11-EDO piece: O Guillerme magister

Hello, everyone, and special thanks to Dan Stearns for his previous posts
on what I termed a hexatonic scale in 11-EDO (e.g. 222212), one of which,
interestingly, occurred in a thread about an article Dave Keenan and I
coauthored here on the Noble Mediant (at first called the "Golden
Mediant") in September 2000. Dan, your posts indeed confirm the suspicions
expressed in my post about it that this is a very attractive scale which
could have already been discovered by others at various times and places.

Both Dan and Dave have played a role in the dialogue leading to my
first multi-voice composition in 11-EDO, with their advocacy of a
sonority of 0-4-7 steps (as an approximation of 7:9:11) introducing me
to a great musical resource in this tuning.

Here notes are generally taken to be sustained until the next note in
a given part or the end of the piece or section or a rest sign "r."
The texture is mostly in three voices, but with four-voice sonorities
at certain points; my approach is to use an "r" sign to show that the
fourth voice rests, i.e. a return to the usual three-voice texture.
This convention also permits notes to span a barline, as in some
suspension-type figures, without the need for ties.

There are some passages in "Stearns/Keenan discant" with parallel
0-4-7 and related sonorities; the notation is based on a regular
22-EDO chain of fifths, so that the stable 11-EDO sonority F3-B3-F4
(0-6-11 steps) has its xenofifth F3-B3 spelled as a tritone, which it
literally is. The plus sign (+), e.g. Eb+4, shows a note raised by
1/11 octave.

Measures 3-4 have a form of rhythmic proportion in which each primary
beat is divided into three parts instead of two, like modern triplets;
the apostrophe (') in the metrical line at the end of this passage
shows a prolonging of the sonority C#3-F3-C#4, like a fermata.

Cantilena Sethareana
--------------------

1 2 | 1 2 | 1 + 2 | 1 2 |

Eb+4 F4 r
F4 F4 C#4 B3 F4 F4 Eb4 F4
B3 B3 A3 B3 B3 C#4 B3 C#4
F3 F3 G3 F3 F3 A3 G3 A3

O Guil- ler- me ma- gi- ster con-

1 2 | 1 2 ' | 1 + 2 + | 1 2 |
1 2 3 4 5 6 1 2 3 4 5 6
G4 F4 Eb4 C#4 B3 C#4 F4 F4 Eb4 F4
Eb4 C#4 B3 A3 G3 F3 B3 C#4 B3 B3
B3 A3 G3 F3 Eb3 C#3 F3 A3 G3 F3

cor- di- ae no- vae:

1 2 + | 1 2 | 1 + 2 + | 1 2 |

F4 F4 F4 C#+4 F4 F4 F4 Eb+4 F4
B3 B3 B3 A+3 B3 B3 C#4 B3 B3
F3 F3 F3 F+3 F3 F3 A3 G3 F3

E- gre- di- a- mur in fo- rum;

1 2 | 1 2 | 1 2 + | 1 2 |

G4 G4 r
F4 F4 Eb4 Eb4 G4 F4 Eb4 F4
B3 B3 B3 B3 B3 B3
F3 F3 F3 F3 F3 F3

I- bi da- bo ti- bi

1 + 2 + | 1 + 2 | 1 2 ||

Eb+4 F4
F4 F4 F4 G4 F4 F4 C#4 B3
B3 B3 C#4 Eb4 C#4 C#4 A3 B3
F3 F3 A3 B3 A3 A3 G3 F3

Can- ti- le- nam cu- ri- o- sam.

O Guillermus [William], teacher of new concord:
Let us go out into the forum;
There I will give to you
A curious song.

My apologies for any errors in this notation, often more obvious after
posting. Mainly I want to say that actually composing in 11-EDO is the
best viewpoint for my theorizing about this tuning, but at the same
time, suggestions from others (including both an experienced 11-EDO
composer like Dan, and a creative theorist and musicians such as Dave)
are an invaluable part of the process -- not to mention Paul's
reflections and Jacky's timbres and compositions.

Also, I would like to emphasize that this piece with its
"quasi-cadences" does not make all other approaches to 11-EDO
obsolete, with a recent post by George Secor very eloquently
indicating one such approach stated on the basis of insight and
experience alike.

