Miracle[10]... how are people using it?

Hi all,

A question for anyone who's messed around with or written extensively
on Miracle:

I've been trying to wrap my head around it ever since I heard Chris
Vaisvil's improv in blackjack. I can definitely get into blackjack,
but I'm having more trouble with the 1+9 decatonic MOS, which is
supposed to be "diatonic" basis for miracle, yes? I can't figure out
how to make any sense out of it.

I started messing around with porcupine[7] after seeing the note about
it in the tctmo, and was similarly perplexed with it until I finally
tried having the generators go downward, and came across the beautiful
Lssssss mode (and realizing that it's an 11-limit scale). And since
then I've become more able to understand the porcupine modes, and am
finally working towards a porcupine composition. I figured that
miracle, since it's so popular, would be another "intuitive" scale...
but I've hit a wall.

I can't get my head wrapped around it. What's the basic sonority
supposed to be, the neutral triad? Or is it that people are using
4:5:7 as stable fifthless sonorities? And if so, how are things
supposed to resolve, being as all of the consonant triads are a secor
away from each other? Or, is it that people use constantly shifting
decatonic scales as intermediate reference frames as part of some
larger blackjack structure, similar as to what I was trying to do with
my diatonic-modes-as-chords approach? (Also, why is the sssssssssL
mode the "basic" one used in decimal?)

Right now my approach to miracle has just been a way to use it to
approximate JI. Which is great and all, but I get the feeling there
must be some underlying musical system here that I'm missing.
Porcupine, for example, has turned out to be far more than just a way
to approximate JI with less notes.

Either way, some insight would be appreciated. I've read Graham's
pages on it a zillion times but I'm still not "getting" it. Some
insight into miracle theory would be much appreciated, or some musical
examples in it demonstrating some resolutions perhaps, or entire
pieces of music. Right now I'm having trouble making musical sense of
it, and a neutral triad is just too hard for me to swallow as a I
chord (maybe I'll get used to it).

Thanks
-Mike

Hi Mike,

> I can't get my head wrapped around it. What's the basic sonority
> supposed to be, the neutral triad? Or is it that people are using
> 4:5:7 as stable fifthless sonorities?

Miracle is much more complex than porcupine, so there's no
diatonic-size scale with complete chords. You can make
neutral triads, but you only get them in half the modes
and they're all at one end of the scale. So it requires
chromatic notes for harmonization.

Does that help? -Carl

On Thu, Sep 9, 2010 at 2:58 AM, Carl Lumma <carl@...> wrote:
>
> Hi Mike,
>
> > I can't get my head wrapped around it. What's the basic sonority
> > supposed to be, the neutral triad? Or is it that people are using
> > 4:5:7 as stable fifthless sonorities?
>
> Miracle is much more complex than porcupine, so there's no
> diatonic-size scale with complete chords. You can make
> neutral triads, but you only get them in half the modes
> and they're all at one end of the scale. So it requires
> chromatic notes for harmonization.
>
> Does that help? -Carl

So does the decimal scale function more as just a way of organizing
the larger MOS's? That is, rather than splitting notes up into
"diatonic" ones which are part of the tonal set and "chromatic" ones
which are not, is the distinction made differently in miracle?

I'm trying to find something to relate it to. In expanded diatonic
harmony, you'll have chord progressions like Bm7b5 -> E7b9 -> Am7 ->
D7b9 -> Gm7 -> C7 -> F. Each one of these uses its own scale, but
they're all obviously based in alterations of the underlying F
diatonic scale. Does it work more like that?

-Mike

Mike wrote:

> So does the decimal scale function more as just a way of organizing
> the larger MOS's? That is, rather than splitting notes up into
> "diatonic" ones which are part of the tonal set and "chromatic" ones
> which are not, is the distinction made differently in miracle?

Uh, I would say its purpose (if it has such a thing) is to
provide melodic material, which can be harmonized chromatically.
Much as the diatonic scale can be harmonized chromatically
in 12-ET.

> I'm trying to find something to relate it to. In expanded diatonic
> harmony, you'll have chord progressions like Bm7b5 -> E7b9 -> Am7 ->
> D7b9 -> Gm7 -> C7 -> F. Each one of these uses its own scale, but
> they're all obviously based in alterations of the underlying F
> diatonic scale. Does it work more like that?

