7 and 9 limit theory

> > Is there a non-drone, non-blues theory
> > of 7-limit that describes a body of
> > music?
>
> My paper _Tuning, Tonality, and Twenty-Two-Tone Temperament_ provides
> a theory of 7-limit tonality. So far there's only a small body of
> music for it (some of which you might hear on the 18th!).
>

Probably not me, but I hope many do hear it. (Are you performing
in Israel?:)

> > I suspect that some of the
> > meantone theory dealing with augmented
> > intervals would be as close to a place
> > to start as any.
>
> That's another approach, which is why I got the 31-tone guitar. But
> it's going to be pretty hard to make coherent compositional use of
> all the 7s in 31.
>

Well, the meantone 7'th implications seem pretty obvious even though
I am much more facile with jazz theory (which basically simplifies
everything to "12tet and harmony" rather than noticing all the
evolution from "pre-12 and counterpoint").

So bII7 -> Db-F-Ab-B -> 4-5-6-7
bVI7 -> Ab-C-Eb-F#
bVII7 -> Bb-D-F-G#
etc...

(Note that to some ears, these might fall apart when a ninth
is added and a 'car horn' third appears in the voicing rather
than a major third).

Of course there are a lot of other more modern resources
like the so called altered dominant (or Jimi Hendrix chord)

C-E-G-A#-D#

and triad stacks

C-E-G-B-D#-F# (where 15/8 * 5/4 = 7/3)

This is all well-known to you, but is just to say that by looking
at existing Western theory and or harmonic practice there is are
models on what 7-limit can do.

(This was written from the standpoint of one who does not believ
that a V7 is normally tuned 12-15-18-21. Those who like this
kind of tuning and motion would find that even normal I-V-I
progressions can fit with 7-limit theory).

> > I don't think a
> > similar extension even to 9 occurs.
>
> Hmm?
>

I don't know whether hmmm means you didn't understand me or that
it means you are wanderring off to show a similar extension. My
point was that my concept of a 9-limit music is one where the
comma does not dissappear. The practice in much Western music
is to have it dissappear, so it doesn't give you a lot of help
with what to do whan it doesn't. This is not to say that
microtonalists haven't explored it, but to say that the great
body of traditional theory and existing Western music has
tried to ignore/suppress the 81/80.

Bob Valentine

--- In tuning@y..., Robert C Valentine <BVAL@I...> wrote:

> Probably not me, but I hope many do hear it. (Are you performing
> in Israel?:)

Johnny Reinhard said it was going to be broadcast on the Web, along
with other people's works from the Microthon. So, Johnny, what's the
URL for this again? www.wnyc.org?
>
> Well, the meantone 7'th implications seem pretty obvious even though
> I am much more facile with jazz theory (which basically simplifies
> everything to "12tet and harmony" rather than noticing all the
> evolution from "pre-12 and counterpoint").
>
> So bII7 -> Db-F-Ab-B -> 4-5-6-7
> bVI7 -> Ab-C-Eb-F#
> bVII7 -> Bb-D-F-G#
> etc...
>
Well in Western music theory and practice, chords notated like this
(and that sound 7-limit in meantone theory and practice) are
augmented sixth chords, not seventh chords. And while augmented sixth
chords are recognized in standard Western theory and practice, their
function doesn't derive from the fact that they're consonant in the 7-
limit. On the contrary, the augmented second, augmented fourth, and
augmented sixth are all dissonant intervals, and resolve in a
determinate way: each augmented interval resolves by contrary minor
seconds outwards (unless the composer is subverting expectations):

F#--G
Eb--D
C---B
Ab--G

(the parallel fifths are usually avoided by using a suspension).

> Of course there are a lot of other more modern resources
> like the so called altered dominant (or Jimi Hendrix chord)
>
> C-E-G-A#-D#

That's not a notation I've ever seen for the Jimi Hendrix chord, nor
did Jimi Hendrix ever play a 31-tET guitar.
>
> and triad stacks
>
> C-E-G-B-D#-F# (where 15/8 * 5/4 = 7/3)

Don't know where I'd find that.
>
> This is all well-known to you, but is just to say that by looking
> at existing Western theory and or harmonic practice there is are
> models on what 7-limit can do.

True . . . hopefully, you'll understand me when I say that Western
theory and practice is based on a 5-limit standard of consonance, and
that the diatonic scale is eminently suited for it.

> (This was written from the standpoint of one who does not believ
> that a V7 is normally tuned 12-15-18-21.

Yes, I'll agree with you on that.

> Those who like this
> kind of tuning and motion would find that even normal I-V-I
> progressions can fit with 7-limit theory).

But even then you have only _one_ 1:3:5:7 chord in the diatonic scale.
>
> > > I don't think a
> > > similar extension even to 9 occurs.
> >
> > Hmm?
> >
>
> I don't know whether hmmm means you didn't understand me or that
> it means you are wanderring off to show a similar extension. My
> point was that my concept of a 9-limit music is one where the
> comma does not dissappear.

Really? That's not part of my concept of it at all. I guess you want
to have all the consonant intervals in the limit uniquely
articulated, 9:10 separate from 8:9. Well, my 22-tET proposal
wouldn't qualify in the 7-limit for you, then, because 5:7 and 7:10
are the same in 22-tET. But that doesn't bother me. I usually voice
chords so that the half-octave represents 5:7 rather than 7:10, so
for an otonal chord I'd use a voicing like 2:5:6:7, and for a utonal
chord, say, 1/12:1/7:1/6:1/5. That works out rather well in the
consonance department. Similarly, in a meantone you could always use
9:4s rather than 9:8s, and 9:5s rather than 10:9s, to get 9-limit
consonance really happening.

> From: paul@stretch-music.com
> Subject: Re: 7 and 9 limit theory
>
> --- In tuning@y..., Robert C Valentine <BVAL@I...> wrote:
>
> > Well, the meantone 7'th implications seem pretty obvious even though
> > I am much more facile with jazz theory (which basically simplifies
> > everything to "12tet and harmony" rather than noticing all the
> > evolution from "pre-12 and counterpoint").
> >
> > So bII7 -> Db-F-Ab-B -> 4-5-6-7
> > bVI7 -> Ab-C-Eb-F#
> > bVII7 -> Bb-D-F-G#
> > etc...
> >
> Well in Western music theory and practice, chords notated like this
> (and that sound 7-limit in meantone theory and practice) are
> augmented sixth chords, not seventh chords.

Right, which is why I mentioned that jazz theory (read theory necessary
to play twentieth century popular music) is based on "12tet and
harmony". We would call the bVI7 spelling above a mistake, however, I
am saying that we have forgotten that bVI7 evolved from bVIaugmented6.

> And while augmented sixth
> chords are recognized in standard Western theory and practice, their
> function doesn't derive from the fact that they're consonant in the 7-
> limit. On the contrary, the augmented second, augmented fourth, and
> augmented sixth are all dissonant intervals, and resolve in a
> determinate way: each augmented interval resolves by contrary minor
> seconds outwards (unless the composer is subverting expectations):
>

Right, but it was so much a part of the vocabulary the Tin-Pan-Alley
composers used that they could just use the shorthand bVI7 and ignore
whether that '7' was really an aug6, plus it didn't make any difference
on their target instruments. It DID make a difference with split keys,
even if it was just the first "aug 6-er" saying "I wish I had gramps
split keys here, sigh".

> > Of course there are a lot of other more modern resources
> > like the so called altered dominant (or Jimi Hendrix chord)
> >
> > C-E-G-A#-D#
>
> That's not a notation I've ever seen for the Jimi Hendrix chord, nor
> did Jimi Hendrix ever play a 31-tET guitar.

Sure, but we refer to this chord as "C7 sharp9" or "C7 augmented 9".
This would imply C-E-G-Bb-D#, though no-one would write it out that
way. I'm trying not to necessarily refer to 31tet but more to
meantone 'thinking' (if not theory).

> >
> > and triad stacks
> >
> > C-E-G-B-D#-F# (where 15/8 * 5/4 = 7/3)
>
> Don't know where I'd find that.

This shouldn't be too hard to find in twentieth century classical
music, or jazz that borrows chordal material from similar sounds
(like Dave Leibman I can't recommend any of his CD's, I only have
one which accompanied his book "Twelve Compositions in the
Chromatic Style" which features lots of these polychords).

