> the space, is another question.
>
> I look forward to a positive contribution from you on this Paul,
> when you have more time.
>
>
> You can configure your subscription by sending an empty email to one
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-- -Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com
The Wandering Medicine Show
KXLU 88.9 FM WED 8-9PM PST

Are not the finals in Hebrew only visually different in regard to size on
only a few of the letters?
That might make it hard , if one ever got up to this many symbols.
This would be especially good for 22 tone systems , and think of the
peoples name we could spell besides Bach, not to mention correspondences
to the major arcana cards of the tarot deck for others. One more symbol we
could start plotting our DNA!

Dave Keenan wrote:

>
>
> uppercase Greek
> lowercase Greek
> uppercase Roman
> standard Hebrew
> final Hebrew
>
> or some approximation thereof.
>
>

-- -Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com
The Wandering Medicine Show
KXLU 88.9 FM WED 8-9PM PST

--- In tuning@yahoogroups.com, kraig grady <kraiggrady@a...> wrote:
> Are not the finals in Hebrew only visually different in regard to
size on
> only a few of the letters?

That's true, but so far it has been fotuitous that the ones we need
do have finals. And in the case where they don't (alef), I just use
another character (ayin) that has some claim to being transliterated
by the associated roman or greek characters. The finals don't only
differ in size. In general the finals have a descender while the
standard ones don't. See
http://www.njop.org/jsAlephbet/sound_main.html

> That might make it hard , if one ever got up to this many symbols.
> This would be especially good for 22 tone systems , and think of
the
> peoples name we could spell besides Bach,

Unfortunately we don't really get many new sounds this way. But
that's how you know that both alef and alpha are close in pitch to A
etc., whereas if you start interleaving the rest of the Roman
alphabet H to Z between the existing A to G, then you'd have a very
hard time remembering the pitch order.

> not to mention correspondences
> to the major arcana cards of the tarot deck for others.

How does that work?

> One more symbol we
> could start plotting our DNA!

Or playing proteins.

> Dave Keenan wrote:
>
> > uppercase Greek
> > lowercase Greek
> > uppercase Roman
> > standard Hebrew
> > final Hebrew
> >
> > or some approximation thereof.

Not all the Roman letters from A to G need to have all four others
beside them. Some don't need uppercase Greek and some don't need
final Hebrew, for example because E and F are close together and so
are B and C.

Dave Keenan wrote:

>>No, it's the 12-equal C C# Eb E F# G A Bb (C).
> > > So what are the generator and period?

Semitone, minor third.

In the case of the so-called "diminished" temperament (map of periods & generators = [<4, 6, 9, 11|, <0, 1, 1, 1|]), the TOP tuning is 101.4561401 for the generator and 298.5321149 for the period. There are other temperaments that use the octatonic scale, just as there are a number of temperaments with a diatonic scale, but probably not many of them are all that interesting: one of them (known only as "Number 81") has a map of [<4, 6, 9, 11|, <0, 1, 1, 0|], period of the TOP tuning = 303.0961630, and generator = 63.74881402.

Dave Keenan wrote:

> So the above method just makes ABC... correspond to the chain of > generators no matter their size, and would result in no fixed pitch > ordering of the superset and no correspondence whatsoever between > the same letter in different linear temperaments (LTs)?

Right. If I'm looking at a piano roll, I have a pretty good idea of the melodic line, but the harmony is tricky to work out if I'm not using an ET. Labeling the generators in order makes it easier to see what's going on. So it's a pretty good system for what it was intended for, but wouldn't be very good for general-purpose notation.

> I see this as a major advance. But still we don't have much > agreement between LTs, do we? If you were to plot the nominals for > each LT on a pitch line from left to right and then line them all up > vertically, how well would the letters line up?

It depends on how similar the temperaments are. You wouldn't get much agreement between an 8-nominal scale in diminished temperament (g = 101.4561401, p = 298.5321149) and a 10-nominal miracle (g = 116.7206423, p = 1200.631014), but a 7-nominal porcupine (g = 162.3176609, p = 1196.905960) would line up pretty well with a 7-nominal meantone.

> You could do this in ASCII by using 72 positions per line of text > and rounding each nominal's pitch to the nearest degree of 72-ET.

But you'd still have to learn a different set of symbols for each tuning system. And if you use something too fine-grained, like 72-ET, you can't have a set of nominals that's consistent across the useful range of a temperament. A major third in 19-ET is 6/19 = 22.7 steps of 72-ET, but a 12-ET major third is 24 steps. If the temperament you're using isn't consistent with 72-ET, you could end up having to learn two or more different 72-ET intervals corresponding to each one your temperament supports.

>>So taking lemba temperament as an example:
> > ...
> > I'm not familiar with most of these LT names. They seem to keep > changing. It would be useful if you could give an approximate > generator and period of each one you mention whose name is less than > a decade old.

It's pretty close to 26-ET, which is why I use 26-ET notation for it. The TOP tuning is 230.8749260 for the generator and 601.7004928 for the period.

>>Valentine (77.8 cent generator, wedgie <<9, 5, -3, -13, -30, -
> > 21||, map > >>[<1, 1, 2, 3|, <0, 9, 5, -3|]) is going to need at least 15.
> > > OK. So we're in agreement (and Carl too) that we won't want to go > beyond 16 nominals for any given LT (although the superset may be > larger).

I can't think of any off the top of my head, but I haven't exhaustively checked the vast archives of linear temperaments to see if any of them has a smaller generator/period ratio. On the other hand, I can't imagine that one that requires many more than 16 nominals would be of much use.

--- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:
> It depends on how similar the temperaments are. You wouldn't get
much
> agreement between an 8-nominal scale in diminished temperament (g
=
> 101.4561401, p = 298.5321149) and a 10-nominal miracle (g =
116.7206423,
> p = 1200.631014), but a 7-nominal porcupine (g = 162.3176609, p =
> 1196.905960) would line up pretty well with a 7-nominal meantone.

Right. But do you agree that if the superset of nominals is
manageable then it would be nice to have nominals that agreed
substantially across temperaments with different numbers of
nominals? It's just finding the right tradeoff that's tricky. If
we're gonna allow DE cardinalities from 5 to 16 then it seems we
need at least 28 nominals in the superset.

> > You could do this in ASCII by using 72 positions per line of
text
> > and rounding each nominal's pitch to the nearest degree of 72-ET.
>
> But you'd still have to learn a different set of symbols for each
tuning
> system. And if you use something too fine-grained, like 72-ET, you
can't
> have a set of nominals that's consistent across the useful range
of a
> temperament. A major third in 19-ET is 6/19 = 22.7 steps of 72-ET,
but a
> 12-ET major third is 24 steps. If the temperament you're using
isn't
> consistent with 72-ET, you could end up having to learn two or
more
> different 72-ET intervals corresponding to each one your
temperament
> supports.

I agreed with Carl that 72 is too many. I'm now looking at 32
(unequal). The above suggested use of 72 was just for the purpose of
making an ASCII graph that makes good use of the width of a Yahoo
window.

Carl, You may be right that it's no coincidence about 72 being a
good temperament (approximation to JI) and (with 70) a good almost-
LCM for many small divisions of the octave, but I don't see how the
connection works.

It's certainly interesting that the almost-LCM region that I'm
looking at now, the set {27, 28, 30, 32} is in the vicinity of 31.

> On the other hand, I can't imagine
> that one that requires many more than 16 nominals would be of much
use.

Right.

>> >And note that we have so far only considered linear temperaments
>> >where the period is a full octave (or approximation thereof). We
>> >also need to consider the cases where the period is a half-octave
>or
>> >a third of an octave, etc.
>>
>> Why? The temperament maps 2, or it wouldn't have low badness.
>> Isn't this all that matters?
>
>No, Carl -- all of Dave's message previous to this point had assumed
>MOS (in the traditional sense:) rather than DE.

How so?

-C.

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> --- In tuning@yahoogroups.com, kraig grady <kraiggrady@a...> wrote:
> > Are not the finals in Hebrew only visually different in regard to
> size on
> > only a few of the letters?
>
> That's true, but so far it has been fotuitous that the ones we need
> do have finals. And in the case where they don't (alef), I just use
> another character (ayin) that has some claim to being
transliterated
> by the associated roman or greek characters.

They're both silent.

> The finals don't only
> differ in size. In general the finals have a descender while the
> standard ones don't. See
> http://www.njop.org/jsAlephbet/sound_main.html

Click on the letters to hear the sounds (or an annoying voice).

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> >And note that we have so far only considered linear
temperaments
> >> >where the period is a full octave (or approximation thereof).
We
> >> >also need to consider the cases where the period is a half-
octave
> >or
> >> >a third of an octave, etc.
> >>
> >> Why? The temperament maps 2, or it wouldn't have low badness.
> >> Isn't this all that matters?
> >
> >No, Carl -- all of Dave's message previous to this point had
assumed
> >MOS (in the traditional sense:) rather than DE.
>
> How so?

Every bit of it did! Why don't we go over it, sentence by sentence,
after my paper is done.

Dave Keenan wrote:
> Right. But do you agree that if the superset of nominals is > manageable then it would be nice to have nominals that agreed > substantially across temperaments with different numbers of > nominals? It's just finding the right tradeoff that's tricky. If > we're gonna allow DE cardinalities from 5 to 16 then it seems we > need at least 28 nominals in the superset.

Yes, it would be nice to avoid confusion. My 16-ET notation, which I still think is a pretty good notation for mavila (formerly known as pelogic, comma 135;128, map [<1, 2, 1|, <0, -1, 3|]), even though it doesn't agree with my recent thoughts on symmetrical alphabetic notation, is based on a chain of narrow fifths starting on A.

. A E B F
. F C G D

The nice thing about this notation is that most of the thirds, except for D-F, are the same as in meantone notation, but the fifths B-F and D-Ab are different. If you notate mavila like meantone, centered around D, all the major intervals turn to minor and vice versa, but the fifths are the same:

. F C G D
. D A E B

Now, if you had new nominals for the equivalents of F#, C#, Eb, and Bb (say P, Q, X, and Z), you might substitute them for F, C, E, and B:

. P Q G D
. D A X Z

A different set of nominals could support tunings like kleismic (hanson), which tempers out 15625;15552.

. N K
. R D#
. Nb B F#
. Rb D V#
. Bb F K#
. Db V
. N K

But it's hard to imagine a consistent set of rules that would always let you assign nominals to notes in the basic scale of the tuning in all the different cases (even if you just notate the "good" temperaments). And you still need a chart to see the interval relationships between notes.

Maybe another approach would be to use B-E-A-D-G-C-F for fourth-based tunings, E-G-B-D-F-A-C for third-based tunings, and A-B-C-D-E-F-G for second-based tunings. Of course, if your generator is in between the ranges (like semisixths, with a 443-cent generator), this won't be of much help.

>> >> Why? The temperament maps 2, or it wouldn't have low badness.
>> >> Isn't this all that matters?
>> >
>> >No, Carl -- all of Dave's message previous to this point had
>> >assumed MOS (in the traditional sense:) rather than DE.
>>
>> How so?
>
>Every bit of it did! Why don't we go over it, sentence by sentence,
>after my paper is done.

Ok...

-C.

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> > >> >And note that we have so far only considered linear
> temperaments
> > >> >where the period is a full octave (or approximation
thereof).
> We
> > >> >also need to consider the cases where the period is a half-
> octave
> > >or
> > >> >a third of an octave, etc.
> > >>
> > >> Why? The temperament maps 2, or it wouldn't have low badness.
> > >> Isn't this all that matters?
> > >
> > >No, Carl -- all of Dave's message previous to this point had
> assumed
> > >MOS (in the traditional sense:) rather than DE.
> >
> > How so?
>
> Every bit of it did! Why don't we go over it, sentence by
sentence,
> after my paper is done.

I look foward to that (for two reasons). :-)

Carl,

Erv's "fluctuating nominals" diagram (and my extension/alteration of
it) assume the period is an octave. You have to draw another such
diagram for half-octave (twin chain) temperaments and another for
triple-chain etc.

These diagrams have generator size on the vertical axis and (octave-
equivalent) pitch on the horizontal axis. The game is played by
plotting, for every generator-size, the pitches of the nominals you
want in that temperament. So you have to decide what size MOS/DE you
will use for each.

I find it easiest to first plot (as points) the nominals for the
small numbered ETs where every note is a nominal. ETs 2, 3, 4, 5, 6,
7, 8, 9 and maybe 10. Note that some of these appear at more than
one place on the diagram. e.g. 5-ET appears for generator sizes of
1/5 and 2/5 octave. For octave period we only need to look at gens
ranging from 0 to 1/2 octave.

Then I play join the dots to show how the pitches of these nominals
vary smoothly with changing generator size.

Then I look at where the best LTs are and see if their nominals so
far form a Rothenberg-proper set, i.e. if their large gaps are no
more than twice as wide as their small gaps. If not then I look at
the nearby ETs with 10 to 16 notes to see how to add more nominals
in order to give the LT a proper set. In some cases we may prefer to
retain a slightly improper set of nominals rather than use more
nominals. That's what conventional notation does with Pythagorean.

For half-octave period our vertical axis only needs to go from 0 to
1/4 octave and odd numbered ETs won't appear on it at all. It will
have a vertical centerline and the right half will be identical to
the left half.

Drawing one of these diagrams is very educational. I recommend it.

The first stage of some kind of consensus would be to agree on the
form of these diagrams. i.e. Where the lines should actually go. I
suggest we only need to go down to 1/8 octave period. Temperaments
with smaller periods will either have as many nominals as periods in
their octave, or, if this is greater than 16, will need to be dealt
with specially. Fortunately, as the period gets smaller the diagram
gets simpler.

Only after agreeing on where the lines are on all these diagrams, do
we need to consider the thornier question of how the various line
segments should be named. So I've been getting ahead of things
somewhat by this talk of using Greek and Hebrew transliterations of
A thru G.

-- Dave Keenan

>Erv's "fluctuating nominals" diagram (and my extension/alteration of
>it)

Did I miss a graphic?

>assume the period is an octave. You have to draw another such
>diagram for half-octave (twin chain) temperaments and another for
>triple-chain etc.

Yes. What has this got to do with the price of tea in China?

-Carl

Dave Keenan wrote:

> The first stage of some kind of consensus would be to agree on the > form of these diagrams. i.e. Where the lines should actually go. I > suggest we only need to go down to 1/8 octave period. Temperaments > with smaller periods will either have as many nominals as periods in > their octave, or, if this is greater than 16, will need to be dealt > with specially. Fortunately, as the period gets smaller the diagram > gets simpler.

There actually aren't many temperaments with less than 1/8 octave period (probably less than a dozen of any interest). In fact, it doesn't look like there are many useful ones with less than 1/5 octave period; mainly ennealimmal and a few 12-ET based temperaments, plus a few oddballs that haven't seemed to attract much attention (other than the so-called "jamesbond", named after its wedgie <<0, 0, 7, 0, 11, 16||, which has a 1/7 octave period and is close to 14-ET). Hemiennealimmal is one of the very few with more than 16 periods in the octave (18 in that case). If someone really likes it enough to want to use it, 72-ET notation for the 18 periods is an option. Even the 1/5 octave temperaments might best be notated with 5 nominals for the periods and accidentals for the generators.

--- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:
> Yes, it would be nice to avoid confusion. My 16-ET notation, which
I
> still think is a pretty good notation for mavila (formerly known
as
> pelogic, comma 135;128, map [<1, 2, 1|, <0, -1, 3|]), even though
it
> doesn't agree with my recent thoughts on symmetrical alphabetic
> notation, is based on a chain of narrow fifths starting on A.
>
> . A E B F
> . F C G D
>
> The nice thing about this notation is that most of the thirds,
except
> for D-F, are the same as in meantone notation, but the fifths B-F
and
> D-Ab are different. If you notate mavila like meantone, centered
around
> D, all the major intervals turn to minor and vice versa, but the
fifths
> are the same:
>
> . F C G D
> . D A E B

Yes. Both of these "work" in different ways. But wouldn't
the "native" mavila/pelogic notation use 9 nominals?

> Now, if you had new nominals for the equivalents of F#, C#, Eb,
and Bb
> (say P, Q, X, and Z), you might substitute them for F, C, E, and B:
>
> . P Q G D
> . D A X Z

Right. That's where I'd use Hebrew letters fay and chaf for F# and
C# and Greek letters epsilon and beta for Eb and Bb. And change the
staff lines somehow proportionally.

> A different set of nominals could support tunings like kleismic
> (hanson), which tempers out 15625;15552.
>
> . N K
> . R D#
> . Nb B F#
> . Rb D V#
> . Bb F K#
> . Db V
> . N K
>
> But it's hard to imagine a consistent set of rules that would
always let
> you assign nominals to notes in the basic scale of the tuning in
all the
> different cases (even if you just notate the "good" temperaments).

Yes it's hard to imagine. But keep trying. Those diagrams like Ervs
are a wonderful tool for looking at the melodic relationships
between many temperaments at once.

> And
> you still need a chart to see the interval relationships between
notes.
>

I think we have to accept that. I note that this thread isn't about
how best to make temperaments fit a chain-of-fourths-based notation,
but how to notate them using native MOS-based nominals. The interval
relationships for these are neccessarily different from those
between chain-of-fourths nominals.

> Maybe another approach would be to use B-E-A-D-G-C-F for fourth-
based
> tunings,

Yes I'd want to keep that.

> E-G-B-D-F-A-C for third-based tunings,

This really only works for minor third to neutral third generators.
Major thirds are definitely a problem area for notation. Do you use
4 nominals for majic (or whatever its called now) or do you use 13?
A compromise is to use a very improper 10.

> and A-B-C-D-E-F-G for
> second-based tunings.

And this only works for wide neutral seconds to narrow major seconds.

> Of course, if your generator is in between the
> ranges (like semisixths, with a 443-cent generator), this won't be
of
> much help.

Agreed. This is where I'd prefer to introduce new nominal symbols
rather than move A thru G too far from their meantone/12-
ET/Pythagorean positions.

Based on some clues from Kraig Grady and Carl Lumma we can see that
one approach is to have a nominal corresponding to each step of some
good high-limit ET having a manageable number of notes and having
fifths in the meantone-12-ET-pythagorean range. Since 72 is too many
then 31 seems a good choice. To avoid, for now, the problem of what
symbols to use for these, we can temporarily use pairs of ASCII
characters where we put a pseudo-accidental _before_ a letter A thru
G. Any real accidentals can come after, as usual.

So we can write the nominals temporarily as: A ^A #A bB vB B ^B vC C
etc,
read as: A, half-sharp-A, sharp-A, flat-B, half-flat-B, B, half-
sharp-B, half-flat-C, C etc.

It might make sense to put their central positions not at steps of
31-ET, but at Canasta positions (31-of-Miracle) where the generator
is 7/72 octave.

-- Dave Keenan

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >Erv's "fluctuating nominals" diagram (and my extension/alteration
of
> >it)
>
> Did I miss a graphic?

Have you seen page 5 of

http://www.anaphoria.com/xen3a.PDF

?

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >Erv's "fluctuating nominals" diagram (and my extension/alteration
of
> >it)
>
> Did I miss a graphic?

Maybe so. Sthe post that started this thread.
/tuning/topicId_53851.html#53930

> >assume the period is an octave. You have to draw another such
> >diagram for half-octave (twin chain) temperaments and another for
> >triple-chain etc.
>
> Yes. What has this got to do with the price of tea in China?

Are we having miscommunication problems again already?

Perhaps confusion has been caused by my use of the royal "we",
meaning "the reader and I", when I wrote:

"And note that we have so far only considered linear temperaments
where the period is a full octave (or approximation thereof). We
also need to consider the cases where the period is a half-octave or
a third of an octave, etc."

And by "so far" I meant "so far, in this message".

Does that clear it up?

