Constructing a universal 13-limit system of notation

George's saggital system is based on 12-equal, and enharmonic equivalents are genuinely equivalent. However, we could spell things in a way which was more diatonically based, and closer to meantone, by making sharps/flats an instrinsic part of the system.

We can construct a system of notation by starting with a "notation" in my sense; in this case, let us consider a 5-limit system based on
<10/9, 25/24, 81/80>. We can express any 5-limit ratio in the form
(10/9)^a (25/24)^b (81/80)^c, and if we express "a" by position on a standard staff, "b" by sharps (if positive) or flats (if negative), and "c" by some sort of comma symbol, then we have a universal system of notation for the 5-limit which becomes ordinary musical notation in any meantone system. We now may extend it, by means of symbols for
64/63, 33/32, and 40/39, and thereby get the 13-limit. The 7,11 and 13 limit symbols simply show how many of these primes are in the factorization, since <10/9,25/24,81/80,64/63,33/32,40/39>^(-1) =
[h7,-g2,h3,-v7,v11,-v13] where g2 = [2,3,4,6,7,7].

This would be an uncompact form of such a notation; a compact form could then be produced in something like the way George has done--even by modifying his system, if he had no objection. Of course, I don't know if the world *wants* a universal 13-limit notation scheme. :)

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> George's saggital system is based on 12-equal, and enharmonic
>equivalents are genuinely equivalent.

It would seem that the intended applications of saggital to 31-tET
and 41-tET would not have this property.

>However, we could spell things in a way which was more diatonically
>based, and closer to meantone, by making sharps/flats an instrinsic
>part of the system.

This would make notating 41-tET more difficult, no? But it sounds
like it could correspond with the set of Fokker/Keenan interval-names

http://www.uq.net.au/~zzdkeena/Music/IntervalNaming.htm,

which becomes a "notation" if we refer it to the note "C", with the
translations {second, third, . . .} -> {D, E}, and minor -> flat.

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

> This would make notating 41-tET more difficult, no? But it sounds
> like it could correspond with the set of Fokker/Keenan interval-names
>
> http://www.uq.net.au/~zzdkeena/Music/IntervalNaming.htm,
>
> which becomes a "notation" if we refer it to the note "C", with the
> translations {second, third, . . .} -> {D, E}, and minor -> flat.

I was going to check this out, but it seems the url is out of date.

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "paulerlich" <paul@s...> wrote:
>
> > This would make notating 41-tET more difficult, no? But it sounds
> > like it could correspond with the set of Fokker/Keenan interval-
names
> >
> > http://www.uq.net.au/~zzdkeena/Music/IntervalNaming.htm,
> >
> > which becomes a "notation" if we refer it to the note "C", with
the
> > translations {second, third, . . .} -> {D, E}, and minor -> flat.
>
> I was going to check this out, but it seems the url is out of date.

Try it now:

http://www.uq.net.au/~zzdkeena/Music/IntervalNaming.htm

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

> http://www.uq.net.au/~zzdkeena/Music/IntervalNaming.htm

It seems to me that rather than Fokker-Keenan, what I was talking about was close to Manuel's system:

{{Manuel suggested investigating how this system relates to the JI notation to be introduced in version 1.6 of Scala. Here are the modifiers needed for 11-limit.

/ comma sharp, 81/80
\ comma flat, 80/81
) diesis sharp, 128/125
( diesis flat, 125/128
7 septimal comma sharp, 64/63
L septimal comma flat, 63/64
^ undecimal diesis sharp, 33/32
v undecimal diesis flat, 32/33}}

If we use A-G strictly according to what h7 tells us they should be, and substitute ordinary sharps and flats for the diesis symbols (which we then don't need) this would be exactly the universal 11-limit method I proposed, and adding a symbol for 40/39 (what is this, by the way--the triskadecimal diesis?) would extend it to a 13-limit system.

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "paulerlich" <paul@s...> wrote:
>
> > http://www.uq.net.au/~zzdkeena/Music/IntervalNaming.htm
>
> It seems to me that rather than Fokker-Keenan, what I was talking
about was close to Manuel's system:
>
> {{Manuel suggested investigating how this system relates to the JI
notation to be introduced in version 1.6 of Scala. Here are the
modifiers needed for 11-limit.
>
> / comma sharp, 81/80
> \ comma flat, 80/81
> ) diesis sharp, 128/125
> ( diesis flat, 125/128
> 7 septimal comma sharp, 64/63
> L septimal comma flat, 63/64
> ^ undecimal diesis sharp, 33/32
> v undecimal diesis flat, 32/33}}
>
> If we use A-G strictly according to what h7 tells us they should be,

What does h7 tell us they should be? Ratios please.

>and substitute ordinary sharps and flats for the diesis symbols

How would one do that, without contradicting their traditional
meaning?

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

> > If we use A-G strictly according to what h7 tells us they should be,
>
> What does h7 tell us they should be? Ratios please.

It depends on what ratio, of course. If you look at either a JI diatonic or Pthagorean starting at A, you get A,B,C,D,E,F,G.

> >and substitute ordinary sharps and flats for the diesis symbols
>
> How would one do that, without contradicting their traditional
> meaning?

That # = 25/24 is the traditional meaning.

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "paulerlich" <paul@s...> wrote:
>
> > > If we use A-G strictly according to what h7 tells us they
should be,
> >
> > What does h7 tell us they should be? Ratios please.
>
> It depends on what ratio, of course. If you look at either a JI
>diatonic or Pthagorean starting at A, you get A,B,C,D,E,F,G.

