Re: 15 EDO MONZ

MONZ

PERHAPS I CAN FIND A FEW MEASURES OF IT SOMEWHERE ON-LINE. THANKS.

hi Stephen,

--- In tuning@yahoogroups.com, "stephenszpak" <stephen_szpak@h...>
wrote:

> Thanks Carl for getting back to me. This was my first
> post anywhere about anything, so you get a gold star.
> The staff for 15 EDO has NOT been established from what
> I can see so far. I'm not sure if I can take Herman Miller's
> tongue and cheek staff seriously. If Blackwood uses a
> staff I haven't as yet found a image of it. Regardless,
> two composers using 15 EDO, even if they use the same
> staff does not convince me it is a "standard" that should
> be accepted by future musicians. Thanks.

Blackwood's notations for all the EDOs between 13 and 24
use the regular 5-line staff, with unique accidentals for
each tuning.

i have the score of his _Microtonal Etudes_, but unfortunately
my old scanner doesn't work with my new computer.

-monz

_________________________________________________________________
Enjoy the holiday season with great tips from MSN. http://special.msn.com/network/happyholidays.armx

> MONZ
>
> PERHAPS I CAN FIND A FEW MEASURES OF IT SOMEWHERE ON-LINE.
> THANKS.

Oh, you mean musical staff! (?) Well, it would be hard to do
worse than what Blackwood used. I'll eat a bug if you can find
an image online. I suppose I could scan a page and put it up
if you were really interested.

As to which notation should you use, it's a hotly contested
matter. My recommendation is to use a staff suited for the
source scale you're composing with. For me the most interesting
scale in 15 is Blackwood's 10-tone symmetrical scale, which I
map to consecutive staff postions just like the diatonic scale
on the standard staff. IIRC there are only 3 keys of this
scale in 15-tET, so key signatures can be simplified to the
numbers 1-3. Anyway, experimenting is the way to go. Just do
it!

-Carl

> MONZ
>
> PERHAPS I CAN FIND A FEW MEASURES OF IT SOMEWHERE ON-LINE.
> THANKS.

Oh, you mean musical staff! (?) Well, it would be hard to do
worse than what Blackwood used. I'll eat a bug if you can find
an image online. I suppose I could scan a page and put it up
if you were really interested.

As to which notation should you use, it's a hotly contested
matter. My recommendation is to use a staff suited for the
source scale you're composing with. For me the most interesting
scale in 15 is Blackwood's 10-tone symmetrical scale, which I
map to consecutive staff postions just like the diatonic scale
on the standard staff. IIRC there are only 3 keys of this
scale in 15-tET, so key signatures can be simplified to the
numbers 1-3. Anyway, experimenting is the way to go. Just do
it!

-Carl

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

/tuning/topicId_50142.html#50145

I'll eat a bug if you can find
> an image online.

***I put one up, Carl, sooooo....

JP

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

/tuning/topicId_50142.html#50146

> > MONZ
> >
> > PERHAPS I CAN FIND A FEW MEASURES OF IT SOMEWHERE ON-LINE.
> > THANKS.
>
> Oh, you mean musical staff! (?) Well, it would be hard to do
> worse than what Blackwood used. I'll eat a bug if you can find
> an image online. I suppose I could scan a page and put it up
> if you were really interested.
>
> As to which notation should you use, it's a hotly contested
> matter. My recommendation is to use a staff suited for the
> source scale you're composing with. For me the most interesting
> scale in 15 is Blackwood's 10-tone symmetrical scale, which I
> map to consecutive staff postions just like the diatonic scale
> on the standard staff. IIRC there are only 3 keys of this
> scale in 15-tET, so key signatures can be simplified to the
> numbers 1-3. Anyway, experimenting is the way to go. Just do
> it!
>
> -Carl

***Carl sees this issue a little differently than I do. (Sorry, I've
already forgotten the name of the poster, and I'm too lazy to go back
right now...)

