Yahoo Tuning Groups Ultimate Backup tuning Big 72-tET spreadsheet

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> Hi Paul... and anybody else interested.
>
> Might it be possible someday to do a nice big colored spreadsheet
> with all the intervals in 72-tET in the same way that the Blackjack
> lattice was made??

well, that's especially easy -- it's all just diagonal bands! in
other words, each row is the same as the last, just shifted over one.

but what's the point, really? every single 72-equal interval is
available from every single 72-equal pitch. the whole thing seems
kinda unnecessary . . .

> Maybe that's a lot of work. I dream of having something like that,
> though. That might mean more than you could imagine to me someday.

hmm . . . i may be missing something. it seems like all you need is a
*line*, not a *matrix* . . . and this already exists in many forms,
such as my 'intervallic continuum' chart . . .

🔗jpehrson2 <jpehrson@rcn.com>

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

/tuning/topicId_35055.html#35056

> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> > Hi Paul... and anybody else interested.
> >
> > Might it be possible someday to do a nice big colored spreadsheet
> > with all the intervals in 72-tET in the same way that the
Blackjack
> > lattice was made??
>
> well, that's especially easy -- it's all just diagonal bands! in
> other words, each row is the same as the last, just shifted over
one.
>
> but what's the point, really? every single 72-equal interval is
> available from every single 72-equal pitch. the whole thing seems
> kinda unnecessary . . .
>
> > Maybe that's a lot of work. I dream of having something like
that,
> > though. That might mean more than you could imagine to me
someday.
>
> hmm . . . i may be missing something. it seems like all you need is
a
> *line*, not a *matrix* . . . and this already exists in many forms,
> such as my 'intervallic continuum' chart . . .

***I guess I'm not understanding this Paul...

I'd like to see an example.

What I'm looking for is a *big* excel sheet that has all the
intervals and the colors in it just like the one you did for me in
Blackjack.

I'm going to use this in my composing and, yes, I'll probably be
a "turncoat" (throw tomatoes now) and eventually bring all this back
into big 12-tET pieces so that *everybody!!!!* will appreciate the
wonders of microtonality!!!!!

🔗paulerlich <paul@stretch-music.com>

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> --- In tuning@y..., "paulerlich" <paul@s...> wrote:
>
> /tuning/topicId_35055.html#35056
>
> > --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> > > Hi Paul... and anybody else interested.
> > >
> > > Might it be possible someday to do a nice big colored
spreadsheet
> > > with all the intervals in 72-tET in the same way that the
> Blackjack
> > > lattice was made??
> >
> > well, that's especially easy -- it's all just diagonal bands! in
> > other words, each row is the same as the last, just shifted over
> one.
> >
> > but what's the point, really? every single 72-equal interval is
> > available from every single 72-equal pitch. the whole thing seems
> > kinda unnecessary . . .
> >
> > > Maybe that's a lot of work. I dream of having something like
> that,
> > > though. That might mean more than you could imagine to me
> someday.
> >
> > hmm . . . i may be missing something. it seems like all you need
is
> a
> > *line*, not a *matrix* . . . and this already exists in many
forms,
> > such as my 'intervallic continuum' chart . . .
>
>
> ***I guess I'm not understanding this Paul...
>
> I'd like to see an example.

well, give me an example of a specific instance in which you think
the big matrix might be useful . . . ?

> What I'm looking for is a *big* excel sheet that has all the
> intervals and the colors in it just like the one you did for me in
> Blackjack.

i understand that, but i can't imagine why you'd want one. all the
intervals are the same, everywhere in the scale!

> I'm going to use this in my composing and, yes, I'll probably be
> a "turncoat" (throw tomatoes now) and eventually bring all this
back
> into big 12-tET pieces

huh? don't get it. you mean some sections of the 72-equal pieces will
be in 12-equal?