Right, but which? A notation isn't a notation until you specify that
choice.

> > >and substitute ordinary sharps and flats for the diesis symbols
> >
> > How would one do that, without contradicting their traditional
> > meaning?
>
> That # = 25/24 is the traditional meaning.

Right, so you're saying you can avoid using ) and ( for 128/125 and
125/128, if you freely use # and b for 25/24 and 24/25? Or you can't?

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> > --- In tuning@y..., "paulerlich" <paul@s...> wrote:
> >
> > > > If we use A-G strictly according to what h7 tells us they
> should be,
> > >
> > > What does h7 tell us they should be? Ratios please.
> >
> > It depends on what ratio, of course. If you look at either a JI
> >diatonic or Pthagorean starting at A, you get A,B,C,D,E,F,G.
>
> Right, but which? A notation isn't a notation until you specify that
> choice.

Try it on 1-9/8-5/4-4/3-3/2-5/3-15/8 and you get 0,1,2,3,4,5,6; if we start with A, that is A,B,C,D,E,F,G. The same goes for the Pythagorean scale.

> Right, so you're saying you can avoid using ) and ( for 128/125 and
> 125/128, if you freely use # and b for 25/24 and 24/25? Or you can't?

Exactly. Use A-G for the results of h7, use # and b for 25/24 and 24/25, and use + and - or whatever else you might prefer for 81/80 and 80/81. You now have the 5-limit. Adding symbols for 64/63, 33/32 and 40/39 gives you the 7, 11 and 13 limits.

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "paulerlich" <paul@s...> wrote:
> > --- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> > > --- In tuning@y..., "paulerlich" <paul@s...> wrote:
> > >
> > > > > If we use A-G strictly according to what h7 tells us they
> > should be,
> > > >
> > > > What does h7 tell us they should be? Ratios please.
> > >
> > > It depends on what ratio, of course. If you look at either a JI
> > >diatonic or Pthagorean starting at A, you get A,B,C,D,E,F,G.
> >
> > Right, but which? A notation isn't a notation until you specify
that
> > choice.
>
> Try it on 1-9/8-5/4-4/3-3/2-5/3-15/8 and you get 0,1,2,3,4,5,6; if
>we start with A, that is A,B,C,D,E,F,G. The same goes for the
>Pythagorean scale.

Except that some syntonic comma accidentals must be applied to at
least one of these scales. It's not a notation that can encompass,
say, 41-tET, until you say which.

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

> > Try it on 1-9/8-5/4-4/3-3/2-5/3-15/8 and you get 0,1,2,3,4,5,6; if
> >we start with A, that is A,B,C,D,E,F,G. The same goes for the
> >Pythagorean scale.
>
> Except that some syntonic comma accidentals must be applied to at
> least one of these scales. It's not a notation that can encompass,
> say, 41-tET, until you say which.

The "which" is determined by the comma counter, which in this case is the 3-et. We have <10/9, 25/24, 81/80>^(-1) = [h7, -g2, h3] where
g2 = [2,3,4]; this defines the whole 5-limit notation.

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "paulerlich" <paul@s...> wrote:
>
> > > Try it on 1-9/8-5/4-4/3-3/2-5/3-15/8 and you get 0,1,2,3,4,5,6;
if
> > >we start with A, that is A,B,C,D,E,F,G. The same goes for the
> > >Pythagorean scale.
> >
> > Except that some syntonic comma accidentals must be applied to at
> > least one of these scales. It's not a notation that can
encompass,
> > say, 41-tET, until you say which.
>
> The "which" is determined by the comma counter, which in this case
> is the 3-et. We have <10/9, 25/24, 81/80>^(-1) = [h7, -g2, h3] where
> g2 = [2,3,4]; this defines the whole 5-limit notation.

This remains too abstract for me. Let's look at George's notation
again, shall we? Isn't a 7-note scale at the center of it, given that
every pitch must be notated as one of the seven letters, along with a
well-defined accidental, and the notation is supposed to work across
31-, 41-, and 72-tET?

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

> Except that some syntonic comma accidentals must be applied to at
> least one of these scales. It's not a notation that can encompass,
> say, 41-tET, until you say which.

Wait a minute--are you saying you need to decide if diatonic or Pythagorean is your baseline scale? That's true enough, and Pythagorean seems like a reasonable choice.

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

> This remains too abstract for me. Let's look at George's notation
> again, shall we? Isn't a 7-note scale at the center of it, given that
> every pitch must be notated as one of the seven letters, along with a
> well-defined accidental, and the notation is supposed to work across
> 31-, 41-, and 72-tET?

I think A-G as well as "up" and "down" give a total of 21 composite signs which only signify 12 distinct symbols, and those 12 symbols in turn are at the center of the system, just as A-G are in the usual meantone-based system of notation.

[Gene:]
/ comma sharp, 81/80
\ comma flat, 80/81
) diesis sharp, 128/125
( diesis flat, 125/128
7 septimal comma sharp, 64/63
L septimal comma flat, 63/64
^ undecimal diesis sharp, 33/32
v undecimal diesis flat, 32/33}}

If we use A-G strictly according to what h7 tells us they should be, and
substitute ordinary sharps and flats for the diesis symbols (which we then
don't need) this would be exactly the universal 11-limit method I
proposed, and adding a symbol for 40/39 (what is this, by the way--the
triskadecimal diesis?) would extend it to a 13-limit system.