Carl tends to like to design staves and notation to reflect the
structure of the scales he uses. For example, he prefers a *decimal*
notation for the "Blackjack" scale... I think the staff he favors has
only 4 lines, but I could be wrong... (Or Monzo came up with that
one...)

Personally, I'm more in line with Blackwood in that I would prefer
our "regular ol'" 5-line staff and then try to adapt the pitches in
some way with modifying accidentals.

I agree with Carl, though, that Blackwood's system is particularly
arcane...

J. Pehrson

hi Joe,

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:

> Carl tends to like to design staves and notation to
> reflect the structure of the scales he uses. For example,
> he prefers a *decimal* notation for the "Blackjack" scale...
> I think the staff he favors has only 4 lines, but I could
> be wrong... (Or Monzo came up with that one...)

Monzo. (adapted from Breed)

http://tonalsoft.com/enc/decimal.htm

-monz

>> As to which notation should you use, it's a hotly contested
>> matter. My recommendation is to use a staff suited for the
>> source scale you're composing with. For me the most interesting
>> scale in 15 is Blackwood's 10-tone symmetrical scale, which I
>> map to consecutive staff postions just like the diatonic scale
>> on the standard staff. IIRC there are only 3 keys of this
>> scale in 15-tET, so key signatures can be simplified to the
>> numbers 1-3. Anyway, experimenting is the way to go. Just do
>> it!
>
>Carl tends to like to design staves and notation to reflect the
>structure of the scales he uses. For example, he prefers a *decimal*
>notation for the "Blackjack" scale... I think the staff he favors has
>only 4 lines, but I could be wrong... (Or Monzo came up with that
>one...)

The number of lines and spaces doesn't really matter.

-Carl

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

/tuning/topicId_50142.html#50172

> hi Joe,
>
>
> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
>
> > Carl tends to like to design staves and notation to
> > reflect the structure of the scales he uses. For example,
> > he prefers a *decimal* notation for the "Blackjack" scale...
> > I think the staff he favors has only 4 lines, but I could
> > be wrong... (Or Monzo came up with that one...)
>
>
>
> Monzo. (adapted from Breed)
>
> http://tonalsoft.com/enc/decimal.htm
>
>
>
> -monz

***Thanks, Monz! So *you* were the "four line staffer" for Breed's
decimal notation...

Joe P.

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

/tuning/topicId_50142.html#50175

> >> As to which notation should you use, it's a hotly contested
> >> matter. My recommendation is to use a staff suited for the
> >> source scale you're composing with. For me the most interesting
> >> scale in 15 is Blackwood's 10-tone symmetrical scale, which I
> >> map to consecutive staff postions just like the diatonic scale
> >> on the standard staff. IIRC there are only 3 keys of this
> >> scale in 15-tET, so key signatures can be simplified to the
> >> numbers 1-3. Anyway, experimenting is the way to go. Just do
> >> it!
> >
> >Carl tends to like to design staves and notation to reflect the
> >structure of the scales he uses. For example, he prefers a
*decimal*
> >notation for the "Blackjack" scale... I think the staff he favors
has
> >only 4 lines, but I could be wrong... (Or Monzo came up with that
> >one...)
>
> The number of lines and spaces doesn't really matter.
>
> -Carl

***My impression, Carl, is that it *might* to the original poster,
but I could be wrong...

JP

>> >Carl tends to like to design staves and notation to reflect the
>> >structure of the scales he uses. For example, he prefers a
>> >*decimal* notation for the "Blackjack" scale... I think the staff
>> >he favors has only 4 lines, but I could be wrong... (Or Monzo
>> >came up with that one...)
>>
>> The number of lines and spaces doesn't really matter.
>
>***My impression, Carl, is that it *might* to the original poster,
>but I could be wrong...

Indeed, but here I was replying to the statement that I preferred
4 lines.

Monz seems to care, but I can't imagine why -- on another page he
points out how ledger lines are implicit staff lines, and suggests
adding more staff lines to improve the readability of conventional
notation.