>so that *everybody!!!!* will appreciate the
> wonders of microtonality!!!!!
>
> jp

🔗jpehrson2 <jpehrson@rcn.com>

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

/tuning/topicId_35055.html#35056

***But, I just need a big reference chart, so I can *immediately* see
all the "approximate just" colors from every pitch relationship.

I will use this for the rest of my life in my composing... :)

Seriously.

Are you saying I only need a *portion* of this chart? I've been
thinking in terms of *Blackjack* lately, not the full 72-tET, so I'm
a little "fuzzy" on all this.

Any help will be, as ever, very gratefully appreciated!

> > Maybe that's a lot of work. I dream of having something like
that, though. That might mean more than you could imagine to me
someday.
>
> hmm . . . i may be missing something.

***I'll bet it's *me!* instead :)

it seems like all you need is a
> *line*, not a *matrix* . . . and this already exists in many forms,
> such as my 'intervallic continuum' chart . . .

***Could you please show me, Paul, what I could use for this, then?

You obviously know what I mean: it's just a quick reference so that
I could take *any* 72-tET pitch and then know the approximate ratio
relationship (hopefully in colors like the Blackjack chart) with
*any* other 72-tET pitch.

I guess you're saying it's different as a *full ET* to the Blackjack
matrix, that we had to have fully *spelled out* on the Excel.

That really worked wonders for me, and, obviously, I want something
like that for the full 72-tET.

I obviously need to have this clarified in my mind.

Help!!!

thanks!!!

🔗jpehrson2 <jpehrson@rcn.com>

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

/tuning/topicId_35055.html#35058

>
> > ***I guess I'm not understanding this Paul...
> >
> > I'd like to see an example.
>
> well, give me an example of a specific instance in which you think
> the big matrix might be useful . . . ?
>
> > What I'm looking for is a *big* excel sheet that has all the
> > intervals and the colors in it just like the one you did for me
in
> > Blackjack.
>
> i understand that, but i can't imagine why you'd want one. all the
> intervals are the same, everywhere in the scale!
>

***So then, what you're saying is I need a kind of "sliderule" that I
can "slide around" to find out what the intervals are?

Sorry about the "fuzziness." I haven't been thinking about the
*entire* 72-tET set of late...

I just want something, obviously, so that when I'm writing a piece
and I want a certain *near just* interval from ANY 72-tET pitch, I
can easly find it!

Whatever will work is fine with me. I don't even remember what all
the possibilities *are* in 72-tET at the moment, since I've only been
working in the *Blackjack* subset... :(

> > I'm going to use this in my composing and, yes, I'll probably be
> > a "turncoat" (throw tomatoes now) and eventually bring all this
> back into big 12-tET pieces
>
> huh? don't get it. you mean some sections of the 72-equal pieces
will be in 12-equal?
>

***Well, that's probably putting it too strongly. 12-tET will be my
basic *reference point* for notation, as it already *is* in 72-tET.

All I'm saying is this:

If I were to write a *bigger* piece for ensemble than the more
soloistic "experimental" efforts I am doing at present, I feel I need
to simplify matters some.

Let's take woodwinds. I don't want to have a woodwind section where
*everybody* is doing alternate fingerings all the time. I understand
that some composers will do this and I'm sure their pieces are great,
but, for my own personal style, *tuning* in general is only PART of
what I am trying to do, and only *part* of my language! I'm not
saying it's *ornamental* or *incidental*, it's just not the *whole
thing...*

For that reason, I would be *much* happier having, for instance, a
woodwind section *MOSTLY* in 12-tET and letting the *strings* handle
much of the microtonality.

I will have *some* alternate fingerings in the winds, but I just
don't want to have to rehearse an *entire* woodwind section in
alternate tunings. There's not enough rehearsal time for it. Same
with brass, for the most part.

So, what I'm saying is that I will have a, basically, 72-tET
framework, but will keep several instruments more playing the 12-tET
part of it.

Of course, *EVERYBODY* will also be playing quarter-tones so,
essentially I guess I'm saying I will be composing in a 72-tET frame
work using a *24-tET* notational base.