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> --- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:
> > Yes, it would be nice to avoid confusion. My 16-ET notation,
which
> I
> > still think is a pretty good notation for mavila (formerly known
> as
> > pelogic, comma 135;128, map [<1, 2, 1|, <0, -1, 3|]), even though
> it
> > doesn't agree with my recent thoughts on symmetrical alphabetic
> > notation, is based on a chain of narrow fifths starting on A.
> >
> > . A E B F
> > . F C G D
> >
> > The nice thing about this notation is that most of the thirds,
> except
> > for D-F, are the same as in meantone notation, but the fifths B-F
> and
> > D-Ab are different. If you notate mavila like meantone, centered
> around
> > D, all the major intervals turn to minor and vice versa, but the
> fifths
> > are the same:
> >
> > . F C G D
> > . D A E B
>
> Yes. Both of these "work" in different ways. But wouldn't
> the "native" mavila/pelogic notation use 9 nominals?

On page 6 of

http://www.anaphoria.com/meantone-mavila.PDF

it looks like meta-meantone is closer to the 12-equal line than to
the 7-equal line. Meanwhile, meta-mavila is equally close to the 9-
equal line and the 7-equal line. So if you can use 7 nominals to
notate the former, surely you can use 7 nominals to notate the
latter . . .

>> >Erv's "fluctuating nominals" diagram (and my
>> >extension/alteration of it)
>>
>> Did I miss a graphic?
>
>Have you seen page 5 of
>
>http://www.anaphoria.com/xen3a.PDF

It's Dave's extension/alteration that I'm missing.

-Carl

>> >Erv's "fluctuating nominals" diagram (and my extension/alteration
>> >of it)
>>
>> Did I miss a graphic?
>
>Maybe so. Sthe post that started this thread.
>/tuning/topicId_53851.html#53930

You mention that you extended it, then say...

"Unfortunately the only graph paper I had at the time was already
used and so the resulting palimpsest (some would say ratsnest) is
unfortunately unsuitable for anyone but me to follow. And even I am
having trouble a few months down the track. In any case, I'd like to
see what others come up with when they try this (without being
influenced by my version)."

...and then give a bunch of suggestions, which I replied to.

>> >assume the period is an octave. You have to draw another such
>> >diagram for half-octave (twin chain) temperaments and another
>> >for triple-chain etc.
>>
>> Yes. What has this got to do with the price of tea in China?
>
>Are we having miscommunication problems again already?

Miscommunication problems sound like a good thing. :)

-Carl

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> > Yes. Both of these "work" in different ways. But wouldn't
> > the "native" mavila/pelogic notation use 9 nominals?
>
> On page 6 of
>
> http://www.anaphoria.com/meantone-mavila.PDF
>
> it looks like meta-meantone is closer to the 12-equal line than to
> the 7-equal line. Meanwhile, meta-mavila is equally close to the 9-
> equal line and the 7-equal line. So if you can use 7 nominals to
> notate the former, surely you can use 7 nominals to notate the
> latter . . .

Agreed. I wasn't sure of the exact position. You could use either 7
or 9 and I guess 7 wins because it's closer to the magic number for
humans, and because of real-world pelog.

No, wait. 7 wins because 9 becomes improper if you drop below a 7/16
oct generator and such generators can certainly still be considered
pelogic/meta-mavila.

This is exactly the kind of stuff we should nut out between us until
we have the whole LT continuum mapped for nominals.

How come you're calling this mavila when Erv called it meta-mavila?
This imples that Erv alreday used "mavila" for something else.

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> It's Dave's extension/alteration that I'm missing.

You asked for it!

/tuning/files/Keenan/Nomina
lsOctavePeriod.jpg

> Miscommunication problems sound like a good thing. :)

Ah! The double negative. Yes. :-)

>>It's Dave's extension/alteration that I'm missing.
>
>You asked for it!
>
>/tuning/files/Keenan/Nomina
>lsOctavePeriod.jpg

Aha, I understand what you meant now!

By the way, are you familiar with Erv's article, "Straight Line
Patterns of the Scale Tree"?

-Carl

--- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:
> Dave Keenan wrote:
>
> > The first stage of some kind of consensus would be to agree on the
> > form of these diagrams. i.e. Where the lines should actually go. I
> > suggest we only need to go down to 1/8 octave period. Temperaments
> > with smaller periods will either have as many nominals as periods in
> > their octave, or, if this is greater than 16, will need to be dealt
> > with specially. Fortunately, as the period gets smaller the diagram
> > gets simpler.
>
> There actually aren't many temperaments with less than 1/8 octave
period
> (probably less than a dozen of any interest). In fact, it doesn't
look
> like there are many useful ones with less than 1/5 octave period;
mainly
> ennealimmal and a few 12-ET based temperaments, plus a few oddballs
that
> haven't seemed to attract much attention (other than the so-called
> "jamesbond", named after its wedgie <<0, 0, 7, 0, 11, 16||, which has a
> 1/7 octave period and is close to 14-ET). Hemiennealimmal is one of the
> very few with more than 16 periods in the octave (18 in that case). If
> someone really likes it enough to want to use it, 72-ET notation for
the
> 18 periods is an option. Even the 1/5 octave temperaments might best be
> notated with 5 nominals for the periods and accidentals for the
generators.

Good point Herman. So we really only need to look at 4 of these diagrams.

Octave period with 5 to 16 nominals (pref max 10)
1/2 oct period with 3 to 8 nominals per chain (pref max 5)
1/3 oct period with 2 to 5 nominals per chain (pref max 3)
1/4 oct period with 2 to 4 nominals per chain (pref max 2)

and if we really want to
1/5 oct period with 1 to 3 nominals per chain (pref max 2)

By the way Carl,

You mentioned preferring a max of 9 nominals, and I tend to agree, but
miracle (minor seconds) and
twintone/paultone/pajara/whatever-it's-called-now (twin
narrow-fourths) pretty much demand 10, right?

Talking of twin narrow-fourths (2xn4 ?), Paul does this thing where he
has the nominal symbols for one chain being the upside down (rot180?)
version of the symbols on the first chain.

Paul,

how do you typeset these and how do you pronounce them?

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> By the way, are you familiar with Erv's article, "Straight Line
> Patterns of the Scale Tree"?

I wasn't, but I am now.

http://www.anaphoria.com/line.PDF

Yes. That's the same kind of diagram (again assuming the period is a
whole octave). There are a potential infinity of lines that can be
drawn on these diagrams. The question is which ones do we want to
represent nominals?

>You mentioned preferring a max of 9 nominals, and I tend to agree, but
>miracle (minor seconds) and twintone/paultone/pajara pretty much
>demand 10, right?

Yep.

-Carl

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> Major thirds are definitely a problem area for notation. Do you use
> 4 nominals for majic (or whatever its called now) or do you use 13?
> A compromise is to use a very improper 10.

Actually, I think that even 13 nominals is improper for any kind of
optimal majic temperament (major thirds). I think you have to go to 16
nominal to get proper.

The most difficult single-chain LTs to notate with native nominals are
those with generators near 0, 1/4, 1/3, 1/2 octave, since 1, 2, 3 and
4 are too few nominals and the only available alternatives are either
too large or very improper, or both.

Assuming we'd like no more than 10 nominals, the bad ranges are:

0 to 1/11 oct, 0 to 109 c
3/13 to 3/11 oct, 277 to 327 c
4/13 to 4/11 oct, 369 to 436 c
5/11 to 1/2 oct, 545 to 600 c

Kleismic/hanson/keenan/whatever (minor thirds) is just inside the
second range (and so might make do with an improper 7). Majic/whatever
(major thirds) is near the middle of the third range.

For twin chain LTs I think the danger zones are just
0 to 1/11 oct, 0 to 109 c
3/13 to 1/4 oct, 277 to 300 c

For triple and quadruple chains it's just
0 to 1/11 oct, 0 to 109 c

and after that the problem goes away since one nominal per chain is
acceptable when we have 5 or more chains.

So, what good LTs fall in these ranges?

-- Dave Keenan

>Actually, I think that even 13 nominals is improper for any kind of
>optimal majic temperament (major thirds).

Question 1: Can you quantify exactly what is lost by basing a
notation on a non-MOS? I imagine that more than one accidental
pair is then required in many situations. . .

Question 2: Can you quantify exactly what is lost by basing a
notation on an improper MOS? I imagine it introduces anomalies
such as B being higher than C in certain situations. . .

-Carl

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> > --- In tuning@yahoogroups.com, kraig grady <kraiggrady@a...> wrote:
> > > Are not the finals in Hebrew only visually different in regard to
> > size on
> > > only a few of the letters?
> >
> > That's true, but so far it has been fotuitous that the ones we need
> > do have finals. And in the case where they don't (alef), I just use
> > another character (ayin) that has some claim to being
> transliterated
> > by the associated roman or greek characters.
>
> They're both silent.

Yes. What's your point?

This isn't a mistake on the part of the web page designer. When read
in text both of these characters are either silent or take on any of a
large number of different vowel sounds. No one knows for sure what
they were for in ancient Hebrew. As you probably know, spoken Hebrew
is a language that died, and was reinvented from its writing, which
recorded very little information about vowel sounds. Modern Hebrew
uses these two characters for this purpose and puts dots in various
places near them to tell you which sound.

But it's very clear that Hebrew alef and Greek alpha have an
evolutionary connection, and it makes sense to me to use ayin if we
need a second Hebrew character to associate with A, since alef and
ayin are the only such "silent" characters in the alefbet, and they
are the only ones whose English names both start with "a".

-- Dave Keenan

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >Actually, I think that even 13 nominals is improper for any kind of
> >optimal majic temperament (major thirds).
>
> Question 1: Can you quantify exactly what is lost by basing a
> notation on a non-MOS? I imagine that more than one accidental
> pair is then required in many situations. . .
>
> Question 2: Can you quantify exactly what is lost by basing a
> notation on an improper MOS? I imagine it introduces anomalies
> such as B being higher than C in certain situations. . .
>
> -Carl

These are excellent questions. I think I'm going to have to go and
ponder them in the bath.

But I can say that multiple pairs of accidentals isn't a problem to
me. I prefer this to having multiple accidentals against a single
note. And with Sagital there's no shortage.

I assume for question 1 that you would want the non-MOS to at least be
contiguous on the chain(s) of generators. Would you also want the
non-MOS to be proper (like that one you found in the minor thirds
temperament)?

For Q2, It doesn't need to introduce such anomalies, that's an
independent choice. But I feel it loses more, the more improper it is.
A little bit of impropriety seems ok, particularly if it lets you
avoid going to a larger (or in some cases smaller) MOS or a non-MOS,
but I think I'd draw the line at having one gap between nominals being
3 times as wide as another.

But I'll have to get back to you with more. Or wait for someone else
to answer these.

Dave Keenan wrote:

> Actually, I think that even 13 nominals is improper for any kind of
> optimal majic temperament (major thirds). I think you have to go to 16
> nominal to get proper.

Is majic the same as magic (19&22&41)? I don't know if 16 is proper, but it doesn't make much sense with less than 19 notes. The only way to make that digestible is to use a hybrid notation. The most obvious in this case is to notate the core 19 notes using a meantone notation, and use some other comma symbol for the rest.

In practice, that means notating a planar temperament. I don't know if the planar temperament itself is of interest. You'd have to avoid mis-spelled chords.

Graham

Herman Miller wrote:

> There actually aren't many temperaments with less than 1/8 octave period > (probably less than a dozen of any interest). In fact, it doesn't look > like there are many useful ones with less than 1/5 octave period; mainly > ennealimmal and a few 12-ET based temperaments, plus a few oddballs that > haven't seemed to attract much attention (other than the so-called > "jamesbond", named after its wedgie <<0, 0, 7, 0, 11, 16||, which has a > 1/7 octave period and is close to 14-ET). Hemiennealimmal is one of the > very few with more than 16 periods in the octave (18 in that case). If > someone really likes it enough to want to use it, 72-ET notation for the > 18 periods is an option. Even the 1/5 octave temperaments might best be > notated with 5 nominals for the periods and accidentals for the generators.

There's Mystery as well -- 29 equal divisions of the octave. The higher limit searches throw up more of the same. There's one with 31, and another with 41 equal divisions. I don't know if anybody would want to use such a complex temperament, but as we haven't known about them for long I wouldn't like to rule it out either. Even at lower limits, there may be melodic reasons for using such linear temperaments.

But I don't think you would use more than 10 nominals for any of these. Mystery would work fine with the 29 notes as Pythagorean.

Graham

Erv is having some fun here with the 13 tone scale which is why i think he
drew it out. that b is higher that c, e higher than f Etc. He is quite
aware how much this messes with the mind. In the end though i think he
expects us to 'deal with it"

wallyesterpaulrus wrote:

> --- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> > >Erv's "fluctuating nominals" diagram (and my extension/alteration
> of
> > >it)
> >
> > Did I miss a graphic?
>
> Have you seen page 5 of
>
> http://www.anaphoria.com/xen3a.PDF
>
> ?
>
>
>

-- -Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com
The Wandering Medicine Show
KXLU 88.9 FM WED 8-9PM PST

Mavila refers to the tuning that Hugh Tracy collected in the Chopi Village
of that name. He uses meta with pelog and slendro also making the
assumption that one cannot wholly grasp the tuning of another culture as
to exactly how they hear it. The meta- being what he hears or as close as
he can imagine ( at that particular time)

Dave Keenan wrote:

>
>
> How come you're calling this mavila when Erv called it meta-mavila?
> This imples that Erv alreday used "mavila" for something else.
>
>
>

-- -Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com
The Wandering Medicine Show
KXLU 88.9 FM WED 8-9PM PST

--- In tuning@yahoogroups.com, Graham Breed <graham@m...> wrote:
> Dave Keenan wrote:
>
> > Actually, I think that even 13 nominals is improper for any kind
of
> > optimal majic temperament (major thirds). I think you have to go
to 16
> > nominal to get proper.
>
> Is majic the same as magic (19&22&41)?

Yeah. I'm pretty sure I saw it called "majic" somewhere (for MAJor
thirds).

> I don't know if 16 is proper,

Probably depends on the specific choice of generator.

> but it doesn't make much sense with less than 19 notes. The only
way to
> make that digestible is to use a hybrid notation. The most
obvious in
> this case is to notate the core 19 notes using a meantone
notation, and
> use some other comma symbol for the rest.
>
> In practice, that means notating a planar temperament. I don't
know if
> the planar temperament itself is of interest. You'd have to avoid
> mis-spelled chords.

OK. That's a reasonable approach. So this says to me that, for this
thread, we should just ignore those "danger zones" where you need
more than 10 notes to get a proper MOS with more than 4 notes. We
can just assume they will be dealt with by other means.

--- In tuning@yahoogroups.com, Graham Breed <graham@m...> wrote:

> There's Mystery as well -- 29 equal divisions of the octave. The
higher
> limit searches throw up more of the same. There's one with 31, and
> another with 41 equal divisions. I don't know if anybody would
want to
> use such a complex temperament, but as we haven't known about them
for
> long I wouldn't like to rule it out either.

Going up to higher complexities will tend to result in more and more
of these. Equal temperaments which are composite numbers will produce
these, and as numbers get bigger, the percentage of them which are
primes shrinks to 0. We can find lots of examples using period
mappings derived from composite equal temperaments; for instance from
171 we can get

[18, 27, 18, 1, -22, -34]
[[9, 15, 22, 26], [0, -2, -3, -2]]
27 .036378 4.918774

[19, 19, 57, -14, 37, 79]
[[19, 30, 44, 53], [0, 1, 1, 3]]
57 .046052 18.984647

[45, -18, 45, -133, -55, 155]
[[9, 14, 21, 25], [0, 5, -2, 5]]
63 .074136 96.827098

[27, -45, 27, -134, -33, 189]
[[9, 13, 23, 24], [0, 3, -5, 3]]
72 .073107 96.924270

[9, -72, 9, -135, -11, 223]
[[9, 14, 23, 25], [0, 1, -8, 1]]
81 .072392 97.414263

[76, 76, 57, -56, -123, -81]
[[19, 31, 45, 54], [0, -4, -4, -3]]
76 .045310 104.179739

[63, 9, 63, -132, -77, 121]
[[9, 15, 21, 26], [0, -7, -1, -7]]
63 .068943 108.926366

[38, 38, -57, -28, -197, -239]
[[19, 31, 45, 52], [0, -2, -2, 3]]
95 .073774 144.611673

[81, 36, 81, -131, -99, 87]
[[9, 10, 19, 21], [0, 9, 4, 9]]
81 .055913 146.030968

[72, -63, 72, -267, -88, 344]
[[9, 13, 22, 24], [0, 8, -7, 8]]
135 .073571 387.251997

A more highly composite number such as 270 or 612 should do even
better.

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
> > > Yes. Both of these "work" in different ways. But wouldn't
> > > the "native" mavila/pelogic notation use 9 nominals?
> >
> > On page 6 of
> >
> > http://www.anaphoria.com/meantone-mavila.PDF
> >
> > it looks like meta-meantone is closer to the 12-equal line than
to
> > the 7-equal line. Meanwhile, meta-mavila is equally close to the
9-
> > equal line and the 7-equal line. So if you can use 7 nominals to
> > notate the former, surely you can use 7 nominals to notate the
> > latter . . .
>
> Agreed. I wasn't sure of the exact position. You could use either 7
> or 9 and I guess 7 wins because it's closer to the magic number for
> humans, and because of real-world pelog.
>
> No, wait. 7 wins because 9 becomes improper if you drop below a
7/16
> oct generator and such generators can certainly still be considered
> pelogic/meta-mavila.

I don't get it. Surely you're not proposing that an improper-7
system, like Pythagorean, should be notated with something other than
7 nominals?

> This is exactly the kind of stuff we should nut out between us
until
> we have the whole LT continuum mapped for nominals.
>
> How come you're calling this mavila when Erv called it meta-mavila?

Not quite. How come everyone calls the other one meantone when Erv
called it meta-meantone? It's not like that. Erv was focusing here on
a particular tuning strategy, which is what the "meta-" part
signifies, while the other part of the name is the temperament in
general.

> This imples that Erv alreday used "mavila" for something else.

Much as he used "meantone".

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:

> You mentioned preferring a max of 9 nominals, and I tend to agree,
but
> miracle (minor seconds) and
> twintone/paultone/pajara/whatever-it's-called-now (twin
> narrow-fourths) pretty much demand 10, right?
>
> Talking of twin narrow-fourths (2xn4 ?),

??

> Paul does this thing where he
> has the nominal symbols for one chain being the upside down >
(rot180?)

Whichever is distinguishable.

> version of the symbols on the first chain.

I've never done this for "twintone/paultone/pajara/whatever-it's-
called-now (twin narrow-fourths)". I've done it for injera (what you
might call twin wide-fourths), though, with 14 nominals. The 7
diatonic notes and their half-octave mirrors.

> Paul,
>
> how do you typeset these

Paint :)

> and how do you pronounce them?

anti-A, anti-B, etc.

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> --- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> > By the way, are you familiar with Erv's article, "Straight Line
> > Patterns of the Scale Tree"?
>
> I wasn't, but I am now.
>
> http://www.anaphoria.com/line.PDF
>
> Yes. That's the same kind of diagram (again assuming the period is a
> whole octave). There are a potential infinity of lines that can be
> drawn on these diagrams. The question is which ones do we want to
> represent nominals?

You might find this diagram relevant, or at least curious, as well:

http://www.bikexprt.com/tunings/tunings3.htm

--- In tuning@yahoogroups.com, "Carl Lumma" <ekin@l...> wrote:
> > "Dave Keenan" <d.keenan@b...> wrote:
> > See http://dkeenan.com/sagittal/
> >
> > A few items will not be up for another few days. But there's
> > definitely enough there to make a visit worthwhile, and no
> > reason to delay the announcement further.
>
> AWESOME!!!
>
> I can't wait to read it.

Thanks -- and there will be more to come!

> And George, I can't believe you were sitting on those
> recordings since 1976!

