Yahoo Tuning Groups Ultimate Backup tuning Extremely simple and flexible generalized notation

Hi all,

We've dealt plenty with generalized notations here before, but I
wanted to relate an idea I just thought of that's pretty easy,
intuitive, and most importantly very simple to implement. The basic
observations are:

1) Existing notation is built around the meantone/diatonic MOS.
2) The # and b accidentals denote alteration by the chromatic interval
c, which is equal to = L-s.
3) Lines and spaces on the staff just include what position in the MOS
you are. Sharps and flats indicate chromatic alteration as per the
above.
4) The whole thing is defined relative to some "center" note, which is
the tonic for the "unaltered" scale. We call this note "middle C"
(although you can use whatever names you want).
5) By convention, this center note is one ledger line below the treble
clef and one ledger line above the bass clef. We generalize the notion
of "treble" and "bass"

That's it. So to generalize any regular temperament to a similar staff
layout, simply
1) Pick the representative "albitonic" MOS for that temperament
2) Figure out which mode you want to use as the base, tonal mode.
3) Find the tonic of this mode - tune it to 261 Hz (middle C). You
don't have to call it "C," but at least identify the note.
4) This note goes one ledger line below the treble clef and one ledger
line above the bass clef. Tenor and alto clefs are generalized as
you'd expect.
5) Use as many lines as you want for each staff. 5 is standard, but if
you have a larger MOS try 6, 7, etc.
6) Sharps and flats mean alteration by c=L-s. Generalize other
accidentals in the same way - e.g. if you're in meantone, the diesis
is c_2 = |s-c_1|. Pick different symbols if you don't like # and b.

That's it, you're done. Pretty simple, I'm sure someone's talked about
or proposed this before. Note that the MOS you use doesn't have to be
tempered if you really don't want it to; you can come up with a
complex system of accidentals to signify a 3D or 4D temperament if you
want.

-Mike

🔗Carl Lumma <carl@...>

Mike wrote:

> That's it, you're done. Pretty simple, I'm sure someone's talked
> about or proposed this before. Note that the MOS you use doesn't
> have to be tempered if you really don't want it to; you can come
> up with a complex system of accidentals to signify a 3D or 4D
> temperament if you want.

That's what I call "diatonic notation", which has been
proposed several times, including by me. Google have
deleted their Groups "pages" feature, but I've archived
the microtools pages here:

http://lumma.org/music/theory/microtools/

I don't enforce MOS, but you're right that doing so will
require more than one accidental pair. I've posted about
this several times.

The exact staff configuration is open for standardization.
There's something to be said for the following:

* If the base scale has n notes (pitch classes), use a
staff with floor[n/2] lines.

* The space below the bottom line should always be concert
pitch mod some number of octaves (or other interval of
equivalence). For scales where n is odd, the space above
the top line is the octave. Where n is even, the top line
is the octave - it can be dotted to indicate this.

* Clefs are a number specifying the octave register of the
space below the bottom line.

-Carl

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

On Sat, May 21, 2011 at 3:13 PM, Carl Lumma <carl@...> wrote:
>
> That's what I call "diatonic notation", which has been
> proposed several times, including by me.

I was going to propose calling it "albitonic notation," but diatonic's
alright by me!

> Google have
> deleted their Groups "pages" feature, but I've archived
> the microtools pages here:
>
> http://lumma.org/music/theory/microtools/

As a side note about naming, I was talking to a few musician friends
irl and brought the subject up, and we were all pretty much in
agreement that using numbers instead of letters for names is much less
confusing for all of these new scales. E.G. using nominals 1-9 for a 9
note scale seems much more intuitive than ABCDEFGHI. They (not me)
also suggested that for all of these scales, like "the porcupine
scale" as they called it, you could just put a letter after each
number to specify, so it could be like 1p 2p 3p 4p 5p 6p etc, although
that would only be necessary if the scale we were referencing wasn't
obvious from context.

