Notating 15-ED2

I've got a 15-ED2 neck on the way from Ron, and am taking this opportunity to return to messing with 15-ED2 notation.

15 is a PITA to notate, no two ways about it. Porcupine[7] sucks because some chords are spelled like in meantone[7] and some aren't, and going up the circle of generators gets you to flats instead of sharps. Blackwood's notation from the "Microtonal Etudes" is god-awful, it equates E with F and B with C to preserve spellings of most 3/2's, but ends up making spellings of 3rds insane and will make it impossible to notate anything not in 5-ED2 without accidentals. Porcupine[8] is worse than [7], because now you have to learn what an "H" note is. Using 9 or 10 nominals is probably out of the question, because now you have to learn an entirely new set of chord spellings (although, since Blackwood[10] is so even, you wouldn't have any spelling exceptions, i.e. unlike in meantone[7] where B-F is a diminished fifth instead of a perfect fifth). Using fewer than 7 nominals may also be problematic, as Augmented[6] is wildly improper and Triforce[6] has no 5-limit triads.

Using numerals instead of letters is out of the question, because I'm a friggin' guitar player and we use numbers to refer to fret positions, so saying "go to 1" or "go from 3 to 5" will be ambiguous, unless I want to give up on notation entirely and just stick with tablature.

Anyone experienced playing in 15 have any appealing ideas I haven't yet considered? I guess there's Orgone/Keemun[7], too...maybe I should look at that for ideas?

-Igs

On Wed, Nov 28, 2012 at 2:07 PM, cityoftheasleep
<igliashon@...> wrote:
>
> I've got a 15-ED2 neck on the way from Ron, and am taking this opportunity to return to messing with 15-ED2 notation.
>
> 15 is a PITA to notate, no two ways about it. Porcupine[7] sucks because some chords are spelled like in meantone[7] and some aren't, and going up the circle of generators gets you to flats instead of sharps. Blackwood's notation from the "Microtonal Etudes" is god-awful, it equates E with F and B with C to preserve spellings of most 3/2's, but ends up making spellings of 3rds insane and will make it impossible to notate anything not in 5-ED2 without accidentals. Porcupine[8] is worse than [7], because now you have to learn what an "H" note is. Using 9 or 10 nominals is probably out of the question, because now you have to learn an entirely new set of chord spellings (although, since Blackwood[10] is so even, you wouldn't have any spelling exceptions, i.e. unlike in meantone[7] where B-F is a diminished fifth instead of a perfect fifth). Using fewer than 7 nominals may also be problematic, as Augmented[6] is wildly improper and Triforce[6] has no 5-limit triads.

This leaves you with valentine[7], "progress"[7], and orgone[7].
Progress has a generator of 7/5. Of those, the first two are insane,
leaving you with only orgone[7] or something that's not an MOS.

You could always build it around the rank-3 Zarlino JI major scale,
1/1 9/8 5/4 4/3 3/2 5/3 15/8 2/1. For me, I'm more inclined to stick
with porcupine[7] or the occasional blackwood[10]. If you want 4:5:6
and 10:12:15 chords to share the same generic pattern of scale steps,
7 note and 10 note scales are about what you're stuck with.

-Mike

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

> This leaves you with valentine[7], "progress"[7], and orgone[7].
> Progress has a generator of 7/5. Of those, the first two are insane,
> leaving you with only orgone[7] or something that's not an MOS.
>
> You could always build it around the rank-3 Zarlino JI major scale,
> 1/1 9/8 5/4 4/3 3/2 5/3 15/8 2/1. For me, I'm more inclined to stick
> with porcupine[7] or the occasional blackwood[10]. If you want 4:5:6
> and 10:12:15 chords to share the same generic pattern of scale steps,
> 7 note and 10 note scales are about what you're stuck with.

Yep. Any idea which nominal I should start the porcupine generator chain on to preserve the maximum number of familiar ("meantone") chord-spellings? I've just been starting it on "A", but I'm not sure if that's optimal.