Perhaps I am thinking too much in 31, but the idea that SOME
things that are common in 12 (like the above polychord being
"major chords a major seventh apart") crosses into the 7-limit
makes me think that there are links from familiar territory
to new territory.

There is also just the transform of 5-limit minor to 7-limit
minor. We have discussed the JI scale

1/1 9/8 7/6 4/3 3/2 14/9 7/4 1/1

before, (which Micheal Harrison uses on a Numbers Racket
selection, I haven't ordered anything from JIN for awhile
so I don't know how that would go these days). His
composition is very much in a straight minor tonality, with
an awesome diminished chord from a harmonic minor version
of this scale used during a resolution which I believe is
(b6 7 9 11) -> (5 1 b3), so the diminished chord is
probably
112:135:162:192

assuming only the 15/8 was added. This is a little bit
odd, and I wonder if it may not have had a 21/16 fourth, which
would make it a 6/5.6/5.7/6 interval structure...

Okay, just rambling...

> >
> > This is all well-known to you, but is just to say that by looking
> > at existing Western theory and or harmonic practice there is are
> > models on what 7-limit can do.
>
> True . . . hopefully, you'll understand me when I say that Western
> theory and practice is based on a 5-limit standard of consonance, and
> that the diatonic scale is eminently suited for it.
>

I believe we are in violent agreement, however, once you start adding
in sharps and flats, and using them in new manners, there is a great
potential for '7' interpretations and/or extensions.

> > > > I don't think a
> > > > similar extension even to 9 occurs.
> > >
> > > Hmm?
> > >
> >
> > I don't know whether hmmm means you didn't understand me or that
> > it means you are wanderring off to show a similar extension. My
> > point was that my concept of a 9-limit music is one where the
> > comma does not dissappear.
>
> Really? That's not part of my concept of it at all. I guess you want
> to have all the consonant intervals in the limit uniquely
> articulated, 9:10 separate from 8:9. Well, my 22-tET proposal
> wouldn't qualify in the 7-limit for you, then, because 5:7 and 7:10
> are the same in 22-tET.

Yes, that is/was part of my understanding and that was something that
confused me about your paper. If I think of an EDO as representing
9-limit, then I would expect that 9:10 and 8:9 would be unique. I
would similarly expect a 5-limit system to have unique terms for
6:5 and 5:4. You suggest that context may be enough to make these
interpretations aural. And your points about using 9:4 and 9:5 to
do 9-limit in a non-unique 9 environment are clipped, but pondered.
[This is exactly the problem with 31 being 11-limit as it confabulates
12:11 and 11:10, however, context may well make the difference].

Howver, this line of thinking would seem to open the slippery slope
for a lot of abuse by poseurs to try to cash in on the microtonailty
craze. [Just kidding].

Bob Valentine

--- In tuning@y..., Robert C Valentine <BVAL@I...> wrote:

> There is also just the transform of 5-limit minor to 7-limit
> minor. We have discussed the JI scale
>
> 1/1 9/8 7/6 4/3 3/2 14/9 7/4 1/1
>
> before, (which Micheal Harrison uses on a Numbers Racket
> selection, I haven't ordered anything from JIN for awhile
> so I don't know how that would go these days).

I'd consider that a 9-limit minor scale, where the minor triads are
6:7:9. In fact, it works even better in 22-tET.

>
> > >
> > > This is all well-known to you, but is just to say that by
looking
> > > at existing Western theory and or harmonic practice there is
are
> > > models on what 7-limit can do.
> >
> > True . . . hopefully, you'll understand me when I say that
Western
> > theory and practice is based on a 5-limit standard of consonance,
and
> > that the diatonic scale is eminently suited for it.
> >
>
> I believe we are in violent agreement, however, once you start
adding
> in sharps and flats, and using them in new manners, there is a great
> potential for '7' interpretations and/or extensions.

Right -- but it's not quite the same as the way 5-limit became the
_standard_ for diatonic music. If '7' is always achieved through
chromaticism, then it will always be subservient to '5' in stability.
>
> You suggest that context may be enough to make these
> interpretations aural. And your points about using 9:4 and 9:5 to
> do 9-limit in a non-unique 9 environment are clipped, but pondered.

Clipped but pondered?

Paul Erlich wrote,

<<it's not quite the same as the way 5-limit became the _standard_ for
diatonic music. If '7' is always achieved through chromaticism, then
it will always be subservient to '5' in stability.>>

I very much agree with this (guess I might have to upgrade that
5%...).

The problem I think is achieving a new "white key" scale that doesn't
sound chromatic and supports harmonics above the 5-limit as well.

The vertical part is simple enough, but my own experiments and ears
have lead me to 8, 9, 10, and 11 note scales that sound white key like
to me (and by that I mean in a very broad sense not diatonic with
added chromatic tones) but that are not conducive to simple higher
limit tonal types of vertical analysis.

I have little doubt this is something of a problem of habit and
repeated exposure. But I also think it's interesting that I can easily
solve for myself both the horizontal and vertical problems by ear, and
yet it's very hard for me to envision a convincing generalized
diatonic that'll satisfyingly combine the two based on my own
experiences.

--Dan Stearns

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:
>
> The problem I think is achieving a new "white key" scale that
doesn't
> sound chromatic and supports harmonics above the 5-limit as well.
>
> The vertical part is simple enough, but my own experiments and ears
> have lead me to 8, 9, 10, and 11 note scales that sound white key
like
> to me (and by that I mean in a very broad sense not diatonic with
> added chromatic tones) but that are not conducive to simple higher
> limit tonal types of vertical analysis.
>
> I have little doubt this is something of a problem of habit and
> repeated exposure. But I also think it's interesting that I can
easily
> solve for myself both the horizontal and vertical problems by ear,
and
> yet it's very hard for me to envision a convincing generalized
> diatonic that'll satisfyingly combine the two based on my own
> experiences.

How do my decatonic and dodecatonic scales in 22-tET fall short in
this regard?

Paul Erlich wrote,

<<How do my decatonic and dodecatonic scales in 22-tET fall short in
this regard?>>

I've only played with the decatonics, and there my ear keeps wanting
to stick it in a diatonic with chromatic tones type framework
(melodically).

My test for this is just to try taking the scale ascending and
descending and see if I can hear its proportions as independent
entities in a generalized white key sense.

Proportionally the 22-tet decatonics are renderable in 12-tet as well,
so this might have something to do with my reaction too.

--Dan Stearns

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:
> Paul Erlich wrote,
>
> <<How do my decatonic and dodecatonic scales in 22-tET fall short in
> this regard?>>
>
> I've only played with the decatonics, and there my ear keeps wanting
> to stick it in a diatonic with chromatic tones type framework
> (melodically).

It took me a few years to get past that stage -- it's not surprising that a lifetime of diatonic
conditioning will impact how you hear it. It may also be how you're using it. Just think of the scale
as tetrads with passing tones.
>
> My test for this is just to try taking the scale ascending and
> descending and see if I can hear its proportions as independent
> entities in a generalized white key sense.

Are there any scales with 10 or more notes that will do that for you?

Hello there!

I've discovered that the Open_etc.exe program that I did for SCALA
isn't recognising folders / files with spaces in the names.

This is just because I forgot to put them within quotes, as one
has to do in this context.

New version checks if there are any spaces, and if so, puts it in
quotes.

When run with SCALA 1.7 or earlier (for those who haven't yet
upgraded), it converts any paths with spaces into the short form
without spaces. SCALA 1.7 recognises this format (an alternative way
of dealing with spaces), but doesn't recognise the path in quotes
format. SCALA 2.0 recognises both.

The path in quotes format is preferrable as when you reshow the
dialog, it will show any spaces, (e.g. "scottish bagpipe.scl" rather
than "SCOTTI~1.SCL")

If you have downloaded the zip before for use with 1.7 or earlier,
please either delete your old version of the file open_etc.ini, or
else edit it to add the line
ShortPaths
at the end.

Download url as before:
http://members.nbci.com/tune_smithy/open_etc/open_etc.zip

Robert

Hello there!