Sibelius can handle the quarter tones *very* easily...

Just some thoughts for the future, as I am thinking of *larger* works
again at the moment.

🔗paulerlich <paul@stretch-music.com>

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:

> > it seems like all you need is a
> > *line*, not a *matrix* . . . and this already exists in many
forms,
> > such as my 'intervallic continuum' chart . . .
>
> ***Could you please show me, Paul, what I could use for this, then?
>
> You obviously know what I mean: it's just a quick reference so
that
> I could take *any* 72-tET pitch and then know the approximate ratio
> relationship (hopefully in colors like the Blackjack chart) with
> *any* other 72-tET pitch.
>
> I guess you're saying it's different as a *full ET* to the
Blackjack
> matrix, that we had to have fully *spelled out* on the Excel.
>
> That really worked wonders for me, and, obviously, I want something
> like that for the full 72-tET.
>
> I obviously need to have this clarified in my mind.
>
> Help!!!
>
> thanks!!!
>
> jp

joseph, it shouln't be too hard to mentally grasp the interval
between any two 72-equal pitches.

for example, from C> to F#v is a tritone, minus a sixth-tone, minus a
twelfth tone.

so it's a tritone minus a quarter-tone.

look this up on the 'intervallic continuum' chart and you'll
immediately see that it corresponds to the ratio 11:8.

see how simple it is?

🔗paulerlich <paul@stretch-music.com>

🔗jpehrson2 <jpehrson@rcn.com>

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

/tuning/topicId_35055.html#35097

> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
>
> > ***So then, what you're saying is I need a kind of "sliderule"
that
> I
> > can "slide around" to find out what the intervals are?
>
> you should be able to grasp the intervals immediately from their
> notation. a sixth-tone is two twelfth-tones, a quarter-tone is
three
> twelfth-tones, and that's all you need to know to figure out the
> interval size. then look it up in the intervallic continuum chart,
>
> /tuning/files/perlich/secor.gif
>
> to see if it corresponds with a 'consonant ratio'.

***I think you're right, Paul. Using the 1/12 tone base as a grid,
all I really need is this chart. The important thing, though, is
that I forgot about this chart!

Thanks!!!!!

Joseph

🔗dkeenanuqnetau <d.keenan@uq.net.au>

🔗jpehrson2 <jpehrson@rcn.com>

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:

/tuning/topicId_35055.html#35121

> Maybe what Joseph needs is a circular "slide rule". Since it's the
> full 72-tET, the notes don't _need_ to be arranged as a chain (in
this
> case a closed-chain or cycle) of miracle generators and could
instead
> be aranged in pitch order. However, I think it would still be
useful
> to have it in miracle-generator order so you can easily see what
will
> fit in Blackjack, Canasta, Studloco. So the 72 notes would be
around
> the outside disk, and an otonal and a utonal 11-limit hexad (and
maybe
> some ASSes and a hexany and other things) could be marked on the
> inside disk.

***Well, sure, I'd enjoy seeing something like this!

🔗dkeenanuqnetau <d.keenan@uq.net.au>

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> > Maybe what Joseph needs is a circular "slide rule". ...
>
> ***Well, sure, I'd enjoy seeing something like this!

Here's a first pass at it, in a 14KB zipped Excel spreadsheet. This
circular sliderule shows all of 72-EDO against an 11-limit otonality
and utonality and can be ordered by secors or 72-EDO degrees.

http://dkeenan.com/Music/Miracle/Miracle72Sliderule.xls.zip

Just print the chart twice and cut the outside ring of the second one,
then put a pin thru the middle of both.

This could be greatly improved upon. But by tricking Excel into doing
some things that it didn't really want to do, I got the job done
quickly, rather than spending hours drawing it all by hand using some
Paint or Draw program.

The main improvement would be to link up the identities within a given
chord, so it's obvious there are two completely seperate chords there,
then add some ASS and magic chords, maybe on other inner disks. You
could do this by hand with a pen.