> The exact staff configuration is open for standardization.
> There's something to be said for the following:
>
> * If the base scale has n notes (pitch classes), use a
> staff with floor[n/2] lines.

This can't be right, as the diatonic scale would only end up with 3
lines, whereas right now it has 5. Maybe ceil(n/2)+1 would work, which
always gives you one note beyond the octave.

-Mike

🔗Carl Lumma <carl@...>

--- Mike Battaglia <battaglia01@...> wrote:

> As a side note about naming, I was talking to a few musician
> friends irl and brought the subject up, and we were all pretty
> much in agreement that using numbers instead of letters for
> names is much less confusing for all of these new scales.

I don't like that idea because numbers are used for intervals.
Using letters for pitches helps keep them distinct.

> so it could be like 1p 2p 3p 4p 5p 6p etc, although that
> would only be necessary if the scale we were referencing
> wasn't obvious from context.

There are too many scales to name this way, and it uses
more than one syllable, making solfege difficult.

> > * If the base scale has n notes (pitch classes), use a
> > staff with floor[n/2] lines.
>
> This can't be right, as the diatonic scale would only end up
> with 3 lines, whereas right now it has 5.

Yes- it currently has too many. Clearly, only the lines
were used originally, for the pentatonic scale. :)

> Maybe ceil(n/2)+1 would work, which
> always gives you one note beyond the octave.

That's four lines for a 5- or 6-note scale, with nine
lines and spaces before hitting ledgers and so more than
one note beyond the octave in either case.

-Carl

🔗Daniel Nielsen <nielsed@...>

As long as you are changing things, you might as well begin at 0. It just
makes more sense, since you can convert to systems where -1 means the note
below tonic, and you can just perform a simple mod N operation for periods,
etc. Or is that just asking too much?
Dan N

🔗Graham Breed <gbreed@...>

🔗genewardsmith <genewardsmith@...>

🔗Kalle Aho <kalleaho@...>

--- In tuning@yahoogroups.com, Daniel Nielsen <nielsed@...> wrote:
>
> > As a side note about naming, I was talking to a few musician
> > friends irl and brought the subject up, and we were all pretty
> > much in agreement that using numbers instead of letters for
> > names is much less confusing for all of these new scales.
> > E.G. using nominals 1-9 for a 9 note scale seems much more intuitive than
> ABCDEFGHI.
>
> As long as you are changing things, you might as well begin at 0. It just
> makes more sense, since you can convert to systems where -1 means the note
> below tonic, and you can just perform a simple mod N operation for periods,
> etc. Or is that just asking too much?
> Dan N
>

I advocate starting with 0. This works especially well with 10-tone
scales as you can then represent the naturals with base-10 numbers
and the register is represented by positions before the last number.
0 would be the lowest note and 10, 20, 30,... would be its' octaves
(or rather decades, if unisons are 0ths). Likewise for 1, 11, 21, 31
and so on.

I'd use a 4-line staff for 10-tone scales with one ledger line under
the lower staff and between the staves. The pitch classes have the
same positions in the upper and lower staves then.

Kalle

🔗Graham Breed <gbreed@...>

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> "genewardsmith" <genewardsmith@...> wrote:
> >
> > --- In tuning@yahoogroups.com, Graham Breed <gbreed@>
> > wrote:
> >
> > > 0 is used for a rest in jianpu.
> >
> > Which is a bad idea.
>
> This is possibly the most widely used system of musical
> notation in the world. Who cares about your opinion?

Since you are defending a bad idea with a worthless argument, who cares about your opinion? I'm quite happy using "r" for a rest, which I note AJK does also. But whatever you use, it is a terrible idea to use an integer for a rest symbol when you are already using integers for note symbols. If you would switch your brain into the "on" position you would have realized that yourself: it limits the functionality of the notation by grabbing a number which more naturally could be used for extending it, it promotes confusion by using adjacent integers for two different things, and it perpetuates the idea, which arose in the days before zero was invented, of starting a count which should start at zero at one.