Here are the porcupine and blackwood notations I've been playing with,
including key-signatures and 5-limit lattices. I'll work out 11-limit
Keemun notation (which is bad-ass, because every 1-4-6 triad is either
4:5:7, 8:11:14, or 8:11:15) later.
[Use fixed-width if it's not displaying properly]
Porcupine[7] notation:
0 D80 D#/Eb160 E240 E#/Fb320 F400 F#/Gb480 G560 G#/Abb640 Ab/Gx720 A800
A#/Bb880 B960 B#/Cb1040 C1120 C#/Db1200 D
Gb--Db--Ab--E---B---F#--C#--Gx \ / \ / \ / \ / \ / \ / \
Fb--Cb--G---D---A---E#--B# \ / \ / \ / \ / \ / \ / \
Abb-Eb--Bb--F---C---G#--D#--A# \ / \ / \ / \ / \ / \ / \
Gb--Db--Ab--E---B---F#--C#--Gx
Major (Minor)-key signatures based on 0|6 (3|3 for minor) as the tonic
mode:
G# (D#): A#, B#, C#, D#, E#, F#, G#A (E#): B#, C#, D#, E#, F#, G#B (F#):
C#, D#, E#, F#, G#C (G#): D#, E#, F#, G#D (A): E#, F#, G#E (B): F#, G#F
(C): G#G (D): Ab (E): AbBb (F): Ab, BbCb (G): Ab, Bb, CbDb (Ab): Ab, Bb,
Cb, DbEb (Bb): Ab, Bb, Cb, Db, EbFb (Cb): Ab, Bb, Cb, Db, Eb, FbGb (Db):
Ab, Bb, Cb, Db, Eb, Fb, Gb
Blackwood[10] notation:
0 A/K#80 A#/Bb160 B/Cb240 C/B#320 C#/Db400 D/Eb480 E/D#560 E#/Fb640
F/Gb720 G/F#800 G#/Hb880 H/Jb960 J/H#1040 J#/Kb1120 K/Ab1200 A/K#
K#--F#--B#--H#--D#--K# / \ / \ / \ / \ / \ /
G#--C#--J#--E#--A#--G# / \ / \ / \ / \ / \ /
D---K---F---B---H---D / \ / \ / \ / \ / \ / A---G---C---J---E---A
/ \ / \ / \ / \ / \ / Hb--Db--Kb--Fb--Bb--Hb / \ / \ / \ / \ / \ /
Eb--Ab--Gb--Cb--Jb--Eb
Keys:
Only really need 3 key signatures: natural, sharp, and flat:
A/G/C/J/E major or D/K/F/B/H minor: naturalDb/Kb/Fb/Bb/Hb major or
A/G/C/J/E minor: flat D/K/F/B/H major or A#/G#/C#/J#/E# minor: sharp
Eb/Ab/Gb/Cb/Jb major or Hb/Db/Kb/Fb/Bb minor = D/K/F/B/H major or
G#/C#/J#/E#/A# minor, but you can call it double-flat if you
wantA#/G#/C#/J#/E# major or K#/F#/B#/H#/D# minor = Kb/Fb/Bb/Hb/Db major
or A/G/C/J/E minor, but you can call it double-sharp if you want

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
> Yep. Any idea which nominal I should start the porcupine generator chain on to preserve the maximum number of familiar ("meantone") chord-spellings? I've just been starting it on "A", but I'm not sure if that's optimal.

Personally, I hate the idea of anything out of F-C-G-D-A-E-B not being a perfect fifth, which means I'd prefer either blackwood notation (B=C, E=F), or porcupine but with totally separate nominals (e.g. TUVWXYZ).

But that's just my own opinion, and in the future if there's a concensus to use porcupine with A-G I'll certainly use that.

(The dumb temporary notation I've been using in my own notes for marimba keys is C, C#, D-, D+, Eb, E, F, F#-, F#+, G, Ab, A, Bb-, Bb+, B, C.)

Keenan

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:

> Personally, I hate the idea of anything out of F-C-G-D-A-E-B not being a perfect fifth,

Ditto. It definitely bothers me.