[me:]

The diesis symbols are indeed redundant, but I added them to avoid
having more than three comma symbols in a row when the 5-exponent is
higher than 3, one can replace /// with ), for example B#\\\ = C(.
By the way why do you prefer 40/39 over 27/26?

Nice name suggestion for 40/39.

In my opinion there should be a balance in a notation system between the
number of different pairs of accidentals and the number of accidentals
at a note. To take 41-tET as an example, at one end of the spectrum,
only # and b is enough no notate it, but it looks hairy because you
get long strings of sharps and flats. The Sagittal system is at the other
end with its many different accidentals and only one necessary for each
note. I agree with Dave that this is probably difficult to read quickly
too. The optimum is two pairs of symbols, the normal sharp and flat plus
/ and \. Then you have at most a combination of two accidentals for each
note and this can be read quickly.
Another advantage of combinations with # and b is that modulations by a
fifth or fourth, which adds a # or b, is more easily recognisable than
when one unique symbol is replaced with another one.

Manuel

--- In tuning@y..., manuel.op.de.coul@e... wrote:
> In my opinion there should be a balance in a notation system between
the
> number of different pairs of accidentals and the number of
accidentals
> at a note. To take 41-tET as an example, at one end of the spectrum,
> only # and b is enough no notate it, but it looks hairy because you
> get long strings of sharps and flats. The Sagittal system is at the
other
> end with its many different accidentals and only one necessary for
each
> note. I agree with Dave that this is probably difficult to read
quickly
> too. The optimum is two pairs of symbols, the normal sharp and flat
plus
> / and \. Then you have at most a combination of two accidentals for
each
> note and this can be read quickly.

This satisfies the "no more than two of anything" rule, but the
symbols / and \ violate the "don't use left-right reflections" rule.

Note that the Sims notation uses some pairs which are up-down
relections of each other and 180^ rotations of each other (which is
fine), but when a "logical" version of the notation would have one
pair (the quarter-tone symbols) looking like even _approximate_
left-right reflections of each other, one of the "flags" gets flipped
to the opposite side on one symbol of the pair so there is no longer
any danger of this.

So I disagree with Joseph Pehrson that our ASCII approximation of the
Sims accidentals could be used in music intended to be sight-read.

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:

/tuning/topicId_33331.html#33360

> --- In tuning@y..., "paulerlich" <paul@s...> wrote:
>
> > Except that some syntonic comma accidentals must be applied to at
> > least one of these scales. It's not a notation that can
encompass,
> > say, 41-tET, until you say which.
>
> Wait a minute--are you saying you need to decide if diatonic or
Pythagorean is your baseline scale? That's true enough, and
Pythagorean seems like a reasonable choice.

****Isn't this what we were discussing when we were comparing Ben
Johnston's 5-limit diatonic notation with a Pythagorean basis, which
it *should* have been based on to make the notation simpler??

JP

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> --- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
>
> /tuning/topicId_33331.html#33360
>
> > --- In tuning@y..., "paulerlich" <paul@s...> wrote:
> >
> > > Except that some syntonic comma accidentals must be applied to
at
> > > least one of these scales. It's not a notation that can
> encompass,
> > > say, 41-tET, until you say which.
> >
> > Wait a minute--are you saying you need to decide if diatonic or
> Pythagorean is your baseline scale? That's true enough, and
> Pythagorean seems like a reasonable choice.
>
>
> ****Isn't this what we were discussing when we were comparing Ben
> Johnston's 5-limit diatonic notation with a Pythagorean basis,
which
> it *should* have been based on to make the notation simpler??
>
> JP

That's the one!

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

/tuning/topicId_33331.html#33388

> So I disagree with Joseph Pehrson that our ASCII approximation of
the Sims accidentals could be used in music intended to be sight-read.

****Whoaeee... Did *me* say that! If so, I immediately recant!
Where did I say that?? I only use the ascii, personally, for
Internet communication, *never* on a score!

??

JP

--- In tuning@y..., manuel.op.de.coul@e... wrote:

> By the way why do you prefer 40/39 over 27/26?

40/39 is simply what I get by inverting a matrix. I also considered a system which uses 27/26, based on a Pythagorean approach, which pushes this idea about as far as it will push:

<9/8, 2187/2048, 81/80, 64/63, 33/32, 27/26>^(-1) =

[h7, -g2, -v5, -v7, v11, -v13],

where g2 = [2,3,4,6,7,7]

This has a v5 in it, as well as v7, v11, and v13, so it is all based on a bedrock of 3-limit.

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
>
> /tuning/topicId_33331.html#33388
>
> > So I disagree with Joseph Pehrson that our ASCII approximation of
> the Sims accidentals could be used in music intended to be
sight-read.
>
> ****Whoaeee... Did *me* say that! If so, I immediately recant!

OK.

> Where did I say that??

/tuning/topicId_32971.html#32975
about paragraph 12, whic is about 1/3 of the way thru the message.

> I only use the ascii, personally, for
> Internet communication, *never* on a score!