They were released in 1976 as part of a 30-minute cassette demo tape
promoting the Motorola Scalatron.

> Is the Scalatron multi-timbral?

Yes. The 5-octave keyboard can be split into two 2.5-octave halves
with separate timbres and enveloping (but with the same tuning).
Actually, even without the keyboard split the instrument is still
multi-timbral: it's possible to have separate voices in the left and
right channels (controlled by separate volume pedals) or,
alternatively, separate voices in the left and right channels
controlled by the same volume pedal and a third voice in a center
channel (or fed equally into left & right channels) controlled by the
other volume pedal. (In all there are 5 voice groups, including 2
divisions of organ stops, which may be routed separately into the 3
channels.) Thus it's possible to fade voices in and out without
using the hands (or, with only a single voice in the center channel,
to pan from left to right, as I did in the Ivor Darreg 19-tone piece
that plays on the Sagittal homepage).

If you have 11.7 MB available on your website for a few days (so
everyone can listen), I'll send you an mp3 file of that 12.5-minute
JI improvisation I did in 1978 (which I mentioned on mmm a couple
weeks ago) that will illustrate this.

> Or was baroque improv.
> multi-tracked?

No. Only the Partch Greek studies for harmonic canon 2 and bass
marimba (which play during episodes 1 and 2) were multi-tracked (and
only #1 was on the demo tape, because I wasn't very happy with #2),
but everything else I recorded on the Scalatron was in real time, in
a single pass. I'm in the process of making midi files of those two
Partch studies, which will be replacing the Scalatron mp3 files on
the Sagittal website (to save space), so if you want copies of those
mp3 files, get them now, while you can.

--George

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >Actually, I think that even 13 nominals is improper for any kind of
> >optimal majic temperament (major thirds).
>
> Question 1: Can you quantify exactly what is lost by basing a
> notation on a non-MOS?

It can also be based on a DE or even an ET. If none of these, you're
looking at a total mess.

> Question 2: Can you quantify exactly what is lost by basing a
> notation on an improper MOS? I imagine it introduces anomalies
> such as B being higher than C in certain situations. . .

Pythagorean notation is based on an improper MOS, and there's
absolutely nothing wrong or lost. B is higher than C if your notation
is based on an out-of-order scale.

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:

> When read
> in text both of these characters are either silent or take on any
of a
> large number of different vowel sounds. No one knows for sure what
> they were for in ancient Hebrew. As you probably know, spoken Hebrew
> is a language that died, and was reinvented from its writing, which
> recorded very little information about vowel sounds.

You seem to be misinformed. There were only small differences in how
the vowels were pronounced by Hebrew speakers who had lost contact
with one another for 2000 years. For example, one vowel was
pronounced "o" by the Ashkenazis, and "a" by the Sephardics, but the
rest pretty much agree. While the vowel symbols are most often
omitted, they (as well as other symbols that indicate musical
effects) are present in the Bible, for example.

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:
>
> ... Only the Partch Greek studies for harmonic canon 2 and bass
> marimba (which play during episodes 1 and 2) were multi-tracked
(and
> only #1 was on the demo tape, because I wasn't very happy with #2),

When I meant was that I wasn't very happy with *the way I played*
#2. It's working out a lot better as a midi file, now that I'm
taking care to work on the expression in each part.

--George

--- In tuning@yahoogroups.com, Graham Breed <graham@m...> wrote:
> Dave Keenan wrote:
>
> > Actually, I think that even 13 nominals is improper for any kind
of
> > optimal majic temperament (major thirds). I think you have to go
to 16
> > nominal to get proper.
>
> Is majic the same as magic (19&22&41)? I don't know if 16 is
proper,
> but it doesn't make much sense with less than 19 notes. The only
way to
> make that digestible is to use a hybrid notation. The most obvious
in
> this case is to notate the core 19 notes using a meantone notation,
and
> use some other comma symbol for the rest.
>
> In practice, that means notating a planar temperament. I don't
know if
> the planar temperament itself is of interest. You'd have to avoid
> mis-spelled chords.
>
>
> Graham

Certainly if you're willing to use meantone notation for this 19, you
should be willing to use it for a 19-equal chain, which means you
have a way of notating enneadecal temperaments (just add an up
accidental and a down accidental relative to this chain). Correct me
if I'm wrong, Dave, but aren't you already using this basic idea to
notate 36, 48, 60, 72, 84??

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
>
> > Even if you aren't particularly interested in a universal
microtonal
> > notation system, I think you will enjoy the story of its
creation.
> ...
> Hermes, I think most people here are tolerant enough that you could
> have come out of the Olympian closet before now. However, there are
a
> few people you should be wary of, so take care.

Thanks for the warning, Gene, and I'll pass the word on to Zeus, now
that he's expressed an interest in surfing the net.

--"George"

I thought it meant the same thing as in "meta-meantone". I thought
the "meta" referred to the particular tuning scheme which, in the
limit, brings such features as coinciding difference tones and
synchronized beats. Certainly the "meta-meantone and meta-mavila"
article concerns itself with this for both temperaments.

--- In tuning@yahoogroups.com, kraig grady <kraiggrady@a...> wrote:
> Mavila refers to the tuning that Hugh Tracy collected in the Chopi
Village
> of that name. He uses meta with pelog and slendro also making the
> assumption that one cannot wholly grasp the tuning of another
culture as
> to exactly how they hear it. The meta- being what he hears or as
close as
> he can imagine ( at that particular time)
>
> Dave Keenan wrote:
>
> >
> >
> > How come you're calling this mavila when Erv called it meta-
mavila?
> > This imples that Erv alreday used "mavila" for something else.
> >
> >
> >
>
> -- -Kraig Grady
> North American Embassy of Anaphoria Island
> http://www.anaphoria.com
> The Wandering Medicine Show
> KXLU 88.9 FM WED 8-9PM PST

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> --- In tuning@yahoogroups.com, Graham Breed <graham@m...> wrote:
> > Dave Keenan wrote:
> >
> > > Actually, I think that even 13 nominals is improper for any
kind
> of
> > > optimal majic temperament (major thirds). I think you have to
go
> to 16
> > > nominal to get proper.
> >
> > Is majic the same as magic (19&22&41)?
>
> Yeah. I'm pretty sure I saw it called "majic" somewhere (for MAJor
> thirds).

You were the one who came up with the idea of spelling it "majic", as
a tuning-math search reveals.

Apparently, it didn't catch on.

--- In tuning@yahoogroups.com, "Carl Lumma" <ekin@l...> wrote:
> Some comments on the first part of The Gift of the Gods...
>
> > Once the harmonic resources of 12-ET were exhausted (by
> > around 1920),
>
> Is this true? Where do you establish it? If not
> established, does it help or hinder the article?

In the 1950s Henry Pleasants wrote a highly controversial book, _The
Agony of Modern Music_, in which he made a very persuasive case for
the irrelevance of 20th-century "serious music." He placed the
breakdown of harmony somewhere around the 2nd decade of that century,
as evidenced by the emergence of new techniques that completely
discarded existing harmonic norms. Though he conceded that it might
yet be possible to discover some novel harmonic device that
maintained a link with the old order, its novelty would only be short-
lived, and the harmony crisis would then be re-established.

> > the university musical establishment now generally
> > considers any efforts to create music using alternate
> > tunings a complete waste of time,
>
> Again, is this true?

Observing that I used the word "generally" (not "universally"), this
is the impression I got from observations made by others on this list
over the past couple of years, which were allowed to stand
unchallenged.

I will be happy to correct either of these statements if they are
inaccurate or misleading (and that goes for anything else in the
introduction).

--George

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> ...
> BTW, Dave and George, I took a quick peek. Margo usually puts the
> beginning of the meantone era at 1470 or 1480. Are you sure you
want
> to say "17th century"?

I can't find anything about the 17th century. Are you referring to
this sentence?

<< This practice eventually resulted in the general adoption of the
_meantone temperament_ in most of Europe by the 16th century. >>

I was referring to the general adoption of meantone as the tuning
commonly in use, not its first appearance on the scene. Even with a
much earlier date, the statement would still hold.

--George

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
> > ...
> > BTW, Dave and George, I took a quick peek. Margo usually puts the
> > beginning of the meantone era at 1470 or 1480. Are you sure you
> want
> > to say "17th century"?
>
> I can't find anything about the 17th century. Are you referring to
> this sentence?
>
> << This practice eventually resulted in the general adoption of
the
> _meantone temperament_ in most of Europe by the 16th century. >>

You can't find it because Dave has already replied to me and changed
the text on the Sagittal site from "17th century" to "16th century",
as well as some of the surrounding text.

> I was referring to the general adoption of meantone as the tuning
> commonly in use, not its first appearance on the scene. Even with
a
> much earlier date, the statement would still hold.

It's not the statement that was there when I wrote my comment.

>> >Actually, I think that even 13 nominals is improper for any kind of
>> >optimal majic temperament (major thirds).
>>
>> Question 1: Can you quantify exactly what is lost by basing a
>> notation on a non-MOS? I imagine that more than one accidental
>> pair is then required in many situations. . .
>>
>> Question 2: Can you quantify exactly what is lost by basing a
>> notation on an improper MOS? I imagine it introduces anomalies
>> such as B being higher than C in certain situations. . .
>
>These are excellent questions. I think I'm going to have to go and
>ponder them in the bath.

Ah, that takes me back. My apartment has only a stand-up shower!
:(

>But I can say that multiple pairs of accidentals isn't a problem to
>me. I prefer this to having multiple accidentals against a single
>note. And with Sagital there's no shortage.

Noted. [Pun intended.]

>I assume for question 1 that you would want the non-MOS to at
>least be contiguous on the chain(s) of generators.

You may so assume.

>Would you also want the non-MOS to be proper (like that one
>you found in the minor thirds temperament)?

Sure, let's not bite off too big a chew. Besides, Q2 should take
care of impropriety... I don't foresee combination effects.

>For Q2, It doesn't need to introduce such anomalies, that's an
>independent choice.

[sound of gears turning]

-Carl

>OK. That's a reasonable approach. So this says to me that, for this
>thread, we should just ignore those "danger zones" where you need
>more than 10 notes to get a proper MOS with more than 4 notes. We
>can just assume they will be dealt with by other means.

That's the idea...

-Carl

>If you have 11.7 MB available on your website for a few days (so
>everyone can listen), I'll send you an mp3 file of that 12.5-minute
>JI improvisation I did in 1978 (which I mentioned on mmm a couple
>weeks ago) that will illustrate this.

I have the space and am happy to host it, but now that my provider
has canceled anonymous ftp support there's no good way for you to
get it to me. Hey wait: send it to me at clumma at yahoo.com.

FYI, though, here's something I sent to Dave off-list re. the
Sagittal site:

>I don't know if you know, but hosting space is very affordable
>these days...
>
>http://www.geekhosting.com
>
>...I was certainly shocked. This company is one of many, but was
>recommended to me by a friend, and I had an online chat with their
>support dept. and they seem to be on the ball. I'm actually
>planning to switch over to them in the next few weeks myself, from
>my costly, anonftp-retracting provider of many years.

-Carl

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> > --- In tuning@yahoogroups.com, Graham Breed <graham@m...> wrote:
> > > Dave Keenan wrote:
> > >
> > > > Actually, I think that even 13 nominals is improper for any
> kind
> > of
> > > > optimal majic temperament (major thirds). I think you have
to
> go
> > to 16
> > > > nominal to get proper.
> > >
> > > Is majic the same as magic (19&22&41)?
> >
> > Yeah. I'm pretty sure I saw it called "majic" somewhere (for
MAJor
> > thirds).
>
> You were the one who came up with the idea of spelling it "majic",
as
> a tuning-math search reveals.

How embarrassing. Must be the alzheimers. ;-)

> Apparently, it didn't catch on.

Apparently.

Since I've been giving you a hard time lately about renaming things,
I should say, "touche". :-)

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
> > Agreed. I wasn't sure of the exact position. You could use
either 7
> > or 9 and I guess 7 wins because it's closer to the magic number
for
> > humans, and because of real-world pelog.
> >
> > No, wait. 7 wins because 9 becomes improper if you drop below a
> 7/16
> > oct generator and such generators can certainly still be
considered
> > pelogic/meta-mavila.
>
> I don't get it. Surely you're not proposing that an improper-7
> system, like Pythagorean, should be notated with something other
than
> 7 nominals?

No. Because the other options are 5 or 12.

So which do you think is preferable for mavila, 7 or 9? And why?

> Not quite. How come everyone calls the other one meantone when Erv
> called it meta-meantone? It's not like that. Erv was focusing here
on
> a particular tuning strategy, which is what the "meta-" part
> signifies, while the other part of the name is the temperament in
> general.

Thanks for explaining that.

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> You seem to be misinformed.

Maybe so.

Now that I do a Google search on "Hebrew dead language" it seems
that there is an enormous amount of disagreement this question. But
fortunately it doesn't seem relevant to the idea of using ayin after
alef if I need a second Hebrew character to group with A and alpha.

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> Certainly if you're willing to use meantone notation for this 19,
you
> should be willing to use it for a 19-equal chain, which means you
> have a way of notating enneadecal temperaments (just add an up
> accidental and a down accidental relative to this chain). Correct
me
> if I'm wrong, Dave, but aren't you already using this basic idea
to
> notate 36, 48, 60, 72, 84??

I'm not sure which "basic idea" is being referred to here, but
certainly these are all notated by comma inflections from 7 nominals
in a chain of the temperament's best fifths.

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> >I don't know if you know, but hosting space is very affordable
> >these days...
> >
> >http://www.geekhosting.com
> >
> >...I was certainly shocked. This company is one of many, but was
> >recommended to me by a friend, and I had an online chat with their
> >support dept. and they seem to be on the ball. I'm actually
> >planning to switch over to them in the next few weeks myself, from
> >my costly, anonftp-retracting provider of many years.

Way more expensive than my xenharmony web host, which was why I was
unimpressed with McL's argument that money should be charged for
music up on the web. The expense is hardly worth discussing.

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:

> In the 1950s Henry Pleasants wrote a highly controversial book,
_The
> Agony of Modern Music_, in which he made a very persuasive case for
> the irrelevance of 20th-century "serious music." He placed the
> breakdown of harmony somewhere around the 2nd decade of that
century,
> as evidenced by the emergence of new techniques that completely
> discarded existing harmonic norms.

So Shostakovich spent his whole life being irrelevant? Poor fella.

The second decade of the 20th century is way to early to start
kvetching about the death of classical music. Camille Saint-Saens
died in that decade, for gosh sakes, and was composing music right up
to the end not much different than he did when he was 19 and wrote
his Symphony #1. Prokoviev died in 1954, Sibelius in 1957, Vaughan
Williams in 1958 so I suggest at least wait until the 60s.

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:

> So which do you think is preferable for mavila, 7 or 9?

For me, the choice would be between 7 and 5. 9 is too many,
especially considering what the harmonic raison d'etre behind mavila
is ('5' comes at position -3 in the chain of '3's, to use
Wilson's 'terminology' for octave-reduced harmonics), and how quickly
it runs into "inconsistency" when extended to larger numbers of notes.

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
> > Certainly if you're willing to use meantone notation for this 19,
> you
> > should be willing to use it for a 19-equal chain, which means you
> > have a way of notating enneadecal temperaments (just add an up
> > accidental and a down accidental relative to this chain). Correct
> me
> > if I'm wrong, Dave, but aren't you already using this basic idea
> to
> > notate 36, 48, 60, 72, 84??
>
> I'm not sure which "basic idea" is being referred to here, but
> certainly these are all notated by comma inflections from 7
nominals
> in a chain of the temperament's best fifths.

By which you mean one 12-equal subset is notated conventionally,
without any comma inflections, right? So similarly, enneadecal and
the like could be done the same way, with one 19-equal subset notated
conventionally.

>> >Actually, I think that even 13 nominals is improper for any kind of
>> >optimal majic temperament (major thirds).
>>
>> Question 1: Can you quantify exactly what is lost by basing a
>> notation on a non-MOS?
>
>It can also be based on a DE or even an ET. If none of these,
>you're looking at a total mess.

That's not very quantified, but if you want to wait until your
paper's finished I completely understand.

-Carl

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> >Actually, I think that even 13 nominals is improper for any
kind of
> >> >optimal majic temperament (major thirds).
> >>
> >> Question 1: Can you quantify exactly what is lost by basing a
> >> notation on a non-MOS?
> >
> >It can also be based on a DE or even an ET. If none of these,
> >you're looking at a total mess.
>
> That's not very quantified, but if you want to wait until your
> paper's finished I completely understand.
>
> -Carl

Why don't you try working out a notation for, say, 31-equal, using 6
or 8 nominals in a chain of fifths. You'll see some "interesting"
issues arise.

>> >I don't know if you know, but hosting space is very affordable
>> >these days...
>> >
>> >http://www.geekhosting.com
>> >
>> >...I was certainly shocked. This company is one of many, but was
>> >recommended to me by a friend, and I had an online chat with their
>> >support dept. and they seem to be on the ball. I'm actually
>> >planning to switch over to them in the next few weeks myself, from
>> >my costly, anonftp-retracting provider of many years.
>
>Way more expensive than my xenharmony web host, which was why I was
>unimpressed with McL's argument that money should be charged for
>music up on the web. The expense is hardly worth discussing.

Care to share the name of this magical service? I have to say I'm
a bit wary, though, since your apache config is echoing back your
IP address instead of your domain name, and you said you didn't know
how to contact them about it.

-Carl

>> >> Question 1: Can you quantify exactly what is lost by basing a
>> >> notation on a non-MOS?
>> >
>> >It can also be based on a DE or even an ET. If none of these,
>> >you're looking at a total mess.
>>
>> That's not very quantified, but if you want to wait until your
>> paper's finished I completely understand.
>
>Why don't you try working out a notation for, say, 31-equal, using
>6 or 8 nominals in a chain of fifths. You'll see some "interesting"
>issues arise.

I notated 19-tET with a non-MOS chain of minor thirds, apparently
to my satisfaction using three accidental pairs.

Maybe you can give poor old me a hinty hint as to what the hell
you're talking about.

-Carl

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> >> Question 1: Can you quantify exactly what is lost by basing a
> >> >> notation on a non-MOS?
> >> >
> >> >It can also be based on a DE or even an ET. If none of these,
> >> >you're looking at a total mess.
> >>
> >> That's not very quantified, but if you want to wait until your
> >> paper's finished I completely understand.
> >
> >Why don't you try working out a notation for, say, 31-equal, using
> >6 or 8 nominals in a chain of fifths. You'll see
some "interesting"
> >issues arise.
>
> I notated 19-tET with a non-MOS chain of minor thirds, apparently
> to my satisfaction using three accidental pairs.

Could you show me?

> Maybe you can give poor old me a hinty hint as to what the hell
> you're talking about.
>
> -Carl

Well, as I see it, the nominals should be interpretable as a
periodicity block (or strip, etc.). A periodicity
block/strip/whatever tiles with itself, without gaps or overlaps, to
cover the entire lattice. So the entire tuning system becomes notated
as copies of the nominals, with one accidental pair for each
dimension. (The accidentals should be chromatic unison vectors --
otherwise they're not doing their job :) I think you made this entire
argument yourself, at one point . . .

If your nominals don't form a periodic unit, then there will either
be gaps or overlaps. Gaps, where no nominal is really appropriate, or
overlaps, where more than one might be. The former case seems pretty
fatal for notation. The latter seems to be a clear case that at least
one of the nominals (like the German B or H) is best jettisoned
(either use Hb for B or use B# for H).