🔗dkeenanuqnetau <d.keenan@uq.net.au>

🔗jonszanto <JSZANTO@ADNC.COM>

🔗jpehrson2 <jpehrson@rcn.com>

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:

/tuning/topicId_35055.html#35134

>
> http://dkeenan.com/Music/Miracle/Miracle72Sliderule.xls.zip
>

***I don't usually like to shout, but this really "takes the cake..."

This is AMAZING! The *perfect* tool for a 72-tetter.

I did a lot, too.

I pasted it on two cardboards, for one thing, using a glue stick.

Then, I cut the wheel out with sizzors.

Do you realize the extent of the decline in American sizzors, these
days? They are very poor. Very poor quality. Not very sharp... the
sizzors, I mean... the policy is a different matter.

I found an *older* pair. Far superior.

Now (seriously) something important: when printing it out, I
selected "scale to fit page" for the Excel chart. Otherwise, the
font was really getting "funky." I don't know if I would have been
able to use it in that shape.

I didn't bother with putting the "slashes" for utonal chords in
Excel. I just "whited out" the periods and put them in with pen... :)

Now, on to more important matters, like putting the pin in.

I used a "pushpin."

And, pounded the other side with a hammer, so the pin folded over.

Works like a charm.

I intend to use this in my composing for the rest of my life which,
if the terrorists leave me alone, hopefully will be a while.

In fact, as I've been mentioning, I'm hoping to go on to larger
pieces.

My objective, as everybody with half a brain has already intuited, is
to let the instruments which play microtonality *easily* do much of
the work, offset with "quasi just" intervals, etc., against
instruments that will, "mostly" play in the 12-tET subset. But, we
won't call it that... :) I could get a bad reputation that way, at
least around *these* parts. It's in 72.

That's why I need this "Miracle Wheel."

Dave, you've "reinvented the Wheel" and I'm extremely grateful to you
for it!

Joseph

🔗jpehrson2 <jpehrson@rcn.com>

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:

/tuning/topicId_35055.html#35136

> Another improvement would be to mark the notes of the standard
> Blackjack key.

***Well, we could always look that up... :)

I rather like the way this is so direct, simple and "uncluttered."

Dave, if you make other versions with other elaborations, would you
mind keeping *this* generation as well??

I mean, it probably doesn't matter, since I've just saved it in about
10 different places, even on the Web... :) but just for future
reference...

🔗jpehrson2 <jpehrson@rcn.com>

🔗genewardsmith <genewardsmith@juno.com>

🔗dkeenanuqnetau <d.keenan@uq.net.au>

🔗jpehrson2 <jpehrson@rcn.com>

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:

/tuning/topicId_35055.html#35153

> Joseph,
>
> I'm curious, which one did you choose to print out, and why - the
one where the notes are ordered by secors, or the one where they are
> ordered by pitch?

***Hello Dave!

Well, in your "infinite wisdom" I can intuit from this question that
you're asking me if I knew there were two versions of this.

Actually, I didn't... :)

I missed the little macro buttons on the top...

Thanks for pointing this out to me! :)

Well, for my *own* purposes it seems the 72-tET ordered wheel even
works better, since I like to see the ordered 72-tET set, but I can
understand why, from a *theoretical* perspective you would feature
the chain of secors one as the "default" on the chart.

I printed out and made my cardboard wheel for the second version.

I had a couple of questions on the 72-tET ordered one, though:

There is a line that is drawn between the 11 limit and the 1/7 and
similarly between the 1/1 and the 7 limit.

I assume that's just something that Excel did that I shouldn't pay
attention to, and I should just white it out???

Just checking.

I was also curious about your use of enharmonics in the basic 72-tET
scale. Is there an "accepted" way of doing this? Maybe not yet.