The AD/BC numbering of years is also the most widely used. If you want to defend it as a good idea, then, Buster, who cares about your opinion? It's a terrible idea, leads to many errors, even by historians, and its sole virtue is that it is widely used. Widely used but dumb is not the same as good.

🔗Graham Breed <gbreed@...>

"genewardsmith" <genewardsmith@...> wrote:

> Since you are defending a bad idea with a worthless
> argument, who cares about your opinion? I'm quite happy
> using "r" for a rest, which I note AJK does also. But
> whatever you use, it is a terrible idea to use an integer
> for a rest symbol when you are already using integers for
> note symbols. If you would switch your brain into the
> "on" position you would have realized that yourself: it
> limits the functionality of the notation by grabbing a
> number which more naturally could be used for extending
> it, it promotes confusion by using adjacent integers for
> two different things, and it perpetuates the idea, which
> arose in the days before zero was invented, of starting a
> count which should start at zero at one.

Bikeshedding -- check

Strawman -- check

Personal insult -- check

I'm out of here.

Graham

🔗Carl Lumma <carl@...>

🔗genewardsmith <genewardsmith@...>

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

> Bikeshedding -- check

Which you started.

> Strawman -- check

If pointing out that widely used does not equate to good is a strawman, then what was your argument?

> Personal insult -- check

Oh, please. You insult me directly and personally, and now you leave in a minute and a Huff. If you dislike personal insults, stop using them.

🔗Graham Breed <gbreed@...>

"Carl Lumma" <carl@...> wrote:

> Don't go please! I always appreciate your posts.
> Almost always. Your posts are of excellent quality.

I'm not leaving the list. I decided long ago to avoid
stupid terminology arguments, especially with Gene. I
have nothing more to say about this one. Well, okay, I'll
point out that integers from 1 are used here, along with a
solfege system:

http://x31eq.com/magic/tripod.pdf

Nothing went into that paper without a great deal of
thought.

Graham

p.s. I have a reply on observed tunings/spectra in my head
but it'll take some work to finish it off. I have mild
toothache today. I am a little grumpy.

🔗Daniel Nielsen <nielsed@...>

It just seems there are places where 0 would more naturally give rise to the
idea of a rest. For instance, and this is just an example, if we had a
notation "N:M" where N is the EDO number and M is the note number from 0 to
N-1, then 12:0 is tonic in 12-edo, and it would make sense to consider 0:X a
rest. Defining 0 as a rest, although it may preserve current systems, just
doesn't feel like a natural extension.
Graham, I don't think Gene meant as much insult as might be inferred in
online text. It was likely at least partially his respect for you that
desired agreement on this minor but somewhat-foundational point.

🔗Mike Battaglia <battaglia01@...>

On Sun, May 22, 2011 at 1:11 AM, Daniel Nielsen <nielsed@...> wrote:
>
> > As a side note about naming, I was talking to a few musician
> > friends irl and brought the subject up, and we were all pretty
> > much in agreement that using numbers instead of letters for
> > names is much less confusing for all of these new scales.
> > E.G. using nominals 1-9 for a 9 note scale seems much more intuitive than ABCDEFGHI.
>
> As long as you are changing things, you might as well begin at 0. It just makes more sense, since you can convert to systems where -1 means the note below tonic, and you can just perform a simple mod N operation for periods, etc. Or is that just asking too much?
> Dan N

I don't want to change things. The reason I'm proposing a numbered
system is to avoid having to reuse A-G, which is based on the same
reasoning that led everyone to want to call them "albitonic" scales
instead of reusing "diatonic."