It is rather unfortunate that one term refers to a scheme and the other
refers to a village who tuning implies another scheme. I suggest we rename
a city meantone. Mavila is the only use of a 'meta' so far that, as you
point out, refer directly to a tuning scheme

wallyesterpaulrus wrote:

> I thought it meant the same thing as in "meta-meantone". I thought
> the "meta" referred to the particular tuning scheme which, in the
> limit, brings such features as coinciding difference tones and
> synchronized beats. Certainly the "meta-meantone and meta-mavila"
> article concerns itself with this for both temperaments.
>
>

-- -Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com
The Wandering Medicine Show
KXLU 88.9 FM WED 8-9PM PST

I thought "meta-meantone" also refers to a tuning scheme . . . (?)

--- In tuning@yahoogroups.com, kraig grady <kraiggrady@a...> wrote:
> It is rather unfortunate that one term refers to a scheme and the
other
> refers to a village who tuning implies another scheme. I suggest we
rename
> a city meantone. Mavila is the only use of a 'meta' so far that,
as you
> point out, refer directly to a tuning scheme
>
> wallyesterpaulrus wrote:
>
> > I thought it meant the same thing as in "meta-meantone". I thought
> > the "meta" referred to the particular tuning scheme which, in the
> > limit, brings such features as coinciding difference tones and
> > synchronized beats. Certainly the "meta-meantone and meta-mavila"
> > article concerns itself with this for both temperaments.
> >
> >
>
> -- -Kraig Grady
> North American Embassy of Anaphoria Island
> http://www.anaphoria.com
> The Wandering Medicine Show
> KXLU 88.9 FM WED 8-9PM PST

>> I notated 19-tET with a non-MOS chain of minor thirds, apparently
>> to my satisfaction using three accidental pairs.
>
>Could you show me?

This is from the Dec. thread...

Let...

# and b show 648:625 (4 generators, about 63 cents)
^ and v show 419904:390625 (8 generators, about 126 cents)
+ and - show 78125:69984 (7 generators, about 190 cents)

C D E F G H A B

C Cv C# Cv C# Cv C# Cv
D D D# D# D# D# D# D#
E E- E Ev E# Ev E# Ev
F F F F F# F# F# F#
G G- G G- G Gv G# Gv
H H H H H H H# H#
A A- A A- A A- A Av
B B B B B B B B

0 17 1 17 1 17 1 17
1 1 2 2 2 2 2 2
5 2 5 3 6 3 6 3
6 6 6 6 7 7 7 7
10 7 10 7 10 8 11 8
11 11 11 11 11 11 12 12
15 12 15 12 15 12 15 13
16 16 16 16 16 16 16 16

...granted, there's a few degrees missing, but it doesn't seem
like it would be a problem.

>Well, as I see it, the nominals should be interpretable as a
>periodicity block (or strip, etc.). A periodicity block/strip/whatever
>tiles with itself, without gaps or overlaps, to cover the entire
>lattice. So the entire tuning system becomes notated as copies of
>the nominals, with one accidental pair for each dimension. (The
>accidentals should be chromatic unison vectors -- otherwise they're
>not doing their job :) I think you made this entire argument
>yourself, at one point . . .

Yep. Glad we agree! :)

>If your nominals don't form a periodic unit, then there will either
>be gaps or overlaps. Gaps, where no nominal is really appropriate, or
>overlaps, where more than one might be. The former case seems pretty
>fatal for notation. The latter seems to be a clear case that at least
>one of the nominals (like the German B or H) is best jettisoned
>(either use Hb for B or use B# for H).

As we know from the hypothesis, MOS/DE/whatever correspond to linear
temperaments, which only require one accidental pair. I don't know
what happens to the temperament situation at the non-MOS points. I
assume (and if I read Graham right...) that we get planar temperament,
etc., such that the codimension corresponds to the number of
accidentals pairs created as the scale gets rotated around itself.
This is all just guesswork on my part, though. If this is the case,
it doesn't seem so bad, since every accidental pair still corresponds
to a chromatic uv. If it's not the case, it still may be possible
to notate things satisfactorily with a different approach, I don't
know.

-Carl

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> Care to share the name of this magical service?

Onehost.

http://www.onehost.ws/

The prices they list are low, but they are charging me even less,
apparently because I am on the old plan. I'm being charged less than
a dollar a month for more than a gig of downloadable stuff.

I have to say I'm
> a bit wary, though, since your apache config is echoing back your
> IP address instead of your domain name, and you said you didn't know
> how to contact them about it.

That has nothing to do with Onehost; since Onehost was so cheap it
seemed kind of silly not to find a cheap way around the domain name
business also, so I have another outfit forward "xenharmony.org" to
my xenharmony site. Of course, you don't actually need a domain name
to be in business, since an IP address will do you, but I pay extra
to have "xenharmony" forwarded, but without using a more expensive
domain registration company.

--- In tuning@yahoogroups.com, kraig grady <kraiggrady@a...> wrote:

> It is rather unfortunate that one term refers to a scheme and the
other
> refers to a village who tuning implies another scheme. I suggest we
rename
> a city meantone.

San Jose is one of the biggest cities in America and many people
still don't know what or where it is, how to put the accent mark over
the e, or how to pronounce it once they do; let's rename it. Costa
Rica will thank us.

It does as i refer to in the first eleven words of my post. the naming of
the city was a joke

wallyesterpaulrus wrote:

> I thought "meta-meantone" also refers to a tuning scheme . . . (?)
>
> --- In tuning@yahoogroups.com, kraig grady <kraiggrady@a...> wrote:
> > It is rather unfortunate that one term refers to a scheme and the
> other
> > refers to a village who tuning implies another scheme. I suggest we
> rename
> > a city meantone. Mavila is the only use of a 'meta' so far that,
> as you
> > point out, refer directly to a tuning scheme
> >
> > wallyesterpaulrus wrote:
> >
> > > I thought it meant the same thing as in "meta-meantone". I thought
> > > the "meta" referred to the particular tuning scheme which, in the
> > > limit, brings such features as coinciding difference tones and
> > > synchronized beats. Certainly the "meta-meantone and meta-mavila"
> > > article concerns itself with this for both temperaments.
> > >
> > >
> >
> > -- -Kraig Grady
> > North American Embassy of Anaphoria Island
> > http://www.anaphoria.com
> > The Wandering Medicine Show
> > KXLU 88.9 FM WED 8-9PM PST
>
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - leave the group.
> tuning-nomail@yahoogroups.com - turn off mail from the group.
> tuning-digest@yahoogroups.com - set group to send daily digests.
> tuning-normal@yahoogroups.com - set group to send individual emails.
> tuning-help@yahoogroups.com - receive general help information.
>
> Yahoo! Groups Links
>
>
>
>

-- -Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com
The Wandering Medicine Show
KXLU 88.9 FM WED 8-9PM PST

As someone who has used Mavila . the seven tone scales seem to be more
basic and 'useable' than the nine tone. this is just the experience of one
person with this tuning, but thought i should chime in anyway!

> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
>
> > So which do you think is preferable for mavila, 7 or 9?
>
>

-- -Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com
The Wandering Medicine Show
KXLU 88.9 FM WED 8-9PM PST

Dave Keenan wrote:

> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> >>Major thirds are definitely a problem area for notation. Do you use >>4 nominals for majic (or whatever its called now) or do you use 13? >>A compromise is to use a very improper 10.
> > > Actually, I think that even 13 nominals is improper for any kind of
> optimal majic temperament (major thirds). I think you have to go to 16
> nominal to get proper.
> > The most difficult single-chain LTs to notate with native nominals are
> those with generators near 0, 1/4, 1/3, 1/2 octave, since 1, 2, 3 and
> 4 are too few nominals and the only available alternatives are either
> too large or very improper, or both.
> > Assuming we'd like no more than 10 nominals, the bad ranges are:
> > 0 to 1/11 oct, 0 to 109 c
> 3/13 to 3/11 oct, 277 to 327 c
> 4/13 to 4/11 oct, 369 to 436 c
> 5/11 to 1/2 oct, 545 to 600 c
> > Kleismic/hanson/keenan/whatever (minor thirds) is just inside the
> second range (and so might make do with an improper 7). Majic/whatever
> (major thirds) is near the middle of the third range.
> > For twin chain LTs I think the danger zones are just
> 0 to 1/11 oct, 0 to 109 c
> 3/13 to 1/4 oct, 277 to 300 c
> > For triple and quadruple chains it's just
> 0 to 1/11 oct, 0 to 109 c
> > and after that the problem goes away since one nominal per chain is
> acceptable when we have 5 or more chains.
> > So, what good LTs fall in these ranges?

Here's a sample:

"Valentine" g = 77.83315314, p = 1199.792743
[<1, 1, 2, 3|, <0, 9, 5, -3|]

"Nautilus" g = 82.97467050, p = 1202.659696
[<1, 2, 3, 3|, <0, -6, -10, -3|]

"Myna" g = 309.8926610, p = 1198.828458
[<1, -1, 0, 1|, <0, 10, 9, 7|]

"Hanson" g = 316.9063960, p = 1200.536355
[<1, 0, 1, -3|, <0, 6, 5, 22|]

"Kleismic" g = 317.8344609, p = 1203.187309
[<1, 0, 1, 2|, <0, 6, 5, 3|]

"Muggles" g = 379.3931044, p = 1203.148011
[<1, 0, 2, 5|, <0, 5, 1, -7|]

"Magic" g = 380.7957184, p = 1201.276744
[<1, 0, 2, -1|, <0, 5, 1, 12|]

"Squares" g = 426.4581630, p = 1201.698520
[<1, 3, 8, 6|, <0, -4, -16, -9|]

"Shrutar" g = 52.64203308, p = 599.4604367
[<2, 3, 5, 5|, <0, 2, -4, 7|]

"Injera" g = 93.60982493, p = 600.8889070
[<2, 3, 4, 5|, <0, 1, 4, 4|]

"Tripletone" g = 92.45965769, p = 399.0200131
[<3, 5, 7, 8|, <0, -1, 0, 2|]

"Augmented" g = 107.3111730, p = 399.9922103
[<3, 5, 7, 9|, <0, -1, 0, -2|]

Dave Keenan wrote:
> Yes. Both of these "work" in different ways. But wouldn't > the "native" mavila/pelogic notation use 9 nominals?

Either 7 or 9 would work; both are MOS for pelogic/mavila. Some versions of pelog are close to 7 notes of 9-ET. Orwell and negri would still require 9, though.

> I think we have to accept that. I note that this thread isn't about > how best to make temperaments fit a chain-of-fourths-based notation, > but how to notate them using native MOS-based nominals. The interval > relationships for these are neccessarily different from those > between chain-of-fourths nominals.

There are temperaments that work better with chain-of-fourths based notation than an MOS-based approach. A good example is the 5&26 temperament, which Gene is referring to as Mothra and Paul as Cynder (TOP tuning: g = 232.5214630, p = 1201.698520). It has a 5-note MOS, which wouldn't be of much use in notating it. On the other hand, you can use traditional meantone notation with a single extra accidental for 36;35. There probably are temperaments with inconvenient MOS that work better with chain-of-something-else notation.

>>E-G-B-D-F-A-C for third-based tunings, > > > This really only works for minor third to neutral third generators. > Major thirds are definitely a problem area for notation. Do you use > 4 nominals for majic (or whatever its called now) or do you use 13? > A compromise is to use a very improper 10.

Another approach is to notate E = -9, G = -5, B = -4, D = 0, F = +4, A = +5, C = +9, # = -3, b = +3:

. B#
. G# D# A#
. E B F# C#
. G D A
. Eb Bb F C
. Gb Db Ab
. Fb

The E-G-B-D-F-A-C approach would still work, but you start needing lots of double sharps and flats.

. Bx C
. Gx A
. Ex B# F Cb
. G# D Ab
. E# B Fb Cbb
. G Abb
. E Fbb

> Based on some clues from Kraig Grady and Carl Lumma we can see that > one approach is to have a nominal corresponding to each step of some > good high-limit ET having a manageable number of notes and having > fifths in the meantone-12-ET-pythagorean range. Since 72 is too many > then 31 seems a good choice.

I think even 31 might be too many. How about a selection of 19 notes out of 31?

--- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:

> "Nautilus" g = 82.97467050, p = 1202.659696
> [<1, 2, 3, 3|, <0, -6, -10, -3|]

I missed Number 54 getting a name. Why "nautilus"?

Commas: {49/48, 250/243} 15&29
Copop 7&9 limit generator: 13/188
MOS: 14, 15, 29, 43, 72

14 nominals seems over the limit, but 7 and an extra symbol might
work. If we use the 13/188 generator, six of them will give the
94-et fourth, so the fifth in this system is that of 94-equal, a mere
1/6 of a cent sharp. 10 generators takes us to 65/94, 16.1 cents
sharp, so the major third is even flatter than it is sharp in 12-
equal, at 370.2 cents, which is really more a 26/21. The 7 is in this
same territory, 17.8 cents flat. Given that people deal with 12-
equal, I'd presume they could handle this, with the errors in a flat
rather than a sharp direction.

Carl Lumma wrote:

> As we know from the hypothesis, MOS/DE/whatever correspond to linear
> temperaments, which only require one accidental pair. I don't know
> what happens to the temperament situation at the non-MOS points. I
> assume (and if I read Graham right...) that we get planar temperament,
> etc., such that the codimension corresponds to the number of
> accidentals pairs created as the scale gets rotated around itself.
> This is all just guesswork on my part, though. If this is the case,
> it doesn't seem so bad, since every accidental pair still corresponds
> to a chromatic uv. If it's not the case, it still may be possible
> to notate things satisfactorily with a different approach, I don't
> know. Hello!

Um, yes. You need at least one accidental pair to go from an MOS to a linear temperament. I think the nominals do work best as an MOS in this case, for the reasons Paul gave. If the nominals aren't an MOS, that first accidental pair will generally only give you an equal temperament, or something similar like an MOS. So you start counting from there.

Once you have a regular temperament, each new accidental pair can increase the codimension. But it can also be useful to have redundant accidentals, like the comma-shift between Db and C# in Pythagorean.

What I'm suggesting with hybrid notations is that a notation designed for a linear temperament instead gets used for a fixed MOS. This MOS functions like the set of nominals, but is too large to give each note its own symbol or staff position. With mystery, you could really get a planar temperament from the notation because the "MOS" is really 29-equal, and so can be replaced with the MOS you appear to describe. With magic, it would mean a different tuning. The first accidental pair would have to describe some other 19 note MOS than the magic one, most obviously meantone.

Graham

Dave Keenan wrote:

> I'm not sure which "basic idea" is being referred to here, but > certainly these are all notated by comma inflections from 7 nominals > in a chain of the temperament's best fifths.

The problem is, you can't get 7 notes from magic's best fifths within the 19-note MOS. So some of those nominals will have only theoretical existence, or you have to use a Tenney-style system where the nominals are a 5-limit diatonic.

What I worked out is essentially a 225:224-planar notation with 19-equal enharmonies. So all we need is a suitable notation for 5-limit JI and the septimal intervals will take care of themselves. The enharmonic equivalences amount to a tempering out of 3125:3072 in the 5-limit plane.

The trouble is, for the 19 or 22 note MOS, you need 6 lattice rows. This would lead to at least 3 compound comma shifts for HEWM. So what I've done is take the theoretical nominals to be fifth generated, but fudge the sharps and flats so that, for example, A-C#-E is a 5-limit triad (I think this is originally one of Fokker's ideas). This way, all 22 notes can be described with only single sharps and flats and no more than two compound comma shifts (and you only *need* a double comma shift on one note anyway). The 19 note MOS can be notated such that each note is unique if you ignore the comma shifts. Anything in this MOS that's written as a major third really is the best approximation to 5:4, although the same isn't true of fifths (but the comma shifts make this clear).

The idea is that where the notation looks familiar, it can be played assuming meantone or JI without doing much damage. Where a 3125:3072 bridge is crossed, the notation should look weird enough to remind the performer what temperament is actually being used. The only problem is that the sharp and flat symbols don't mean what a performer trained in a Pythagorean-based notation will think they should mean. Am I right in assuming that sagittal will solve this problem? That is, that it supplies convenient symbols for both the usual Pythagorean sharps and flats and these alternative, 5-limit based ones? More generally, all we need is a good way of notating 5-limit JI based on 7 nominals and covering 6 lattice rows.

Graham

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> > I'm not sure which "basic idea" is being referred to here, but
> > certainly these are all notated by comma inflections from 7
> nominals
> > in a chain of the temperament's best fifths.
>
> By which you mean one 12-equal subset is notated conventionally,
> without any comma inflections, right?

Yes. The 12-equal subset called ABCDEFG.

> So similarly, enneadecal and
> the like could be done the same way, with one 19-equal subset
notated
> conventionally.

I assume you mean a 19-equal subset having more than 7 tones, in
which case notating them conventionally will involve the "apotome"
comma inflection as symbolised by conventional sharps and flats. Is
this what you intend? I don't think I'm following. I'm afraid your
posts are a little too terse for me.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
>
> > In the 1950s Henry Pleasants wrote a highly controversial book,
> _The
> > Agony of Modern Music_, in which he made a very persuasive case
for
> > the irrelevance of 20th-century "serious music." He placed the
> > breakdown of harmony somewhere around the 2nd decade of that
century,
> > as evidenced by the emergence of new techniques that completely
> > discarded existing harmonic norms.
>
> So Shostakovich spent his whole life being irrelevant? Poor fella.
>
> The second decade of the 20th century is way to early to start
> kvetching about the death of classical music. Camille Saint-Saens
> died in that decade, for gosh sakes, and was composing music right
up
> to the end not much different than he did when he was 19 and wrote
> his Symphony #1. Prokoviev died in 1954, Sibelius in 1957, Vaughan
> Williams in 1958 so I suggest at least wait until the 60s.

Gene:

I didn't say that I was agreeing with the proposition that
all "serious music" after 1920 is irrelevant. I was only using this
as the source of my statement that the breakdown of the traditional
harmonic system occurred by 1920 (I think Pleasants actually puts it
about a decade earlier, so I allowed another 10 years, just to be on
the safe side).

But I would date this as late as the 1960s, because the book came out
in 1955, and it would not have been written if the author did not
already have grounds to make the statement that much of 20th-century
music was irrelevant, as evidenced by the fact that it had lost its
audience.

Pleasants also observed that those 20th-century composers who still
wrote diatonically tended to be regarded "less seriously" than those
who discarded traditional tonality in favor of new compositional
techniques, so he was not making a blanket dismissal of all 20th-
century music.

Since we can't agree on a date, then may I suggest that this sentence:

"Once the harmonic resources of 12-ET were exhausted (by around
1920), there was no way to progress further harmonically within 12-ET
other than to discard existing harmonic norms in favor of new
techniques that produced music that was (and still is)
incomprehensible to the great majority of listeners."

be changed to:

"As composers in the first half of the 20th century realized that the
harmonic resources of 12-ET were nearing exhaustion, many of them
began discarding existing harmonic norms in favor of new techniques
that resulted in music that was (and still is) often incomprehensible
to the great majority of listeners."

You can read some comments (both pro and con) about the book here:
http://www.kafalas.com/urbcol72.htm
and I would highly recommend that you (and anyone else who hopes that
the microtonal movement would some day be more than a niche market)
get a copy (out of print, but available used) and read it, because
Pleasants writes from an academic background, but (as a music critic)
addresses the problem of a lost audience for "serious music" from the
perspective of a typical concert-goer.

BTW, he never once mentioned (or even hinted) that microtonality
might hold the answer to the several "crises" he describes, so I
think we are in a good position to remedy some of those things. But
I believe that we need to be aware of the issues and views he brought
up, whether or not we agree with them.

--George

George,

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:
> You can read some comments (both pro and con) about the book here:
> http://www.kafalas.com/urbcol72.htm
> and I would highly recommend that you (and anyone else who hopes that
> the microtonal movement would some day be more than a niche market)
> get a copy (out of print, but available used) and read it, because
> Pleasants writes from an academic background, but (as a music critic)
> addresses the problem of a lost audience for "serious music" from the
> perspective of a typical concert-goer.