I've discovered that the new Open_etc program doesn't recognise
folders or files with spaces in the names.

This new version fixes it. Works with SCALA 2.0 or SCALA 1.7 or
earlier.

Same url as before:
http://members.nbci.com/tune_smithy/open_etc/open_etc.zip

Unzip all the files into the same folder as your SCALA.EXE file.

When making a SCALA shortcut, if you use the method of dragging
from Windows explorer, use Rt click, and then Create Shortcut(s).

It is very easy to drag the Scala app instead, and it looks much
the same as a shortcut on the desktop. Look closely and you'll
see some of them have small curved arrows on them, they are the
genuine shortcuts. If you've used this method of dragging from
Windows Explorer before, you may find some icons on your desktop you
thought were shortcuts are actually copies of the apps themselves.

They will all be running using the desktop as their working
directory (not necessarily much of a problem, depending on what
they do and what they expect to find in their working directories).

Robert

I've discovered, Open_etc.exe doesn't recognise names of folders and
files if they have spaces in them.

New version fixes this:

Same url as before:
http://members.nbci.com/tune_smithy/open_etc/open_etc.zip

Do say if anything doesn't work at all - it is easy to fix,
and I really like hearing any bug reports and dealing with
them, and it is of great value to other users of my
programs too.

Robert

I've discovered, Open_etc.exe doesn't recognise names of folders and
files if they have spaces in them.

New version fixes this:

Same url as before:
http://members.nbci.com/tune_smithy/open_etc/open_etc.zip

Do say if anything doesn't work at all - it is easy to fix,
and I really like hearing any bug reports and dealing with
them, and it is of great value to other users of my
programs too.

Robert

I've discovered, Open_etc.exe doesn't recognise names of folders and
files if they have spaces in them.

New version fixes this:

Same url as before:
http://members.nbci.com/tune_smithy/open_etc/open_etc.zip

Do say if anything doesn't work at all - it is easy to fix,
and I really like hearing any bug reports and dealing with
them, and it is of great value to other users of my
programs too.

Robert

Sorry everyone.

I've been doing this on-line from web page and kept getting an
error message, so thought the messages weren't being sent.

The first post about needing to delete open_etc.ini
or edit it for Scala 1.7 no longer applies because
I thought of another method that meant no-one needs
to do that.

(it now passes the short form of any name with spaces in it
to Scala, whichever version of SCALA it is, and saves
the file name with spaces in the open_etc.ini file
from one session to the next to use for the dialogs).

Robert

Paul Erlich wrote,

<<Are there any scales with 10 or more notes that will do that for
you?>>

I'll dig around and look for some of these. I do know that a lot of
these were non-octave scales which kind of unfairly resets the rules a
bit.

Here's an example in cents of two related scales along a very similar
line that I'm using in a current piece,

30, 405, 720, 890, 1183, 1417, 1597, 1831, 2050, 2266, 2451

30, 223, 405, 608, 720, 890, 1116, 1183, 1417, 1597

These scales, and many like them, are culled from very large ascending
and descending melodic strings or sequences that I find by ear and
intuition on the fretless guitar.

Trusting that they'll sound good on most any instrument and with most
any timbre (as I believe most all tunings do), I'll often then take
these tunings to the sound module and the keyboard and start to
compose.

--Dan Stearns

> > Bob
> Paul
Bob
> >
> > You suggest that context may be enough to make these
> > interpretations aural. And your points about using 9:4 and 9:5 to
> > do 9-limit in a non-unique 9 environment are clipped, but pondered.
>
> Clipped but pondered?
>

Yes, I clipped the comments from my reply, but am ponderring the
implications. However YOU clipped the following paragraph without
a comment (and I expected a shout of 'touche' or a quiet 'check').

I quote below :

> > Yes, that is/was part of my understanding and that was something that
> > confused me about your paper. If I think of an EDO as representing
> > 9-limit, then I would expect that 9:10 and 8:9 would be unique. I
> > would similarly expect a 5-limit system to have unique terms for
> > 6:5 and 5:4.
>

Can any neutral third composers can comment on
creating a clear 5-limit music with 6:5 and 5:4 mapped to the
same note?

Bob Valentine

--- In tuning@y..., robertinventor@h... wrote:

/tuning/topicId_22836.html#22893

> I've discovered, Open_etc.exe doesn't recognise names of folders
and
> files if they have spaces in them.
>
> New version fixes this:
>
> Same url as before:
> http://members.nbci.com/tune_smithy/open_etc/open_etc.zip
>
> Do say if anything doesn't work at all - it is easy to fix,
> and I really like hearing any bug reports and dealing with
> them, and it is of great value to other users of my
> programs too.
>
> Robert

Hello Robert!

I just downloaded your most recent version of open_etc.zip which is,
to my mind, the best invention for SCALA since equally sliced bread...

"Open" works just great in BOTH version of SCALA. I'm sure to use it
a lot, and I certainly hope that Manuel incorporates it in a revision
of his program. It really helps get scales "in a hurry" and you know
how we need these in our "heated" discussions!

However, I STILL can't get COPY to work properly. I've tried it BOTH
ways @c first and @copy first... It SAYS that material is being
copied to the clipboard, but then when I paste into my favorate text
utility I get nothing.

Similarly, when I try to open the .txt file that is made in my SCALA
directory there is nothing in it.

Of course, I don't like the idea AT ALL of making text files when all
I wanted to do is COPY AND PASTE something from the SCALA screen as I
could do in the previous version 1.7.

I thought it was somehow going to be possible to just copy the
screen text to the windows buffer to be used anyplace?? Maybe I was
wrong in that.

If it is necessary to always make .txt files, then surely I will want
to stick with SCALA version 1.7 for this COPY function.

Any suggestions?

Thanks!

_________ _______ ____
Joseph Pehrson

--- In tuning@y..., Robert C Valentine <BVAL@I...> wrote:
>
> Can any neutral third composers can comment on
> creating a clear 5-limit music with 6:5 and 5:4 mapped to the
> same note?
>
> Bob Valentine

Daniel Wolf has remarked on this list (it's in a footnote in my
paper) how he feels the Thai 7-tET music has 5-limit implications,
which are reflected better by the Thai vocalists than by the fixed-
pitch instruments that accompany them.

Hi Joseph!

Glad you like it, the part that is working!

I wonder about the copy.

It's @c first.

@c
then the scala commands to show the scale,
then
@copy

E.g. to show the scale and copy it to the clipboard
@c
show
@copy

Something to check:

Are you doing the @c first, then the scala commands such as show,
_then_ the @copy?

the @c and @copy mark the beginning and end of the section to be
copied.

Perhaps you are highlighting the text? This method doesn't
pay any attention to the highlighting, as that is something
that wouldn need to be done in GTk. My program has no
way of finding out what selection of text is highlighted.

Perhaps I should have made that clear in the readme, didn't
think to explain it, sorry.

If you do it as
@c
show
@copy
then it should work. If not, could do some more detailed
trouble shooting to find out what exactly is happening.

.............................

As for saving to text files - programs do this all the time in the
form of .ini files - it is normal for a program to save one or
more .ini text files on exit, to keep a record of all the settings
for the next session.

Similarly, if one records an audio file, it is very common that
the program will first record to a temporary file, perhaps in
your Windows temp folder, and then copy it to the proper file name
when it is finished. This is the default windows way of doing it
in fact.

So temporary files are very common.

Only one text file is ever created, ~copy.txt, and it is
overwritten each time it is used.

However, maybe what you mean is that you don't want it to be
listed with all the other text files in that folder.

If so, could rename it to ~copy.tmp, say.

It is a common convention to use "tmp" extensions for temporary
files as then if one sees any files with that ext. one knows one
can delete them, as they
must have been left by some program or other that was using
them as a temporary file. Do a search for files of type
*.tmp in Windows Explorer, and if one hasn't cleaned them out,
chances are that there are a fair number of .tmp files.
It should be safe to delete them all.

Tere are a few other extensions used in that way - for example
some programs use .$$$ for temporary files I believe, and
Word has its own convention for temporary files - whenever
you edit a document, it makes another copy of it with a
special file extension, which is how it can "recover" it
later if needed.

I think you can get spring clean programs to delete them
all for you.