Most appreciatively,

Margo Schulter
mschulter@value.net

Dear Margo,

I would dearly love to hear your 'Cantilena Sethareana' via a .MP3 or
similar. I'm sure I'm not the only one. Maybe someone else on the list
can help.

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> Dear Margo,
>
> I would dearly love to hear your 'Cantilena Sethareana' via a .MP3
> or similar. I'm sure I'm not the only one. Maybe someone else on the
> list can help.

I'm not sure on the notation, but if Margo can post it as a midi sequencer file (.mid) as she has in the past (and *wants* to do this), I'll take the midi file, digitize the audio and upload it to [somewhere] as an .mp3 file...

Cheers,
Jon

Hi Margo,

You always manage to set such a wonderful, neighborly example... it
really is a pleasure and an honor to have you around, thanks.

I must admit though that your recent absence at the list has led me to
secretly wonder what you've been toiling away at all this time! I just
know I'll someday be thumbing through some mammoth and cheerfully
verbose Margo Schulter microtonal book, and I for one can hardly wait!

take care,

--Dan Stearns

----- Original Message -----
From: "M. Schulter" <MSCHULTER@VALUE.NET>
To: <tuning@yahoogroups.com>
Sent: Thursday, May 09, 2002 2:55 PM
Subject: [tuning] 11-EDO piece: O Guillerme magister

> Hello, everyone, and special thanks to Dan Stearns for his previous
posts
> on what I termed a hexatonic scale in 11-EDO (e.g. 222212), one of
which,
> interestingly, occurred in a thread about an article Dave Keenan and
I
> coauthored here on the Noble Mediant (at first called the "Golden
> Mediant") in September 2000. Dan, your posts indeed confirm the
suspicions
> expressed in my post about it that this is a very attractive scale
which
> could have already been discovered by others at various times and
places.
>
> Both Dan and Dave have played a role in the dialogue leading to my
> first multi-voice composition in 11-EDO, with their advocacy of a
> sonority of 0-4-7 steps (as an approximation of 7:9:11) introducing
me
> to a great musical resource in this tuning.
>
> Here notes are generally taken to be sustained until the next note
in
> a given part or the end of the piece or section or a rest sign "r."
> The texture is mostly in three voices, but with four-voice
sonorities
> at certain points; my approach is to use an "r" sign to show that
the
> fourth voice rests, i.e. a return to the usual three-voice texture.
> This convention also permits notes to span a barline, as in some
> suspension-type figures, without the need for ties.
>
> There are some passages in "Stearns/Keenan discant" with parallel
> 0-4-7 and related sonorities; the notation is based on a regular
> 22-EDO chain of fifths, so that the stable 11-EDO sonority F3-B3-F4
> (0-6-11 steps) has its xenofifth F3-B3 spelled as a tritone, which
it
> literally is. The plus sign (+), e.g. Eb+4, shows a note raised by
> 1/11 octave.
>
> Measures 3-4 have a form of rhythmic proportion in which each
primary
> beat is divided into three parts instead of two, like modern
triplets;
> the apostrophe (') in the metrical line at the end of this passage
> shows a prolonging of the sonority C#3-F3-C#4, like a fermata.
>
>
> Cantilena Sethareana
> --------------------
>
> 1 2 | 1 2 | 1 + 2 | 1 2 |
>
> Eb+4 F4 r
> F4 F4 C#4 B3 F4 F4 Eb4 F4
> B3 B3 A3 B3 B3 C#4 B3 C#4
> F3 F3 G3 F3 F3 A3 G3 A3
>
> O Guil- ler- me ma- gi- ster con-
>
>
>
> 1 2 | 1 2 ' | 1 + 2 + | 1
2 |
> 1 2 3 4 5 6 1 2 3 4 5 6
> G4 F4 Eb4 C#4 B3 C#4 F4 F4 Eb4 F4
> Eb4 C#4 B3 A3 G3 F3 B3 C#4 B3 B3
> B3 A3 G3 F3 Eb3 C#3 F3 A3 G3 F3
>
> cor- di- ae no-
vae:
>
>
>
> 1 2 + | 1 2 | 1 + 2 + | 1 2 |
>
> F4 F4 F4 C#+4 F4 F4 F4 Eb+4 F4
> B3 B3 B3 A+3 B3 B3 C#4 B3 B3
> F3 F3 F3 F+3 F3 F3 A3 G3 F3
>
> E- gre- di- a- mur in fo- rum;
>
>
> 1 2 | 1 2 | 1 2 + | 1 2 |
>
> G4 G4 r
> F4 F4 Eb4 Eb4 G4 F4 Eb4 F4
> B3 B3 B3 B3 B3 B3
> F3 F3 F3 F3 F3 F3
>
> I- bi da- bo ti- bi
>
>
> 1 + 2 + | 1 + 2 | 1 2 ||
>
> Eb+4 F4
> F4 F4 F4 G4 F4 F4 C#4 B3
> B3 B3 C#4 Eb4 C#4 C#4 A3 B3
> F3 F3 A3 B3 A3 A3 G3 F3
>
> Can- ti- le- nam cu- ri- o- sam.
>
> O Guillermus [William], teacher of new concord:
> Let us go out into the forum;
> There I will give to you
> A curious song.
>
> My apologies for any errors in this notation, often more obvious
after
> posting. Mainly I want to say that actually composing in 11-EDO is
the
> best viewpoint for my theorizing about this tuning, but at the same
> time, suggestions from others (including both an experienced 11-EDO
> composer like Dan, and a creative theorist and musicians such as
Dave)
> are an invaluable part of the process -- not to mention Paul's
> reflections and Jacky's timbres and compositions.
>
> Also, I would like to emphasize that this piece with its
> "quasi-cadences" does not make all other approaches to 11-EDO
> obsolete, with a recent post by George Secor very eloquently
> indicating one such approach stated on the basis of insight and
> experience alike.
>
> Most appreciatively,
>
> Margo Schulter
> mschulter@value.net
>
>
>
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Margo,