Especially in a historical context, I believe that is true. In the
time that Pleasants wrote the book, some trends in contemporary music
reversed themselves against the modernist/serialist strain, and have
created a body of work that isn't reviled as the
Darmstadt/serialist/complexity camp became. Some of these trends would
be the minimalist and 'downtown' composers (Kyle Gann is a good source
on many of these trends). There are still big problems with the book,
mostly that it is dated and pretty conservative, but worth a read.

> BTW, he never once mentioned (or even hinted) that microtonality
> might hold the answer to the several "crises" he describes, so I
> think we are in a good position to remedy some of those things.

George, I think that is true to a point, but not only harmonic
language has become wrung out - styles have passed as well. If one
simply puts old wine in new bottles, the audience will remain small.
One would hope that composers and musicians would seize a new universe
of tunings in a manner that opens up new forms of musical expression
as well. Just my $0.02...

Cheers,
Jon

hi George,

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:

> Since we can't agree on a date, then may I suggest that
> this sentence:
>
> "Once the harmonic resources of 12-ET were exhausted
> (by around 1920), there was no way to progress further
> harmonically within 12-ET other than to discard existing
> harmonic norms in favor of new techniques that produced
> music that was (and still is) incomprehensible to the
> great majority of listeners."
>
> be changed to:
>
> "As composers in the first half of the 20th century realized
> that the harmonic resources of 12-ET were nearing exhaustion,
> many of them began discarding existing harmonic norms in favor
> of new techniques that resulted in music that was (and still is)
> often incomprehensible to the great majority of listeners."

i think that is a *superb* re-write !!!!! good job.

as you may glean from my big historical chronology
"A Century of New Music in Vienna" (and even from its filename!),
i think 1905 was the year that traditional harmonic concepts
really started breaking down. by 1908, Schoenberg had
written his first really "atonal" (pantonal) compositions.
and they had a huge influence: by 1920 it was common for
composers to be writing atonal music.

http://www.tonalsoft.com/monzo/schoenberg/Vienna1905.htm

Schoenberg introduced his "12-tone method" shortly after 1920.
but atonality was part of the musical language (at least in
German-speaking countries) well before World War I.

-monz

> You can read some comments (both pro and con) about the book here:
> http://www.kafalas.com/urbcol72.htm
> and I would highly recommend that you (and anyone else who hopes
that
> the microtonal movement would some day be more than a niche market)
> get a copy (out of print, but available used) and read it, because
> Pleasants writes from an academic background, but (as a music
critic)
> addresses the problem of a lost audience for "serious music" from
the
> perspective of a typical concert-goer.
>
> BTW, he never once mentioned (or even hinted) that microtonality
> might hold the answer to the several "crises" he describes, so I
> think we are in a good position to remedy some of those things. But
> I believe that we need to be aware of the issues and views he
brought
> up, whether or not we agree with them.
>
> --George

--- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:

> George, I think that is true to a point, but not only harmonic
> language has become wrung out - styles have passed as well.

I would far rather write like a microtonal Beethoven than do trance in
22.

If one
> simply puts old wine in new bottles, the audience will remain small.

The trouble is, not only does the "high" stuff often get weird,
the "low" stuff often gets bad. The same is true in the case of
poetry, where popular poetry mostly simply stinks; in the art world,
low art is often barf city, though one sees interesting graffiti or
auto decoration. It's not therefore just classical music which has
experienced a death of high culture problem. I think the most viable
art form today is film, where the dichotomy of high and low is not
really establised; that is, there are a lot of clearly lowbrow movies
made, but it is hardly the case that the only good movies are indie
films no one will watch.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> I would far rather write like a microtonal Beethoven than do trance in
> 22.

An admirable goal, and I'm sure along the way you'll find plenty of
things that please you. It doesn't invalidate the argument that those
pieces will probably be of limited interest and impact (which is
neither here nor there on a personal level, only on the level that
George was talking about). IOW, I don't think that simply changing the
tuning system of a long-gone style is going to cause a rebirth.

But who knows - its all conjecture.

> The trouble is, not only does the "high" stuff often get weird,
> the "low" stuff often gets bad.

Well, the old "x% of everything is crap" can apply across the board.
And I don't think the film analogy is very valid, because it is quite
easy to be exposed to a lot of the music that is made (by virtue of
the delivery methods) than film - the barriers to making film are
still higher, and it is not possible to see all the bad stuff that
gets made that never goes into the distribution pipeline. Maybe
digital film/delivery will change as broadband becomes ubiquitous.

Gosh, this isn't proper for this list anymore. Sorry.

Cheers,
Jon

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> I notated 19-tET with a non-MOS chain of minor thirds, apparently
> >> to my satisfaction using three accidental pairs.
> >
> >Could you show me?
>
> This is from the Dec. thread...
>
> Let...
>
> # and b show 648:625 (4 generators, about 63 cents)
> ^ and v show 419904:390625 (8 generators, about 126 cents)
> + and - show 78125:69984 (7 generators, about 190 cents)
>
> C D E F G H A B
>
> C Cv C# Cv C# Cv C# Cv
> D D D# D# D# D# D# D#
> E E- E Ev E# Ev E# Ev
> F F F F F# F# F# F#
> G G- G G- G Gv G# Gv
> H H H H H H H# H#
> A A- A A- A A- A Av
> B B B B B B B B

What a strange table? Where did this come from?

> 0 17 1 17 1 17 1 17
> 1 1 2 2 2 2 2 2
> 5 2 5 3 6 3 6 3
> 6 6 6 6 7 7 7 7
> 10 7 10 7 10 8 11 8
> 11 11 11 11 11 11 12 12
> 15 12 15 12 15 12 15 13
> 16 16 16 16 16 16 16 16
>
> ...granted, there's a few degrees missing, but it doesn't seem
> like it would be a problem.

Try writing a two-bar melodic figure, using the nominals, and then
transpose it to a different pitch level. You might see things don't
work out so nice.

> >Well, as I see it, the nominals should be interpretable as a
> >periodicity block (or strip, etc.). A periodicity
block/strip/whatever
> >tiles with itself, without gaps or overlaps, to cover the entire
> >lattice. So the entire tuning system becomes notated as copies of
> >the nominals, with one accidental pair for each dimension. (The
> >accidentals should be chromatic unison vectors -- otherwise they're
> >not doing their job :) I think you made this entire argument
> >yourself, at one point . . .
>
> Yep. Glad we agree! :)
>
> >If your nominals don't form a periodic unit, then there will
either
> >be gaps or overlaps. Gaps, where no nominal is really appropriate,
or
> >overlaps, where more than one might be. The former case seems
pretty
> >fatal for notation. The latter seems to be a clear case that at
least
> >one of the nominals (like the German B or H) is best jettisoned
> >(either use Hb for B or use B# for H).
>
> As we know from the hypothesis, MOS/DE/whatever correspond to linear
> temperaments, which only require one accidental pair.

You're forgetting the hypothesis again. It involves Fokker
periodicity blocks.

> I don't know
> what happens to the temperament situation at the non-MOS points. I
> assume (and if I read Graham right...) that we get planar
temperament,
> etc.,

Hmm? If it's generated "linearly", then of course it's
still "linear", in the sense you meant above.

Hi Kraig,

I agree with this, but the question was about the number of nominals
in the notation, not the number of notes in the scale.

7 nominals certainly works, but I think a case could be made for 5 as
well . . .

-Paul

--- In tuning@yahoogroups.com, kraig grady <kraiggrady@a...> wrote:
> As someone who has used Mavila . the seven tone scales seem to be
more
> basic and 'useable' than the nine tone. this is just the experience
of one
> person with this tuning, but thought i should chime in anyway!
>
>
>
> > --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...>
wrote:
> >
> > > So which do you think is preferable for mavila, 7 or 9?
> >
> >
>
> -- -Kraig Grady
> North American Embassy of Anaphoria Island
> http://www.anaphoria.com
> The Wandering Medicine Show
> KXLU 88.9 FM WED 8-9PM PST

--- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:

> There are temperaments that work better with chain-of-fourths based
> notation than an MOS-based approach. A good example is the 5&26
> temperament, which Gene is referring to as Mothra and Paul as
Cynder
> (TOP tuning: g = 232.5214630, p = 1201.698520). It has a 5-note
MOS,
> which wouldn't be of much use in notating it.

Hmm? Why not? Seems perfect.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:
>
> > "Nautilus" g = 82.97467050, p = 1202.659696
> > [<1, 2, 3, 3|, <0, -6, -10, -3|]
>
> I missed Number 54 getting a name. Why "nautilus"?

Wow -- I just answered this on tuning-math, and you replied
affirmatively!

Remember?

This is what the floragram for this temperament looks like:

/tuning-math/files/Paul/nautilus.gif

Thus . . . nautilus.

> Commas: {49/48, 250/243} 15&29
> Copop 7&9 limit generator: 13/188
> MOS: 14, 15, 29, 43, 72
>
> 14 nominals seems over the limit, but 7 and an extra symbol might
> work. If we use the 13/188 generator, six of them will give the
> 94-et fourth, so the fifth in this system is that of 94-equal, a
mere
> 1/6 of a cent sharp. 10 generators takes us to 65/94, 16.1 cents
> sharp, so the major third is even flatter than it is sharp in 12-
> equal, at 370.2 cents, which is really more a 26/21. The 7 is in
this
> same territory, 17.8 cents flat. Given that people deal with 12-
> equal, I'd presume they could handle this, with the errors in a
flat
> rather than a sharp direction.

I've lost your train of thought. Too many numbers meaning too many
different things.

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
> > --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...>
wrote:
> > > I'm not sure which "basic idea" is being referred to here, but
> > > certainly these are all notated by comma inflections from 7
> > nominals
> > > in a chain of the temperament's best fifths.
> >
> > By which you mean one 12-equal subset is notated conventionally,
> > without any comma inflections, right?
>
> Yes. The 12-equal subset called ABCDEFG.

I meant all 12 notes of a 12-equal subset. Could you respond again
with this clarification?

> > So similarly, enneadecal and
> > the like could be done the same way, with one 19-equal subset
> notated
> > conventionally.
>
> I assume you mean a 19-equal subset having more than 7 tones,

Yes, I mean one having 19 notes.

> in
> which case notating them conventionally will involve the "apotome"
> comma inflection as symbolised by conventional sharps and flats.

Yes, I meant the conventional notation with sharps and flats.

> Is
> this what you intend?

Yes.

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>

> > I missed Number 54 getting a name. Why "nautilus"?
>
> Wow -- I just answered this on tuning-math, and you replied
> affirmatively!
>
> Remember?

No.

> This is what the floragram for this temperament looks like:
>
> /tuning-math/files/Paul/nautilus.gif
>
> Thus . . . nautilus.

It does indeed make sense. Very cool. Thanks!

wallyesterpaulrus wrote:
> --- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:
> > >>There are temperaments that work better with chain-of-fourths based >>notation than an MOS-based approach. A good example is the 5&26 >>temperament, which Gene is referring to as Mothra and Paul as > > Cynder > >>(TOP tuning: g = 232.5214630, p = 1201.698520). It has a 5-note > > MOS, > >>which wouldn't be of much use in notating it.
> > > Hmm? Why not? Seems perfect.

If you carry it out to 26 notes, which seems like a reasonable size of a scale, you'll need two accidentals for 10 of the pitches, and three for two of them (+13 and -13). The meantone notation doesn't require any triple accidentals, and only 6 of the pitches need double accidentals (Ab< = -13, Eb< = -10, Bb< = -7, F#> = +7, C#> = +10, and G#> = +13).

Most consonant intervals around D are represented more neatly in the meantone system. Only a few like 7/4 and 9/7 are simpler in the MOS-based notation.

................. ratio .. meantone .. 5-note MOS
minor third ...... 6/5 D - F D - E>>
major third ...... 5/4 D - F# D - G<<
diminished fourth 9/7 D - F#> D - G<
perfect fourth ... 4/3 D - G D - G>
augmented fourth . 7/5 D - Ab< D - A>>>
diminished fifth 10/7 D - G#> D - A<<<
perfect fifth .... 3/2 D - A D - A<
minor sixth ...... 8/5 D - Bb D - A>>
major sixth ...... 5/3 D - B D - C<<
augmented sixth .. 7/4 D - C< D - C
minor seventh .... 9/5 D - C D - C>

But in practice you'd probably use a distinct 21;20 accidental in place of the double 36;35, so the advantage of meantone is slight.

Herman Miller wrote:
> Dave Keenan wrote:
>>This really only works for minor third to neutral third generators. >>Major thirds are definitely a problem area for notation. Do you use >>4 nominals for majic (or whatever its called now) or do you use 13? >>A compromise is to use a very improper 10.
> > > Another approach is to notate E = -9, G = -5, B = -4, D = 0, F = +4, A = > +5, C = +9, # = -3, b = +3:
> > . B#
> . G# D# A#
> . E B F# C#
> . G D A
> . Eb Bb F C
> . Gb Db Ab
> . Fb

It occurred to me that notating the 5-limit lattice with a periodicity block like this might make a good system of selecting a notation for an MOS, rather than a linear series like the traditional fourth-based notation. Magic would be a good candidate, since it's a good 5-limit approximation that's otherwise tricky to notate. Since we need to represent half-octave temperaments, we'd need to use magic[16] or magic[22]. 22 is especially attractive, since 16 only works with the 5-limit version of magic, and if we notate 22-ET we can treat it as magic, pajara, or porcupine, whichever works out best for a particular temperament. If you extend my porcupine notation by adding successive letters of the alphabet for every third step of 22-ET:

| 1 2 2
|0....5....0....5....0.2
|A B C D E F G H
| I J K L M N O
| P Q R S T U V A

you can use these letters to fill a magic-porcupine block:

+---------------+
| /Q\__ |
| /V S P\_ |
| /E B U R(O) |
| /J G D A T/ |
| (O)L I F C/ |
| \N_K H/ |
| \M/ |
+---------------+

and tile it to fill the 5-limit lattice space.

+-------------------------+
|R(O)L I F C/V S P\M/J G D|
| T/Q\N_K H/E B U R(O)L I |
|C/V S P\M/J G D A T/Q\N_K|
| E B U R(O)L I F C/V S P\|
|J G D A T/Q\N_K H/E B U R|
|)L I F C/V S P\M/J G D A |
|Q\N_K H/E B U R(O)L I F C|
| S P\M/J G D A T/Q\N_K H/|
|B U R(O)L I F C/V S P\M/J|
| D A T/Q\N_K H/E B U R(O)|
|I F C/V S P\M/J G D A T/Q|
| K H/E B U R(O)L I F C/V |
|P\M/J G D A T/Q\N_K H/E B|
| R(O)L I F C/V S P\M/J G |
|A T/Q\N_K H/E B U R(O)L I|
+-------------------------+

For chains of minor thirds, you have up to 11 nominals to pick from: P R T V B D F H J L N. Coincidentally (?), 11 is the size of an MOS of the best-known chain-of-minor-thirds temperament (kleismic). Chains of fourths or major thirds give you the whole 22-nominal range to use as needed. Half-octave temperaments would center one chain on D and the other one on O. Three-per-octave would use D, U, and I; four per octave could start with D and O, and add either B and M, or F and Q.

Note that intervals like A-C, G-I, K-M, and so on (skipping a letter) are all minor thirds! This useful property is a consequence of using porcupine notation. Fourths are like A-D, H-K, and so on. Major thirds are a little trickier: you have to go back five letters (F-A, H-C, etc). Of course, when you notate temperaments, there will be all those enharmonic equivalents to learn, but it's good to have a basic set that's relatively easy to figure out.

How's that for a start?

>The second decade of the 20th century is way to early to start
>kvetching about the death of classical music. Camille Saint-Saens
>died in that decade, for gosh sakes, and was composing music right
>up to the end not much different than he did when he was 19 and
>wrote his Symphony #1. Prokoviev died in 1954, Sibelius in 1957,
>Vaughan Williams in 1958 so I suggest at least wait until the 60s.

Norman Henry's idea is that hindsight is necessary to inform
judgements of greatness. There may be some truth to that.
Classical music does seem to be dying, though. Actually in
the US it's already dead, perhaps even entering the revival
phase. This was a cultural thing, though. Rock music uses
the same tuning as classical music, with the same harmonic
resources, and it took off like thunder.

As for harmonic resources, I don't think they run out. The
things you have to do to differentiate yourself just get more
subtle. The kinds of decisions you make in voicings, for
example -- jazz musicians can often recognize dozens of artists
this way. But they might have to listen for a while to pick
it up.

-Carl

hi Gene,

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> --- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:
>
> The trouble is, not only does the "high" stuff often get
> weird, the "low" stuff often gets bad. The same is true in
> the case of poetry, where popular poetry mostly simply stinks;
> in the art world, low art is often barf city, though one sees
> interesting graffiti or auto decoration. It's not therefore
> just classical music which has experienced a death of high
> culture problem. I think the most viable art form today is
> film, where the dichotomy of high and low is not really
> establised; that is, there are a lot of clearly lowbrow
> movies made, but it is hardly the case that the only good
> movies are indie films no one will watch.

i think these are some really perceptive comments.
further comment is banished to metatuning.

-monz

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> Hi Kraig,
>
> I agree with this, but the question was about the number of
nominals
> in the notation, not the number of notes in the scale.

But shouldn't these be closely related?

--- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:
> wallyesterpaulrus wrote:
> > --- In tuning@yahoogroups.com, Herman Miller <hmiller@I...>
wrote:
> >>(TOP tuning: g = 232.5214630, p = 1201.698520). It has a 5-note
> >> MOS, which wouldn't be of much use in notating it.
> >
> > Hmm? Why not? Seems perfect.
>
> If you carry it out to 26 notes, which seems like a reasonable
size of a
> scale, you'll need two accidentals for 10 of the pitches, and
three for
> two of them (+13 and -13).
...
> But in practice you'd probably use a distinct 21;20 accidental in
place
> of the double 36;35, so the advantage of meantone is slight.

Yes. With the sagittal set of comma symbols now available (and those
still to come) there is no need to ever use triple (or even double)
accidentals.

So I agree with Paul that 5 nominals is ideal for this one.

--- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:
> Herman Miller wrote:
> > . B#
> > . G# D# A#
> > . E B F# C#
> > . G D A
> > . Eb Bb F C
> > . Gb Db Ab
> > . Fb
>
> It occurred to me that notating the 5-limit lattice with a
periodicity
> block like this might make a good system of selecting a notation
for an
> MOS, rather than a linear series like the traditional fourth-based
> notation.
...
> How's that for a start?

I don't want to be too negative about this since you've obviously
put a lot of though into it, and I haven't yet understood your
proposal completely, but ...

Having the nominals be a 2D periodicity block has already been tried
in Ben Johnston's JI notation, and in my not so humble opinion it
results in a complete mess as soon as you want to modulate away from
the basic PB.

This was discussed on this list some months back. I believe Paul
Erlich agreed with me.

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> > --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
> wrote:
> > > --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...>
> wrote:
> > > > I'm not sure which "basic idea" is being referred to here,
but
> > > > certainly these are all notated by comma inflections from 7
> > > nominals
> > > > in a chain of the temperament's best fifths.
> > >
> > > By which you mean one 12-equal subset is notated
conventionally,
> > > without any comma inflections, right?
> >
> > Yes. The 12-equal subset called ABCDEFG.
>
> I meant all 12 notes of a 12-equal subset. Could you respond again
> with this clarification?

Aha! I was parsing "12-equal subset" as "subset of 12-equal", but
now I see you mean "subset of X which is equivalent to 12-equal".

So, to answer your original question:

It depends.

If you are talking about the mixed Sagittal notation, that uses
conventional sharps and flats combined with single-shaft Sagittal
symbols, then the answer is yes.

If you are talking about the pure Sagittal notation, that never has
more than one accidental per note, then the answer is no.

In pure Sagittal, the symbols that replace the conventional sharp
and flat (the double-shafted arrow up and down) are considered to be
just another pair of comma inflection symbols off the 7 nominals. In
their case the comma represented is the apotome (2048:2147 =
2^11:3^7).