Good idea. :-)

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

/tuning/topicId_33331.html#33481

> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> > --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> >
> > /tuning/topicId_33331.html#33388
> >
> > > So I disagree with Joseph Pehrson that our ASCII approximation
of
> > the Sims accidentals could be used in music intended to be
> sight-read.
> >
> > ****Whoaeee... Did *me* say that! If so, I immediately recant!
>
> OK.
>
> > Where did I say that??
>
> /tuning/topicId_32971.html#32975
> about paragraph 12, whic is about 1/3 of the way thru the message.
>
> > I only use the ascii, personally, for
> > Internet communication, *never* on a score!
>
> Good idea. :-)

Hmmm. I can't believe I said that... I hope nobody *saves* these
archives.... :)

I think you're right about the left-right business....

Oh... by the way, I'm enjoying the "standard" lattice for Blackjack,
C-G-D-A...

I meant to ask you, Dave: if you get a chance, could you please make
a chart of all the possible *Blackjack* intervals??

I know you have one for "Miracle 31" ("Canasta")

I was going to make a "Blackjack" one from that, but got composing
instead, and I don't seem to be getting around to it. Besides, you
could make it a *lot* faster than I could!

In addition (I don't ask a lot do I??) would you mind actually
*writing out* the interval names rather than just using letters where
I have to refer back to a "legend...??"

I'll remember them *much* better that way...

I guess if you don't have time to do this, I will *eventually* get
around to figuring it out...

Thanks, Dave!

Joseph

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

> I meant to ask you, Dave: if you get a chance, could you please
make
> a chart of all the possible *Blackjack* intervals??

Monz did that, about 1/3 of the way down this page. You'll have to
label it using the particular "key" you're using -- in your case, the
key where B[ is 0, 0.

> In addition (I don't ask a lot do I??) would you mind actually
> *writing out* the interval names rather than just using letters
where
> I have to refer back to a "legend...??"

Oops . . . so this is not quite what you wanted . . . but maybe 9.67
semitones is good enough a name for you for the "subminor
seventh" . . . or if you prefer ratios, there's a version like that
in the Files folder.

I wrote,

> or if you prefer ratios, there's a version like that
> in the Files folder.

It's

/tuning/files/monz/blackjackintmat3.xls

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> Oh... by the way, I'm enjoying the "standard" lattice for Blackjack,
> C-G-D-A...

I'm glad.

> I meant to ask you, Dave: if you get a chance, could you please
make
> a chart of all the possible *Blackjack* intervals??

I assume you mean those less than an octave or a 12th or something?

> I know you have one for "Miracle 31" ("Canasta")

I'm not sure which one you mean. URL?

I give only the Blackjack ones on the keyboard colouring diagram.

Then there's the table of abbreviated names for all of 72-EDO which
would also be sufficient for Miracle-37, so I suppose that's the one
you mean.

> I was going to make a "Blackjack" one from that, but got composing
> instead, and I don't seem to be getting around to it. Besides, you
> could make it a *lot* faster than I could!
>
> In addition (I don't ask a lot do I??) would you mind actually
> *writing out* the interval names rather than just using letters
where
> I have to refer back to a "legend...??"

Oh yeah. Sorry about that.

Ok. Just tell me what you want in all the columns. With blackjack, I
can't always give the note that forms that interval above C since many
blackjack intervals are impossible with a C root.

I could do it as a bunch of sliderules, i.e. on the open chain of
secors in the standard key. One sliderule for each interval so you can
slide it along to figure out every instance of that interval.

I'm open to suggestions.

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

> I'm open to suggestions.

How about a big matrix, with abbreviations for the names (such as
sm7) in the cells.

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
>
> > I'm open to suggestions.
>
> How about a big matrix, with abbreviations for the names (such as
> sm7) in the cells.

Feel free to do that, but Joseph asked for the names to be spelled in
full. When I think about my time constraints I have to retract the
offer re slide-rules. Joseph, I could either just spell the names in
full on the keyboard colouring diagram (you can print it and cut the
interval thingies off so you can slide them along the keyboard), or I
can take that table for 72-EDO and delete all the intervals you can't
get in blackjack and then add the full spellings. To bad about the
"note from C" column. It will just have some notes that aren't in the
standard blackjack key.

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> --- In tuning@y..., "paulerlich" <paul@s...> wrote:
> > --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> >
> > > I'm open to suggestions.
> >
> > How about a big matrix, with abbreviations for the names (such as
> > sm7) in the cells.
>
> Feel free to do that, but Joseph asked for the names to be spelled
in
> full.

Considering how much you've changed Joseph's mind about other things,
you'd think a few little abbreviations wouldn't hurt him too bad?
I'll see what I can do . . .

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> Joseph, I could either just spell the names in
> full on the keyboard colouring diagram (you can print it and cut the
> interval thingies off so you can slide them along the keyboard), or
I
> can take that table for 72-EDO and delete all the intervals you
can't
> get in blackjack and then add the full spellings. To bad about the
> "note from C" column. It will just have some notes that aren't in
the
> standard blackjack key.

Well I just choosed one and I done it. Try

http://dkeenan.com/Music/Miracle/BlackjackIntervalNaming.txt

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> > Joseph, I could either just spell the names in
> > full on the keyboard colouring diagram (you can print it and cut
the
> > interval thingies off so you can slide them along the keyboard),
or
> I
> > can take that table for 72-EDO and delete all the intervals you
> can't
> > get in blackjack and then add the full spellings. To bad about
the
> > "note from C" column. It will just have some notes that aren't in
> the
> > standard blackjack key.
>
> Well I just choosed one and I done it. Try
>
> http://dkeenan.com/Music/Miracle/BlackjackIntervalNaming.txt

This looks the same as it did before . . . hmm . . .