The readme says how to rename the files if one wants.

Just thought people might appreciate being able to see
the text files and be able to double click on them to see them
- you never know, might be useful to have a backup of ones
most recent SCALA copy command at all times.

Starting the file name with ~ was meant to indicate that it
is okay to delete it if one wants to, as that is another
convention that is sometimes used (though maybe less universal
- I'd hesitate before deleteing all files beginning with ~
on your computer just in case some programmer is using some
other the convention).

Another possibility would be to get Open_etc to delete ~copy.txt
after copying to clipboard.

But, is a tiny file, gets overwritten each time, and I thought the
benefits of keeping it, just in case it was needed ever by anyone,
outweighed the benefits of cointinually deleteing it each time.

Easily changed. Or made configurable for that matter.

What do you think, now that I've explained a bit more about why
it is done that way?

If you think ~copy.txt (and ~paste.txt) are best deleted after use,
that is an easy one line change to the program, and I'll do it,
or if both methods are particularly desired by anyone, could
make it configurable by adding a line to the .ini file.

Robert

--- In tuning@y..., robertinventor@h... wrote:

/tuning/topicId_22836.html#22980
>
> I wonder about the copy.
>
> It's @c first.
>
> @c
> then the scala commands to show the scale,
> then
> @copy
>

Hi Robert!

Everything is working now!

This, actually, was very funny. I thought when you went @c it
started the process of storing what was ALREADY on the screen!

I didn't realize you then had to SHOW the scale again! (I already
had it up once on the screen before I tried to copy it!)

So, obviously, I was copying a blank screen. Probably it did a good
job of it, but, of course, I couldn't see anything!

I'm not sure whether that is unclear in the original "instructions"
or if I was more confused than most possible users would be... (maybe
a little doubtful, though..)

> .............................
>
> As for saving to text files - programs do this all the time in the
> form of .ini files - it is normal for a program to save one or
> more .ini text files on exit, to keep a record of all the settings
> for the next session.
>
> Similarly, if one records an audio file, it is very common that
> the program will first record to a temporary file, perhaps in
> your Windows temp folder, and then copy it to the proper file name
> when it is finished. This is the default windows way of doing it
> in fact.
>
> So temporary files are very common.
>
> Only one text file is ever created, ~copy.txt, and it is
> overwritten each time it is used.
>

Well, this is something I didn't initially understand, although I
suppose I should have intuited it...

I thought it was going to do something like ~copy.txt, ~copy1.txt,
~copy2.txt, and fill up my directories with this stuff!

Naturally, I wouldn't like THAT, but since it is just overwriting, it
makes no difference, of course.

>
> It is a common convention to use "tmp" extensions for temporary
> files as then if one sees any files with that ext. one knows one
> can delete them, as they
> must have been left by some program or other that was using
> them as a temporary file. Do a search for files of type
> *.tmp in Windows Explorer, and if one hasn't cleaned them out,
> chances are that there are a fair number of .tmp files.
> It should be safe to delete them all.
>

Thanks, Robert. Actually I *do* know that. Sometimes they get quite
large... Same with temporary Internet files, although when you
delete "cookies," of course, you have to put information back in when
visiting certain Internet sites.

A funny thing happened with that. I got the advice from mp3.com to
delete all my "corrupted" cookies, which is what they thought my
problem was with playing mp3 files. I deleted everything according
to their instructions, and then the problem started AGAIN. Only when
I went into the "administration" area of mp3.com and tried to play a
mp3 from THERE, where the sign-in screen doesn't pertain, would the
mp3s play. THEN, they would play ANYPLACE, and the sign-in, info.
screen never appeared again. Isn't that strange??

> Tere are a few other extensions used in that way - for example
> some programs use .$$$ for temporary files I believe, and
> Word has its own convention for temporary files - whenever
> you edit a document, it makes another copy of it with a
> special file extension, which is how it can "recover" it
> later if needed.
>

Yes, I do know this.. and it has been a "lifesaver" during power
outages upon occasion...

>
> Just thought people might appreciate being able to see
> the text files and be able to double click on them to see them
> - you never know, might be useful to have a backup of ones
> most recent SCALA copy command at all times.
>

Oh sure... now that I know it's only ONE file!

> Starting the file name with ~ was meant to indicate that it
> is okay to delete it if one wants to, as that is another
> convention that is sometimes used (though maybe less universal
> - I'd hesitate before deleteing all files beginning with ~
> on your computer just in case some programmer is using some
> other the convention).
>

OK!

>
> What do you think, now that I've explained a bit more about why
> it is done that way?
>
> If you think ~copy.txt (and ~paste.txt) are best deleted after use,
> that is an easy one line change to the program, and I'll do it,
> or if both methods are particularly desired by anyone, could
> make it configurable by adding a line to the .ini file.
>

Oh no... now that I understand it is only ONE file being overwritten,
there is no reason for this!

I do have one final question for you, though.

The @c and @copy function does NOT work on SCALA 1.7.

Did you mention this before and I missed it??

I get an error message "cannot find the .txt file..."

Of course, it makes little difference, since in THAT version of
SCALA, I can cut and paste right from the screen, anyway.

I was just curious about that.

Thanks for all the help. These are BIG, BIG, BIG improvements in
SCALA, and I hope you can help Manuel implement them in his program,
so that they are in ALL the releases of BOTH 1.7 and 2.0! This is
very important... It makes life SO much easier... particularly the
loading in of files...

Well, and, of course the copying in SCALA 2.0 which is, otherwise,
considerably more difficult. I still haven't figured out how to get
the interface to do it.

What are the letters abbreviating this non-Windows development tool??
And what do those letter stand for again??

THANKS!!!!!

_______ ______ ______ ____
Joseph Pehrson

Hi Joseph,

> Everything is working now!
Great.

> So, obviously, I was copying a blank screen. Probably it did a
good
> job of it, but, of course, I couldn't see anything!

:-)

> I'm not sure whether that is unclear in the original "instructions"
> or if I was more confused than most possible users would be...

Very likely was unclear.

I'll look at the readme in the zip too, and see if it can be better
espressed.

> Thanks, Robert. Actually I *do* know that. Sometimes they get
quite
> large... Same with temporary Internet files, although when you
> delete "cookies," of course, you have to put information back in
when
> visiting certain Internet sites.

Yes, indeed, one needs to take care before deleting all ones cookies,
though they are tiny files.

> A funny thing happened with that. I got the advice from mp3.com to
> delete all my "corrupted" cookies, which is what they thought my
> problem was with playing mp3 files. I deleted everything according
> to their instructions, and then the problem started AGAIN. Only
when
> I went into the "administration" area of mp3.com and tried to play
a
> mp3 from THERE, where the sign-in screen doesn't pertain, would the
> mp3s play. THEN, they would play ANYPLACE, and the sign-in, info.
> screen never appeared again. Isn't that strange??

Yes!

> Yes, I do know this.. and it has been a "lifesaver" during power
> outages upon occasion...
>
> >
> > Just thought people might appreciate being able to see
> > the text files and be able to double click on them to see them
> > - you never know, might be useful to have a backup of ones
> > most recent SCALA copy command at all times.
> >
>
> Oh sure... now that I know it's only ONE file!

Okay fine, can see how one would have trepidations about
filling a directory with hundreds of text files! Never find
anything in it...

>

> Oh no... now that I understand it is only ONE file being
overwritten,
> there is no reason for this!

Great.
>
> I do have one final question for you, though.
>
> The @c and @copy function does NOT work on SCALA 1.7.
>
> Did you mention this before and I missed it??

Yes, I did.

It's the @c that doesn't work.
Instead you need to do

file ~copy.txt
show
@copy

That will work in 1.7.

Not sure why the @c doesn't work, but as you say, can
do the usual highlight method, and this method would
mainly be useful if one wants to copy a long list
spanning many screens (e.g. Show Int for a large scale)

I'll check the readme for this too, may have forgotten toupdate it.
Did post to the TL, but with the huge number of e-mails right
now, I think a few replies to posts are getting missed.

I think I'll do another update of the archive tomorrow as a zip for
the most recent posts, last month or so, for downloading, to help
everyone with this.