But there's nothing stopping you from using two pure Sagittal
accidentals per note if that's what you think works best.

> > > So similarly, enneadecal and
> > > the like could be done the same way, with one 19-equal subset
> > notated
> > > conventionally.
> >
> > I assume you mean a 19-equal subset having more than 7 tones,
>
> Yes, I mean one having 19 notes.

OK. So you mean one subset of enneadecal that is equivalent to 19-
equal. I don't know what enneadecal is, so I didn't know it had one.

But given that it does, your analogy to notating 72-ET in mixed
Sagittal certainly works, since no Sagittal symbols are needed to
notate 19-equal in the mixed notation, and only apotome symbols are
needed for it in the pure.

I think it may well make sense to use (up to) two accidentals per
note for LTs having more than 5 parallel chains. The nominals form
a "MOS" on one chain, one accidental extends that chain, the other
jumps you to other chains.

--- In tuning@yahoogroups.com, I wrote:
> I think it may well make sense to use (up to) two accidentals per
> note for LTs having more than 5 parallel chains. The nominals form
> a "MOS" on one chain, one accidental extends that chain, the other
> jumps you to other chains.

Oops! That's not what you meant at all. You meant the nominals would
all be in different chains and they wouldn't cover all the chains,
but would be a manageable (5 to 10 note) MOS of the best temperament
consistent with n-ET where n is the number of chains, and one
accidental would extend this to one note per chain (the full n-ET),
while the other accidental would move you along the chains.

Yes. I agree with this. I believe this is exactly what Graham Breed
proposed.

--- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:
> Dave Keenan wrote:
> > Based on some clues from Kraig Grady and Carl Lumma we can see
that
> > one approach is to have a nominal corresponding to each step of
some
> > good high-limit ET having a manageable number of notes and
having
> > fifths in the meantone-12-ET-pythagorean range. Since 72 is too
many
> > then 31 seems a good choice.
>
> I think even 31 might be too many. How about a selection of 19
notes out
> of 31?

That's not a bad idea. We should at least see how far we can get
with only 19. The "Greek for flats, Hebrew for sharps" idea allows
for extending it later if necessary.

I note that the standard Windows fonts "Arial" and "Times New Roman"
contain both Greek and Hebrew alphabets (along with Arabic and
Cyrillic). We could still use the method of putting sharps or flats
_before_ the letters A to G to represent these extra nominals in
ASCII.

One would hope so . even when i use seven tone scales i do modulate around
to the higher ones but don't think of them as my base scale. As paul
pointed out 5 's are good if you are not going to be 7 heavy

Dave Keenan wrote:

> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> > Hi Kraig,
> >
> > I agree with this, but the question was about the number of
> nominals
> > in the notation, not the number of notes in the scale.
>
> But shouldn't these be closely related?
>
>
>

-- -Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com
The Wandering Medicine Show
KXLU 88.9 FM WED 8-9PM PST

hi Dave and Herman,

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:

> --- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:
> > Herman Miller wrote:
> > > . B#
> > > . G# D# A#
> > > . E B F# C#
> > > . G D A
> > > . Eb Bb F C
> > > . Gb Db Ab
> > > . Fb
> >
> > It occurred to me that notating the 5-limit lattice with
> > a periodicity block like this might make a good system of
> > selecting a notation for an MOS, rather than a linear series
> > like the traditional fourth-based notation.
> ...
> > How's that for a start?
>
> I don't want to be too negative about this since you've
> obviously put a lot of though into it, and I haven't yet
> understood your proposal completely, but ...

Herman, i have to make that same disclaimer ...

> Having the nominals be a 2D periodicity block has already
> been tried in Ben Johnston's JI notation, and in my not so
> humble opinion it results in a complete mess as soon as you
> want to modulate away from the basic PB.
>
> This was discussed on this list some months back. I believe
> Paul Erlich agreed with me.

i think i missed that particular discussion, but i've been
arguing for a HEWM-type (1D-basis) notation, and specifically
*against* Johnston's notation (2D-basis), since 1994.

-monz

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> --- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:
> > Dave Keenan wrote:
> > > Based on some clues from Kraig Grady and Carl Lumma
> > > we can see that one approach is to have a nominal
> > > corresponding to each step of some good high-limit ET
> > > having a manageable number of notes and having fifths
> > > in the meantone-12-ET-pythagorean range. Since 72 is
> > > too many then 31 seems a good choice.
> >
> > I think even 31 might be too many. How about a selection
> > of 19 notes out of 31?
>
> That's not a bad idea. We should at least see how far we
> can get with only 19. The "Greek for flats, Hebrew for sharps"
> idea allows for extending it later if necessary.

i don't know where i saw this (i'm sure Kraig can help),
but Erv Wilson used the first five Greek letters along
with the usual first 7 Roman letters, and two accidentals
which i'll render here as - and + , to notate modulus-31
as follows:

0 C
30 C -
29 B +
28 B
27 beta +
26 beta
25 beta -
24 A +
23 A
22 alpha +
21 alpha
20 alpha -
19 G +
18 G
17 gamma +
16 gamma
15 gamma -
14 F +
13 F
12 F -
11 E +
10 E
9 epsilon +
8 epsilon
7 epsilon -
6 D +
5 D
4 delta +
3 delta
2 delta -
1 C +
0 C

note that Wilson used both accidentals for all five
of the Greek letters, but only with C and F out of
the Roman set; the other Roman letters use only the
plain letter and the plus sign, but not the minus sign.
C and F are also the two Roman letters which do not
have associated Greek equivalents here.

also note that Wilson's ordering of the Greek letters
follows the Roman alphabetization and not the Greek.

regarding 19edo: i've just recently added circular
enharmonicity diagrams to the bottom of my 19edo page,
which might be of help:

http://www.tonalsoft.com/enc/19edo.htm

-monz

hi Paul,

i only realized just now that your "zoom" charts
on my "equal-temperament" page

http://www.tonalsoft.com/enc/eqtemp.htm

don't have a line for the MIRACLE family plotted on them.

-monz

oops, sorry ... sent before with the wrong subject line.

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> hi Paul,
>
>
> i only realized just now that your "zoom" charts
> on my "equal-temperament" page
>
> http://www.tonalsoft.com/enc/eqtemp.htm
>
> don't have a line for the MIRACLE family plotted on them.
>
>
>
> -monz

>> C D E F G H A B
>>
>> C Cv C# Cv C# Cv C# Cv
>> D D D# D# D# D# D# D#
>> E E- E Ev E# Ev E# Ev
>> F F F F F# F# F# F#
>> G G- G G- G Gv G# Gv
>> H H H H H H H# H#
>> A A- A A- A A- A Av
>> B B B B B B B B
>
>What a strange table? Where did this come from?
>
>> 0 17 1 17 1 17 1 17
>> 1 1 2 2 2 2 2 2
>> 5 2 5 3 6 3 6 3
>> 6 6 6 6 7 7 7 7
>> 10 7 10 7 10 8 11 8
>> 11 11 11 11 11 11 12 12
>> 15 12 15 12 15 12 15 13
>> 16 16 16 16 16 16 16 16
>>
>> ...granted, there's a few degrees missing, but it doesn't seem
>> like it would be a problem.
>
>Try writing a two-bar melodic figure, using the nominals, and then
>transpose it to a different pitch level. You might see things don't
>work out so nice.

The above table should takes care of the natural keys. I'll
work out the others in a few days.

>> >If your nominals don't form a periodic unit, then there will
>> >either be gaps or overlaps. Gaps, where no nominal is really
>> >appropriate, or overlaps, where more than one might be. The
>> >former case seems pretty fatal for notation. The latter seems
>> >to be a clear case that at least one of the nominals (like
>> >the German B or H) is best jettisoned (either use Hb for B
>> >or use B# for H).
>>
>> As we know from the hypothesis, MOS/DE/whatever correspond to linear
>> temperaments, which only require one accidental pair.
>
>You're forgetting the hypothesis again. It involves Fokker
>periodicity blocks.

...with all but one of their unison vectors tempered out, which
is to say linear temperaments.

>> I don't know
>> what happens to the temperament situation at the non-MOS points.
>> I assume (and if I read Graham right...) that we get planar
>> temperament, etc.,
>
>Hmm? If it's generated "linearly", then of course it's
>still "linear", in the sense you meant above.

If its pitches move by two different commas under a transposition
of a just interval, it can't be a linear temperament, can it?

The simple question I'm getting at here is: what happens in
PB terms at non-MOS points?

-Carl

>> hi Paul,
>>
>>
>> i only realized just now that your "zoom" charts
>> on my "equal-temperament" page
>>
>> http://www.tonalsoft.com/enc/eqtemp.htm
>>
>> don't have a line for the MIRACLE family plotted on them.

Probably because they're 5-limit graphs, and miracle is
a lousy 5-limit temperament.

-Carl

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> hi Paul,
> >>
> >>
> >> i only realized just now that your "zoom" charts
> >> on my "equal-temperament" page
> >>
> >> http://www.tonalsoft.com/enc/eqtemp.htm
> >>
> >> don't have a line for the MIRACLE family plotted on them.
>
> Probably because they're 5-limit graphs, and miracle is
> a lousy 5-limit temperament.
>
> -Carl

but you can still easily see on the "zoom: 10" graph
that 21, 31, 41, 51, 52, and 72 all lie on the same
straight line. why not label it?

-monz

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
>
> > perhaps families of tunings should be named and classified
> > according to the ways that sagittal works, since it's such
> > a broad-based notation.
>
> For any family not based on a single chain of fifths, it works
quite
> awkwardly. That one reason Carl and I weren't too crazy about it --
> it favors systems like pythagorean, meantone, and
> helmholtz/groven/schismic, at the expense of miracle, magic,
pajara,
> etc....

As Dave replied earlier, the problem is not really with the Sagittal
system itself (which is basically a set of accidentals capable of
modifying tones in a single chain of fifths), but with having the
nominals in a chain of fifths.

While the rest of you have been addressing the issue of how to name
the nominals when other generators are used, I took a few minutes to
look through some of my files for something I worked out a little
over a month ago.

Here are the Sagittal accidentals that would be used for Miracle (for
10 nominals). Using "N" as the name for a given nominal, here's a
table of how to notate various tones in the Miracle chain G
generators from N (along with the principal JI ratio for each tone):

-41G 100/99 N'|~
-31G 80/81 N\!
-30G 256/243 N.||\
-21G 32/33 N\!/
-20G 28/27 N.(|\
-11G 20/21 N'!!)
-10G 64/63 N|)
-1G 15/16 N'\!!/
0G 1/1 N
1G 16/15 N./||\
10G 63/64 N!)
11G 21/20 N.||)
20G 27/28 N'(!/
21G 33/32 N/|\
30G 243/256 N'!!/
31G 81/80 N/|
41G 99/100 N.!~

Note that since symbols are specified for both 10 and 11 generators
(and also for 20 and 21G, and for 30 and 31G), there are alternate
spellings for each tone.

This is given in high-precision Sagittal notation, which employs
accent marks to notate most (if not all) of these ratios *exactly*.
In the medium-precision (Athenian-level) notation, the accents
(indicated by "." and "'", a 5-schisma down and up, respectively) are
simply omitted.

This is just one example of what can be done with these accidentals,
which are ready for your use -- once you've settled on how to name
and notate your nominals.

--George

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
> > Hi Kraig,
> >
> > I agree with this, but the question was about the number of
> nominals
> > in the notation, not the number of notes in the scale.
>
> But shouldn't these be closely related?

Yes.

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> --- In tuning@yahoogroups.com, I wrote:
> > I think it may well make sense to use (up to) two accidentals per
> > note for LTs having more than 5 parallel chains. The nominals
form
> > a "MOS" on one chain, one accidental extends that chain, the
other
> > jumps you to other chains.
>
> Oops! That's not what you meant at all. You meant the nominals
would
> all be in different chains and they wouldn't cover all the chains,
> but would be a manageable (5 to 10 note) MOS of the best
temperament
> consistent with n-ET where n is the number of chains, and one
> accidental would extend this to one note per chain (the full n-ET),
> while the other accidental would move you along the chains.
>
> Yes. I agree with this. I believe this is exactly what Graham Breed
> proposed.

I have no idea what this means. I guess I meant the nominals would
all be within a single chain of *periods*, if the period of the "LT"
is, say, 1/6 octave or smaller.

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> hi Paul,
>
>
> i only realized just now that your "zoom" charts
> on my "equal-temperament" page
>
> http://www.tonalsoft.com/enc/eqtemp.htm
>
> don't have a line for the MIRACLE family plotted on them.
>
>
>
> -monz

MIRACLE isn't a 5-limit temperament. The 5-limit comma of MIRACLE has
been called 'ampersand', and if we were to include that, there are
tons of simpler and/or smaller commas that we would then
be "obligated", I feel, to include. I'd rather not go down that path,
cluttered as the chart is already.

Perhaps it would be worthwhile to make separate sets of charts for
higher limits, such as 7-limit. In that case, and especially for 11-
limit, MIRACLE would certainly need to be included.

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> >You're forgetting the hypothesis again. It involves Fokker
> >periodicity blocks.
>
> ...with all but one of their unison vectors tempered out, which
> is to say linear temperaments.

Nope. For one thing, "linear temperaments" and the like are infinite,
while Fokker periodicity blocks are finite. Meantone, for example,
has an infinite number of pitches per octave (assuming you don't have
a restriction on the number of sharps or flats), while the diatonic
periodicity block has 7 pitches per octave, whether or not you temper
anything out.

If we restrict our attention to infinite tuning systems, the
hypothesis is completely irrelevant. It has nothing to say in this
area.

> >> I don't know
> >> what happens to the temperament situation at the non-MOS points.
> >> I assume (and if I read Graham right...) that we get planar
> >> temperament, etc.,
> >
> >Hmm? If it's generated "linearly", then of course it's
> >still "linear", in the sense you meant above.
>
> If its pitches move by two different commas under a transposition
> of a just interval,

I'm not following. Can you describe this process in more detail?

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> --- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> > >> hi Paul,
> > >>
> > >>
> > >> i only realized just now that your "zoom" charts
> > >> on my "equal-temperament" page
> > >>
> > >> http://www.tonalsoft.com/enc/eqtemp.htm
> > >>
> > >> don't have a line for the MIRACLE family plotted on them.
> >
> > Probably because they're 5-limit graphs, and miracle is
> > a lousy 5-limit temperament.
> >
> > -Carl
>
>
>
> but you can still easily see on the "zoom: 10" graph
> that 21, 31, 41, 51, 52, and 72 all lie on the same
> straight line. why not label it?

I could ask you the same question about tons of other straight lines
on there. Only so many before it gets too cluttered.

Let's put together some 7-limit graphs sometime soon, OK?

Meanwhile, I have an old issue with the zoom: 100 graph, which I
might as well bring up again:

Look at my original. It has a "counterschismic" line connecting 306
with 53.

Now look at your negative. The "counterschismic" line is missing.

Would you re-do your negative?

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> I have no idea what this means. I guess I meant the nominals would
> all be within a single chain of *periods*, if the period of
the "LT"
> is, say, 1/6 octave or smaller.

Yes. That's what I meant.

And then I understand you were proposing to use one set of
accidentals (conventional sharps and flats in the case of
enneadecal) to extend this "chain" of periods to a full octave cycle
of periods (equiv to 19-ET), and use a different set of accidentals
to move up or down the chains of generators from these 19.

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

> MIRACLE isn't a 5-limit temperament.

I don't agree; it has the same TOP tuning in the 5-limit as in the 7
and 11 limits. It isn't a very good 5-limit temperament, but it seems
absurd, given that it uses the same tuning and mapping, not to call
it miracle.

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
> > I have no idea what this means. I guess I meant the nominals
would
> > all be within a single chain of *periods*, if the period of
> the "LT"
> > is, say, 1/6 octave or smaller.
>
> Yes. That's what I meant.
>
> And then I understand you were proposing to use one set of
> accidentals (conventional sharps and flats in the case of
> enneadecal) to extend this "chain" of periods to a full octave
cycle
> of periods (equiv to 19-ET), and use a different set of accidentals
> to move up or down the chains of generators from these 19.

Well, I wasn't making any firm proposals, I was just asking if this
is similar to stuff that's already done in Sagittal. And I guess, in
one version, it is . . .

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
>
> > MIRACLE isn't a 5-limit temperament.
>
> I don't agree; it has the same TOP tuning in the 5-limit as in the
7
> and 11 limits.

The stuff on Monz's page in question all assumes pure octaves.

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> Question 1: Can you quantify exactly what is lost by basing a
> >> notation on a non-MOS? I imagine that more than one accidental
> >> pair is then required in many situations. . .
> >>
> >> Question 2: Can you quantify exactly what is lost by basing a
> >> notation on an improper MOS? I imagine it introduces anomalies
> >> such as B being higher than C in certain situations. . .
> >
> >These are excellent questions. I think I'm going to have to go and
> >ponder them in the bath.
>
> Ah, that takes me back. My apartment has only a stand-up shower!
> :(
>
> >But I can say that multiple pairs of accidentals isn't a problem
to
> >me. I prefer this to having multiple accidentals against a single
> >note. And with Sagital there's no shortage.
>
> Noted. [Pun intended.]
>
> >I assume for question 1 that you would want the non-MOS to at
> >least be contiguous on the chain(s) of generators.
>
> You may so assume.
>
> >Would you also want the non-MOS to be proper (like that one
> >you found in the minor thirds temperament)?
>
> Sure, let's not bite off too big a chew. Besides, Q2 should take
> care of impropriety... I don't foresee combination effects.
>
> >For Q2, It doesn't need to introduce such anomalies, that's an
> >independent choice.
>
> [sound of gears turning]
>
> -Carl

Well it's been a long bath, and my answers are "no" and "no". That
is, I can't quantify them.

The best I can do is to say that they would be "icky". :-)

Seriously, if I was a congnitive psychologist then maybe I'd be able
to quantify the cognitive load causes by having to remember where 3
different step-sizes (L M s) fell in a non-MOS set of nominal,
instead of only having to worry about 2 (L s).

I think David Rothenberg had some reasonable goes at quantifying
some things based on information theory. His stuff about stability
etc. i.e. whatever tends to make a good recognisable melodic object
or scale will tend to make a good set of nominals too.

I'd rather use a slightly improper MOS than use a proper non-MOS
because of the more than 2 step sizes thing, and how hard this gets
to remember, when you modulate.

There are some limits I would put on how improper a set of MOS/DE
nominals with 5 to 10 notes can be.
(a) I would want L/s to be less than 3 for all reasonable values of
the generator, i.e. for any kind of optimum.
(b) When you list the cardinalities of all the MOS/DE for a
temperament in order, I would like the cardinality of the nominals
MOS/DE to be no more than one position away from the cardinality of
a proper MOS/DE.

Otherwise I would rather use a proper MOS/DE that has more than 10
notes (or maybe even one with only 4 notes), or for LTs with more
than5 periods to the ocatve, use the method Paul just described, of
notating a chain (or the whole cycle) of _periods_ with nominals,
rather than a chain of generators.

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> > --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
> wrote:
> > > I have no idea what this means. I guess I meant the nominals
> would
> > > all be within a single chain of *periods*, if the period of
> > the "LT"
> > > is, say, 1/6 octave or smaller.
> >
> > Yes. That's what I meant.
> >
> > And then I understand you were proposing to use one set of
> > accidentals (conventional sharps and flats in the case of
> > enneadecal) to extend this "chain" of periods to a full octave
> cycle
> > of periods (equiv to 19-ET), and use a different set of
accidentals
> > to move up or down the chains of generators from these 19.
>
> Well, I wasn't making any firm proposals, I was just asking if
this
> is similar to stuff that's already done in Sagittal. And I guess,
in
> one version, it is . . .