> which means I'd prefer either blackwood notation (B=C, E=F),

I thought I was okay with it until I realized what it does to triads. Here's all 15 notes:

0 B/C
80 B#/C#
160 Db
240 D
320 D#
400 Eb/Fb
480 E/F
560 E#/F#
640 Gb
720 G
800 G#
880 Ab
960 A
1040 A#
1120 Bb/Cb
1200 B/C

So, what's a C major triad? C-Eb-G. What about a B major triad? B-Dx-Fx#. See, with this notation, B-F is a perfect fourth, B-G is a perfect fifth, B-F# is a tritone, but a lower tritone than B-Gb...it's a nightmare. And this is just one example. It's waaaaay worse than porcupine A-G.

> or porcupine but with totally separate nominals (e.g. TUVWXYZ).

I hate the idea of using different letters. I hated P-Z for Pajara[10] 7 years ago, and I still hate it today. I have to sing the friggin' alphabet song every time just to remember the order of non-consecutive letters.

However, one thing I've thought about it is using a solfeggio system instead of letter nominals. Seemed to work well enough for Jacob and Andrew. But I haven't put much thought in yet.

> But that's just my own opinion, and in the future if there's a concensus to use porcupine with A-G I'll certainly use that.
>

It's probably the closest thing we have to a consensus so far, but I don't think any people have gotten together to play in 15-ET yet.

> (The dumb temporary notation I've been using in my own notes for marimba keys is C, C#, D-, D+, Eb, E, F, F#-, F#+, G, Ab, A, Bb-, Bb+, B, C.)
>

Yeah, that's kind of how I intuitively think of 15, and I would love to come up with a notation that can capture that consistently across keys. I took a stab at an Augmented[12] notation, using the 12 nominals from 12-TET (A-G, with 5 enharmonically-equivalent sharps and flats) and an additional accidental for the three extra notes, but it did not go well. I might take another stab at it, though....

-Igs

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@> wrote:
> > which means I'd prefer either blackwood notation (B=C, E=F),
>
> I thought I was okay with it until I realized what it does to triads. Here's all 15 notes:
>
> 0 B/C
> 80 B#/C#
> 160 Db
> 240 D
> 320 D#
> 400 Eb/Fb
> 480 E/F
> 560 E#/F#
> 640 Gb
> 720 G
> 800 G#
> 880 Ab
> 960 A
> 1040 A#
> 1120 Bb/Cb
> 1200 B/C
>
> So, what's a C major triad? C-Eb-G. What about a B major triad? B-Dx-Fx#. See, with this notation, B-F is a perfect fourth, B-G is a perfect fifth, B-F# is a tritone, but a lower tritone than B-Gb...it's a nightmare. And this is just one example. It's waaaaay worse than porcupine A-G.

I propose to change this insane nightmare by making it even more insane. =)

I like # and b always to represent the apotome (as in Sagittal) - meaning they would be useless in 15edo. So my version would be:

0 A#/B/C/Db (really only call it C)
80 A#^/B^/C^/Db^ (really only call it C^)
160 Dv (or a bunch of others, omitted for brevity...)
240 B#/C#/D/Eb/Fb (really only call it D)
320 D^
400 Ev
480 D#/E/F/Gb (really only call it E)
560 E^
640 Gv
720 E#/F#/G/Ab (really only call it G)
800 G^
880 Av
960 G#/A/Bb/Cb (really only call it A)
1040 A^
1120 Cv
1200 A#/B/C/Db (really only call it C)

C major: C-Ev-G (makes perfect sense because v is the syntonic comma)

B major: same as C major! All right, if you insist: B-D#v-F# (But really it's the same as C major.)

You can tell at a glance that anything that looks like a normal note is part of one 5edo, anything with a ^ is another, and anything with v is another.

As I said, this is even more insane, but don't deny its merits!