For me, it is not clear how that notation for 11 EDO (or 22 EDO)
works. Could you explain it, or point to an article describing it ?

Bart Pauwels

Hello, there, Bart Pauwels -- and welcome to the Tuning List,
Bart. Thank you for asking about a notation which I tend to take for
granted for 22-EDO, but is by no means "universal" or anything like
it, making your question all the more helpful and appropriate.

/tuning/topicId_36888.html#36908

Here's my 11-EDO/22-EDO notation scheme show with a keyboard layout
(on the Web, there might be an "Expand Messages" option to get this to
display more accurately):

273 491 600 981 1091
5 9 11 18 20
F#+/Ab G#+/Bb Bb+/A# C#+/Eb Eb+/D#
F+ G+ A+ B+/Db C+ D+ E+/Gb F+
2 6 10 14 15 19 23 24
109 327 545 764 818 1036 1255 1309
------------------------------------------------------------------
164 382 491 873 982
3 7 9 16 18
F# G# Bb C# Eb
F G A B C D E F
0 4 8 12 13 17 21 22
0 218 436 655 709 927 1145 1200

The numbers show the distance in 22-EDO steps and cents for each note
with reference to an octave of F-F. Note that an asterisk (*) shows a
note raised by 1/11 octave, or 2 steps in 22-EDO.

The rule for this notation is that a flat lowers a note by 3 steps,
while a sharp raises it by three steps -- the chromatic semitone in
22-EDO -- while diatonic semitones (e.g. E-F, B-C, Ab-G, G#-A) are
always equal to a single step, or literally a "quartertone" in
relation to the regular major second or whole-tone of 4 steps.

Here's the 11-EDO subset of 22-EDO that I'm using, with notes shown in
11-EDO steps with reference to F:

873 1091
9 10
C#+/Eb Eb+
F+ G+ A+ B+ F+
1 3 5 7 12
109 327 545 764 1309
---------------------------------------------------------------
873 982
8 9
C# Eb
F G A B F
0 2 4 6 11
0 218 436 655 1200

For a fuller discussion, please see

/tuning/topicId_36697.html#36697

Most appreciatively,

Margo Schulter
mschulter@value.net