Anyway, I noticed that from every enharmonic you used one version of
the 12th of a tone down and 6th of a tone down, and then used the
*OTHER* variant of the enharmonic for the 12th of a tone up and the
6th of a tone up... i.e.:

C], C#<, C#v, C#, Db^, Db>, D[

Is there some principle at work here, or is the idea just to
differentiate the pitches more by using this??

I CAUGHT A MISTAKE!

Note you have TWO D]'s !!

I think that probably should be corrected in the original Excel file,
no?

I corrected my two wheels. The Miracle generator correction was a
slight bit more challenging, but I managed it... :)

I guess I'm also asking about the basic choice of enharmonics for the
72-tET scale. You have:

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

Generally speaking, you are *so* systematic, that I'm inclined to
believe you have a reason for this choice.

What is it (again)?

Oh... for the boys and girls who are making their "wheels" at home, I
would advise one thing:

Start by gluing the FULL PAGE 8 1/2 X 11 to the same sized
cardboard. THEN cut the wheel out, using sharp sizzors, if you can
find any. That worked best for me. I made the *second* wheel in no
time.

Thanks so much again, Dave, for pointing the second wheel out to me!
Probably I'll be using BOTH quite a bit!

Joseph

🔗dkeenanuqnetau <d.keenan@uq.net.au>

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> Well, for my *own* purposes it seems the 72-tET ordered wheel even
> works better, since I like to see the ordered 72-tET set, but I can
> understand why, from a *theoretical* perspective you would feature
> the chain of secors one as the "default" on the chart.
>
> I printed out and made my cardboard wheel for the second version.
>
> I had a couple of questions on the 72-tET ordered one, though:

> There is a line that is drawn between the 11 limit and the 1/7 and
> similarly between the 1/1 and the 7 limit.
>
> I assume that's just something that Excel did that I shouldn't pay
> attention to, and I should just white it out???

Right.

> I was also curious about your use of enharmonics in the basic 72-tET
> scale. Is there an "accepted" way of doing this? Maybe not yet.

I don't know. I can only argue convincingly for the choice used in the
standard CGDA Blackjack key and the alternate (violin/guitar)
blackjack key based on GDAE.

> Anyway, I noticed that from every enharmonic you used one version of
> the 12th of a tone down and 6th of a tone down, and then used the
> *OTHER* variant of the enharmonic for the 12th of a tone up and the
> 6th of a tone up... i.e.:
>
> C], C#<, C#v, C#, Db^, Db>, D[
>
> Is there some principle at work here, or is the idea just to
> differentiate the pitches more by using this??

Differentiate the pitches more. Yes. I figure it's preferable that a
performer see something notated as a kind of D if it's closer to D
than C. Introduces some redundancy in the notation to help avoid
mistakes. And, at least within those two Blackjack keys, it results in
the most thirds being spelled correctly. _All_ the neutral thirds are
spelled correctly. This does not apply thru the whole of 72-tET. I
haven't really given much time to optimising the notation for the
whole of 72-tET. Feel free to use enharmonics to spell intervals
correctly if you think it helps.

> I CAUGHT A MISTAKE!
>
> Note you have TWO D]'s !!
>
> I think that probably should be corrected in the original Excel
file,
> no?

Thanks very much for that. I've uploaded a corrected version. Fixed
the font size problem too I hope.
http://dkeenan.com/Music/Miracle/Miracle72Sliderule.xls.zip
I also spaced the otonal and utonal a bit better for the pitch-order
wheel (since they overlap on that one). I recommend using two
different colours to loop together the otonal identities vs. the
utonal, and make them visually separate from each other.

> I guess I'm also asking about the basic choice of enharmonics for
the
> 72-tET scale. You have:
>
> C, C#, D, Eb, E, F, F#, G, G#, A, Bb, B
>
> Generally speaking, you are *so* systematic, that I'm inclined to
> believe you have a reason for this choice.