You are advocating something that you think would be superior because
it is "simpler," or more "sensible," or more mathematically elegant -
which, in a certain sense, it is. However. simplicity means nothing to
a corpse - you need a real live human being that can derive order out
of things in order to pick up on the elegance of a particular
solution. Unfortunately, everyone has different ways of perceiving
order in things - mathematicians have one way of doing it, and working
musicians have another. It will not seem simple at all to a musician
who's spent most of his life referring to the tonic as "the I chord"
to suddenly shift to 0 because someone's telling him that it happens
to be more mathematically elegant to perform the modulo operation for
the equivalence interval. That's where I'm coming from with all of
this.

-Mike

🔗Mike Battaglia <battaglia01@...>

On Sun, May 22, 2011 at 12:45 AM, Carl Lumma <carl@...> wrote:
>
> > As a side note about naming, I was talking to a few musician
> > friends irl and brought the subject up, and we were all pretty
> > much in agreement that using numbers instead of letters for
> > names is much less confusing for all of these new scales.
>
> I don't like that idea because numbers are used for intervals.
> Using letters for pitches helps keep them distinct.

Nominals would be used for pitches, ordinals would be used for
interval classes. But the reason I don't want to use letters is the
same reason everyone didn't want to call albitonic scales "diatonic"
scales. Except in this case, the "literature" in which A-G means the
notes of the diatonic scale is the vocabulary of almost every
practicing musician in any part of the world used to the western
system of notation. I do think that they'd have caught onto the notion
that porcupine[7] is a "porcupine diatonic," but I don't think they'll
enjoy so much the notion that C-E in Pajara now corresponds to a 9/8
rather than a 5/4. And I think that if we push that system, they'll
eventually start using numbers anyway, or maybe devise a notation
whereby everything relates to meantone[7].

> > so it could be like 1p 2p 3p 4p 5p 6p etc, although that
> > would only be necessary if the scale we were referencing
> > wasn't obvious from context.
>
> There are too many scales to name this way, and it uses
> more than one syllable, making solfege difficult.

It would only be necessary to tack on the letter if the scale we were
referencing wasn't obvious from context.

> Yes- it currently has too many. Clearly, only the lines
> were used originally, for the pentatonic scale. :)

I see I've opened the floodgates for lots of innovative ideas. I was
getting at a different goal, which was figuring out an optimal system
for existing musicians to adapt to, given what they already find
"simple" and intuitive. In other words, I am coming from the exact
opposite direction as the "jammer"/Janko/etc paradigm, which aims to
rebuild things in a more intuitive way from the ground up.

> > Maybe ceil(n/2)+1 would work, which
> > always gives you one note beyond the octave.
>
> That's four lines for a 5- or 6-note scale, with nine
> lines and spaces before hitting ledgers and so more than
> one note beyond the octave in either case.

Yeah, I screwed up. I meant more to suggest having the lines on the
staff reaching an octave in span from the top note to the bottom note,
rounding up in the case of odd-numbered scales. So decatonic scales
would have six lines and five spaces, spanning in total an octave.
9-note scales would also have 6 lines, except in this case the scale
would span an octave + one note. If the staff can't even represent an
octave, I don't think it's going to be very useful.

-Mike

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> Unfortunately, everyone has different ways of perceiving
> order in things - mathematicians have one way of doing it, and working
> musicians have another. It will not seem simple at all to a musician
> who's spent most of his life referring to the tonic as "the I chord"
> to suddenly shift to 0 because someone's telling him that it happens
> to be more mathematically elegant to perform the modulo operation for
> the equivalence interval. That's where I'm coming from with all of
> this.

Unfortunately, even musicians sometimes get confused by the fact that a third is two steps, a fifth four steps, an octave seven steps, and a twelfth eleven steps. We are used to seeing things like <7 11 16|, but how many people just automatically add one and see it as "8 12 17"?

1500 years ago Brahmagupta invented zero and negative numbers. This was a good idea. We constantly screw up if we ignore this good idea.

Let me tell a sad story about that. Back in 1981, there was a big do over the 2000th anniversary of the death of Virgil. Unfortunately, Virgil died in 19 BC, which is the same as -18 AD, which means the 2000th anniversary was really in the year 1982. This affair was attended by hundreds of scholars, many of them professional historians. Not one of them noticed until it was pointed out after the whole thing had started. Don't mess with zero.