Not quite ready for the Mills + Tuning, what with one thing or
another, plan a spot of FTS programming right now, then prob.
come back to it at the weekend or thereabouts, and finish it.

> Thanks for all the help. These are BIG, BIG, BIG improvements in
> SCALA, and I hope you can help Manuel implement them in his
program,
> so that they are in ALL the releases of BOTH 1.7 and 2.0! This is
> very important... It makes life SO much easier... particularly the
> loading in of files...

I'm very happy to help in whatever way may be needed, depending on
what his researches into it unearth.

> What are the letters abbreviating this non-Windows development
tool??

Gtk

> And what do those letter stand for again??

Never thought to ask. Manuel, what does Gtk stand for?

Robert

> > Bob
> Paul
Bob
>
> > There is also just the transform of 5-limit minor to 7-limit
> > minor. We have discussed the JI scale
> >
> > 1/1 9/8 7/6 4/3 3/2 14/9 7/4 1/1
> >
>
> I'd consider that a 9-limit minor scale, where the minor triads are
> 6:7:9. In fact, it works even better in 22-tET.
>

Well.. let me expose my ignorance again.

14/9--- 7/6--- 7/4
| | | 15/8
| | | /
| | | /
4/3--- 1/1--- 3/2---9/8

In the piece I was referring to, these were the notes that I
believe were used, and this is a lattice diagram of how I
think they were related (I know, its tipped over and not
terribly good ascii art, so sue me).

Where do you see (hear) 9-limit from and is that information
present in the lattice or not? I don't want to get into a
big debate on the audability of primes or '9'-ness or anything
like that, however, the '9' (like the '15') does seem to be
a side effect of having the 3-5-7 prime limits present.

Bob Valentine

Drat... I had been trying my best to stay out of this thread
(because I can't keep up with the one's I'm already in),
but I just couldn't resist...

--- In tuning@y..., Robert C Valentine <BVAL@I...> wrote:

/tuning/topicId_22836.html#22999

>
> > > Bob
> > Paul
> Bob
> >
> > > There is also just the transform of 5-limit minor to 7-limit
> > > minor. We have discussed the JI scale
> > >
> > > 1/1 9/8 7/6 4/3 3/2 14/9 7/4 1/1
> > >
> >
> > I'd consider that a 9-limit minor scale, where the minor
> > triads are 6:7:9. In fact, it works even better in 22-tET.
> >
>
> Well.. let me expose my ignorance again.
>
> 14/9--- 7/6--- 7/4
> | | | 15/8
> | | | /
> | | | /
> 4/3--- 1/1--- 3/2---9/8
>
> In the piece I was referring to, these were the notes that I
> believe were used, and this is a lattice diagram of how I
> think they were related (I know, its tipped over and not
> terribly good ascii art, so sue me).
>
> Where do you see (hear) 9-limit from and is that information
> present in the lattice or not? I don't want to get into a
> big debate on the audability of primes or '9'-ness or anything
> like that, however, the '9' (like the '15') does seem to be
> a side effect of having the 3-5-7 prime limits present.
>
> Bob Valentine

Hi Bob,

Anytime you take the 3-dimension of the lattice out further
than 2 steps, you'll get 9. So it doesn't take much extension
of that dimension (hey, that has a nice ring to it...) to
produce a "9-ness" in even a small scale like this.

Three of the 6:7:9 chords described by Paul are present:
4/3 - 14/9 - 1/1
1/1 - 7/6 - 3/2
3/2 - 7/4 - 9/8

So there's plenty of "9-ness" in this particular lattice.

The answer to your question of whether this, and 15-ness,
is inherent in the lattice or is a side-effect is an interesting
one. I think it depends most on how much relative importance
you place in the dichotomy of odd- vs. prime-limit.

This lattice, like all the ones we draw here, is a prime-limit
one. Each dimension of the lattice represents a different
prime-factor.

An odd-limit diagram such as Partch's Tonality Diamond gives
each odd number its own dimension.

I find both useful, for different purposes.

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

--- In tuning@y..., Robert C Valentine <BVAL@I...> wrote:
>
> > > Bob
> > Paul
> Bob
> >
> > > There is also just the transform of 5-limit minor to 7-limit
> > > minor. We have discussed the JI scale
> > >
> > > 1/1 9/8 7/6 4/3 3/2 14/9 7/4 1/1
> > >
> >
> > I'd consider that a 9-limit minor scale, where the minor triads
are
> > 6:7:9. In fact, it works even better in 22-tET.
>>
> Where do you see (hear) 9-limit from

I just meant that it acts like a regular diatonic minor scale, except
that the three minor triads, instead of being complete 5-limit
utonalities (1/6:1/5:1/4), are incomplete 9-limit otonalities
(6:7:9). In 22-tET, all three major triads in the scale are very
nearly 1/9:1/7:1/6. I'm sticking with the original meaning of the
word "limit" here (due to Partch).

> and is that information
> present in the lattice or not?

No. The lattice represents the entire tuning system, and for tuning
systems, it's the _prime_ limit which is relevant (see Monz'
dictionary entry for "limit"). Prime limit is not very clearly
expressed by Partch but has become (unfortunately) the only meaning
of "limit" for many subsequent theorists.

On 5/16/01 3:03 AM, "Robert C Valentine" <BVAL@IIL.INTEL.COM> wrote:

> Can any neutral third composers can comment on
> creating a clear 5-limit music with 6:5 and 5:4 mapped to the
> same note?

But now that you mention it, I *have* done this!
It's kind of frightening when you see it work.
It's one of the ugliest microtonal things to play on guitar.
By the time you're done, you *know* it's the same note,
but you can hear the difference in function.

Sort of a primal meantonomaly,
But in the harmonic convergence ascension for {2:1,5:3,3:2} it shows up.
Too often I fly past 10 into the 22/34/46 strain of [2m2 = M2]...
Like I've said it gets my blood pumping.
But the "6:5=5:4" anomaly is much more apparent if you sit there.
Think, 10, 7, 10, 7. Why not.
Try it in 17 (10 + 7).

What I saw as obvious was that chordally, it's a half-fifth.
What I saw as not so obvious was that melodically,
it was a bisection of a minor 3rd (the 32:27).

The 7 tone level at first glance:

F, Bb,
D E or G A or C D
,F# ,B

0 3 5 7 10 12 14 17

Then the ten... watch how fugly:

F, Bb,
D Eb, E or G ? A or C ,C# D
,F# ,B

0 (2) 3 5 7 (8-9) 10 12 14 (15) 17

Refining from the convergence,
by the time you hit 22, the 1/4 from 12 splits into F *or* F,
and conversely the 3/4 splits into ,B or B
Because of all the even temperaments,
the semioctave doesn't actually split until 53.
I can never remember which nests
wind up with [Ab, or ,G#] or [,,G# or Ab,,];
in this case it's the latter.

0 D
2 Eb,
3 E
5 F F, ,F#
7 G
8 ,,G#
9 Ab,,
10 A
12 Bb, ,B B
14 C
15 ,C#
17 D

Sooo... you wind up with the 5/17 able to represent
not only 6:5 and 5:4, but 32:27 as well.

This is as unsightly as the Jordan shuffle, if you know card tricks.

My melodic strategy, squeeze the stone until your hand bleeds
and say you got the blood from the stone...
I'll speak in n/17:
play through 0 3 5... 0 3 5... 0 3 5... it'll sound like an [F,];
play through 10 7 5... 0 10 7 5... 10 7 5... it'll sound like an [,F#].
Repeat this several times.
Now play 0 3 5 7 10. Your ears should fall off.

You can either be gentle with the dual agency,
or neutralize it by treating 2/17 as a legal melodic interval.
It's almost all the way back to playing in different "keys".
In a sense, maybe... in one section,
sell off the 5/17 like it's a minor third,
try to convince with the next section it's a major third...
in some kind of passage fly through some neutral thoughts;
anywhere you can find three notes in a row
with 2 equal spaces of 2/17 between.

It's a very difficult strain for me.
I'm so tempted to work in some 3rd limit 17...
but it kills my sinuses.
Just the clear obscenity, of using the FIVE/17 as a 32:27.
I keep reaching for the 4/17...
play in the strain, play in the strain...

