More miracle scale blasts from the past

These were optimized to have as much 11-limit dyadic, triadic and tetradic harmony as possible, so they should be about as good as it gets for the size of the scale. Expressed in secors.

9 notes
[-6 -5 -4 0 1 2 3 8 9]

10 notes
[-2 -1 0 4 5 6 7 11 12 13]

11 notes
[0 2 4 6 8 10 11 13 15 17 19]

12 notes
[-3 -2 -1 0 3 4 5 6 7 11 12 13]

On Thu, Sep 9, 2010 at 8:52 PM, genewardsmith
<genewardsmith@...> wrote:
>
> These were optimized to have as much 11-limit dyadic, triadic and tetradic harmony as possible, so they should be about as good as it gets for the size of the scale. Expressed in secors.
>
> 9 notes
> [-6 -5 -4 0 1 2 3 8 9]
>
> 10 notes
> [-2 -1 0 4 5 6 7 11 12 13]
>
> 11 notes
> [0 2 4 6 8 10 11 13 15 17 19]
>
> 12 notes
> [-3 -2 -1 0 3 4 5 6 7 11 12 13]

Hi Gene,

I'm technologically stupid here, how do I load this up into Scala? Is
there some way to type in the generator size and the scale factors and
use it to make a scale? Scala's the only software I really use.

Also I know you have an enormous amount of music written... have you
done anything in miracle?

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Thu, Sep 9, 2010 at 8:52 PM, genewardsmith
> <genewardsmith@...> wrote:
> >
> > These were optimized to have as much 11-limit dyadic, triadic and tetradic harmony as possible, so they should be about as good as it gets for the size of the scale. Expressed in secors.
> >
> > 9 notes
> > [-6 -5 -4 0 1 2 3 8 9]

! mir9.scl
Mir9
9
!
116.7156
233.4312
350.1468
499.7064
616.4220
733.1376
933.7248
1050.4403
1200.0000

> > 10 notes
> > [-2 -1 0 4 5 6 7 11 12 13]

! mir10.scl
Mir10
10
!
83.8715
200.5871
317.3027
466.8624
583.578
700.2936
817.0092
966.5688
1083.2844
1200.0000

> > 11 notes
> > [0 2 4 6 8 10 11 13 15 17 19]

! mir11.scl
Mir11
11
!
83.8715
233.4312
317.3027
466.8624
550.7339
700.2936
784.1651
933.7248
1017.5963
1167.1559
1200.0000

> > 12 notes
> > [-3 -2 -1 0 3 4 5 6 7 11 12 13]

! mir12.scl
Mir12
12
!
83.8715
200.5871
317.3027
350.1468
466.8624
583.5780
700.2936
817.0092
849.8532
966.5688
1083.2844
1200.0000

> Also I know you have an enormous amount of music written... have you
> done anything in miracle?

Several pieces. Here's one:

http://www.archive.org/details/RachmaninoffPlaysBlackjack

On Fri, Sep 10, 2010 at 12:16 AM, genewardsmith
<genewardsmith@...> wrote:
>
> > > 10 notes
> > > [-2 -1 0 4 5 6 7 11 12 13]
>
> ! mir10.scl
> Mir10
> 10
> !
> 83.8715
> 200.5871
> 317.3027
> 466.8624
> 583.578
> 700.2936
> 817.0092
> 966.5688
> 1083.2844
> 1200.0000

^ I found this one really interesting. If you start on second mode of
the scale, it turns into a miracle re-tempering of Paul's pajara
standard pentachordal major scale, with some maj/minor triads replaced
with neutral ones. Perhaps Paul's scale has something of an ideal
miracle re-tempering.

> > > 11 notes
> > > [0 2 4 6 8 10 11 13 15 17 19]
>
> ! mir11.scl
> Mir11
> 11
> !
> 83.8715
> 233.4312
> 317.3027
> 466.8624
> 550.7339
> 700.2936
> 784.1651
> 933.7248
> 1017.5963
> 1167.1559
> 1200.0000

This one is really magical, my favorite of the lot. I just wish I
could wrap my head around what miracle -is-, rather than just a neat
way to get arbitrarily close to JI. Are there any really intuitive
miracle "puns" that can be taken advantage of?

> > > 12 notes
> > > [-3 -2 -1 0 3 4 5 6 7 11 12 13]

This one was nice as well.

> > Also I know you have an enormous amount of music written... have you
> > done anything in miracle?
>
> Several pieces. Here's one:
>
> http://www.archive.org/details/RachmaninoffPlaysBlackjack

Thanks for this, I really enjoyed it. I'm not hip enough to know the
reference - what was the original piece that was mutated?

BTW, I sent you an offlist about your "Ostinato" piece... hopefully
you got it, I know there was some email trouble last time :)

-Mike

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

> This one is really magical, my favorite of the lot. I just wish I
> could wrap my head around what miracle -is-, rather than just a neat
> way to get arbitrarily close to JI. Are there any really intuitive
> miracle "puns" that can be taken advantage of?

Miracle tempers out 225/224, 1029/1024, 243/242, 385/384, 441/440, 540/539 and 2401/2400, all of which have their puns. 1029/1024 tells us that three 8/7s make up a 3/2, and there is an 8/7-8/7-8/7-8/7-7/6 chord. 225/224 tells us that 15/14 and 16/15 are identified, and that there is a 5/4-5/4-9/7 augmented triad, whereas 441/440 tells us that 21/20 and 22/21 are identified. 385/384 tells us that 48/35, which like 15/14 nd 21/20 is a diagonal of the hexany, and related to voice leading questions, may be identified with 11/8. 243/242 tells us that 11/9 is identified as a half-fifth neutral third.

> > > Also I know you have an enormous amount of music written... have you
> > > done anything in miracle?
> >
> > Several pieces. Here's one:
> >
> > http://www.archive.org/details/RachmaninoffPlaysBlackjack
>
> Thanks for this, I really enjoyed it. I'm not hip enough to know the
> reference - what was the original piece that was mutated?

The second theme of the third movement of Rachmaninoff's second piano oncerto.

> BTW, I sent you an offlist about your "Ostinato" piece... hopefully
> you got it, I know there was some email trouble last time :)

Just checked, and I got it.