Well, I started doing what I said I would do, and I decided your
interval names are not really well-suited for Joseph or for me. Why
would the difference between a M2 and a M6 not be a P5? It seems that
the line of thinking that preserves 12-tET _notation_ for the subset
of 72-tET pitches falling within the 12-tET _pitch_ universe, should
also employ 12-tET _interval names_ for the subset of 72-tET pitches
falling within the 12-tET _interval_ universe.

So I suggest we retain the 12-tET interval names intact, and add
modifiers for the small modifiers. This is already done in Boston:

"twelfth-low minor sixth" = 783 cents
"sixth-high major third" = 433 cents
"quarter-high perfect fourth" = 550 cents

Isn't this much better for Joseph?

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

/tuning/topicId_33331.html#33485

> I wrote,
>
> > or if you prefer ratios, there's a version like that
> > in the Files folder.
>
> It's
>
> /tuning/files/monz/blackjackintmat3.xls

*****This is actually a great and useful chart, and probably more
useful than what *I* was thinking about, which, as you surmised later
on, was a "naming convention" for Blackjack intervals.

However, this chart is an *older* one in the old F-C-G Blackjack key,
so it's not so useful for me anymore.

I know Monz is overburdened with activities, but it would be
*wonderful* if this chart could be transposed into what we consider
now the "standard" C-G-D-A Blackjack key!

Thanks!

JP

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

/tuning/topicId_33331.html#33491

> --- In tuning@y..., "paulerlich" <paul@s...> wrote:
> > --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> >
> > > I'm open to suggestions.
> >
> > How about a big matrix, with abbreviations for the names (such as
> > sm7) in the cells.
>
> Feel free to do that, but Joseph asked for the names to be spelled
in
> full. When I think about my time constraints I have to retract the
> offer re slide-rules. Joseph, I could either just spell the names
in
> full on the keyboard colouring diagram (you can print it and cut
the
> interval thingies off so you can slide them along the keyboard), or
I
> can take that table for 72-EDO and delete all the intervals you
can't
> get in blackjack and then add the full spellings. To bad about the
> "note from C" column. It will just have some notes that aren't in
the
> standard blackjack key.

****So, Dave, if you began on *G* would that mean that you could
illustrate *all* the intervals??

JP

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

/tuning/topicId_33331.html#33494

> --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> > Joseph, I could either just spell the names in
> > full on the keyboard colouring diagram (you can print it and cut
the
> > interval thingies off so you can slide them along the keyboard),
or
> I
> > can take that table for 72-EDO and delete all the intervals you
> can't
> > get in blackjack and then add the full spellings. To bad about
the
> > "note from C" column. It will just have some notes that aren't in
> the
> > standard blackjack key.
>
> Well I just choosed one and I done it. Try
>
> http://dkeenan.com/Music/Miracle/BlackjackIntervalNaming.txt

****Hi Dave.

Thanks for doing this. Originally, though, I found it rather
confusing, since it *is* for "Miracle 41" "Studloco," yes?

I guess the point is to show all the possibilities in the naming
system. Anyway, I deleted the pitches that weren't *specifically*
part of Blackjack.

Speaking of "conventions" though, I thought we had been using Dbv
rather than C#v and Ab^ rather than G#^ for Blackjack.

I realize it doesn't really make any difference, but it might be nice
to "settle" on something, just for quick reference in writing and
conversation...

??

BTW-- What does "Studloco" mean again?? "Crazy" of course, but
what's the rest?? I forgot.

JP

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

/tuning/topicId_33331.html#33496

> >
http://dkeenan.com/Music/Miracle/BlackjackIntervalNaming.txt
>
> This looks the same as it did before . . . hmm . . .
>
> Well, I started doing what I said I would do, and I decided your
> interval names are not really well-suited for Joseph or for me. Why
> would the difference between a M2 and a M6 not be a P5? It seems
that the line of thinking that preserves 12-tET _notation_ for the
subset of 72-tET pitches falling within the 12-tET _pitch_ universe,
should also employ 12-tET _interval names_ for the subset of 72-tET
pitches falling within the 12-tET _interval_ universe.
>
> So I suggest we retain the 12-tET interval names intact, and add
> modifiers for the small modifiers. This is already done in Boston:
>
> "twelfth-low minor sixth" = 783 cents
> "sixth-high major third" = 433 cents
> "quarter-high perfect fourth" = 550 cents
>
> Isn't this much better for Joseph?

****This makes a *lot* more sense, Paul, and the fact that is is
*already* in use makes a potent case for its adoption.

So, would you please mind listing these for me?? I guess this is
really all I need, although Monz' reworking of the big Blackjack
color ratio chart would be cool, too...

JP

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

>http://dkeenan.com/Music/Miracle/BlackjackIntervalNaming.txt
>
>
> ****Hi Dave.
>
> Thanks for doing this. Originally, though, I found it rather
> confusing, since it *is* for "Miracle 41" "Studloco," yes?

Well, it's the _pitches_ of StudLoco, or the _intervals_ of
Blackjack. However, note that it conflicts with the "Boston" system
of naming intervals, which I thought you agreed was better.

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

> So, would you please mind listing these for me?? I guess this is
> really all I need, although Monz' reworking of the big Blackjack
> color ratio chart would be cool, too...
>
> JP

Joseph, shouldn't these be ONE AND THE SAME project?