Arranged a a chain of fifths that's Eb Bb F C G D A E B F# C# G#. You
could equally well use Ab instead of G# but the idea is to deviate as
little at possible from the naturals in either direction, on a chain
of fifths (the most likely modulation). Preferring the G# over the Ab
dates from the meantone era and probably relates to wanting both
melodic and harmonic minor keys.

🔗dkeenanuqnetau <d.keenan@uq.net.au>

🔗monz <joemonz@yahoo.com>

> From: dkeenanuqnetau <d.keenan@uq.net.au>
> To: <tuning@yahoogroups.com>
> Sent: Sunday, March 03, 2002 7:36 PM
> Subject: [tuning] Re: 72-EDO 11-limit circular sliderule
> (was: Big 72-tET spreadsheet)
>
>
> At Monz's request, I've just uploaded GIFs of the two sliderules for
> those who can't read Excel spreadsheets, or have trouble with
> spreadsheets with Macros. They are:
>
> in pitch order
> http://dkeenan.com/Music/Miracle/72Sliderule.gif
> and in secor order
> http://dkeenan.com/Music/Miracle/Miracle72Sliderule.gif

THANK YOU, THANK YOU, THANK YOU, DAVE !!

i can't wait to construct my own sliderule like Joe P. did.

-monz

_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at http://mail.yahoo.com

🔗jpehrson2 <jpehrson@rcn.com>

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:

/tuning/topicId_35055.html#35185

>
> > I was also curious about your use of enharmonics in the basic 72-
tET scale. Is there an "accepted" way of doing this? Maybe not yet.
>
> I don't know. I can only argue convincingly for the choice used in
the standard CGDA Blackjack key and the alternate (violin/guitar)
> blackjack key based on GDAE.
>

***Oh... gee. I was't thinking of that. Why, of course! Glad you
did it that way, Dave!

>
> > I CAUGHT A MISTAKE!
> >
> > Note you have TWO D]'s !!
> >
> > I think that probably should be corrected in the original Excel
> file, no?
>
> Thanks very much for that. I've uploaded a corrected version. Fixed
> the font size problem too I hope.
> http://dkeenan.com/Music/Miracle/Miracle72Sliderule.xls.zip
> I also spaced the otonal and utonal a bit better for the pitch-
order wheel (since they overlap on that one). I recommend using two
> different colours to loop together the otonal identities vs. the
> utonal, and make them visually separate from each other.
>

****This new version seemed rather *strange* since it looks so
different on the *surface* from the internal wheel of the other one.
You must have just found *other places* that these
identities "worked" and used those instead to solve the "spacing"
problem. ??

Unfortunately, the entire wheel, not just the FONT is somewhat
smaller, but I guess we can live with that...

> > I guess I'm also asking about the basic choice of enharmonics for
> the
> > 72-tET scale. You have:
> >
> > C, C#, D, Eb, E, F, F#, G, G#, A, Bb, B
> >
> > Generally speaking, you are *so* systematic, that I'm inclined to
> > believe you have a reason for this choice.
>
> Arranged a a chain of fifths that's Eb Bb F C G D A E B F# C# G#.
You could equally well use Ab instead of G# but the idea is to
deviate as little at possible from the naturals in either direction,
on a chain of fifths (the most likely modulation). Preferring the G#
over the Ab dates from the meantone era and probably relates to
wanting both melodic and harmonic minor keys.

***Oh... got it. With *D* in the very middle, which is
the "traditional" way.

Thanks again, Dave!

🔗jpehrson2 <jpehrson@rcn.com>

--- In tuning@y..., "monz" <joemonz@y...> wrote:

/tuning/topicId_35055.html#35187

>
> THANK YOU, THANK YOU, THANK YOU, DAVE !!
>
> i can't wait to construct my own sliderule like Joe P. did.
>
>
> -monz
>

***Another tip for the boys and girls in front of the cathode ray
tube who are trying this...

Gluestick the *cardboard*, *not* the paper, when you put them
together.

A silly thing to mention?

Well, maybe... but it took me makeing about 3 of them before I did
this...