Yes, though I don't think of each of those chords having its
own scale! Like b9 is in which scale of D7? Here your
understanding of jazz theory may just blow me away, I mean,
probably there is some mode that has a b9 in it that you can
think of D7b9 coming from... but to me its just a chord
which needs a chromatic interval (b9). If there is some way
to think of 7-limit tetrads as coming from a related sequence
of miracle[10] modes, I suppose that'd be pretty dope, but
you'll have to discover it because my lazy approach is more
chord-centric and involves remembering as few scales as
possible :0 -Carl

On Thu, Sep 9, 2010 at 3:41 AM, Carl Lumma <carl@...> wrote:
>
> Mike wrote:
>
> > So does the decimal scale function more as just a way of organizing
> > the larger MOS's? That is, rather than splitting notes up into
> > "diatonic" ones which are part of the tonal set and "chromatic" ones
> > which are not, is the distinction made differently in miracle?
>
> Uh, I would say its purpose (if it has such a thing) is to
> provide melodic material, which can be harmonized chromatically.
> Much as the diatonic scale can be harmonized chromatically
> in 12-ET.

I see. That makes sense. Do you know of any good examples of how this
could be used in miracle...?

> > I'm trying to find something to relate it to. In expanded diatonic
> > harmony, you'll have chord progressions like Bm7b5 -> E7b9 -> Am7 ->
> > D7b9 -> Gm7 -> C7 -> F. Each one of these uses its own scale, but
> > they're all obviously based in alterations of the underlying F
> > diatonic scale. Does it work more like that?
>
> Yes, though I don't think of each of those chords having its
> own scale! Like b9 is in which scale of D7? Here your
> understanding of jazz theory may just blow me away, I mean,
> probably there is some mode that has a b9 in it that you can
> think of D7b9 coming from...

There are a few scales that you could use over it. But the "simplest"
scale (and hence the most intuitive sounding, with the most common
tones pivoting between the two adjacent chords) that supports D7 is D
phrygian dominant, as in D Eb F# G A Bb C D. This is the fifth mode of
G harmonic minor, and resolves beautifully to Gm as such. Just for
fun, try this voicing:

D-G-C-Eb-Bb-D -> D-F#-C-Eb-A-C -> G-Bb-D-E-A-C#

You can either then resolve the C# at the end up to D or revel in the
sweet, sweet dissonance contained therein. Either way, D phrygian
dominant (G harmonic minor) will be simplest over the first 2 chords,
and G dorian #4 (mode of D harmonic minor) will work best over the
last one. Make it G dowian #4 #7 if you want, it's up to you.

This isn't the usual canon jazz, trick, however. This is like the
"halfway between jazz and classical" trick that I've come to really
enjoy playing in - what guys like Bill Evans, Keith Jarrett, Brad
Mehldau got amazingly good at. But the usual canon jazz trick,
however, is probably more interesting from a microtonal theory
standpoint.

The usual canon jazz trick here is to use the altered scale over a
dom7 going to minor, as in D Eb F Gb Ab Bb C D. Since jazz people know
all about Rothenberg and regular tempering (lol, I wish), they've made
use of the fact that 128/125 is tempered out, and hence D-Gb is an
ambiguous interval and could also be D-F#, and so they do use it that
way. This has a different sound to it than the other one - it's a bit
more poignant and in some cases a bit "dirtier" sounding.

The other canon jazz trick, which isn't used so much when a dom7 is
going to minor but rather as an alternate way to go to major, is to
use the octatonic scale (the one that starts on a half step and then a
whole step). So if you're going Dm7->G7->Cmaj, and you want to put a
b9 and a and say a natural 13 (or any other extension in that scale),
you can use the G octatonic scale. So play a G7omit 5 in the left
hand, and on top of it play C#maj -> Bbmaj -> Gmaj -> Emaj or any of
the usual diminished scale "tricks" that people love to abuse, and
then voice lead to Cmaj and you win internets.

So if you're going to play a dom7 chord with a b or a #9, and a #11,
and a b13, you're taught to use the octatonic scale instead of
something like C Db E F# G A Bb C. Note also that said scale is
improper, but if you add the ornamental D# you get the proper
octatonic scale. So knowing all about Rothenberg, they wanted to prove
him wrong in his paper 50 years in the future at the footnote at the
bottom of page 231 when he says that no examples have been studied in
which ornamental tones have been added to turn an improper scale into
a proper scale. They also place the octatonic scale in the middle of a
diatonic chord progression to take advantage of the fact that 648/625
and 81/80 are both tempered out in 12-tet. I mean, they didn't know
what the hell they were doing and just stumbled on it.