A big matrix, with the new blackjack key along the top and along the
left, and then the Boston-style interval names in the cells -- with
the colors the same as they are now.

Two birds with one stone!

I'll get on this right away -- but first I need to know how we're
going to abbreviate the intervals.

Would you prefer to see

"twelfth-low minor sixth"

abbreviated as

m6-1/12

or as

tlm6

??

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

/tuning/topicId_33331.html#33520

> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
>
>
>http://dkeenan.com/Music/Miracle/BlackjackIntervalNaming.txt
> >
> >
> > ****Hi Dave.
> >
> > Thanks for doing this. Originally, though, I found it rather
> > confusing, since it *is* for "Miracle 41" "Studloco," yes?
>
> Well, it's the _pitches_ of StudLoco, or the _intervals_ of
> Blackjack.

Huh? Don get it. How can it be the *pitches* of *one* system and
the *intervals* of another simultaneously?? And, if this is somehow
so, wouldn't that be a pretty *bad* chart?? (And I don't mean *bad*
as *good* in this case... :) )

However, note that it conflicts with the "Boston" system
> of naming intervals, which I thought you agreed was better.

****Yes, I do, so I guess I'll forget about Dave's system...

Sorry, Dave! :)

JP

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

/tuning/topicId_33331.html#33522

> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
>
> > So, would you please mind listing these for me?? I guess this is
> > really all I need, although Monz' reworking of the big Blackjack
> > color ratio chart would be cool, too...
> >
> > JP
>
> Joseph, shouldn't these be ONE AND THE SAME project?
>
> A big matrix, with the new blackjack key along the top and along
the left, and then the Boston-style interval names in the cells --
with the colors the same as they are now.
>
> Two birds with one stone!

*****Bright, man, bright...

>
> I'll get on this right away -- but first I need to know how we're
> going to abbreviate the intervals.
>
> Would you prefer to see
>
> "twelfth-low minor sixth"
>
> abbreviated as
>
> m6-1/12
>
> or as
>
> tlm6
>
> ??

Doesn't the former one look a little too much like a Utonal "tuning
ratio...??" rather than a fraction of a tone?

JP

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

> > m6-1/12
> >
> > or as
> >
> > tlm6
> >
> > ??
>
> Doesn't the former one look a little too much like a Utonal "tuning
> ratio...??" rather than a fraction of a tone?

Not really . . . but I take it you'd prefer to see

tlm6 for "twelfth-low minor sixth"

and

qha4 for "quarter-high augmented fourth"

etc.?

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

/tuning/topicId_33331.html#33528

> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
>
> > > m6-1/12
> > >
> > > or as
> > >
> > > tlm6
> > >
> > > ??
> >
> > Doesn't the former one look a little too much like a
Utonal "tuning
> > ratio...??" rather than a fraction of a tone?
>
> Not really . . . but I take it you'd prefer to see
>
> tlm6 for "twelfth-low minor sixth"
>
> and
>
> qha4 for "quarter-high augmented fourth"
>
> etc.?

****Yes. They will fit in the chart better, too. However, they will
take a little getting used to...

JP

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> --- In tuning@y..., "paulerlich" <paul@s...> wrote:
>
> /tuning/topicId_33331.html#33520
>
> > --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> >
> >
>
>http://dkeenan.com/Music/Miracle/BlackjackIntervalNaming.txt
> > >
> > >
> > > ****Hi Dave.
> > >
> > > Thanks for doing this. Originally, though, I found it rather
> > > confusing, since it *is* for "Miracle 41" "Studloco," yes?
> >
> > Well, it's the _pitches_ of StudLoco, or the _intervals_ of
> > Blackjack.
>
>
> Huh? Don get it. How can it be the *pitches* of *one* system and
> the *intervals* of another simultaneously??

If you took all 41 of the intervals in Blackjack, and built them up
from a fixed tonic, you'd get the 41 pitches of StudLoco.

BTW, I think Blackjack is a "deep scale" (in the Carlton Gamer, et
al. sense) when tuned in 41-tET.

> And, if this is somehow
> so, wouldn't that be a pretty *bad* chart?? (And I don't mean
*bad*
> as *good* in this case... :) )

Well, it's good in that it's giving you two different ways of using
the chart . . .

> However, note that it conflicts with the "Boston" system
> > of naming intervals, which I thought you agreed was better.
>
> ****Yes, I do, so I guess I'll forget about Dave's system...
>
> Sorry, Dave! :)

Dave also constructed his StudLoco scale to be centered on C, which
one may object to for various reasons . . .

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> > Well I just choosed one and I done it. Try
> >
> >
http://dkeenan.com/Music/Miracle/BlackjackIntervalNaming.txt
>
> This looks the same as it did before . . . hmm . . .

Look again. The other is at
http://dkeenan.com/Music/Miracle/MiracleIntervalNaming.txt

I took out the intervals that don't occur in Blackjack and spelled the
names in full, as I said I would.

By the way folks, these have now been corrected (thanks to Paul). I
had "E" where it should have been "Ev" for the major third (4:5).

> Well, I started doing what I said I would do, and I decided your
> interval names are not really well-suited for Joseph or for me. Why
> would the difference between a M2 and a M6 not be a P5?