The property of notation that we usually debate, generalized vs.
'extra accidentals', is independent of the number of lines actually
drawn on the staff.

-Carl

hi Carl,

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

> Indeed, but here I was replying to the statement that
> I preferred 4 lines.
>
> Monz seems to care, but I can't imagine why -- on another
> page he points out how ledger lines are implicit staff
> lines, and suggests adding more staff lines to improve the
> readability of conventional notation.
>
> The property of notation that we usually debate,
> generalized vs. 'extra accidentals', is independent
> of the number of lines actually drawn on the staff.

the reason why the number of staff-lines matters to me
is because i want to *avoid* using ledger-lines.

by adjusting the number of staff-lines to fit the
cardinality of the tuning, staves can simply be stacked
one on top of the other to cover the various 8ve registers.

i usually try to have one ledger-line between staves,
which represents the various 8ves of "C".

-monz

>> Indeed, but here I was replying to the statement that
>> I preferred 4 lines.
>>
>> Monz seems to care, but I can't imagine why -- on another
>> page he points out how ledger lines are implicit staff
>> lines, and suggests adding more staff lines to improve the
>> readability of conventional notation.
>>
>> The property of notation that we usually debate,
>> generalized vs. 'extra accidentals', is independent
>> of the number of lines actually drawn on the staff.
>
>the reason why the number of staff-lines matters to me
>is because i want to *avoid* using ledger-lines.
>
>by adjusting the number of staff-lines to fit the
>cardinality of the tuning, staves can simply be stacked
>one on top of the other to cover the various 8ve registers.
>
>i usually try to have one ledger-line between staves,
>which represents the various 8ves of "C".

Right, but it has nothing to do with what we're discussing.

-Carl

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

/tuning/topicId_50142.html#50209

> >> Indeed, but here I was replying to the statement that
> >> I preferred 4 lines.
> >>
> >> Monz seems to care, but I can't imagine why -- on another
> >> page he points out how ledger lines are implicit staff
> >> lines, and suggests adding more staff lines to improve the
> >> readability of conventional notation.
> >>
> >> The property of notation that we usually debate,
> >> generalized vs. 'extra accidentals', is independent
> >> of the number of lines actually drawn on the staff.
> >
> >the reason why the number of staff-lines matters to me
> >is because i want to *avoid* using ledger-lines.
> >
> >by adjusting the number of staff-lines to fit the
> >cardinality of the tuning, staves can simply be stacked
> >one on top of the other to cover the various 8ve registers.
> >
> >i usually try to have one ledger-line between staves,
> >which represents the various 8ves of "C".
>
> Right, but it has nothing to do with what we're discussing.
>
> -Carl

***Carl, I don't believe this is entirely true. The original poster
(who by now is probably way too frightened to make another
appearance... :) gave me the impression that he thought that
different ETs had different kinds of *staves...* That implied to me
that he thought that the accidentals and even the *lines and spaces*
would be different depending on the kind of scale used.

Sometimes, of course, it is, as in the case of Monz's quartertone
notation.

Sometimes, Carl, I wonder if you've really read and played enough
music to understand how *basic* the notion of the 5-line staff is in
the consciousness, and how important the number of lines can be to
comprehension...

(I admit I'm falling a bit into the Johnny Reinhard camp in making
this pronouncement... :)

JP

>***Carl, I don't believe this is entirely true. The original poster
>(who by now is probably way too frightened to make another
>appearance... :) gave me the impression that he thought that
>different ETs had different kinds of *staves...*

Yes, right, I got that impression too. But they don't, and the
core issue which has been mentioned by Mark, Dave, myself, and
you has been that of generalized-diatonic vs. extra-accidentals,
which is independent of the particular staff entirely.