Anyways, I'm completely rambling now, but point is: if I could figure
out how to generalize the above to miracle and porcupine and such, I'd
be a happy, happy man :) And also, theories of how tonality works that
I've read so far generally leave all of the above out, and hence leave
me unsatisfied. And also hence why I am so adamant that scales besides
aeolian and ionian can be used to form tonal systems. I mean, when the
scale is changing on every chord like this and yet one note still ends
up being emphasized mentally as the tonic, the whole concept seems to
become meaningless...

> but to me its just a chord
> which needs a chromatic interval (b9). If there is some way
> to think of 7-limit tetrads as coming from a related sequence
> of miracle[10] modes, I suppose that'd be pretty dope, but
> you'll have to discover it because my lazy approach is more
> chord-centric and involves remembering as few scales as
> possible :0 -Carl

That's pretty much my life's mission right now, haha. :)

-Mike

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Hi Mike,
>
> > I can't get my head wrapped around it. What's the basic sonority
> > supposed to be, the neutral triad? Or is it that people are using
> > 4:5:7 as stable fifthless sonorities?
>
> Miracle is much more complex than porcupine, so there's no
> diatonic-size scale with complete chords. You can make
> neutral triads, but you only get them in half the modes
> and they're all at one end of the scale. So it requires
> chromatic notes for harmonization.

You are assuming you must use a MOS. In fact, there are non-MOS scales of about the same size using miracle tunings. I did a bunch of stuff along those lines, which was posted years ago. Digging it out might be a pain.

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

> > Miracle is much more complex than porcupine, so there's no
> > diatonic-size scale with complete chords. You can make
> > neutral triads, but you only get them in half the modes
> > and they're all at one end of the scale. So it requires
> > chromatic notes for harmonization.
>
> You are assuming you must use a MOS. In fact, there are non-MOS
> scales of about the same size using miracle tunings. I did a
> bunch of stuff along those lines, which was posted years ago.
> Digging it out might be a pain.

I never assume that, having been the first to describe,
for example, hanson[8]. The upper limit on "diatonic-size"
is in fact 10. There may be better miracle scales smaller
than 10, I haven't looked lately, but IIRC the small
generator makes them rather unlikely candidates. -Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:

> > You are assuming you must use a MOS. In fact, there are non-MOS
> > scales of about the same size using miracle tunings. I did a
> > bunch of stuff along those lines, which was posted years ago.
> > Digging it out might be a pain.
>
> I never assume that, having been the first to describe,
> for example, hanson[8]. The upper limit on "diatonic-size"
> is in fact 10. There may be better miracle scales smaller
> than 10, I haven't looked lately, but IIRC the small
> generator makes them rather unlikely candidates. -Carl
>

You're still assuming generated scales.

Gene wrote:
> You're still assuming generated scales.

That I am. What's the alternative? -Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Gene wrote:
> > You're still assuming generated scales.
>
> That I am. What's the alternative? -Carl

Here's one alternative: in terms of secors, the scale [-2 0 2 4 6 7 9 11 13 15]. There are 4 copies inside Blackjack, 14 inside Canasta, and so forth. It's a miracle tempering (or a portent tempering) of [21/20 8/7 6/5 21/16 11/8 3/2 8/5 7/4 11/6 2]. Here's something from the archives about it:

/tuning-math/message/2467

Gene wrote:

> > > You're still assuming generated scales.
> >
> > That I am. What's the alternative? -Carl
>
> Here's one alternative: in terms of secors, the scale
> [-2 0 2 4 6 7 9 11 13 15]. There are 4 copies inside
> Blackjack, 14 inside Canasta, and so forth. It's a miracle
> tempering (or a portent tempering) of [21/20 8/7 6/5
> 21/16 11/8 3/2 8/5 7/4 11/6 2]. Here's something from
> the archives about it:
>
> /tuning-math/message/2467

Leading to this?

!
Gene's decatonic
10
!
83.7
233.4
317.1
466.8
550.5
700.2
816.9
966.6
1050.3
2/1
!

Pretty interesting scale. Probably an improvement
on miracle[10] in many ways. -Carl

Bless you Carl, scl format I know how to deal with.

I'll give it a shot in the next few days.

Chris

>
> Leading to this?
>
> !
> Gene's decatonic
> 10
> !
> 83.7
> 233.4
> 317.1
> 466.8
> 550.5
> 700.2
> 816.9
> 966.6
> 1050.3
> 2/1
> !
>
> Pretty interesting scale. Probably an improvement
> on miracle[10] in many ways. -Carl
>
>

Shure. Note though, it doesn't solve the problem Mike
originally complained of -- the lack of complete chords in
a reasonable-size scale. That's unavoidable due to the
complexity of miracle tempering. However, as I said, this
may be an improvement on the 10-note MOS.

