A piece in Wurschmidt temperament

Cross-posted to the Xenharmonic Alliance on Facebook.

I have to just publish this thing before I overtweak it. It's a piece in
Wurschmidt temperament in 31 EDO.

https://soundcloud.com/jdfreivald/extrospection

Wurschmidt has a near-just 5/4 as generator, with eight making a 3/2. In 31
EDO, carried out to a 16-note MOS, it has excellent seven-limit harmonies,
and even some 11-limit as well. It also has little-itty-bitty steps,
though, and not a lot of perfect fifths except on chords that are pretty
close together (e.g., major chords 40 cents apart).

Because of the excellent 5- and 7-limit harmonies, I went for heavy strings
and a slowish tempo, so you can really hear and feel the sound. This isn't
the boldest thing I've ever done, and I may modify it with different chords
in the future, but I like the sounds anyway.

Part of my goal is always to do something that I couldn't do in 12 EDO. I
don't feel like I fully exploited that, but I did somewhat. Here, although
the main chords (C#m and A) are essentially the same as (though in better
tune than) in 12 EDO, you couldn't get the same sound -- the seven limit (a
bit of 7/6 and 10/7) and a few excellent augmented chords (truly two 5/4s
stacked, meaning you hear the 25th harmonic clearly) just wouldn't be the
same. I used eight (octave-equivalent) tones of the 16-tone MOS.

Written in Lilypond, using Saggital notation that was pre-processed to
scordatura before compiling. Rendered with Timidity++.

Regards,
Jake

On 09/20/2013 02:42 AM, Jake Freivald wrote:

> Written in Lilypond, using Saggital notation that was pre-processed to
> scordatura before compiling. Rendered with Timidity++.

Why the scordatura and not MTS? Is something about my microtonal support not working for you?

Graham

>
> > Written in Lilypond, using Saggital notation that was pre-processed to
> > scordatura before compiling. Rendered with Timidity++.
>
> Why the scordatura and not MTS? Is something about my microtonal
> support not working for you?
>

I just haven't figured it out yet. I tried following your instructions a
year+ ago, before I knew anything about Saggital, or enough about Lilypond
to do more than use it to generate output for Timidity. I didn't get
instant gratification from it, so I quit trying after a short time. I
haven't even tried to understand Saggital until a few weeks ago.

On the other hand, I know a little Perl and can easily set up the
replacement tables that I need in Excel, so making the text-based
substitutions was relatively quick.

Actually, I should make sure I'm using my terms right. What I meant by
"scordatura" is that each note gets mapped to / replaced by a different
tone in the alternate tuning: C --> c, C/|\ --> cis, C/||\ --> d, E\!!/ -->
dis, etc. That's relatively easy to make happen with a Perl script. Then
the c, cis, d, etc. are output to a MIDI file, and during Timidity's
rendering process, they're tuned to c = 0 cents, cis = 39 cents, d = 77
cents, dis = 310 cents by Timidity.

Anyway, the downside to this, of course, is that I don't have a Saggital
score. That *is* important to me, so I'll probably try to figure it out
again someday.

Regards,
Jake

I enjoyed that.  Different enough from the usual 12EDO to be striking, but it sounded good, or "right" enough.  That's not easy, as we know.

The little same-note (tritone-ish) in the guitar figuration sounded funny to me the first time, then when you repeated it it sounded right.

When the lower bell-like sounds happen, they are a magical weirdness. They're not bells exactly, not sure what they are. 

And the doubling of guitar and strings brings things together in a nice way.

When the piece finished, it jumped right into Mike Battaglia's first Comma pump in Hanson/Kleismic, which I also liked.

________________________________
From: Jake Freivald <jdfreivald@...>
To: makemicromusic@yahoogroups.com
Sent: Thursday, September 19, 2013 9:42 PM
Subject: [MMM] A piece in Wurschmidt temperament

 
Cross-posted to the Xenharmonic Alliance on Facebook.