-Carl

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

/tuning/topicId_50142.html#50234

> >***Carl, I don't believe this is entirely true. The original
poster
> >(who by now is probably way too frightened to make another
> >appearance... :) gave me the impression that he thought that
> >different ETs had different kinds of *staves...*
>
> Yes, right, I got that impression too. But they don't, and the
> core issue which has been mentioned by Mark, Dave, myself, and
> you has been that of generalized-diatonic vs. extra-accidentals,
> which is independent of the particular staff entirely.
>
> -Carl

***Carl, sorry, you're losing me a bit here. What, specifically, do
you have in mind??

Thanks!

JP

>> >***Carl, I don't believe this is entirely true. The original
>> >poster (who by now is probably way too frightened to make
>> >another appearance... :) gave me the impression that he thought
>> >that different ETs had different kinds of *staves...*
>>
>> Yes, right, I got that impression too. But they don't, and the
>> core issue which has been mentioned by Mark, Dave, myself, and
>> you has been that of generalized-diatonic vs. extra-accidentals,
>> which is independent of the particular staff entirely.
>
>***Carl, sorry, you're losing me a bit here. What, specifically,
>do you have in mind??

As you explained, I am one of those who like to to base notation
on scales ("generalized-diatonic") while some others prefer to
outfit standard notation with "extra accidentals". That's one
question; the number of staff lines is a separate question.

To answer your question about Dave's Sagittal suggestions, I think
they are both manifestly inferior to Herman Miller's porcupine
notation, which you can do without any new accidentals or nominals
at all (since porcupine has a 7-tone MOS).

-Carl

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

/tuning/topicId_50142.html#50286

> >> >***Carl, I don't believe this is entirely true. The original
> >> >poster (who by now is probably way too frightened to make
> >> >another appearance... :) gave me the impression that he thought
> >> >that different ETs had different kinds of *staves...*
> >>
> >> Yes, right, I got that impression too. But they don't, and the
> >> core issue which has been mentioned by Mark, Dave, myself, and
> >> you has been that of generalized-diatonic vs. extra-accidentals,
> >> which is independent of the particular staff entirely.
> >
> >***Carl, sorry, you're losing me a bit here. What, specifically,
> >do you have in mind??
>
> As you explained, I am one of those who like to to base notation
> on scales ("generalized-diatonic") while some others prefer to
> outfit standard notation with "extra accidentals". That's one
> question; the number of staff lines is a separate question.
>

***Got it. Tx!

JP

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> >***Carl, I don't believe this is entirely true. The original
> >> >poster (who by now is probably way too frightened to make
> >> >another appearance... :) gave me the impression that he thought
> >> >that different ETs had different kinds of *staves...*
> >>
> >> Yes, right, I got that impression too. But they don't, and the
> >> core issue which has been mentioned by Mark, Dave, myself, and
> >> you has been that of generalized-diatonic vs. extra-accidentals,
> >> which is independent of the particular staff entirely.
> >
> >***Carl, sorry, you're losing me a bit here. What, specifically,
> >do you have in mind??
>
> As you explained, I am one of those who like to to base notation
> on scales ("generalized-diatonic") while some others prefer to
> outfit standard notation with "extra accidentals". That's one
> question; the number of staff lines is a separate question.
>
> To answer your question about Dave's Sagittal suggestions, I think
> they are both manifestly inferior to Herman Miller's porcupine
> notation, which you can do without any new accidentals or nominals
> at all (since porcupine has a 7-tone MOS).

This is certainly a valid and logical approach when the music is
actually based around that MOS, but it isn't without its problems in
general.

Redefining existing nominals and accidentals so that the familiar
harmonic relationships no longer apply, has its own problems.

And what about all the other MOS of all the other linear temperaments
of which 15-ET is a member? (I count 7). We then would not only have
to learn a new notation for every ET (they may use the same symbols
but the symbols would have different sounds) but we would have to
learn a new notation for every different way of viewing a single ET as
a linear temperament. One persons "manifest inferiority" is anothers ...

