Miracle scales in Miracle notation

Inspired by Graham's webpage, I made an attempt at a systematic
Miracle notation. The 4:5:6:7:11 chord is spelled C F# J L# Hb.
Here are the three scales with ASCII equivalents:

21-tone Miracle scale "Blackjack"
0: 1/1 C unison, perfect prime
1: 33.333 cents C# Dbb;
2: 116.667 cents D
3: 150.000 cents D# Ebb;
4: 233.333 cents E
5: 266.667 cents E# Fbb;
6: 350.000 cents F
7: 383.333 cents F# Gbb;
8: 466.667 cents G
9: 500.000 cents G# Hbb;
10: 583.333 cents H
11: 616.667 cents H# Jbb;
12: 700.000 cents J
13: 733.333 cents J# Kbb;
14: 816.667 cents K
15: 850.000 cents K# Lbb;
16: 933.333 cents L
17: 966.667 cents L# Abb;
18: 1050.000 cents A
19: 1083.333 cents A# Bbb;
20: 1166.667 cents B Cb
21: 2/1 C octave

31-tone Miracle scale
0: 1/1 C unison, perfect prime
1: 33.333 cents C# Dbb;
2: 83.333 cents Cx| Db
3: 116.667 cents D
4: 150.000 cents D# Ebb;
5: 200.000 cents Dx| Eb
6: 233.333 cents E
7: 266.667 cents E# Fbb;
8: 316.667 cents Ex| Fb
9: 350.000 cents F
10: 383.333 cents F# Gbb;
11: 433.333 cents Fx| Gb
12: 466.667 cents G
13: 500.000 cents G# Hbb;
14: 550.000 cents Gx| Hb
15: 583.333 cents H
16: 616.667 cents H# Jbb;
17: 650.000 cents Hx Jb;
18: 700.000 cents J
19: 733.333 cents J# Kbb;
20: 766.667 cents Jx Kb;
21: 816.667 cents K
22: 850.000 cents K# Lbb;
23: 883.333 cents Kx Lb;
24: 933.333 cents L
25: 966.667 cents L# Abb;
26: 1000.000 cents Lx Ab;
27: 1050.000 cents A
28: 1083.333 cents A# Bbb;
29: 1116.667 cents Ax Bb;
30: 1166.667 cents B Cb
31: 2/1 C octave

41-tone Miracle scale
0: 1/1 C unison, perfect prime
1: 33.333 cents C# Dbb;
2: 66.667 cents Cx Db;
3: 83.333 cents Cx| Db
4: 116.667 cents D
5: 150.000 cents D# Ebb;
6: 183.333 cents Dx Eb;
7: 200.000 cents Dx| Eb
8: 233.333 cents E
9: 266.667 cents E# Fbb;
10: 300.000 cents Ex Fb;
11: 316.667 cents Ex| Fb
12: 350.000 cents F
13: 383.333 cents F# Gbb;
14: 416.667 cents Fx Gb;
15: 433.333 cents Fx| Gb
16: 466.667 cents G
17: 500.000 cents G# Hbb;
18: 533.333 cents Gx Hb;
19: 550.000 cents Gx| Hb
20: 583.333 cents H
21: 616.667 cents H# Jbb;
22: 650.000 cents Hx Jb;
23: 666.667 cents Hx| Jb
24: 700.000 cents J
25: 733.333 cents J# Kbb;
26: 766.667 cents Jx Kb;
27: 783.333 cents Jx| Kb
28: 816.667 cents K
29: 850.000 cents K# Lbb;
30: 883.333 cents Kx Lb;
31: 900.000 cents Kx| Lb
32: 933.333 cents L
33: 966.667 cents L# Abb;
34: 1000.000 cents Lx Ab;
35: 1016.667 cents Lx| Ab
36: 1050.000 cents A
37: 1083.333 cents A# Bbb;
38: 1116.667 cents Ax Bb;
39: 1133.333 cents Ax| Bb
40: 1166.667 cents B Cb
41: 2/1 C octave

Manuel

Manuel Op De Coul wrote:

> Inspired by Graham's webpage, I made an attempt at a systematic
> Miracle notation. The 4:5:6:7:11 chord is spelled C F# J L# Hb.
> Here are the three scales with ASCII equivalents:

Manuel, you seem to have changed every possible aspect of my notation!
I'll explain my logic, so you can say why you disagree

Using 10 symbols for an octave:

The 10 note scale in 31 or 41 is an approximation to 10-equal.
There's a word for this, I forget what, but it's useful for notation.

Using numbers for names:

There are 10 notes to my scale and we have 10 digits. So make it
digital! It also happens that the numbers denote generators from the
root, which is an elegant feature that I find makes the notation much
easier to use. Numbers also mean there's no confusion with existing
note names.

Placing the "wolf" between 9 and 0:

In this case, a chain of generators is also a melodic scale, so you
don't have to remember both a diatonic or chromatic scale and a cycle
of fifths. Except in your notation, the discontinuity is between B
and C, so A to L isn't a chain of generators.

Using ^ and v for raising and lowering

Although we can't be fully consistent with all existing notations, ^
and v have some history of use for shifts of around the size I use
them for. That also leaves # and b free for a chromatic semitone-like
shift, probably ^^^ and vvv. You're also using ; for a reason I don't
fully understand. I thought about / for the difference between 0 and
1vvv, but decided it isn't needed yet and wouldn't always have that
meaning when it is used.

I think that covers it,

Graham

Graham, thanks for the critique.

>Using 10 symbols for an octave

I chose to have 11 symbols because I wanted to extend the chain
of generators as far as to the point of getting a smaller interval.
The generator is the "whole tone" in this case, and the "semitone"
what's left over (2/72 octave). Then we can think of the Blackjack
scale being made of 11 "diatonic" tones and 10 "chromatic" ones.
The 31-tone Miracle scale then adds 10 more "chromatic" tones and
the 41-tone 10 more than those.
Then a modulation down one generating interval introduces one sharp
more in the "diatonic" scale. Ok, that's the opposite of what we're
used to, but not a major drawback I think. The alternative would mean
that the sharp is much higher than the flat of the next tone, with a
"semitone" of 5/72 octave.
By the way I thought it probably better to rearrange the names to
C H D E F J G K A L B C
making them easier to recognise.

>There are 10 notes to my scale and we have 10 digits.

I agree being able to use numbers is elegant.

>Placing the "wolf" between 9 and 0:
> In this case, a chain of generators is also a melodic scale, so you
>don't have to remember both a diatonic or chromatic scale and a cycle
>of fifths. Except in your notation, the discontinuity is between B
>and C, so A to L isn't a chain of generators.

I don't see your point? In any case B is the endpoint of both the
major diatonic chain and the 11-tone Miracle chain.

>Using ^ and v for raising and lowering

I used b and # because it's the chromatic alteration belonging to
this systematisation.

>You're also using ; for a reason I don't fully understand.

It's the ascii equivalent of a semiflat, and b; that of a sesquiflat.
I prefer to reserve / and \ for usage for the syntonic comma only.
Then the semiflat and -sharp can be used for the general case of
1/n part of a semitone where 1/n is one step, in this case of 72-tET.

Manuel

--- In tuning@y..., <manuel.op.de.coul@e...> wrote:

/tuning/topicId_22397.html#22453

Then we can think of the Blackjack
> scale being made of 11 "diatonic" tones and 10 "chromatic" ones.

Thank you, Manuel... This answered my previous question...

_________ _____ ____ _
Joseph Pehrson