Keenan

On Wed, Nov 28, 2012 at 2:47 PM, cityoftheasleep <igliashon@...>
wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > This leaves you with valentine[7], "progress"[7], and orgone[7].
> > Progress has a generator of 7/5. Of those, the first two are insane,
> > leaving you with only orgone[7] or something that's not an MOS.
> >
> > You could always build it around the rank-3 Zarlino JI major scale,
> > 1/1 9/8 5/4 4/3 3/2 5/3 15/8 2/1. For me, I'm more inclined to stick
> > with porcupine[7] or the occasional blackwood[10]. If you want 4:5:6
> > and 10:12:15 chords to share the same generic pattern of scale steps,
> > 7 note and 10 note scales are about what you're stuck with.
>
> Yep. Any idea which nominal I should start the porcupine generator chain
> on to preserve the maximum number of familiar ("meantone") chord-spellings?
> I've just been starting it on "A", but I'm not sure if that's optimal.

G-G for Lssssss is what strikes me as closest, intuitively, to what we
have now (It's kind of like G lydian dominant or something). I don't
mind C-C for Lssssss either. I actually enjoy using the familiar
letter names for such an exotic scale to some extent, but if you're
not a fan you can always go with nominals 1-7 instead. I also like the
chroma for porcupine[7] being ^ and v, since it's so small, as opposed
to # and b.

So if I were writing a book for beginners and looking for a beginner
notation for 15-EDO, that would be my personal preference, with
blackwood coming in second. Nominals G-G for Lssssss, chroma is ^ and
v.

Outside of the scope of a book for beginners specifically, it's also
useful to note that this system can easily be extended to porcupine[8]
by adding an additional nominal H and additional symbols (I prefer
#/b) for the porcupine[8] chroma. So if you want to work within
porcupine[7], you get G A B C D E F G for Lssssss, and if you want
porcupine[8], G H A B C D E F G gives you LsLLLLLL. And since
porcupine[8] MODMOS's that modify things by the porcupine[7] chroma
can be useful, then you can just write things like G H A Bv C D E F G
for a scale that's like G H A B C D E F G, but which replaces the 5/4
with a 6/5. (Note that Bv is the same note as A# but spelled a
different way).

I find that in some sense it's more natural for me to think along the
latter terms if I'm in a porcupine[8] section and within the former
terms if I'm in a porcupine[7] section. To actually pull this off in
notation, though, would require you to switch staffs to accommodate
the extra nominal. I don't know if it'll be easier to do things that
way, or if people will instead be more inclined to notate porcupine[8]
and its MODMOS's just using porcupine[7] notation. I certainly know I
find it more natural to think in terms of porcupine[7], but I have yet
to write a composition around porcupine[8] so I don't know how hard
it'd be to notate the whole thing using only porcupine[7] notation.

To be blunt the whole thing is a pain in the ass. But, there's no
point complaining because porcupine[7] and porcupine[8] and their
respective MODMOS's are both beautiful scale systems, so there's no
getting around it. The same situation presents itself whenever you
have two MOS's that are both viable "diatonic" sized MOS's, especially
those that are just one note apart, like porcupine[7/8], bleu[8/9],
negri[9/10], miracle[10/11], etc. In one sense this is a prime feature
of those tunings; in another it makes notation difficult.

I still think that for beginners, simplifying the above to have
porcupine[7] with G-G nominals for Lssssss and ^/v accidentals is the
best way to go.

-Mike

On Wed, Nov 28, 2012 at 5:38 PM, Keenan Pepper <keenanpepper@...>
wrote:
>
> (The dumb temporary notation I've been using in my own notes for marimba
> keys is C, C#, D-, D+, Eb, E, F, F#-, F#+, G, Ab, A, Bb-, Bb+, B, C.)