I have to just publish this thing before I overtweak it. It's a piece in Wurschmidt temperament in 31 EDO. 

https://soundcloud.com/jdfreivald/extrospection

Wurschmidt has a near-just 5/4 as generator, with eight making a 3/2. In 31 EDO, carried out to a 16-note MOS, it has excellent seven-limit harmonies, and even some 11-limit as well. It also has little-itty-bitty steps, though, and not a lot of perfect fifths except on chords that are pretty close together (e.g., major chords 40 cents apart).

Because of the excellent 5- and 7-limit harmonies, I went for heavy strings and a slowish tempo, so you can really hear and feel the sound. This isn't the boldest thing I've ever done, and I may modify it with different chords in the future, but I like the sounds anyway. 

Part of my goal is always to do something that I couldn't do in 12 EDO. I don't feel like I fully exploited that, but I did somewhat. Here, although the main chords (C#m and A) are essentially the same as (though in better tune than) in 12 EDO, you couldn't get the same sound -- the seven limit (a bit of 7/6 and 10/7) and a few excellent augmented chords (truly two 5/4s stacked, meaning you hear the 25th harmonic clearly) just wouldn't be the same. I used eight (octave-equivalent) tones of the 16-tone MOS.

Written in Lilypond, using Saggital notation that was pre-processed to scordatura before compiling. Rendered with Timidity++.

Regards,

Jake

Thank you, Caleb, for the feedback and appreciation.

> That's not easy, as we know.

I would be embarrassed to tell you how long it took. :)

> The little same-note (tritone-ish) in the guitar figuration sounded
> funny to me the first time, then when you repeated it it sounded right.

Interesting. It's a 10/7. I really liked the sound of that (1/1 - 10/7 -
3/2) in the strings, and emphasized the 10/7 in the guitar part. It sounded
right to me from the beginning, but I already knew the piece well enough to
know that's what *had* to be there.

> When the lower bell-like sounds happen, they are a magical weirdness.
> They're not bells exactly, not sure what they are.

Those are the tubular bells in the soundfont I use. They're not great as
bells, but they have a nice non-harmonic quality to them. (The chimes that
go in the B part of the piece are a nylon-stringed guitar being played
impossibly high. I've always liked that sound, but it's an abuse of the
soundfont.) "Magical weirdness" is a wonderful thing.

> When the piece finished, it jumped right into Mike Battaglia's first
> Comma pump in Hanson/Kleismic, which I also liked.

I like that too -- it has an interesting sound to it.

I have three more projects to do: One in Kleismic (Keemun, specifically),
one in Magic, and one in extended Meantone. All four of these have nice
thirds, so part of the job is comparing them compositionally.

Thanks again.

Regards,
Jake

On 09/20/2013 02:24 PM, Jake Freivald wrote:

> Actually, I should make sure I'm using my terms right. What I meant by
> "scordatura" is that each note gets mapped to / replaced by a different
> tone in the alternate tuning: C --> c, C/|\ --> cis, C/||\ --> d, E\!!/ -->
> dis, etc. That's relatively easy to make happen with a Perl script. Then
> the c, cis, d, etc. are output to a MIDI file, and during Timidity's
> rendering process, they're tuned to c = 0 cents, cis = 39 cents, d = 77
> cents, dis = 310 cents by Timidity.

This is what I call "scordablature" and I support it directly. So you can write in your Wurschmidt notation and write like this or as Sagittal or whatever else you program in. And you can output as MTS to work with Timidity, which you're using anyway, so you won't have to worry about tuning tables.

> Anyway, the downside to this, of course, is that I don't have a Saggital
> score. That *is* important to me, so I'll probably try to figure it out
> again someday.

Okay. Writing the Wurschmidt support shouldn't be harder than what you're already doing with Perl. You'll have to think up alphabetical note names, though.

Graham

Well done! Good timbres, and given the way it was created, it sounds
surpsisingly "unmechanical". The chord progression first appearing at 1:32
really catches the ear.

Yeah, to do something that you cannot in 12 EDO is usually one of my goals, too.
Funny thing is here that large parts of the piece (I have to confess) sound
"conventional" to me - although I am quite sure they are not. I have run into
the same problem in my stuff, maybe it's the conventional-sounding chords that
trick the hearing habits.

But keep going anyway!