>And what about all the other MOS of all the other linear temperaments
>of which 15-ET is a member? (I count 7). We then would not only have
>to learn a new notation for every ET (they may use the same symbols
>but the symbols would have different sounds) but we would have to
>learn a new notation for every different way of viewing a single ET as
>a linear temperament. One persons "manifest inferiority" is anothers ...

You're still thinking of ETs as the notation targets. If I write
music in porcupine with your 15-tET notation, what happens when I
want to play it in 22 or 37?

-Carl

On Sun, 21 Dec 2003 22:56:54 -0000, "Dave Keenan" <d.keenan@bigpond.net.au>
wrote:

>Redefining existing nominals and accidentals so that the familiar
>harmonic relationships no longer apply, has its own problems.
>
>And what about all the other MOS of all the other linear temperaments
>of which 15-ET is a member? (I count 7). We then would not only have
>to learn a new notation for every ET (they may use the same symbols
>but the symbols would have different sounds) but we would have to
>learn a new notation for every different way of viewing a single ET as
>a linear temperament. One persons "manifest inferiority" is anothers ...

It wouldn't be quite so bad; you'd have to learn a new notation for every
linear temperament, but the same notation would cover multiple ET's using
that temperament, and most of the "good" ET's would be taken care of by a
fairly small number of temperaments (meantone, schismic, diaschismic,
kleismic, Orwell, magic, Wuerschmidt). A few of the more "interesting"
temperaments (miracle, porcupine, pelogic, etc) might be worth notating
even though there aren't many ET's that use them. If you have a real
interest in oddball divisions of the octave like 47-ET, though, which don't
fit into one of the more productive linear temperaments, you're going to
need a more general notation like cents. Ultimately it might be easiest to
use cents for everything (especially for performance), but at least for
theoretical purposes, it'd be nice to have standard notations for some of
the more useful linear and planar temperaments.

Kleismic in particular is one that I'd like to have a good notation for. I
like your 8-naturals scheme, but notating it on a staff presents some
difficulties. For practical purposes, I skip four notes in the series and
use a 7-natural scheme: D F A C D#/Eb F#/Gb A#/Bb C# E G B, mainly because
this makes a good keyboard mapping. But Graham Breed's keyboard mapping
seems like it would work just as well, and I may end up switching to it;
it's certainly adequate for the 15-note kleismic scale.

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >And what about all the other MOS of all the other linear temperaments
> >of which 15-ET is a member? (I count 7). We then would not only have
> >to learn a new notation for every ET (they may use the same symbols
> >but the symbols would have different sounds) but we would have to
> >learn a new notation for every different way of viewing a single ET as
> >a linear temperament. One persons "manifest inferiority" is
anothers ...
>
> You're still thinking of ETs as the notation targets. If I write
> music in porcupine with your 15-tET notation, what happens when I
> want to play it in 22 or 37?

Carl,

Stephen asked for notations for 15-tET, not porcupine-LT (linear
temperament). I already said it makes sense to use a porcupine-LT
notation when that's what you're writing for.

But there are still two ways to do that, as Herman has described on
his website.
http://www.io.com/~hmiller/music/temp-porcupine.html

One has the 7 nominals being the 7-tone MOS of the porcupine
temperament. But these are not our usual 7 nominals, and Herman is
careful to say so and to use lowercase letters a to g rather than
uppercase (but I wonder if this is enough distinction). The step from
g to a is around 228 cents while all the others are around 162 cents.

The other retains the familiar relationship of fifths between the
nominals FCGDAE, but still uses porcupine-7 chromatic accidentals so
the notation stays the same in any porcupine tuning including 15-ET,
22-ET, 37-ET.

The notation of mine that Herman kindly gives is now outdated only in
that I would not now use the Sims arrows for the 5-comma (81/80), but
rather the sagittal left-barbs. I would only use the arrows for the
11-M-diesis (33/32). As Herman says, both of these commas correspond
to the natural chromatic alteration of the porcupine temperament,
since they both correspond to 7 of its approx 162 cent generators
(octave reduced), given that its 3,5,7,11-generator-mapping is [-3 -5
6 -4].