🔗Mike Battaglia <battaglia01@...>

On Sun, May 22, 2011 at 2:50 PM, genewardsmith
<genewardsmith@...> wrote:
>
> > Unfortunately, everyone has different ways of perceiving
> > order in things - mathematicians have one way of doing it, and working
> > musicians have another. It will not seem simple at all to a musician
> > who's spent most of his life referring to the tonic as "the I chord"
> > to suddenly shift to 0 because someone's telling him that it happens
> > to be more mathematically elegant to perform the modulo operation for
> > the equivalence interval. That's where I'm coming from with all of
> > this.
>
> Unfortunately, even musicians sometimes get confused by the fact that a third is two steps, a fifth four steps, an octave seven steps, and a twelfth eleven steps. We are used to seeing things like <7 11 16|, but how many people just automatically add one and see it as "8 12 17"?

OK, these are good points, but I think that if the goal is to avoid
musicians getting confused, making the "I chord" now mean the old "ii
chord" isn't going to further that ideal.

I made a post about how people hated the "supermajor"/"subminor"
terminology, and that's where I'm coming from. It doesn't matter if we
invent the best mathematical system in the world if existing musicians
hate it. Janko keyboards have been around for over a century and have
never caught on for this very reason. I doubt "jammers" will catch on
either. In fact, I doubt microtonal music itself will catch on unless
we can get existing musicians to understand it.

> Let me tell a sad story about that. Back in 1981, there was a big do over the 2000th anniversary of the death of Virgil. Unfortunately, Virgil died in 19 BC, which is the same as -18 AD, which means the 2000th anniversary was really in the year 1982. This affair was attended by hundreds of scholars, many of them professional historians. Not one of them noticed until it was pointed out after the whole thing had started. Don't mess with zero.

LOL, wow. Never heard that one.

-Mike

🔗Carl Lumma <carl@...>

--- Mike Battaglia <battaglia01@...> wrote:

> Yeah, I screwed up. I meant more to suggest having the lines
> on the staff reaching an octave in span from the top note to
> the bottom note, rounding up in the case of odd-numbered scales.
> So decatonic scales would have six lines and five spaces,
> spanning in total an octave. 9-note scales would also have
> 6 lines, except in this case the scale would span an
> octave + one note. If the staff can't even represent an octave,
> I don't think it's going to be very useful.

I think the difference is, I'm counting the spaces below
and above the outside lines.

E
--D----
C
--B----
A

is a pentatonic scale. Perhaps what you'd do is make the
thing above E another space with a ledger line above it.
It would be A', the bottom space of the staff above.

_
A'
E
--D----
C
--B----
A

For a four note scale, it'd be

A'
--D----
C
--B----
A

You could print two octaves worth of staff in either case,
or use ledger lines, or use a clef to switch octaves.
Since clefs can only switch octaves, they're not confusing.

> In other words, I am coming from the exact opposite
> direction as the "jammer"/Janko/etc paradigm, which aims to
> rebuild things in a more intuitive way from the ground up.

Whereas I once thought the jammer type approach hopelessly
outgunned by the weight of tradition, my feeling now is that
there aren't enough musicians left in the world to put up
a fight and the entire thing should in fact be simplified
in order to save it.

-Carl

🔗Mike Battaglia <battaglia01@...>

On Sun, May 22, 2011 at 3:43 PM, Carl Lumma <carl@...> wrote:
>
> I think the difference is, I'm counting the spaces below
> and above the outside lines.
>
> E
> --D----
> C
> --B----
> A
>
> is a pentatonic scale.

Calling the notes in a pentatonic scale A-E is a prime example of why
the letter idea sucks. I did not find any part of this intuitive at
all. For anyone following this, go to a piano, call the black keys
A-E, and see how much you like it.