It's difficult but like I said, don't forget how primal it is.
See this is why I said try it in 17.
It's like a forensic operation.
Adding back 7 or 10 gives you 24 and 27.
Once you *have* the genus of the distribution, yeah,
try doing it in 24... but eesh... [7/24 = 3/12] ??

Unless... you can avoid the temptation
of using the 1/3 (9/27) as a major third.
If you train a little with the 8/27,
it's actually the major third from 54, 16/54,
very very right brain... (8 8 7 8 8 8 7)
you can see the half-minor-third element (in 27) a little better.
If you can withstand that... ha ha...
try it in 31 and stay away from the 10/31!!!

Kind of reminds me of Für Elise,
how many times you hear that hovering haunting leading D#,
and when it turns into an Eb, the context has changed
to the point where it doesn't even register.
Unless you're following along with it.
Ehh... same dual agency, different meantone strain.
crunchhh

It would be almost like, in Für,
instead of playing E D# E D# E D# E D# E D# ...
throw in a little E D# D D# E D# D D# E D# D D#...
then when you get to the ...E B "D" C A etc,
see how weird that D in quotes sounds.

Bless the tone deaf.

All present
or accounted for,
Marc Jones.

Marc Jones wrote:

> Sort of a primal meantonomaly,
> But in the harmonic convergence ascension for {2:1,5:3,3:2} it shows up.
> Too often I fly past 10 into the 22/34/46 strain of [2m2 = M2]...
> Like I've said it gets my blood pumping.
> But the "6:5=5:4" anomaly is much more apparent if you sit there.
> Think, 10, 7, 10, 7. Why not.
> Try it in 17 (10 + 7).

Really fascinating post about neutrals. Enjoyed it a lot. But I must confess I have very little
idea what the above paragraph means. I do have some idea of what you mean by the 6:5=5:4 anomaly,
and have experienced it myself. It's all the other stuff around it I don't get. Could you
explain, or point to a previous post or a URL explaining, what "harmonic convergence ascension" is,
and how it's done? What is a strain? How does one "think, 10, 7, 10, 7"? Maybe you went over the
background to this recently - if so, forgive, I just had to dump about half a Meg of TLs into the
"Finish Reading Later" folder (ah, *there's* a bit of wishful thinking...) in order to get to the
current stuff.

> I'll speak in n/17:
> play through 0 3 5... 0 3 5... 0 3 5... it'll sound like an [F,];
> play through 10 7 5... 0 10 7 5... 10 7 5... it'll sound like an [,F#].
> Repeat this several times.

Hey! That'll be enough outa you, Mister. This is too practical. Belongs on the other list! ;-)

> Now play 0 3 5 7 10. Your ears should fall off.

LOL! I love your writing style. (Both of you (?!))

--
David J. Finnamore
Nashville, TN, USA
http://personal.bna.bellsouth.net/bna/d/f/dfin/index.html
--

On 5/18/01 11:36 AM, "David J. Finnamore" <daeron@bellsouth.net> wrote:

> Marc Jones wrote:
>
>> Sort of a primal meantonomaly,
>> But in the harmonic convergence ascension for {2:1,5:3,3:2} it shows up.

DAMMIT ADDAM... it's not that, it's {2:1,5:3,4:3} ! ! ! ! ! ! ! !
BEHOLD BEHOLD BEHOLD...
whom???
* * * * * Typos, the Greek God of Error. :-P * * * * *

>> Too often I fly past 10 into the 22/34/46 strain of [2m2 = M2]...
>> Like I've said it gets my blood pumping.
>> But the "6:5=5:4" anomaly is much more apparent if you sit there.
>> Think, 10, 7, 10, 7. Why not.
>> Try it in 17 (10 + 7).
>
> Really fascinating post about neutrals. Enjoyed it a lot. But I must confess
> I have very little
> idea what the above paragraph means.

I apologize for the fact that we've talked to no one else but ourselves
for the last ten years or so. As for last night, it was late late late and
this is what came out.

We shall try to serviceably clarify.

> I do have some idea of what you mean by
> the 6:5=5:4 anomaly,
> and have experienced it myself.

Four [3:2]s modulo [2:1] don't equal [5:4], they equal [81:64].
The Lab calls it Syntonic Meantone.
The idea of meantone, as far as how many of one interval
makes how many of another interval in certain temperaments,

> It's all the other stuff around it I don't
> get. Could you
> explain, or point to a previous post or a URL explaining, what "harmonic
> convergence ascension" is,
> and how it's done? What is a strain?

We're working on the website.
After 10 years in the Lab, it should be interesting.

Okay... harmonic convergence ascension.
Joel Mandelbaum, in "Division of the Octave",
briefly quoted a Euclidian algorithm of Viggo Brun's.
Historically, We see it as one of the most useful tools
as far as doing what we have to musically to stay healthy.
In 1960, when "Division" was written, however,
people were only carrying their calculations out
to a few decimal points, and with no error function,
so everyone was getting different results.
In 1988, We started working with it, and hoo boy.
Lots and lots of fun. It's a way of life.
To this day, We *still* think, because it came from Brun,
that there's resources untapped in the algorithm.
Every few years we find something else in it.

Works kinda a little like this:

inta a1 a2 a3
intb b1 b2 b3
intc c1 c2 c3

Where inta is just interval "a", and there's a matrix
corresponding to the number of notes in each interval.
Stack the intervals largest to smallest.
Perform this operation:

inta/intb a1 a2 a3
intb a1+b1 a2+b2 a3+b3
intc c1 c2 c3

Assuming you start with inta = the octave,
or whatever the largest interval you want to dissect is,
keep performing the operation,
resorting the list after every time.
Easy to set up a macro in Excel, but I use HyperCard.

What the algorithm does, or a blunt interpretation,
is it finds temperaments in which these intervals
are becoming more and more and more accurate.
(There's a *little* cross reference around,
in something we just wrote about Relative Cents.)

First thing you find is the largest number at any one sort,
in the first column (a1, b1, c1) is a convergent temperament.
After that, there emerges two classes:
one, when the a1+b1 yields the highest number and intb > inta/intb,
and the other when it doesn't.
There's a condition of strength there,
We've worked with it for 10 years in plain text temperaments
and bold text temperaments. Never named it, did We.
Main and Auxiliary, maybe.
The main ones, the map spills into easily,
the auxiliary, you have to spill from above,
as was shown in 17 as a compound of 10+7,
spilling all the way down from 53,46,34,22,12.

HUH? I said as I read...

This would be {2:1,3:2,5:4}...
the example shown in the book somewhat.

2:1 1 0 0
3:2 0 1 0
5:4 0 0 1

perform...

4:3 1 0 0
3:2 1 1 0
5:4 0 0 1

resort...

3:2 1 1 0
4:3 1 0 0
5:4 0 0 1

etc...

4:3 2 1 0
5:4 0 0 1
9:8 1 1 0

5:4 2 1 1
9:8 1 1 0
16:15 2 1 0

9:8 3 2 1
10:9 2 1 1
16:15 2 1 0

10:9 5 3 2
16:15 2 1 0
81:80 3 2 1

16:15 7 4 2
25:24 5 3 2
81:80 3 2 1

25:24 12 7 4
128:125 7 4 2
81:80 3 2 1

Rest Area, 1 Mile.
Okay, at this point, it's shaping up a little.
Remember the first three intervals?
There you are, 12 notes in the [2:1],
7 in the [3:2], 4 in the [5:4].

This has no auxiliaries for quite some time.
Here's the series you get, auxiliaries in parentheses:

1,2,3,5,7,12,19,31,34,53,118,(205),(323),(441),559...

Cool. A list of temperaments to screw around with for a few years.

Until we took the term Harmonic Convergence literally.

If you ROUND the temperaments up and back,
(that is, rounding, finding the nearest note
from one temperament in another;
I think Johnny Reinhard calls this immigration.)

If you ROUND the temperaments up and back,
wouldn't it make a little surface sense,
that if you could round these to infinity and back,
that you would have intervals expressable
in terms of the ones you used in the algorithm?

If you round 12 up to 19, then even up to 31,
you wind up with two... oh no another Orphonic term ugh...
please accept Our dialect, we only mangle English...
you wind up with WHAT WE CALL an Interval Genus of 2.
One larger interval, one smaller interval.