Yes. But sort of by accident. That is, we didn't have any thoughts
of periods and generators in mind at the time, since it was just
notating ETs, not LTs. But I agree it would be sensible to extend
this method of notation to LT's whose periods form an ET with
reasonable fifths, e.g. 12, 17, 19, 22, 24, 29, etc

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

> The stuff on Monz's page in question all assumes pure octaves.

Assuming pure octaves, 41/422 is copoptimal for the 5 and 7 limit,
and 7/72 is a fine choice in 5, 7, 9 or 11. The rationale for calling
the 5-limit temperament miracle is quite strong.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
>
> > The stuff on Monz's page in question all assumes pure octaves.
>
> Assuming pure octaves, 41/422 is copoptimal for the 5 and 7 limit,
> and 7/72 is a fine choice in 5, 7, 9 or 11. The rationale for
calling
> the 5-limit temperament miracle is quite strong.

How about using words for what they were intended? MIRACLE always
implied 7-limit or 11-limit, while "ampersand" was all 5-limit.

hi Paul,

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

> Let's put together some 7-limit graphs sometime soon, OK?

sounds good to me!

> Meanwhile, I have an old issue with the zoom: 100 graph,
> which I might as well bring up again:
>
> Look at my original. It has a "counterschismic" line
> connecting 306 with 53.
>
> Now look at your negative. The "counterschismic" line is
> missing.
>
> Would you re-do your negative?

hmm, that's really strange ... wonder what happened.
sure, i'll redo it ... i can't guarantee how soon, but
it won't take long to do.

i'm really working hard on the Encyclopaedia of Tuning
right now, and pretty soon i'll want the whole list of
all the corrections you've been "reminding" me about for
such a long time.

-monz

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:

> i'm really working hard on the Encyclopaedia of Tuning
> right now, and pretty soon i'll want the whole list of
> all the corrections you've been "reminding" me about for
> such a long time.

Well, I hoped you've saved them, because I sure don't have access to
the whole list. Much of it resided in the sent items folder of my now-
defunct stretch e-mail account. Many of the others were sent directly
to you by clicking on this web server, so I never had any record of
them whatsoever.

hi Paul and Gene,

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:

> > --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
> wrote:
> >
> > > The stuff on Monz's page in question all assumes pure octaves.
> >
> > Assuming pure octaves, 41/422 is copoptimal for the
> > 5 and 7 limit, and 7/72 is a fine choice in 5, 7, 9 or 11.
> > The rationale for calling the 5-limit temperament miracle
> > is quite strong.
>
> How about using words for what they were intended? MIRACLE
> always implied 7-limit or 11-limit, while "ampersand" was
> all 5-limit.

is it not possible that ampersand is a sub-family under the
larger miracle family?

-monz

hi Paul,

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
>
> > i'm really working hard on the Encyclopaedia of Tuning
> > right now, and pretty soon i'll want the whole list of
> > all the corrections you've been "reminding" me about for
> > such a long time.
>
> Well, I hoped you've saved them, because I sure don't have
> access to the whole list. Much of it resided in the sent
> items folder of my now-defunct stretch e-mail account. Many
> of the others were sent directly to you by clicking on this
> web server, so I never had any record of them whatsoever.

well, hmm ... i save every non-spam email i get, so hopefully
i do have them all. unfortunately my computer suffered a
rather serious virus attack recently, and quite a few files
did get corrupted. i'll have to search for them.

-monz

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
>
> How about using words for what they were intended? MIRACLE always
> implied 7-limit or 11-limit, while "ampersand" was all 5-limit.

How about using words in a logical way?

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:

> is it not possible that ampersand is a sub-family under the
> larger miracle family?

Not really. It uses the same tuning and the same mapping. It's just
miracle, where you ignore any 7 or 11 limit interpretations of the
same notes.

the closest thing i am seeing off the cuff is
http://www.anaphoria.com/xen3a.PDF
monz wrote:

> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> > --- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:
> > > Dave Keenan wrote:
> > > > Based on some clues from Kraig Grady and Carl Lumma
> > > > we can see that one approach is to have a nominal
> > > > corresponding to each step of some good high-limit ET
> > > > having a manageable number of notes and having fifths
> > > > in the meantone-12-ET-pythagorean range. Since 72 is
> > > > too many then 31 seems a good choice.
> > >
> > > I think even 31 might be too many. How about a selection
> > > of 19 notes out of 31?
> >
> > That's not a bad idea. We should at least see how far we
> > can get with only 19. The "Greek for flats, Hebrew for sharps"
> > idea allows for extending it later if necessary.
>
> i don't know where i saw this (i'm sure Kraig can help),
> but Erv Wilson used the first five Greek letters along
> with the usual first 7 Roman letters, and two accidentals
> which i'll render here as - and + , to notate modulus-31
> as follows:
>
> 0 C
> 30 C -
> 29 B +
> 28 B
> 27 beta +
> 26 beta
> 25 beta -
> 24 A +
> 23 A
> 22 alpha +
> 21 alpha
> 20 alpha -
> 19 G +
> 18 G
> 17 gamma +
> 16 gamma
> 15 gamma -
> 14 F +
> 13 F
> 12 F -
> 11 E +
> 10 E
> 9 epsilon +
> 8 epsilon
> 7 epsilon -
> 6 D +
> 5 D
> 4 delta +
> 3 delta
> 2 delta -
> 1 C +
> 0 C
>
> note that Wilson used both accidentals for all five
> of the Greek letters, but only with C and F out of
> the Roman set; the other Roman letters use only the
> plain letter and the plus sign, but not the minus sign.
> C and F are also the two Roman letters which do not
> have associated Greek equivalents here.
>
> also note that Wilson's ordering of the Greek letters
> follows the Roman alphabetization and not the Greek.
>
> regarding 19edo: i've just recently added circular
> enharmonicity diagrams to the bottom of my 19edo page,
> which might be of help:
>
> http://www.tonalsoft.com/enc/19edo.htm
>
> -monz
>
>
>
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - leave the group.
> tuning-nomail@yahoogroups.com - turn off mail from the group.
> tuning-digest@yahoogroups.com - set group to send daily digests.
> tuning-normal@yahoogroups.com - set group to send individual emails.
> tuning-help@yahoogroups.com - receive general help information.
>
> Yahoo! Groups Links
>
>
>
>

-- -Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com
The Wandering Medicine Show
KXLU 88.9 FM WED 8-9PM PST

Page 8 seems to confirm exactly what Monz posted below.

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@a...> wrote:
> the closest thing i am seeing off the cuff is
> http://www.anaphoria.com/xen3a.PDF
> monz wrote:
>
> > --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...>
wrote:
> > > --- In tuning@yahoogroups.com, Herman Miller <hmiller@I...>
wrote:
> > > > Dave Keenan wrote:
> > > > > Based on some clues from Kraig Grady and Carl Lumma
> > > > > we can see that one approach is to have a nominal
> > > > > corresponding to each step of some good high-limit ET
> > > > > having a manageable number of notes and having fifths
> > > > > in the meantone-12-ET-pythagorean range. Since 72 is
> > > > > too many then 31 seems a good choice.
> > > >
> > > > I think even 31 might be too many. How about a selection
> > > > of 19 notes out of 31?
> > >
> > > That's not a bad idea. We should at least see how far we
> > > can get with only 19. The "Greek for flats, Hebrew for sharps"
> > > idea allows for extending it later if necessary.
> >
> > i don't know where i saw this (i'm sure Kraig can help),
> > but Erv Wilson used the first five Greek letters along
> > with the usual first 7 Roman letters, and two accidentals
> > which i'll render here as - and + , to notate modulus-31
> > as follows:
> >
> > 0 C
> > 30 C -
> > 29 B +
> > 28 B
> > 27 beta +
> > 26 beta
> > 25 beta -
> > 24 A +
> > 23 A
> > 22 alpha +
> > 21 alpha
> > 20 alpha -
> > 19 G +
> > 18 G
> > 17 gamma +
> > 16 gamma
> > 15 gamma -
> > 14 F +
> > 13 F
> > 12 F -
> > 11 E +
> > 10 E
> > 9 epsilon +
> > 8 epsilon
> > 7 epsilon -
> > 6 D +
> > 5 D
> > 4 delta +
> > 3 delta
> > 2 delta -
> > 1 C +
> > 0 C
> >
> > note that Wilson used both accidentals for all five
> > of the Greek letters, but only with C and F out of
> > the Roman set; the other Roman letters use only the
> > plain letter and the plus sign, but not the minus sign.
> > C and F are also the two Roman letters which do not
> > have associated Greek equivalents here.
> >
> > also note that Wilson's ordering of the Greek letters
> > follows the Roman alphabetization and not the Greek.
> >
> > regarding 19edo: i've just recently added circular
> > enharmonicity diagrams to the bottom of my 19edo page,
> > which might be of help:
> >
> > http://www.tonalsoft.com/enc/19edo.htm
> >
> > -monz
> >
> >
> >
> >
> > You can configure your subscription by sending an empty email to
one
> > of these addresses (from the address at which you receive the
list):
> > tuning-subscribe@yahoogroups.com - join the tuning group.
> > tuning-unsubscribe@yahoogroups.com - leave the group.
> > tuning-nomail@yahoogroups.com - turn off mail from the group.
> > tuning-digest@yahoogroups.com - set group to send daily digests.
> > tuning-normal@yahoogroups.com - set group to send individual
emails.
> > tuning-help@yahoogroups.com - receive general help information.
> >
> > Yahoo! Groups Links
> >
> >
> >
> >
>
> -- -Kraig Grady
> North American Embassy of Anaphoria Island
> http://www.anaphoria.com
> The Wandering Medicine Show
> KXLU 88.9 FM WED 8-9PM PST

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:

/tuning/topicId_53851.html#53876

> One feature that may be less than obvious on the Sagittal home
page,
> is that you can click on the image that shows an example phrase
> designed to show lots of Sagittal symbols, to hear it played in
> various tunings.
> http://dkeenan.com/sagittal/exmp/
>

***It sure isn't... :(

How about "(click here for example tunings)"

??

JP

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:

/tuning/topicId_53851.html#53897

>
> --- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:
>
> > --- In tuning@yahoogroups.com, "Carl Lumma" <ekin@l...> wrote:
>
> > > > the university musical establishment now generally
> > > > considers any efforts to create music using alternate
> > > > tunings a complete waste of time,
> > >
> > > Again, is this true?
> >

***I also found this to be a bit exaggerated, but it was funny to
read at the time... :)

JP

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:

/tuning/topicId_53851.html#53905

> hi Paul,
>
>
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
>
> > --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> >
> > > perhaps families of tunings should be named and classified
> > > according to the ways that sagittal works, since it's such
> > > a broad-based notation.
> >
> > For any family not based on a single chain of fifths, it works
quite
> > awkwardly. That one reason Carl and I weren't too crazy about it -
-
> > it favors systems like pythagorean, meantone, and
> > helmholtz/groven/schismic, at the expense of miracle, magic,
pajara,
> > etc....
>
>
> but there's the beginning of a classification right there !!
>
> pythagorean, meantone, and schismic could all be subsets of
> a larger "sagittal" category, and those with multiple
> chains would have other name(s).
>

***That's rather putting the back of the horse before the arrow,
isn't it?? :)

J. Pehrson

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
>
> /tuning/topicId_53851.html#53876
>
> > One feature that may be less than obvious on the Sagittal home
> page,
> > is that you can click on the image that shows an example phrase
> > designed to show lots of Sagittal symbols, to hear it played in
> > various tunings.
> > http://dkeenan.com/sagittal/exmp/
> >
>
> ***It sure isn't... :(
>
> How about "(click here for example tunings)"

Hi Joseph. We'll fix it.

But you should at least have seen a popup saying something similar when you mouse over
the figure. Do you see that?

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

/tuning/topicId_53851.html#54100

> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
>
> > In the 1950s Henry Pleasants wrote a highly controversial book,
> _The
> > Agony of Modern Music_, in which he made a very persuasive case
for
> > the irrelevance of 20th-century "serious music." He placed the
> > breakdown of harmony somewhere around the 2nd decade of that
> century,
> > as evidenced by the emergence of new techniques that completely
> > discarded existing harmonic norms.
>
> So Shostakovich spent his whole life being irrelevant? Poor fella.
>
> The second decade of the 20th century is way to early to start
> kvetching about the death of classical music. Camille Saint-Saens
> died in that decade, for gosh sakes, and was composing music right
up
> to the end not much different than he did when he was 19 and wrote
> his Symphony #1. Prokoviev died in 1954, Sibelius in 1957, Vaughan
> Williams in 1958 so I suggest at least wait until the 60s.

***The Pleasants book is an intellectually specious and vapid read...
(most *un* pleasant...)

J. Pehrson

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
>
> > >You're forgetting the hypothesis again. It involves Fokker
> > >periodicity blocks.
> >
> > ...with all but one of their unison vectors tempered out, which
> > is to say linear temperaments.
>
> Nope. For one thing, "linear temperaments" and the like are
infinite,
> while Fokker periodicity blocks are finite. Meantone, for example,
> has an infinite number of pitches per octave (assuming you don't
have
> a restriction on the number of sharps or flats), while the diatonic
> periodicity block has 7 pitches per octave, whether or not you
temper
> anything out.

To attempt to make something positive out of this . . . If you start
with an infinite JI system (basically, all the rationals within some
prime limit, or anything like that), and it's N-dimensional
(including prime 2 in the count), then tempering out N-2 independent
commas (N *minus* 2) *will* yield what you call a "linear
temperament", which is what my paper calls a 2-dimensional
temperament (since I count prime 2).

But that's not the hypothesis, that's just a standard result in
linear algebra, basically . . .

> If we restrict our attention to infinite tuning systems, the
> hypothesis is completely irrelevant. It has nothing to say in this
> area.

Dave Keenan wrote:

> I don't want to be too negative about this since you've obviously > put a lot of though into it, and I haven't yet understood your > proposal completely, but ...
> > Having the nominals be a 2D periodicity block has already been tried > in Ben Johnston's JI notation, and in my not so humble opinion it > results in a complete mess as soon as you want to modulate away from > the basic PB.
> > This was discussed on this list some months back. I believe Paul > Erlich agreed with me.

I don't think that any arbitrary periodicity block would be useful, and I'd agree with the assessment that Ben Johnston's notation in particular is confusing. But it's like saying that having the nominals in a linear chain has already been tried, if the only example you have is the diatonic scale. That approach makes a "complete mess" with third-based temperaments, half-octave temperaments, and pretty much anything that isn't diatonic. Pretty much everything that's "already been tried" has problems with one temperament or another. I think you should give this one another look.

You can look at this "magic/porcupine/pajara" notation in more than one way. Above all, it's a neat way of notating each note of 22-ET, which is one of the smaller good 7-limit ET's with an exact half-octave. These same 22 nominals can be used to name degrees of Orwell[31], Pajara[34], Porcupine[37], or Magic[41]. You could go to 26-ET and use the whole alphabet, but there aren't as many good temperaments with 26-ET compared with 22-ET. Or you could stick with 12-ET and just add a few extra names for the black notes, but a few odd temperaments still need more than 12 nominals to notate.

Take mavila as an example of how this notation is intended to work: if you round to the nearest 22-ET degree, you get 15-3-12-0-10-19-7 (I E H D V C U). The thirds D-U, E-V, H-C and I-D are notated consistently with major thirds as in porcupine or magic. In pitch order this is H I C D E U V: the difference between the steps I-C and E-U compared with the other steps is clear.

D S L E T M F U N G V O H A P I B Q J C R K D
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
D E U V H I C D

Now, this isn't a perfect system (23-ET notation is clearly better for mavila), but it still seems pretty good. The one deficiency is that the step V-H appears to be different from the other small steps, and consequently the minor thirds U-H and V-I are notated inconsistently.

This system even turns out to be acceptable for "gawel", the cumbersome temperament with the approx. 569-cent generator, when mapped to steps of magic[41]:

D S L E T M F U N G V O H A P I B Q J C R K D
0 2 4 6 7 9 11 13 15 17 19 22 24 26 28 30 32 34 35 37 39 41
B
M I
T P
L A
S H D
D V K
G R
N J
U Q
F

As you can see, the match isn't perfect, but it's still pretty good for a generic all-purpose LT notation system.

>> >You're forgetting the hypothesis again. It involves Fokker
>> >periodicity blocks.
>>
>> ...with all but one of their unison vectors tempered out, which
>> is to say linear temperaments.
>
>Nope. For one thing, "linear temperaments" and the like are infinite,
>while Fokker periodicity blocks are finite. Meantone, for example,
>has an infinite number of pitches per octave (assuming you don't have
>a restriction on the number of sharps or flats), while the diatonic
>periodicity block has 7 pitches per octave, whether or not you temper
>anything out.

You're right, I shouldn't say "linear temperament" and "planar
temperament". I should say periodicity strip, etc. etc. But what
I said (IIRC) remains true despite this foible.

>> >> I don't know
>> >> what happens to the temperament situation at the non-MOS points.
>> >> I assume (and if I read Graham right...) that we get planar
>> >> temperament, etc.,
>> >
>> >Hmm? If it's generated "linearly", then of course it's
>> >still "linear", in the sense you meant above.
>>
>> If its pitches move by two different commas under a transposition
>> of a just interval,
>
>I'm not following. Can you describe this process in more detail?

Sorry, this is wrong, transposing by any just interval doesn't
necessarily get you over to the next tile. I think transposing by
the generator does change at most one note, though.

-Carl

>> >> Question 1: Can you quantify exactly what is lost by basing a
>> >> notation on a non-MOS? I imagine that more than one accidental
>> >> pair is then required in many situations. . .
>> >>
>> >> Question 2: Can you quantify exactly what is lost by basing a
>> >> notation on an improper MOS? I imagine it introduces anomalies
>> >> such as B being higher than C in certain situations. . .

>Well it's been a long bath, and my answers are "no" and "no". That
>is, I can't quantify them.
>
>The best I can do is to say that they would be "icky". :-)
>
>Seriously, if I was a congnitive psychologist then maybe I'd be able
>to quantify the cognitive load causes by having to remember where 3
>different step-sizes (L M s) fell in a non-MOS set of nominal,
>instead of only having to worry about 2 (L s).
>
>I think David Rothenberg had some reasonable goes at quantifying
>some things based on information theory. His stuff about stability
>etc. i.e. whatever tends to make a good recognisable melodic object
>or scale will tend to make a good set of nominals too.
>
>I'd rather use a slightly improper MOS than use a proper non-MOS
>because of the more than 2 step sizes thing, and how hard this gets
>to remember, when you modulate.
>
>There are some limits I would put on how improper a set of MOS/DE
>nominals with 5 to 10 notes can be.
>(a) I would want L/s to be less than 3 for all reasonable values of
>the generator, i.e. for any kind of optimum.
>(b) When you list the cardinalities of all the MOS/DE for a
>temperament in order, I would like the cardinality of the nominals
>MOS/DE to be no more than one position away from the cardinality of
>a proper MOS/DE.

Sounds good.

>Otherwise I would rather use a proper MOS/DE that has more than 10
>notes (or maybe even one with only 4 notes), or for LTs with more
>than5 periods to the ocatve, use the method Paul just described, of
>notating a chain (or the whole cycle) of _periods_ with nominals,
>rather than a chain of generators.

Yes. Of course I've always looked at periods as generators.
In fact I apparently caused a lot of confusion on tuning-math
by calling them generators.

Thanks for your reply,

-Carl

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:

/tuning/topicId_53851.html#54262

> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
> > --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...>
wrote:
> >
> > /tuning/topicId_53851.html#53876
> >
> > > One feature that may be less than obvious on the Sagittal home
> > page,
> > > is that you can click on the image that shows an example
phrase
> > > designed to show lots of Sagittal symbols, to hear it played
in
> > > various tunings.
> > > http://dkeenan.com/sagittal/exmp/
> > >
> >
> > ***It sure isn't... :(
> >
> > How about "(click here for example tunings)"
>
> Hi Joseph. We'll fix it.
>
> But you should at least have seen a popup saying something similar
when you mouse over
> the figure. Do you see that?