It's certainly debatable whether the 5-comma symbol should be used
because of its lower prime limit or the 11-M-diesis symbol because its
rational size is much closer to its size in porcupine.

Comparison of the two notations is clearer if we use the same comma
and the same ASCII symbol for the accidental in both cases. It's
essentially only the nominals that change between the two. I'll use
the 11-M-diesis below (as Herman does) but will use the sagittal
symbols for it, whose ASCII shorthand are ^ and v. Here's a chain of
porcupine generators showing both notations. If you're reading on the
web, hit the Reply button to see it formatted correctly.

a^ b^ c^ d^ e^ f^ g^ a b c d e f g av bv cv dv ev fv gv
9--5--11-3--------1-----------------7
A^ B C#v D^ E F#v G^ A Bv C^ D Ev F^ G Av Bb^ C Dv Eb^ F Gv
| | | | | | |

Note that, in the second notation, C#v and F#v are equivalent to C^^
and F^^. Similarly Eb^ and Bb^ are equivalent to Evv and Bvv.

I've shown a slide-rule in between the two notations, that shows the
11-limit ratio approximations. Below the second notation I've
indicated the nominals in their chain of fifths/fourths. Unfortunately
only three of them are in the central 7-tone MOS. The whole sequence
can be seen as 3 interleaved chains of fifths, in the second notation.

When you are told that in porcupine the 5-comma is the same as the
11-M-diesis and the 7-comma vanishes, then you see that the second
notation preserves the familiar notation of all the harmonic
relationships.

Clearly the first notation has the advantage of fewer accidentals for
someone who uses porcupine temperament a lot. But the second is likely
to be more readily understood by someone who has to cope with a lot of
different tunings, whether composer or performer or both.

>You're still thinking of ETs as the notation targets. If I write
>music in porcupine with your 15-tET notation, what happens when I
>want to play it in 22 or 37?

Put another way, when porcupine notation is 'broken' (you're using
it for non-porcupine music) the result about the same as Sagittal
for music written in any tuning.

Or is it?

-Carl

--- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:
> It wouldn't be quite so bad; you'd have to learn a new notation for
every
> linear temperament, but the same notation would cover multiple ET's
using
> that temperament, and most of the "good" ET's would be taken care of
by a
> fairly small number of temperaments (meantone, schismic, diaschismic,
> kleismic, Orwell, magic, Wuerschmidt).

Good point. I did overstated the case somewhat, didn't I.

> A few of the more "interesting"
> temperaments (miracle, porcupine, pelogic, etc) might be worth notating
> even though there aren't many ET's that use them. If you have a real
> interest in oddball divisions of the octave like 47-ET, though,
which don't
> fit into one of the more productive linear temperaments, you're going to
> need a more general notation like cents. Ultimately it might be
easiest to
> use cents for everything (especially for performance), but at least for
> theoretical purposes, it'd be nice to have standard notations for
some of
> the more useful linear and planar temperaments.

Sure. But it's possible to do these with either MOS nominals or
chain-of-fifth nominals.

> Kleismic in particular is one that I'd like to have a good notation
for. I
> like your 8-naturals scheme, but notating it on a staff presents some
> difficulties. For practical purposes, I skip four notes in the
series and
> use a 7-natural scheme: D F A C D#/Eb F#/Gb A#/Bb C# E G B, mainly
because
> this makes a good keyboard mapping. But Graham Breed's keyboard mapping
> seems like it would work just as well, and I may end up switching to it;
> it's certainly adequate for the 15-note kleismic scale.

Yes, kleismic is a bastard for doing a MOS-based notation, since there
are proper MOS with 4 and 15 notes but nothing in between. Only the
improper 7 and 11. The chain-of-fifths notation for it isn't much
better since this needs 3 pairs of accidentals.