---In makemicromusic@yahoogroups.com, <gbreed@...> wrote:

On 09/20/2013 02:24 PM, Jake Freivald wrote:

> > Actually, I should make sure I'm using my terms right. What I meant by
> "scordatura" is that each note gets mapped to / replaced by a different
> tone in the alternate tuning: C --> c, C/|\ --> cis, C/||\ --> d, E\!!/ -->
> dis, etc. That's relatively easy to make happen with a Perl script. Then
> the c, cis, d, etc. are output to a MIDI file, and during Timidity's
> rendering process, they're tuned to c = 0 cents, cis = 39 cents, d = 77
> cents, dis = 310 cents by Timidity.

This is what I call "scordablature" and I support it directly. So you
can write in your Wurschmidt notation and write like this or as Sagittal
or whatever else you program in. And you can output as MTS to work with
Timidity, which you're using anyway, so you won't have to worry about
tuning tables.

> > Anyway, the downside to this, of course, is that I don't have a Saggital
> score. That *is* important to me, so I'll probably try to figure it out
> again someday.

Okay. Writing the Wurschmidt support shouldn't be harder than what
you're already doing with Perl. You'll have to think up alphabetical
note names, though.

Graham

Hans,

> Well done! Good timbres, and given the way it was created, it sounds
surpsisingly "unmechanical".

Thank you. The timbres are by choice; the "unmechanicalness" is luck. :)

> The chord progression first appearing at 1:32 really catches the ear.

It's a cool sequence, I think, but it's also pretty straightforward:

A major, voiced as 1:4:6:20
C# "Genus", 1:3:5:15
A major with an added 8/7, voiced as 7:21:35:128
C# major, voiced as 1:3:5:16
A "Genus", 1:3:5:15

Genus, of course, is just a particular voicing of the major seventh chord.

So the only distinctly non-twelve aspect of this progression is the 8/7;
however, since there's also a 5/4 (relative to the root, voiced below it),
we get an approximate 11/3 (1044 cents + an octave) out of the deal.
Without worrying about prime limits, though, it's worth noting that the
ratio-oriented microtonal mindset (and Scala) led me to those chord
voicings.

> Yeah, to do something that you cannot in 12 EDO is usually one of my
goals, too.
> Funny thing is here that large parts of the piece (I have to confess)
sound
> "conventional" to me - although I am quite sure they are not.

In several ways, it *is* conventional. The base chord sequence is simple
C#m -> A, and even the chord sequence I've described above is mostly
something that could be done in 12 EDO. In that sense, much of what you
hear is microtonal only because it's in better tune than usual.

On the other hand, the second chord you hear is a G# augmented chord,
0-387-774 cents -- solidly non-twelve with a very nice 25th harmonic.
There's also an A septimal minor chord at 0-271-697 cents, an A with a 10/7
tritone and no third at 0-620-697 cents (though voiced as 0-620-1897 cents,
so you don't get the 77-cent clash), and the A major with the added 8/7
above: That's three seven-limit tones that are important to the sound of
the piece.

I guess I'm happy enough that it sounds "conventional". If it's microtonal
and sounds appealing without sounding "xenharmonic", that's one form of
success.

Regards,
Jake

Thanks for the info, Jake! My 31-EDO guitar arrived a few weeks ago, and I'm
very interested

in discussions related to this tuning.

If I interpreted the data correctly, your scale is the following 9-note scale,
starting on "A",

in 31-EDO steps: 0 6 7 10 16 17 18 20 28 31

(though earlier you stated that it's 8 notes?)

I wondered what would be a good base scale for a notation. I noticed that the
scale has a large

gap when expressed as a chain of major thirds, but can be represented as two
almost

uninterrupted chains of major thirds, separated by a perfect fifth, like
following:

-- 16
-- 6
-- --
-- 17
20 7
10 28
0 18

I tried to find a max-variety-3 scale with a similar structure, and came up with
the following

7-note scale:

(31-EDO steps, marvel ratios and possible Sagittal note names, resp.)