-Carl

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> Bless you Carl, scl format I know how to deal with.
>
> I'll give it a shot in the next few days.
>
> Chris
>
>
> >
> > Leading to this?
> >
> > !
> > Gene's decatonic
> > 10
> > !
> > 83.7
> > 233.4
> > 317.1
> > 466.8
> > 550.5
> > 700.2
> > 816.9
> > 966.6
> > 1050.3
> > 2/1
> > !
> >
> > Pretty interesting scale. Probably an improvement
> > on miracle[10] in many ways. -Carl
> >
> >
>

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

> Here's one alternative: in terms of secors, the scale [-2 0 2 4 6 7 9 11 13 15]. There are 4 copies inside Blackjack, 14 inside Canasta, and so forth. It's a miracle tempering (or a portent tempering) of [21/20 8/7 6/5 21/16 11/8 3/2 8/5 7/4 11/6 2].

Along the same lines, the miracle tempering of [12/11 8/7 5/4 21/16 10/7 3/2 80/49 7/4 15/8 2], which in terms of secors is [-9 -7 -5 -3 -2 -1 0 2 4 6], where now there are 6 copies in Blackjack and 16 in Canasta.

It occurs to me that looking for strictly proper scales in a linear temperament (with a given tuning) might actually be a bit easier than for equal temperaments, so I might give it a try. Certainly one way to generate scales appropriate to the temperament. There are already six 7-note proper scales of "miracle type" listed here:

http://xenharmonic.wikispaces.com/Strictly+proper+7-note+31edo+scales

On 9 September 2010 14:36, Mike Battaglia <battaglia01@...> wrote:

> I've been trying to wrap my head around it ever since I heard Chris
> Vaisvil's improv in blackjack. I can definitely get into blackjack,
> but I'm having more trouble with the 1+9 decatonic MOS, which is
> supposed to be "diatonic" basis for miracle, yes? I can't figure out
> how to make any sense out of it.

I used it as a basis for notation, and also as a diatonic basis for
chromatic alterations. It's like in a minor key, you have a 7 note
diatonic as the natural scale, but there are really 9 notes in the
gamut, and more as chromatic alterations. With Miracle, I'd write
with 10 notes to the octave, and use quommatic alterations freely.
So, you can think of major and minor triads as a altered versions of
the neutral triad. 6:7:9 is a different kind of chord because 6:7 is
two decimal steps instead of three.

What I've also done is write melodies in 10 notes to the octave
without alterations, and then fill in the accidentals so that the
harmony works. And I took 7 out of those 10 alterable notes to be the
equivalent of a diatonic, not the decimal scale.

I tended towards 4:6:7 as the basic chord, because it's easy to switch
between 8:7 and 7:6. I have examples of this under "Decimal
Counterpoint" but not with the notation. I do have notated Miracle
pieces, though.

Graham

On Thu, Sep 9, 2010 at 10:12 PM, Graham Breed <gbreed@...> wrote:
>
> I tended towards 4:6:7 as the basic chord, because it's easy to switch
> between 8:7 and 7:6. I have examples of this under "Decimal
> Counterpoint" but not with the notation. I do have notated Miracle
> pieces, though.
>
> Graham

I just heard the Decimal Counterpoint stuff for the first time -
really interesting. Do you have any examples of 4-voice counterpoint
or the like? Or any rendered examples of music in Miracle? It has a
very dissonant and dark sound to it, much more so than either diatonic
or porcupine.

-Mike

PS: How are you writing this stuff, in Scala? I need to figure something out.

On Thu, Sep 9, 2010 at 10:35 PM, Mike Battaglia <battaglia01@...> wrote:
> PS: How are you writing this stuff, in Scala? I need to figure something out.

PPS: I just heard this too, this is awesome:
http://x31eq.com/music/dingsheng.mp3

Is this in some kind of 7-limit version of magic temperament? Did you
do this with a generalized keyboard?

-Mike

On 10 September 2010 10:35, Mike Battaglia <battaglia01@...> wrote:

> I just heard the Decimal Counterpoint stuff for the first time -
> really interesting. Do you have any examples of 4-voice counterpoint
> or the like? Or any rendered examples of music in Miracle? It has a
> very dissonant and dark sound to it, much more so than either diatonic
> or porcupine.

No, I didn't get to 4 voice counterpoint, at least in the exercises.

My music's here:

http://x31eq.com/music/

When I Set Out for Lyonnesse is in miracle, with notation, and some
counterpoint.

> PS: How are you writing this stuff, in Scala? I need to figure something out.

The decimal counterpoint was step-recorded through MIDI and played with Kyma.

Graham