***Hi Dave,

Yes, that works, but the "problem" is that there is no incentive
to "mousey over" those staves. They just look like graphics. At
least, *I* didn't do it; I went right to the bottom part for
the "stuff..."

Joseph

--- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:

> This system even turns out to be acceptable for "gawel", the
cumbersome
> temperament with the approx. 569-cent generator, when mapped to
steps of
> magic[41]:
>
> D S L E T M F U N G V O H A P I B Q J C R K D
> 0 2 4 6 7 9 11 13 15 17 19 22 24 26 28 30 32 34 35 37 39 41
> B
> M I
> T P
> L A
> S H D
> D V K
> G R
> N J
> U Q
> F
>
> As you can see, the match isn't perfect, but it's still pretty good
for
> a generic all-purpose LT notation system.

I'm not exactly following all this, but I'd like to point out every
third note (generatorwise) of gawel[19] is a single diatonic scale.
So it would be nice, ideally, for this diatonic scale to
be "nominalled" in a familiar way.

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> Sorry, this is wrong, transposing by any just interval doesn't
> necessarily get you over to the next tile. I think transposing by
> the generator does change at most one note, though.

What if the period is 1/2 octave, or 1/3 octave, or . . . ?

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
>
> /tuning/topicId_53851.html#53897
>
> >
> > --- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:
> >
> > > --- In tuning@yahoogroups.com, "Carl Lumma" <ekin@l...> wrote:
> >
> > > > > the university musical establishment now generally
> > > > > considers any efforts to create music using alternate
> > > > > tunings a complete waste of time,
> > > >
> > > > Again, is this true?
> > >
>
> ***I also found this to be a bit exaggerated, but it was funny to
> read at the time... :)
>
> JP

The whole "mythology" piece has several purposes:

1) To serve as an easy-to-read, gentle, and (especially) entertaining
introduction to the Sagittal notation for musicians (both performers
and composers) who will be using it for the first time;

2) To provide some background information about alternate tunings in
general and issues pertinent to microtonal notation in particular;

3) To motivate musicians and music students to tell others about the
Sagittal website;

4) To garner sympathy and support for our cause;

and, of course, last but not least:

5) To regain a respectable share of the religious market for the
Pantheon on Mount Olympus. ;-)

If there are others outside our alternate tunings group(s) who think
that the opening statement above is exaggerated, then I would hope
that they might want to stop by here and perhaps put in a message of
encouragement.

--"George"

--- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:
> George,
>
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
> > You can read some comments (both pro and con) about the book here:
> > http://www.kafalas.com/urbcol72.htm
> > and I would highly recommend that you (and anyone else who hopes
that
> > the microtonal movement would some day be more than a niche
market)
> > get a copy (out of print, but available used) and read it,
because
> > Pleasants writes from an academic background, but (as a music
critic)
> > addresses the problem of a lost audience for "serious music" from
the
> > perspective of a typical concert-goer.
> ...
> > BTW, he never once mentioned (or even hinted) that microtonality
> > might hold the answer to the several "crises" he describes, so I
> > think we are in a good position to remedy some of those things.
>
> George, I think that is true to a point, but not only harmonic
> language has become wrung out - styles have passed as well. If one
> simply puts old wine in new bottles, the audience will remain small.

Jon,

I have put off replying to this and subsequent comments because I
didn't want to "shoot from the hip" before I had thought everything
through sufficiently. Unfortunately, there have been too many other
things going on this week that I have had to finish up by today,
which has not given me sufficient time to address this topic. I
believe that musical style is critical to the ability of any music,
microtonal or not, to be relevant to those outside that particular
group in which it is being created, so I very definitely wish to
pursue this topic once I have sorted through my many (and sometimes
conflicting) thoughts about this.

Unfortunately, due to circumstances beyond my control, I expect to be
away from the tuning lists for most of the next 1.5 weeks, and when I
return I will have a lot of catching up to do. But hopefully I will
be able to reply soon after that.

I want everyone to know that I'll be missing you all -- but I'll be
getting back in tune -- soon!

--George

George,

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:
> I have put off replying to this and subsequent comments because I
> didn't want to "shoot from the hip"

I've gotten powder burns around the crotch when I tried that - you're
a smart guy.

But seriously, I'll look forward to your thoughts on the matter,
either here or at MMM. I honestly hold nothing against anyone in their
chosen style(s) of composing/performing, and I was simply addressing
this as a music that has some function in our life as a general
populous beyond simply illustrating a tuning.

We all need to make music that pleases us (personally) first; if it
fails that, no one else would be likely to enjoy it. But if all this
tuning stuff really has a meaning aside from the joy of calculation,
it would be folly to ignore the potential for more listeners, for
whatever reason.

I'll see you down the road...

Cheers,
Jon

--- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:

> We all need to make music that pleases us (personally) first; if it
> fails that, no one else would be likely to enjoy it. But if all this
> tuning stuff really has a meaning aside from the joy of calculation,
> it would be folly to ignore the potential for more listeners, for
> whatever reason.

I don't think being trendy and now is the magic answer, as it seemed
to me you were suggesting; in fact I think Margo's stuff shows the
potential of doing the exact opposite.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:
>
> > We all need to make music that pleases us (personally) first; if
it
> > fails that, no one else would be likely to enjoy it. But if all
this
> > tuning stuff really has a meaning aside from the joy of
calculation,
> > it would be folly to ignore the potential for more listeners, for
> > whatever reason.
>
> I don't think being trendy and now is the magic answer, as it
seemed
> to me you were suggesting; in fact I think Margo's stuff shows the
> potential of doing the exact opposite.

I don't equate "music with meaning" with "trendy and now", though I
can see why one might infer "trendy and now" from "potential for more
listeners".

--- In tuning@yahoogroups.com, Graham Breed <graham@m...> wrote:
...
> Am I right in
> assuming that sagittal will solve this problem? That is, that it
> supplies convenient symbols for both the usual Pythagorean sharps
and
> flats and these alternative, 5-limit based ones? More generally,
all we
> need is a good way of notating 5-limit JI based on 7 nominals and
> covering 6 lattice rows.

Yes. Sagittal provides suitable accidentals.

You can try it in Scala. Set up a scale with the ratios you're
interested in and SET NOTATION SAJI1.

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

> I don't equate "music with meaning" with "trendy and now", though I
> can see why one might infer "trendy and now" from "potential for
more
> listeners".

I was really responding mostly to this:

/tuning/topicId_53851.html#54146

I don't think new tunings lead automatically to new forms of
expression, and that if it doesn't, your music is doomed to failure.
Quite the opposite, I think the most interesting microtonal music is
one that puts old wine in new bottles, because then the potential of
the old wine is finally realized, and vast possibilities are opened
up.

Anyway, I suggest people write what they would like to listen to
themselves, and not try to be a microtonal Britney Spears unless that
music speaks to you.

Gene,

As I kindly pointed out, to each his own. However, you and I
completely disagree as to what will intrigue a listener's ear and
experience, something that doesn't surprise me. I also believe that
the idea of applying new tunings to old forms of music and reaping
enormous rewards, untold vistas of expression, is overstated.

But one thing I think everyone can agree on: the music that will
appeal the most, and will last the longest, will be the *best* music
one can possibly make. And to do that, each of us will want to make
the music that we feel the closest to, that speaks to us, and will
hopefully speak to others.

> Anyway, I suggest people write what they would like to listen to
> themselves, and not try to be a microtonal Britney Spears unless that
> music speaks to you.

I wouldn't take to the witness stand on this, but I'm willing to bet
you don't know a whole lot about the music of today, much less the
last couple of decades. To make a comment about Ms. Spears would be
about as appropriate as me suggesting people revisit the fine works of
Leroy Anderson in a microtonal fashion. Pop acts, both of 'em. I'm
sure anyone's wine can find better bottles than those.

Cheers,
Jon

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
> > > How about "(click here for example tunings)"
> >
> > Hi Joseph. We'll fix it.
> >
> > But you should at least have seen a popup saying something
similar
> when you mouse over
> > the figure. Do you see that?
>
>
> ***Hi Dave,
>
> Yes, that works, but the "problem" is that there is no incentive
> to "mousey over" those staves. They just look like graphics. At
> least, *I* didn't do it; I went right to the bottom part for
> the "stuff..."

I've now put a link for it among the "stuff ...". Thanks.

--- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:
> I don't think that any arbitrary periodicity block would be
useful, and
> I'd agree with the assessment that Ben Johnston's notation in
particular
> is confusing. But it's like saying that having the nominals in a
linear
> chain has already been tried, if the only example you have is the
> diatonic scale. That approach makes a "complete mess" with third-
based
> temperaments, half-octave temperaments, and pretty much anything
that
> isn't diatonic.
> Pretty much everything that's "already been tried" has
> problems with one temperament or another. I think you should give
this
> one another look.

OK. But I'm pretty sure I can see with Johnston notation that it's
fundamentally the 2-dimensionality of the nominal set that causes
the problems.

> You can look at this "magic/porcupine/pajara" notation in more
than one
> way. Above all, it's a neat way of notating each note of 22-ET,
which is
> one of the smaller good 7-limit ET's with an exact half-octave.
These
> same 22 nominals can be used to name degrees of Orwell[31], Pajara
[34],
> Porcupine[37], or Magic[41]. You could go to 26-ET and use the
whole
> alphabet, but there aren't as many good temperaments with 26-ET
compared
> with 22-ET. Or you could stick with 12-ET and just add a few extra
names
> for the black notes, but a few odd temperaments still need more
than 12
> nominals to notate.
>
> Take mavila as an example of how this notation is intended to
work: if
> you round to the nearest 22-ET degree, you get 15-3-12-0-10-19-7
(I E H
> D V C U). The thirds D-U, E-V, H-C and I-D are notated
consistently with
> major thirds as in porcupine or magic. In pitch order this is H I
C D E
> U V: the difference between the steps I-C and E-U compared with
the
> other steps is clear.
>
> D S L E T M F U N G V O H A P I B Q J C R K D
> 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
> D E U V H I C D
>
> Now, this isn't a perfect system (23-ET notation is clearly better
for
> mavila), but it still seems pretty good. The one deficiency is
that the
> step V-H appears to be different from the other small steps, and
> consequently the minor thirds U-H and V-I are notated
inconsistently.
>
> This system even turns out to be acceptable for "gawel", the
cumbersome
> temperament with the approx. 569-cent generator, when mapped to
steps of
> magic[41]:
>
> D S L E T M F U N G V O H A P I B Q J C R K D
> 0 2 4 6 7 9 11 13 15 17 19 22 24 26 28 30 32 34 35 37 39 41
> B
> M I
> T P
> L A
> S H
D
> D V K
> G R
> N J
> U Q
> F
>
> As you can see, the match isn't perfect, but it's still pretty
good for
> a generic all-purpose LT notation system.

If we forget about whether this is a PB or not, then I totally agree
that this is the right way to go about using the rest of the Roman
alphabet as nominal (if you must use the rest of the Roman alphabet).

i.e. I agree with "O" as the half-octave, since it's like zero. I
have misgivings about using "H" at all due to the German usage, but
what the heck, we're never going to use "B" to mean what we usually
call "Bb" so we might as well do what we like with "H", and we won't
get "O" to fall in the right place unless we do.

So what I see you as doing is using the 7 letters A to G in pretty
much their usual positions (although tending more towards their 7-ET
positions) and then using the 7 letters H to N for pitches flat of A
to G, and using P to V for pitches sharp of A to G. This may be the
best we can do in ASCII, but otherwise I prefer Greek
transliterations of A to G instead of H to N, and the Hebrew instead
of P to V. It is good not to use X or Y because these are the only
uppercase used in the ASCIIfication of sagittal accidentals.

--- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:

> I wouldn't take to the witness stand on this, but I'm willing to bet
> you don't know a whole lot about the music of today, much less the
> last couple of decades. To make a comment about Ms. Spears would be
> about as appropriate as me suggesting people revisit the fine works
of
> Leroy Anderson in a microtonal fashion. Pop acts, both of 'em. I'm
> sure anyone's wine can find better bottles than those.

Now you change your tune. Britney Spears tops the charts; if
popularity now is what counts, she has it. What criterion is your
real one--writing music of the kind Jon Szanto likes?

Gene,

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> Now you change your tune.

No, I just think writing music that relates to one's own time makes
sense. I never said it has to pander to the lowest common denomenator
- there is a hell of a lot of music being made today, outside of
Britney and Justin and Janet, etc.

> What criterion is your real one--writing music of the kind Jon
Szanto likes?

Now you're getting silly and personal, and I won't go there any more.
I simply think that the resources that are opening up (around here)
also open up a lot of possibilities, and I don't think tht boldly
striding forward into the past is going to do anything except make the
author and a few other people cozy.

Not that there is anything wrong with that in the least.

Cheers,
Jon

--- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:
> Gene,
>
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> > Now you change your tune.
>
> No, I just think writing music that relates to one's own time makes
> sense.

What does that mean? Does Margo's music relate to our time, for
instance? Does relating to our time carry harmonic implications--for
example, is it possible or impossible to relate to our time using
only 5-limit triadic harmony?

> Now you're getting silly and personal, and I won't go there any
more.
> I simply think that the resources that are opening up (around here)
> also open up a lot of possibilities, and I don't think tht boldly
> striding forward into the past is going to do anything except make
the
> author and a few other people cozy.

First you say I'm getting silly and personal, and in the next
sentence you get downright insulting. Who, specifically, are you
talking about here? Who is failing the Jon Szanto test by striding
boldly into the past?

Gene,

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:
> > No, I just think writing music that relates to one's own time
> > makes sense.
>
> What does that mean? Does Margo's music relate to our time, for
> instance?

Not really, but that doesn't devalue it at all for me. But by
consciously focusing on a 'neo' style that definitely points to the
past, it means far less to anyone who is steeped (daily, inexorably)
in music of a more current style.

> Does relating to our time carry harmonic implications--for
> example, is it possible or impossible to relate to our time using
> only 5-limit triadic harmony?

Harmony is only one small part of music.

> First you say I'm getting silly and personal, and in the next
> sentence you get downright insulting.

I apologize if it came off as an insult. I look at your
accomplishments in tuning as prodigious and important (boldly), and
the style(s) you profess to aspire to compositionally are mostly from
great composers of the past. Sure, you could say I was referring to
you, but I meant it in the most general of meanings, as there are
other microtonal composers (not on this list) that take this rear-view
look at past forms and styles.

And, from our conversations elsewhere, I have a large love for many of
our past composers. I just don't want to be one before my time is up.

Cheers,
Jon

--- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:

> > Does relating to our time carry harmonic implications--for
> > example, is it possible or impossible to relate to our time using
> > only 5-limit triadic harmony?
>
> Harmony is only one small part of music.

Which fails to answer my question. What does one need to do
harmonically, if anything, in order not to stride boldly into the
past?

> > First you say I'm getting silly and personal, and in the next
> > sentence you get downright insulting.
>
> I apologize if it came off as an insult. I look at your
> accomplishments in tuning as prodigious and important (boldly), and
> the style(s) you profess to aspire to compositionally are mostly
from
> great composers of the past. Sure, you could say I was referring to
> you, but I meant it in the most general of meanings, as there are
> other microtonal composers (not on this list) that take this rear-
view
> look at past forms and styles.

I took it as directed at several of us, in particular me, Margo and
Aaron.

> And, from our conversations elsewhere, I have a large love for many
of
> our past composers. I just don't want to be one before my time is
up.

How do you prevent that?

Gene,

Let's wrap it up, because I've said all I need to say. When George
comes back we can start a new thread, with a proper title and
everything. If you like.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> > Harmony is only one small part of music.
>
> Which fails to answer my question.

That is correct, and intentional.

> I took it as directed at several of us, in particular me, Margo and
> Aaron.

Well, then you took it wrongly.

> > And, from our conversations elsewhere, I have a large love for
> > many of our past composers. I just don't want to be one before
> > my time is up.
>
> How do you prevent that?

Live in the here and now, to the best of my ability.

Cheers,
Jon

>> Sorry, this is wrong, transposing by any just interval doesn't
>> necessarily get you over to the next tile. I think transposing
>> by the generator does change at most one note, though.
>
>What if the period is 1/2 octave, or 1/3 octave, or . . . ?

Er, I meant "change at most one note per period". That is, the
denominator there tells you how many.

I think you and Dave were just talking about this re. notation?

-Carl

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:

/tuning/topicId_53851.html#54351

> --- In tuning@yahoogroups.com, Graham Breed <graham@m...> wrote:
> ...
> > Am I right in
> > assuming that sagittal will solve this problem? That is, that it
> > supplies convenient symbols for both the usual Pythagorean sharps
> and
> > flats and these alternative, 5-limit based ones? More generally,
> all we
> > need is a good way of notating 5-limit JI based on 7 nominals and
> > covering 6 lattice rows.
>
> Yes. Sagittal provides suitable accidentals.
>
> You can try it in Scala. Set up a scale with the ratios you're
> interested in and SET NOTATION SAJI1.

***So what is the status right now of Scala as pertains to Sagittal
notation? Does it include it now? Which version of Scala has it? I
guess I should download the most recent version if so, yes? What
number is it? What other questions can I ask?

Thanks!

Joseph

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
> ***So what is the status right now of Scala as pertains to
Sagittal
> notation? Does it include it now?

Yes.

> Which version of Scala has it? I
> guess I should download the most recent version if so, yes? What
> number is it? What other questions can I ask?

Just download the latest.
http://www.xs4all.nl/~huygensf/scala/

Hi there.
Since I really don't know who were the authors of the following words, I'll
just hope they're gonna read this message in order they could respond to my
questions.

> >Blackwood claims to have discovered an essentially new chord
> >progression in 12-equal:
> >
> >http://www.bruceduffie.com/blackwood.html
> >
> >You probably have to purchase his very expensive, self-published
> >treatise to find out what it is. Oh wait, you could just listen to
> >the piece in question!

Great, so where can I find the recording?

> "I had discovered some chord progressions in 12 notes in the
> process of looking at some of the other equal tunings, which,
> oddly enough, were never exploited or used by composers between
> 1904 and 1915 when they would have been idiomatic. And I
> thought, well, to write an etude to explore these, obviously,
> you don't need electronic media. You can just write it for piano.
> So I wrote a piano piece in that idiom and the piece came out
> sounding slightly like Scriabin with a little Milhaud perhaps
> thrown in. Then it occurred to me, 'Wait a moment. I can't make
> do with just one etude. I need a set.' So I wrote some more
> etudes in tonal idiom that sound rather like Russian music
> in 1905.'"

Have you got these as MIDI files somewhere? I'd like to hear them.
Petr

>> >Blackwood claims to have discovered an essentially new chord
>> >progression in 12-equal:
>> >
>> >http://www.bruceduffie.com/blackwood.html
>> >
>> >You probably have to purchase his very expensive, self-published
>> >treatise to find out what it is. Oh wait, you could just listen
>> >to the piece in question!
>
>Great, so where can I find the recording?

Easley Blackwood is on Cedille records...

https://www.cedillerecords.org/blackwood.html

They used to sell his recordings direct.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <ekin@l...> wrote:

/tuning/topicId_53851.html#54716

> >> >Blackwood claims to have discovered an essentially new chord
> >> >progression in 12-equal:
> >> >
> >> >http://www.bruceduffie.com/blackwood.html
> >> >
> >> >You probably have to purchase his very expensive, self-published
> >> >treatise to find out what it is. Oh wait, you could just listen
> >> >to the piece in question!
> >
> >Great, so where can I find the recording?
>
> Easley Blackwood is on Cedille records...
>
> https://www.cedillerecords.org/blackwood.html
>
> They used to sell his recordings direct.
>
> -Carl

***Amazon.com also has these, but don't buy his talented father's
bridge books by mistake... :)

JP