-- 27
-- 17
20 7
10 28
0 --

0 7 10 17 20 27 28 31

-- 49/27
-- 35/24
14/9 7/6
5/4 15/8
1/1

1/1 7/6 5/4 35/24 14/9 49/27 15/8 2/1

-- B)||(
-- G||\
A E
F/| C/|
D)!!( --

D)!!( E F/| G||\ A B)||( C/| D)!!(

You can use those accidentals in a global key signature, s.th. D E F G A B C D
expresses

the above scale, and you can use different key signatures to indicate
modulations.

For "vertical" modulations in major third direction, we need two pairs of
accidentals.

The first is )||( and )!!(, representing 25/24, e.g. to modulate to D E F G A B
C)||( D.

What happened here is that the C/| a major third below E became the C||\ a major
third

above A. The resulting scale is a mirrored version of the original scale.

To get a scale with the same structure as the original scale again, we can
define a second

pair of accidentals >, <, and use > to increase D)!!( by an approximate 8/7 to
the note

a major third above B)||(, so the scale becomes D> E F G A B C)||( D>.

(not sure if it's possible to express this in Sagittal w/o user-defined
accidentals)

Assuming this global key signature, the 9-note scale can be expressed as
following:

-- C>)||(

-- A>

-- --

-- D>

E)||( B
C)||( G
A E

A A> B C)||( C>)||( D> E E)||( G A

This is a general marvel notation using two kinds of accidentals, which means
you can apply

any marvel temperament you want, including wuerschmidt, orwell, meantone, magic
or 31et.

You can use the wuerschmidt interpretation, but you didn't make much use of the
mapping that

8 stacked thirds make a fifth, and the interpretation for 8/7 and 10/7 is -
strictly speaking - not

legitimate in my scale arrangement, and also doesn't occur in wuerschmidt[16].

In orwell, on the other hand, this interpretation works with my notation, since
there a fifth plus

5 major thirds makes a 8/7, and the major third above is a 10/7, of course. When
it comes to

the mapping, this seems to be a very fitting interpretation, especially if you
want to think of

the accidental ">" as 8/7.

31et allows much freedom of interpretation, but is very restricting from the
tuning perspective,

especially if you want better fifths (though 5/4 and 7/4 are great).

Regards

- Geddy

P.S.: I hope I didn't make many errors, this small editor window and the missing
preview button

are a great annoyance

---In MakeMicroMusic@yahoogroups.com, <makemicromusic@yahoogroups.com> wrote:

Hans,
> Well done! Good timbres, and given the way it was created, it sounds
surpsisingly "unmechanical".
Thank you. The timbres are by choice; the "unmechanicalness" is luck. :)
> The chord progression first appearing at 1:32 really catches the ear.
It's a cool sequence, I think, but it's also pretty straightforward:
A major, voiced as 1:4:6:20C# "Genus", 1:3:5:15A major with an added 8/7, voiced
as 7:21:35:128C# major, voiced as 1:3:5:16A "Genus", 1:3:5:15
Genus, of course, is just a particular voicing of the major seventh chord.
So the only distinctly non-twelve aspect of this progression is the 8/7;
however, since there's also a 5/4 (relative to the root, voiced below it), we
get an approximate 11/3 (1044 cents + an octave) out of the deal. Without
worrying about prime limits, though, it's worth noting that the ratio-oriented
microtonal mindset (and Scala) led me to those chord voicings.
> Yeah, to do something that you cannot in 12 EDO is usually one of my goals,
too.> Funny thing is here that large parts of the piece (I have to confess)
sound> "conventional" to me - although I am quite sure they are not.
In several ways, it *is* conventional. The base chord sequence is simple C#m ->
A, and even the chord sequence I've described above is mostly something that
could be done in 12 EDO. In that sense, much of what you hear is microtonal only
because it's in better tune than usual.
On the other hand, the second chord you hear is a G# augmented chord, 0-387-774
cents -- solidly non-twelve with a very nice 25th harmonic. There's also an A
septimal minor chord at 0-271-697 cents, an A with a 10/7 tritone and no third
at 0-620-697 cents (though voiced as 0-620-1897 cents, so you don't get the
77-cent clash), and the A major with the added 8/7 above: That's three
seven-limit tones that are important to the sound of the piece.
I guess I'm happy enough that it sounds "conventional". If it's microtonal and
sounds appealing without sounding "xenharmonic", that's one form of success.
Regards,Jake