A few slight modifications to that would make for a perfectly regular
notation system built around Ares temperament:

http://x31eq.com/cgi-bin/rt.cgi?ets=7p_12p_15p&limit=11

If the +/- accidental is 81/80, the #/b accidental is 25/24, and the
nominals C-C represent the tempered version of the scale whose
transversal is 1/1 9/8 5/4 4/3 3/2 5/3 15/8 2/1, then you get

C C# D- D Eb E F F#- F# G Ab A Bb- Bb B C

This is, of course only one way to spell things, just like there's
more than one way to spell things based around meantone[12] in 12-EDO.
You could also try 7p&12e&15p if you want to count 11/8 as a type of
5\12 instead of as a type of 6\12, which as one option gives you

C C# D- D Eb E F F+ F# G Ab A Bb- Bb B C

I don't think that this is any worse than any rank-2 based system,
really. The only issue is that there's a lot more ways to
enharmonically respell things now. To fix this, you might notice that
#/b and +/- are tempered to be the same size in 15-EDO; tempering them
together and using the symbol ^/v for both gives you porcupine
temperament, but where the nominals C-C now reflect the porcupine[7]
6|0 v4 ^7 MODMOS as a base, which would ordinarily be spelled C D E Fv
G A B^ C using the usual porcupine notation. This

Looking at 7&12&x rank-3 temperaments is another way to find useful
notation systems which happen to use more than one accidental. Here's
16-EDO http://x31eq.com/cgi-bin/rt.cgi?ets=7p_12p_16p&limit=11

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Wed, Nov 28, 2012 at 2:47 PM, cityoftheasleep <igliashon@...>
> wrote:
> >
> > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> > > This leaves you with valentine[7], "progress"[7], and orgone[7].
> > > Progress has a generator of 7/5. Of those, the first two are insane,
> > > leaving you with only orgone[7] or something that's not an MOS.
> > >
> > > You could always build it around the rank-3 Zarlino JI major scale,
> > > 1/1 9/8 5/4 4/3 3/2 5/3 15/8 2/1. For me, I'm more inclined to stick
> > > with porcupine[7] or the occasional blackwood[10]. If you want 4:5:6
> > > and 10:12:15 chords to share the same generic pattern of scale steps,
> > > 7 note and 10 note scales are about what you're stuck with.
> >
> > Yep. Any idea which nominal I should start the porcupine generator chain
> > on to preserve the maximum number of familiar ("meantone") chord-spellings?
> > I've just been starting it on "A", but I'm not sure if that's optimal.
>
> G-G for Lssssss is what strikes me as closest, intuitively, to what we
> have now (It's kind of like G lydian dominant or something). I don't
> mind C-C for Lssssss either. I actually enjoy using the familiar
> letter names for such an exotic scale to some extent, but if you're
> not a fan you can always go with nominals 1-7 instead. I also like the
> chroma for porcupine[7] being ^ and v, since it's so small, as opposed
> to # and b.

I agree with G-A being the large step. It doesn't jive with standard notation, but if you forget standard music notation and just think about the alphabet, it makes sense. G-A is the only step that is not consecutive letters in the alphabet, so it should be the odd step. Actually I'm sure I've seen a porcupine notation before where G-A was the large step, so can we set that in stone right now?

Also agree with ^ and v for the accidentals (or the fancy sagittal symbols /| and \| if you prefer).

This means my marimba will be a transposing instrument where the near row of keys is nominally G A B C D E F G but sounds Cv D E F G Av Bv Cv. I'm fine with that.

Keenan

On Thu, Nov 29, 2012 at 11:22 AM, Keenan Pepper <keenanpepper@...>
wrote:
> Actually I'm sure
> I've seen a porcupine notation before where G-A was the large step, so can
> we set that in stone right now?

A bunch of people have independently come up with the same scheme. At
least in Scala, M37 is called "Miller" notation, so I assume Herman
Miller invented it. Miller porcupine notation has consecutive
generators going from A-G so that Lssssss is G-A-B-C-D-E-F-G, and the
accidentals are #/b. Then there's also Paul's 8-note notation system,
which is the same idea, except it's now going from A-H instead of A-G.
So LsLLLLLL is G-H-A-B-C-D-E-F-G. Accidentals are also #/b, but this
time they represent 16/15 instead of 25/24.

The thing I outlined in my post to Igs is something I worked out a
while ago based on Paul's system, which I posted about here
(/tuning/topicId_104583.html#104583). The only
difference is that I suggested ^/v be the standard accidental for
porcupine[7] and that #/b be the standard accidental for porcupine[8].

Since all these schemes end up calling Lssssss G-A-B-C-D-E-F-G, I
don't mind it being made standard.