Atonal 12 would be a genus of 1,
12 equal could be saying 12 minor seconds,
12 fifths, whatever, equal an octave.
Equal temperament is really just a meantone strain.
::ducking::

Rounding 12 up to 19 would be a genus of 2, same with 31,
and this is what We call Syntonic Meantone.
What most people call meantone, that is, [4P5 = M3].
There are 2 different sizes of intervals.
Meantone spoken as an "anomaly",
is that it's an intervallic anomaly,
you wind up at a note by cutting corners.

When you round up to 34, though, in {2:1,3:2,5:4}
and even if you round all the way up to 559, 4296, or 78005;
it doesn't matter after 34 as far as the genus of 12 goes.
At 34, you have a genus of 3, which is the full convergence.
You have 3 different size intervals making up the rounded scale.
At this point, if you impose a table of legal intervals
derived from the intervals implied by the convergence,
then you're tapping into a discreet just intonation grid.
Back up, back up... which means you can play it in
[2:1\12], [3:2\7], [5:4\4], or even in just intonation.
It's a plateau of semblage.

> How does one "think, 10, 7, 10, 7"?

Stream of consciousness babble.
Wasn't supposed to be typed really.
Depends on who's listening and who's dictating.

Looking at the {2:1,5:3,4:3},
HO HO HO HO HO HO HO... oh boy...

Something we call Chromatic Meantone, usually [2m2 = M2],
that is, around 22, 34, 46, maybe even 70,
that two 16:15 can be used and wind up at a 9:8.
Pretty hairy, but the idea is the LOGIC TABLE implied,
leaves you able to substitute half-octaves,
run around rampant bisecting *any* two major seconds,
it's completely seductive.

Calling it a meantone "strain" came from the lab
around the time We figured out CMT, Chromatic meantone...
Since the just intonation web is a sort of monolith, a purity,
then really heh heh meantone is a sort of a contamination,
a virus of sorts, so We call them STRAINNNNS.

I'm saying, once you're familiar with these nests,
and you know the convergent just intonation grids,
and especially once you know the meantone corners you can cut,
if you LOOK at this, which is the list for {2:1,5:3,4:3},
PREVIOUSLY CONFUSED BY CERTAIN PEOPLE AS {2:1,5:3,3:2}!!!!

1,2,3,(4),7,10,12,(22),(34),46,53,(65),(118),171...

You have five even temperaments, in easy guitar fingering range,
that are even in number. Zero modulo two... even.
The Chromatic meantone strain is found from 10 through 46.

On another topic We've put a chip on the table about,
it stands to mention that the "Hendrix chord",
suggested to Paul he try it in 22,
is absolutely a legal construct in CMT,
which is often easier to visualize that you can simply
throw semi-octaves in and their ambiguity
is instantly accomodatable as per the logic grid.

Anyway anyway, I'm serious, there's too much excitement in that list,
and whenever anyone over here sees it, we start jumping right for that.
We head right for 22, 34, 46.
If you were here, YOU WOULD HAVE TO say "10,7,10,7,calm down, 10,7",
to remember that this is ALSO the place,
that causes the meantone strain that two equal thirds equals a fifth.

As I said,

>> Too often I fly past 10 into the 22/34/46 strain of [2m2 = M2]...
>> Like I've said it gets my blood pumping.
>> But the "6:5=5:4" anomaly is much more apparent if you sit there.
>> Think, 10, 7, 10, 7. Why not.
>> Try it in 17 (10 + 7).

...fast thoughts from the Lab often sound like slow insanity.

In many other words:
[2M3 = P5]
or
[2m3 = P5]
or
"The anomaly 5:4=6:5"
or...
"6:5 and 5:4 mapped to the same note."

...all of these are expressing the exact same thing.

We might also now add "VMT" for Valentine meantone? :P
Or at least Neutral Third Meantone. (possibly N3MT)

Ever heard "shoot first, ask questions later?"
With the amount of mental stuff We have going on,
We find it best to eject the ideas, even if rushed,
and be ready to explain later, should anyone (thank you)
see something interesting in the symbolism of Our glyphs.

> Maybe you went over the
> background to this recently - if so, forgive, I just had to dump about half a
> Meg of TLs into the
> "Finish Reading Later" folder (ah, *there's* a bit of wishful thinking...) in
> order to get to the
> current stuff.

Nah We just started posting the last couple days.

Hyuk. We am new in town.

>
>
>> I'll speak in n/17:
>> play through 0 3 5... 0 3 5... 0 3 5... it'll sound like an [F,];
>> play through 10 7 5... 0 10 7 5... 10 7 5... it'll sound like an [,F#].
>> Repeat this several times.
>
> Hey! That'll be enough outa you, Mister. This is too practical. Belongs on
> the other list! ;-)
>

After reading through the o**** list last night, Some thought as much.

>
>> Now play 0 3 5 7 10. Your ears should fall off.
>
> LOL! I love your writing style. (Both of you (?!))

Both is correct in that there are more than one.

"We are many, We are one,
Orphaned souls congealed as none."

‡

--- In tuning@y..., "Orphon Soul, Inc." <tuning@o...> wrote:

> Something we call Chromatic Meantone, usually [2m2 = M2],
> that is, around 22, 34, 46, maybe even 70,
> that two 16:15 can be used and wind up at a 9:8.

Hi Marc.

I think Meantone already has enough meanings . . .
What you're talking about, two 16:15s corresponding to a 9:8, of
course implies that

16/15 ~= (9/8)^(1/2)
256/225 ~= 9/8
2048/2025 ~= 1/1.

2048/2025 is called the diaschisma.

So in the langauge of many of us on this list, you're saying,
"Temperaments in which the diaschisma vanishes".

We've talked about these quite a bit (as you might expect, since I
use 22).

Graham Breed made nice page about these temperaments (which he
sometimes calls diaschismic temperaments, for obvious reasons) at:

http://www.cix.co.uk/~gbreed/diaschis.htm

I'm sure you'll enjoy it.

>
> Calling it a meantone "strain" came from the lab
> around the time We figured out CMT, Chromatic meantone...
> Since the just intonation web is a sort of monolith, a purity,
> then really heh heh meantone is a sort of a contamination,
> a virus of sorts, so We call them STRAINNNNS.

Looks like you're in good company.
The new "MIRACLE" strain is based on a remarkably good set of
approximations consistent with:

(3/2)^(1/6) ~= (8/5)^(1/7) ~= (8/7)^(1/2) ~= (11/4)^(1/15)
>
> On another topic We've put a chip on the table about,
> it stands to mention that the "Hendrix chord",
> suggested to Paul he try it in 22,

My interpretation as 1/1-5/4-7/4-7/6 is well approximated in 22.

I tried Purple Haze in 22 but I found both possibilities for the
pitch level of the second chord (the bIII) unsatisfactory.
>
>
>
>
> Ever heard "shoot first, ask questions later?"
> With the amount of mental stuff We have going on,
> We find it best to eject the ideas, even if rushed,
> and be ready to explain later, should anyone (thank you)
> see something interesting in the symbolism of Our glyphs.

Keep it up! Communication will only improve as we learn one another's
languages.

On 5/18/01 8:13 PM, "paul@stretch-music.com" <paul@stretch-music.com> wrote:

> I think Meantone already has enough meanings . . .
> What you're talking about, two 16:15s corresponding to a 9:8, of
> course implies that
>
> 16/15 ~= (9/8)^(1/2)
> 256/225 ~= 9/8
> 2048/2025 ~= 1/1.
>
> 2048/2025 is called the diaschisma.
>
> So in the langauge of many of us on this list, you're saying,
> "Temperaments in which the diaschisma vanishes".
>

If I knew that, it might have been called Diaschismatic Meantone here,
as you said, Graham calls them something similar.

Ahh... but thank you for the vocabulary and web links.
Is there any kind of dictionary of microtonal chatter anywhere?
A lot of the reason I've been holding back so long is
I'm not sure if there's a name for all of these ratios.
Seemingly though, after a few expressive posts,
I'm at least able to put out the mathematics of the thought,
and try to English around it a bit.