Because it's essentially based on giving the most consonant just
intervals the simplest names, not based on 12-tET, and as such it is
applicable to almost any scale, not only those containing significant
12-tET subsets. M2 is 8:9, M6 is 3:5. The difference between them is a
comma short of a 2:3. Definitely not a P5.

> It seems
that
> the line of thinking that preserves 12-tET _notation_ for the subset
> of 72-tET pitches falling within the 12-tET _pitch_ universe, should
> also employ 12-tET _interval names_ for the subset of 72-tET pitches
> falling within the 12-tET _interval_ universe.

Tee hee. :-) Once again Paul and Dave (who agree on most things)
struggle for control of the mind of Joseph Pehrson.

Sorry folks. Not really.

> So I suggest we retain the 12-tET interval names intact, and add
> modifiers for the small modifiers. This is already done in Boston:
>
> "twelfth-low minor sixth" = 783 cents
> "sixth-high major third" = 433 cents
> "quarter-high perfect fourth" = 550 cents
>
> Isn't this much better for Joseph?

Only Joseph and time can tell.

Notice that with this system Blackjack has no major third, minor
sixth, major seventh. Although Blackjack certainly does contain
excellent approximations to 4:5 and 5:8 and a reasonable approximation
to 8:15.

What will you call a 4:5:6 chord? etc.

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> ****So, Dave, if you began on *G* would that mean that you could
> illustrate *all* the intervals??

No. There's no single such note. But G would probably make more sense
than C. But no time, sorry.

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> ****Hi Dave.
>
> Thanks for doing this. Originally, though, I found it rather
> confusing, since it *is* for "Miracle 41" "Studloco," yes?

No.

> I guess the point is to show all the possibilities in the naming
> system.

No. Only Blackjack.

> Anyway, I deleted the pitches that weren't *specifically*
> part of Blackjack.

That won't work. You will have deleted intervals that _are_ avaiable
in blackjack, just not on C.

> Speaking of "conventions" though, I thought we had been using Dbv
> rather than C#v and Ab^ rather than G#^ for Blackjack.
>
> I realize it doesn't really make any difference, but it might be
nice
> to "settle" on something, just for quick reference in writing and
> conversation...

Good point. Thanks. I think the list of interval names predated the
standardisation effort. I'll fix 'em.

> BTW-- What does "Studloco" mean again?? "Crazy" of course, but
> what's the rest?? I forgot.

I guess it's a card game that has some relationship with the number
41???

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> Speaking of "conventions" though, I thought we had been using Dbv
> rather than C#v and Ab^ rather than G#^ for Blackjack.

Er no. In the standard key we have #v and b^ but never #^ or bv.

So C#v is correct but G#^ is wrong.

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

/tuning/topicId_33331.html#33533

> >
> > Huh? Don get it. How can it be the *pitches* of *one* system
and the *intervals* of another simultaneously??
>
> If you took all 41 of the intervals in Blackjack, and built them up
> from a fixed tonic, you'd get the 41 pitches of StudLoco.
>

***Got it! Thanks.

However, the beautiful new Blackjack interval matrix works *best* for
me!

Joseph

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

/tuning/topicId_33331.html#33537

> > It seems that the line of thinking that preserves 12-tET
_notation_ for the subset of 72-tET pitches falling within the 12-tET
_pitch_ universe, should also employ 12-tET _interval names_ for the
subset of 72-tET pitches falling within the 12-tET _interval_
universe.
>
> Tee hee. :-) Once again Paul and Dave (who agree on most things)
> struggle for control of the mind of Joseph Pehrson.
>

****Gee... I hope it will be worth it when you get there... :)

Seriously, though, I'm only "regurgitating" practical concerns
of "traditionally trained" musicians... so I guess my "pea brain"
manages to drag along a lot of pretty significant "excess
baggage..." :)
>

> > So I suggest we retain the 12-tET interval names intact, and add
> > modifiers for the small modifiers. This is already done in Boston:
> >
> > "twelfth-low minor sixth" = 783 cents
> > "sixth-high major third" = 433 cents
> > "quarter-high perfect fourth" = 550 cents
> >
> > Isn't this much better for Joseph?
>
> Only Joseph and time can tell.
>

****And, of course, I'm *wild* about this idea and the new color
matrix. Not only that, but I believe every *practicing* musician
will feel the same way. (We should ask Ted Mook on this point not
mute).

JP

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

/tuning/topicId_33331.html#33539

> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> > ****Hi Dave.
> >
> > Thanks for doing this. Originally, though, I found it rather
> > confusing, since it *is* for "Miracle 41" "Studloco," yes?
>
> No.
>
> > I guess the point is to show all the possibilities in the naming
> > system.
>
> No. Only Blackjack.
>
> > Anyway, I deleted the pitches that weren't *specifically*
> > part of Blackjack.
>
> That won't work. You will have deleted intervals that _are_
avaiable in blackjack, just not on C.

*****That's funny. I can't believe I did that! :) Now that Paul
explained what you were doing with that...

>
> > Speaking of "conventions" though, I thought we had been using Dbv
> > rather than C#v and Ab^ rather than G#^ for Blackjack.
> >
> > I realize it doesn't really make any difference, but it might be
> nice to "settle" on something, just for quick reference in writing
and conversation...
>
> Good point. Thanks. I think the list of interval names predated the
> standardisation effort. I'll fix 'em.
>
> > BTW-- What does "Studloco" mean again?? "Crazy" of course, but
> > what's the rest?? I forgot.
>
> I guess it's a card game that has some relationship with the number
> 41???