> Also agree with ^ and v for the accidentals (or the fancy sagittal symbols
> /| and \| if you prefer).

Do those sagittal symbols represent the porcupine chroma?

> This means my marimba will be a transposing instrument where the near row
> of keys is nominally G A B C D E F G but sounds Cv D E F G Av Bv Cv. I'm
> fine with that.

Ugh.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> A bunch of people have independently come up with the same scheme. At
> least in Scala, M37 is called "Miller" notation, so I assume Herman
> Miller invented it. Miller porcupine notation has consecutive
> generators going from A-G so that Lssssss is G-A-B-C-D-E-F-G, and the
> accidentals are #/b. Then there's also Paul's 8-note notation system,
> which is the same idea, except it's now going from A-H instead of A-G.
> So LsLLLLLL is G-H-A-B-C-D-E-F-G. Accidentals are also #/b, but this
> time they represent 16/15 instead of 25/24.
>
> The thing I outlined in my post to Igs is something I worked out a
> while ago based on Paul's system, which I posted about here
> (/tuning/topicId_104583.html#104583). The only
> difference is that I suggested ^/v be the standard accidental for
> porcupine[7] and that #/b be the standard accidental for porcupine[8].

And in any closed 15-note system, both accidentals are the same interval, so you can just say IDGAF.

> Since all these schemes end up calling Lssssss G-A-B-C-D-E-F-G, I
> don't mind it being made standard.

I hereby proclaim this "standard Miller nominals". Let them be used throughout the land.

> > Also agree with ^ and v for the accidentals (or the fancy sagittal symbols
> > /| and \| if you prefer).
>
> Do those sagittal symbols represent the porcupine chroma?

Yes, because they represent 81/80.

Keenan

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
> I like # and b always to represent the apotome (as in Sagittal) - meaning they would be useless in 15edo. So my version would be:
>
> 0 A#/B/C/Db (really only call it C)
> 80 A#^/B^/C^/Db^ (really only call it C^)
> 160 Dv (or a bunch of others, omitted for brevity...)
> 240 B#/C#/D/Eb/Fb (really only call it D)
> 320 D^
> 400 Ev
> 480 D#/E/F/Gb (really only call it E)
> 560 E^
> 640 Gv
> 720 E#/F#/G/Ab (really only call it G)
> 800 G^
> 880 Av
> 960 G#/A/Bb/Cb (really only call it A)
> 1040 A^
> 1120 Cv
> 1200 A#/B/C/Db (really only call it C)
>
> C major: C-Ev-G (makes perfect sense because v is the syntonic comma)
>
> B major: same as C major! All right, if you insist: B-D#v-F# (But really it's the same as C major.)
>
> You can tell at a glance that anything that looks like a normal note is part of one 5edo, anything with a ^ is another, and anything with v is another.
>
> As I said, this is even more insane, but don't deny its merits!

I tried a similar approach too--it's basically pentatonic notation, based on the three disjunct circles of fifths--and was pretty sold on it for a while. As you imply with your "really only call it..." notes, I basically just used 5 nominals, and figured "what the heck, you just gotta learn that what looks like a minor 6th is also a perfect 5th, because this is 5-ED2 and the limma is tempered out". So you get A-A^-Cv-C-C^-Dv-D-D^-Ev-E-E^-Gv-G-G^-A. W00t, it's so simple! You have to learn FEWER note-names, not more!

But then I realized--it's not just fifths and minor sixths that get conflated (spelling-wise), it's pretty much everything. A-C looks like a minor 3rd but sounds like a major 2nd; A-C^ looks like a major 3rd but sounds like a minor 3rd. D^ to Ev is the same distance as A^ to Cv. It's annoying and counter-intuitive. Your approach is a way around this, but really, your notation is just 5-limit JI notation, not based on any temperament, so any comma pump will cause notational drift. That, I think, is a bigger problem than working out a new set of spellings.

Another way around it is to use nominals A-E, but that's even more ridiculous, because nothing is spelled familiar at all anymore. Aaaaaand, another problem with pentatonic notations in general is that you need accidentals for literally *every* 5-limit chord. There's no "white key" scale.