> You could print two octaves worth of staff in either case,
> or use ledger lines, or use a clef to switch octaves.
> Since clefs can only switch octaves, they're not confusing.

I think if you need to throw in tons of ledger lines and clef
switching, it will be confusing. This is bikeshedding, however,
because no matter what either you or I decide, the public will decide
at the end of the day.

> > In other words, I am coming from the exact opposite
> > direction as the "jammer"/Janko/etc paradigm, which aims to
> > rebuild things in a more intuitive way from the ground up.
>
> Whereas I once thought the jammer type approach hopelessly
> outgunned by the weight of tradition, my feeling now is that
> there aren't enough musicians left in the world to put up
> a fight and the entire thing should in fact be simplified
> in order to save it.

What's the entire thing that needs simplifying in order to be saved?

-Mike

🔗Carl Lumma <carl@...>

🔗cityoftheasleep <igliashon@...>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
>
> > What's the entire thing that needs simplifying in order to
> > be saved?
>
> The idea of reading music.

Almost every piano player I know reads music fluently, as does everyone I know who went through a few years of band class in high school. The only musicians who seem to have whole-sale abandoned music-reading are guitar players, who tend to opt for the "tablature + recording" approach...which works a lot better for guitar anyway. I bemoaned my poor music-reading skills for a while, even tried (recently) to take some classical guitar lessons to try to improve, but after a few months I was not making any progress and I realized that this method was totally non-intuitive and archaic, as well as unnecessary given the abundance of tablature available. So I gave it up.

-Igs

🔗lobawad <lobawad@...>

For some reason I had assumed that pretty much everyone here is well-versed in reading and writing music. Not that it really matters.

If you're fluent in guitar tab, you're also fluent at reading and writing music, by the way- have you seen old lute notation? Same goes for the various Asian notation systems, Nashville notation, etc.

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> >
> > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> > > What's the entire thing that needs simplifying in order to
> > > be saved?
> >
> > The idea of reading music.
>
> Almost every piano player I know reads music fluently, as does everyone I know who went through a few years of band class in high school. The only musicians who seem to have whole-sale abandoned music-reading are guitar players, who tend to opt for the "tablature + recording" approach...which works a lot better for guitar anyway. I bemoaned my poor music-reading skills for a while, even tried (recently) to take some classical guitar lessons to try to improve, but after a few months I was not making any progress and I realized that this method was totally non-intuitive and archaic, as well as unnecessary given the abundance of tablature available. So I gave it up.
>
> -Igs
>

🔗lobawad <lobawad@...>

Best of all, you could check to see if you wrote a good composition by casting out nines.

Seriously, musical set theory doesn't have a problem with zero, it's not like its an unprecedented novelty musicians won't grasp.

--- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, Daniel Nielsen <nielsed@> wrote:
> >
> > > As a side note about naming, I was talking to a few musician
> > > friends irl and brought the subject up, and we were all pretty
> > > much in agreement that using numbers instead of letters for
> > > names is much less confusing for all of these new scales.
> > > E.G. using nominals 1-9 for a 9 note scale seems much more intuitive than
> > ABCDEFGHI.
> >
> > As long as you are changing things, you might as well begin at 0. It just
> > makes more sense, since you can convert to systems where -1 means the note
> > below tonic, and you can just perform a simple mod N operation for periods,
> > etc. Or is that just asking too much?
> > Dan N
> >
>
> I advocate starting with 0. This works especially well with 10-tone
> scales as you can then represent the naturals with base-10 numbers
> and the register is represented by positions before the last number.
> 0 would be the lowest note and 10, 20, 30,... would be its' octaves
> (or rather decades, if unisons are 0ths). Likewise for 1, 11, 21, 31
> and so on.
>
> I'd use a 4-line staff for 10-tone scales with one ledger line under
> the lower staff and between the staves. The pitch classes have the
> same positions in the upper and lower staves then.
>
> Kalle
>