>> Since the just intonation web is a sort of monolith, a purity,
>> then really heh heh meantone is a sort of a contamination,
>> a virus of sorts, so We call them STRAINNNNS.
>
> Looks like you're in good company.
> The new "MIRACLE" strain is based on a remarkably good set of
> approximations consistent with:
>
> (3/2)^(1/6) ~= (8/5)^(1/7) ~= (8/7)^(1/2) ~= (11/4)^(1/15)

Well thanks... I was wondering.
Notice how I didn't actually ask though.

That's a pretty interesting set of equivalences.
I might run it through the Brun-o-matic
and see what temperaments show up.

OHHHHH okay NOW I get why you're talking about 7/72... ok...

> I tried Purple Haze in 22 but I found both possibilities for the
> pitch level of the second chord (the bIII) unsatisfactory.

HAAA yes that G.
That would perturb.
Well how did the chord work out heh.

>> We find it best to eject the ideas, even if rushed,
>> and be ready to explain later, should anyone (thank you)
>> see something interesting in the symbolism of Our glyphs.
>
> Keep it up! Communication will only improve as we learn one another's
> languages.

I agree.
Seems like mathematics is the common denominator.
Translating it into a spoken language, classifying, naming things,
that's where there's been the most blockage.
But that shouldn't matter since there hasn't been anyone around
to talk to about it who might have a vocabulary already.

Thank you for your encouragement.

Marc

--- In tuning@y..., "Orphon Soul, Inc." <tuning@o...> wrote:

> Is there any kind of dictionary of microtonal chatter anywhere?

You might want to try <http://www.ixpres.com/interval/dict>.

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

--- In tuning@y..., "Orphon Soul, Inc." <tuning@o...> wrote:
> On 5/18/01 8:13 PM, "paul@s..." <paul@s...> wrote:
>
> > I think Meantone already has enough meanings . . .
> > What you're talking about, two 16:15s corresponding to a 9:8, of
> > course implies that
> >
> > 16/15 ~= (9/8)^(1/2)
> > 256/225 ~= 9/8
> > 2048/2025 ~= 1/1.
> >
> > 2048/2025 is called the diaschisma.
> >
> > So in the langauge of many of us on this list, you're saying,
> > "Temperaments in which the diaschisma vanishes".
> >
>
> If I knew that, it might have been called Diaschismatic Meantone
here,

Well . . . meantone kinda means that the 81/80 vanishes.

> as you said, Graham calls them something similar.
>
> Ahh... but thank you for the vocabulary and web links.
> Is there any kind of dictionary of microtonal chatter anywhere?

You could try Monz' dictionary: http://www.ixpres.com/interval/dict/.

> A lot of the reason I've been holding back so long is
> I'm not sure if there's a name for all of these ratios.

See http://www.xs4all.nl/~huygensf/doc/intervals.html.

> > I tried Purple Haze in 22 but I found both possibilities for the
> > pitch level of the second chord (the bIII) unsatisfactory.
>
> HAAA yes that G.
> That would perturb.
> Well how did the chord work out heh.

The lower version didn't work because the major third is lower than
the fifth of the first chord.

The higher version didn't work because the root is higher than the
7/6 of the first chord.

On 5/18/01 8:44 PM, "paul@stretch-music.com" <paul@stretch-music.com> wrote:

>>> I tried Purple Haze in 22 but I found both possibilities for the
>>> pitch level of the second chord (the bIII) unsatisfactory.
>>
>> HAAA yes that G.
>> That would perturb.
>> Well how did the chord work out heh.
>
> The lower version didn't work because the major third is lower than
> the fifth of the first chord.

Yeah it's tricky but if you play the E+9 with no 5th... EHHHH...
::squeak::
Yeah I know not unless you layer it.
Doesn't really work in 34 either.
But 46 isn't so bad.

--- In tuning@y..., "Orphon Soul, Inc." <tuning@o...> wrote:
> On 5/18/01 8:44 PM, "paul@s..." <paul@s...> wrote:
>
> >>> I tried Purple Haze in 22 but I found both possibilities for the
> >>> pitch level of the second chord (the bIII) unsatisfactory.
> >>
> >> HAAA yes that G.
> >> That would perturb.
> >> Well how did the chord work out heh.
> >
> > The lower version didn't work because the major third is lower than
> > the fifth of the first chord.
>
> Yeah it's tricky but if you play the E+9 with no 5th...

I do . . . I still hear the "false fifth" between the E and the following B as a contrapuntally
awkward cross-relation.

> Yeah I know not unless you layer it.

What do you mean by layering it?

On 5/19/01 12:36 AM, "paul@stretch-music.com" <paul@stretch-music.com>
wrote:

>> Yeah it's tricky but if you play the E+9 with no 5th...
>
> I do . . . I still hear the "false fifth" between the E and the following B as
> a contrapuntally
> awkward cross-relation.
>

Good ear. That E...... B... A... melodic combination
with the B being flat one note, that *is* kind of menacing.

>> Yeah I know not unless you layer it.
>
> What do you mean by layering it?

So sorry...

I meant you can get away with a lot of things like this in 22,
if you overdub the same structure in something like 34, 46, or 56.

Orphon Soul wrote:

> If I knew that, it might have been called Diaschismatic Meantone here,
> as you said, Graham calls them something similar.

I'm still avoiding calling them anything on the web page. But
"diaschismic" or "double positive" would be fine on me, depending on
whether you're thinking of the harmonic or melodic definition. In this
case, it's harmonic so "diaschismic".

It shouldn't be "meantone". It doesn't even have one chain of fifths.

Graham

On 5/19/01 5:00 PM, "graham@microtonal.co.uk" <graham@microtonal.co.uk>
wrote:

> It shouldn't be "meantone". It doesn't even have one chain of fifths.

Does meantone generally imply using fifths?
I didn't know, I was just going by the word,
some tone, split into some mean.

‡

It all depends on which list you are.
In a practical context, mean tone gets a whole different meaning.

----- Original Message -----
From: "Orphon Soul, Inc." <tuning@orphonsoul.com>
To: "Tuning List" <tuning@yahoogroups.com>
Sent: Saturday, May 19, 2001 6:12 PM
Subject: Re: [tuning] Re: Valentine - 6:5 and 5:4 mapped to the same note

> On 5/19/01 5:00 PM, "graham@microtonal.co.uk" <graham@microtonal.co.uk>
> wrote:
>
> > It shouldn't be "meantone". It doesn't even have one chain of fifths.
>
> Does meantone generally imply using fifths?
> I didn't know, I was just going by the word,
> some tone, split into some mean.
>
> ?
>
>
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--- In tuning@y..., "Orphon Soul, Inc." <tuning@o...> wrote:
> BEHOLD BEHOLD BEHOLD...
> whom???
> * * * * * Typos, the Greek God of Error. :-P * * * * *

I love it!

I can't take time right now to respond line by line, but please accept
my thanks for that lengthy and illuminating (and poetic!) post. I've
printed it out for study and quick reference. It may take me awhile
to absorb it all but I'm sure it will be worth the effort.

> "We are many, We are one,
> Orphaned souls congealed as none."

Uh, OK. Y'all be careful, now, ya hear?

--
David F. (just me, all by my lonesome)
Nashville, TN, USA
http://personal.bna.bellsouth.net/bna/d/f/dfin/index.html
--
"Seems like mathematics is the common denominator." (recognize that
statement, Marc? :-)

On 5/20/01 12:00 AM, "David J. Finnamore" <daeron@bellsouth.net> wrote:

> "Seems like mathematics is the common denominator." (recognize that
> statement, Marc? :-)

Oh I tend to think so, yeah.
I was just saying this to Johnny today over sushi.
I struggle with terminology,
and eventually a lot of this all boils down to math.

--- In tuning@y..., graham@m... wrote:
> Orphon Soul wrote:
>
> > If I knew that, it might have been called Diaschismatic Meantone here,
> > as you said, Graham calls them something similar.
>
> I'm still avoiding calling them anything on the web page. But
> "diaschismic" or "double positive" would be fine on me,

On one of your other web pages, Graham, you do call them "diaschismic". Can you find it?

Anyhow, if "double positive" meant "Pyth. comma represented by +2 degrees", it wouldn't be
synonymous with diaschismic. So what do you mean by "double positive"?