Speaking of which, it's also important to consider the musicians who are going to be using 15-ET, and the interface they will have with their instrument. Are we expecting the 5w10b (or 10w5b) keyboard to be the favored choice, when 7w8b or 8w7b are both way more compact, or when 9w6b (i.e. Triforce) seems a more optimal mix of regularity and compactness? My current thinking is that anyone who plays 15-ED2 on a 7w8b keyboard (or an 8w7b) will gravitate naturally to Porcupine notation. I mean, you obviously want the white keys to be the naturals, right? And you want spellings of chords to easily indicate fingerings, right? I mean, imagine you're reading a piece of 15-tone sheet music for keyboard (or marimba, as the case may be). What's more important, that the fifths are all spelled the way they are in 12-TET, or that you can find the notes on your instrument more easily? Considering your marimba is in 7w8b, how do you feel about applying a pentatonic notation to it?

Of course, any keyboard other than 5w10b (or 10w5b) will put keyboardists and guitarists at odds, because on guitar, Blackwood[10] (or just 5-ET) has all the open-position chords. And blackwood[10] in the major mode is basically a super-position of all the major-type modes of the 5-limit JI diatonic scale (as well as the 7- and 11-limit variations on said diatonic scale), so if you're just noodling diatonically in 15-ET on guitar, odds are you're just staying in a 7-note subset of Blackwood[10]. Thus I generally find that, on guitar, the wonky inconsistent A-G pentatonic notation actually does the best job, because I don't think in terms of all three note-names in a triad, just root and chord-type--i.e., I don't think of C-Ev-G, I just think "C major". And it's way easier to just be able to say "all the naturals in this key are major, and all the v's are minor". For writing guitar chord charts, this notation is tough to beat. In Porcupine notation, you'd basically have to abandon all-4ths tuning, or accept some accidentals on the open strings, and get used to a sort of diagonal mapping of accidentals across the strings.

So, I hope you can understand my dilemma. I'm trying to choose the notation very carefully in case I end up setting the convention.

-Igs

On Thu, Nov 29, 2012 at 12:31 PM, Keenan Pepper <keenanpepper@...>
wrote:
>
> And in any closed 15-note system, both accidentals are the same interval,
> so you can just say IDGAF.

I assume that snooty 15-EDO classical musicians will GAF, since snooty
12-EDO classical musicians today GAF about enharmonic respellings.

> > Since all these schemes end up calling Lssssss G-A-B-C-D-E-F-G, I
> > don't mind it being made standard.
>
> I hereby proclaim this "standard Miller nominals". Let them be used
> throughout the land.

The standardization of those nominals is fine with me, but Herman
Miller if you read this at some point, can you weigh in on if you
actually invented these nominals? I'm still not sure if it's you or
Paul who came up with it.

-Mike

On 11/30/2012 10:46 AM, Mike Battaglia wrote:
> On Thu, Nov 29, 2012 at 12:31 PM, Keenan Pepper<keenanpepper@...>
> wrote:
>>
>> And in any closed 15-note system, both accidentals are the same interval,
>> so you can just say IDGAF.
>
> I assume that snooty 15-EDO classical musicians will GAF, since snooty
> 12-EDO classical musicians today GAF about enharmonic respellings.
>
>>> Since all these schemes end up calling Lssssss G-A-B-C-D-E-F-G, I
>>> don't mind it being made standard.
>>
>> I hereby proclaim this "standard Miller nominals". Let them be used
>> throughout the land.
>
> The standardization of those nominals is fine with me, but Herman
> Miller if you read this at some point, can you weigh in on if you
> actually invented these nominals? I'm still not sure if it's you or
> Paul who came up with it.

I believe I may have come up with the A-G notation for porcupine (with the large step between G and A), but my email archive only goes back as far as 2004, when I referred to "my porcupine notation, which uses the letters A-G for the basic 7-note MOS" in a message in February. Which suggests that I must have discussed that notation in an earlier message.

Herman