****Yes, Monz says it's wild Mexican poker or some such. That
evening remains a distant memory....

JP

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

> Notice that with this system Blackjack has no major third, minor
> sixth, major seventh.

Not in the sense that musicians today understand them, no.

> Although Blackjack certainly does contain
> excellent approximations to 4:5 and 5:8 and a reasonable
approximation
> to 8:15.
>
> What will you call a 4:5:6 chord?

root, twelfth-low major third, fifth

p1, tlM3, P5

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
>
> > Notice that with this system Blackjack has no major third, minor
> > sixth, major seventh.
>
> Not in the sense that musicians today understand them, no.

But it has things that _sound_ just like them, only better.

"Musicians today" (i.e 12-tET musicians) are just a blip on the map as
far as the history of tuning goes.

> > Although Blackjack certainly does contain
> > excellent approximations to 4:5 and 5:8 and a reasonable
> approximation
> > to 8:15.
> >
> > What will you call a 4:5:6 chord?
>
> root, twelfth-low major third, fifth
>
> p1, tlM3, P5

So you're gonna call it a "root, twelfth-low major third, fifth
chord"? I don't think so.

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
>
>
>http://dkeenan.com/Music/Miracle/BlackjackIntervalNaming.txt
> >
> >
> > ****Hi Dave.
> >
> > Thanks for doing this. Originally, though, I found it rather
> > confusing, since it *is* for "Miracle 41" "Studloco," yes?
>
> Well, it's the _pitches_ of StudLoco, or the _intervals_ of
> Blackjack. However, note that it conflicts with the "Boston" system
> of naming intervals, which I thought you agreed was better.

No it's just the intervals of Blackjack. It's not the pitches of
anything.

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

> Why would the difference between a M2 and a M6 not be a P5?

It's because Miracle temperament is not meantone temperament. That
should have been obvious.

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

> No it's just the intervals of Blackjack. It's not the pitches of
> anything.

i see 41 pitches starting from C. whether you meant it or not, this
is going to be interpreted as a studloco scale.

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> > --- In tuning@y..., "paulerlich" <paul@s...> wrote:
>
> > Why would the difference between a M2 and a M6 not be a
P5?
>
> It's because Miracle temperament is not meantone
temperament. That
> should have been obvious.

it was obvious to me. but it won't be obvious to any musician that
didn't study with ben johnston or someone like that. it was a
rhetorical question. every tuning system that's been used in the
west, pythagorean, meantone, well-temperament, had the
property M6 - M2 = P5. so it's entrenched not only in modern
musicians in general but even in those specializing in early
music. if you try to change this now, you'll be greeted with
puzzlement, disbelief, skepticism, and most likely, rejection.

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

/tuning/topicId_33331.html#33587

> "Musicians today" (i.e 12-tET musicians) are just a blip on the map
as far as the history of tuning goes.

****Hi Dave!

Do you really think so?? I rather doubt it, since 12-tET has been so
ingrained for 100 years now.

Sure, maybe on the overview since *prehistory* :) but if we have to
start someplace to educate people *right now* to do something *new*
I, personally, would start with a 12-tET basis and I bet anything
that many other people would agree with me.

Wanna place some bets...? $ :)

> > > Although Blackjack certainly does contain
> > > excellent approximations to 4:5 and 5:8 and a reasonable
> > approximation
> > > to 8:15.
> > >
> > > What will you call a 4:5:6 chord?
> >
> > root, twelfth-low major third, fifth
> >
> > p1, tlM3, P5
>
> So you're gonna call it a "root, twelfth-low major third, fifth
> chord"? I don't think so.

****Well, by now I think you know I *would...*!

Joseph

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

/tuning/topicId_33331.html#33592

> --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
>
> > No it's just the intervals of Blackjack. It's not the pitches of
> > anything.
>
> i see 41 pitches starting from C. whether you meant it or not, this
> is going to be interpreted as a studloco scale.

***Well, that's how *I* saw it, too, which is why I was so confused...

Joseph

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

/tuning/topicId_33331.html#33593

> --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> > --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> > > --- In tuning@y..., "paulerlich" <paul@s...> wrote:
> >
> > > Why would the difference between a M2 and a M6 not be a
> P5?
> >
> > It's because Miracle temperament is not meantone
> temperament. That
> > should have been obvious.
>
> it was obvious to me. but it won't be obvious to any musician that
> didn't study with ben johnston or someone like that. it was a
> rhetorical question. every tuning system that's been used in the
> west, pythagorean, meantone, well-temperament, had the
> property M6 - M2 = P5. so it's entrenched not only in modern
> musicians in general but even in those specializing in early
> music. if you try to change this now, you'll be greeted with
> puzzlement, disbelief, skepticism, and most likely, rejection.

*REJECTION* People just won't want to play your music...

JP

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
>
> > No it's just the intervals of Blackjack. It's not the pitches of
> > anything.
>
> i see 41 pitches starting from C. whether you meant it or not, this
> is going to be interpreted as a studloco scale.

Ok. I fixed that problem. I've changed the offending column to
"Example" where I give an example of each interval within the standard
Blackjack key. Both notes are shown every time. The root is G whenever
possible, but otherwise another natural (C, D or A) except for those
few that don't occur on any natural. It's at

http://dkeenan.com/Music/Miracle/BlackjackIntervalNaming.txt