Miracle scale comparison

For Dave Keenan I did a "fuzzy" scale comparison with two Miracle
scales. The maximum difference has been set to 5 cents. This doesn't
say how close the scales actually are, only that the corresponding
tones for both are inside a small hypercube if you know what I mean.
The results for the two have been combined to save bandwidth.

(1) = only Miracle-21
(2) = only Miracle-31
= both

KEENAN5.SCL : approximate equal in key 0, diff. 3.1899 cents (2)
approximate subset of FJ-72TET.SCL size: 72, diff. 2.9804 cents
approximate subset of FJ-96TET.SCL size: 96, diff. 4.9354 cents (1)
approximate subset of KEENAN5.SCL size: 31, diff. 3.1899 cents (1)
approximate subset of PARTCH-UR.SCL size: 39, diff. 4.9354 cents
approximate subset of PARTCH_39.SCL size: 39, diff. 4.9354 cents
approximate subset of PARTCH_41A.SCL size: 41, diff. 4.9354 cents
approximate subset of PARTCH_43A.SCL size: 43, diff. 4.9354 cents
approximate superset of AL-FARABI.SCL size: 7, diff. 4.9354 cents
approximate superset of AL-FARABI_CHROM2.SCL size: 7, diff. 4.9354 cents
approximate superset of AL-FARABI_DIAT.SCL size: 7, diff. 4.3185 cents
approximate superset of AL-FARABI_DOR2.SCL size: 7, diff. 4.3185 cents
approximate superset of AL-FARABI_G5.SCL size: 7, diff. 3.9100 cents (2)
approximate superset of AL-FARABI_G6.SCL size: 7, diff. 3.9100 cents (2)
approximate superset of AL-FARABI_G7.SCL size: 7, diff. 4.7513 cents (2)
approximate superset of AUGTETK.SCL size: 6, diff. 3.9100 cents (2)
approximate superset of AWRAAMOFF.SCL size: 12, diff. 4.9354 cents (2)
approximate superset of CHIN_BRONZE.SCL size: 7, diff. 2.9804 cents (2)
approximate superset of CKRING1.SCL size: 13, diff. 2.9804 cents (2)
approximate superset of CLUSTER6A.SCL size: 6, diff. 4.9354 cents (2)
approximate superset of CLUSTER6B.SCL size: 6, diff. 4.9354 cents (2)
approximate superset of COHENF_11.SCL size: 11, diff. 2.9804 cents (2)
approximate superset of CONS11.SCL size: 7, diff. 2.9804 cents (2)
approximate superset of CONS12.SCL size: 8, diff. 2.9804 cents (2)
approximate superset of CONS13.SCL size: 10, diff. 2.9804 cents (2)
approximate superset of CONS8.SCL size: 4, diff. 1.9550 cents (2)
approximate superset of CONS9.SCL size: 5, diff. 2.9804 cents (2)
approximate superset of CONS_7.SCL size: 10, diff. 2.9804 cents (2)
approximate superset of CONS_7A.SCL size: 11, diff. 2.9804 cents (2)
approximate superset of CROSS2_5.SCL size: 9, diff. 4.9354 cents (2)
approximate superset of CROSS_7.SCL size: 7, diff. 2.9804 cents
approximate superset of CROSS_72.SCL size: 13, diff. 4.9354 cents (2)
approximate superset of DEKANY.SCL size: 10, diff. 3.1847 cents (2)
approximate superset of DEKANY2.SCL size: 10, diff. 4.9354 cents (2)
approximate superset of DEKANY3.SCL size: 10, diff. 4.9354 cents (2)
approximate superset of DIAMOND_CHESS.SCL size: 11, diff. 2.1592 cents (2)
approximate superset of DIAPHONIC_5.SCL size: 5, diff. 2.1592 cents
approximate superset of DIAPHONIC_7.SCL size: 7, diff. 3.9100 cents (2)
approximate superset of DIAT_SMAL.SCL size: 7, diff. 2.9804 cents (2)
approximate superset of DIMTETB.SCL size: 5, diff. 3.9100 cents (2)
approximate superset of DIV_FIFTH2.SCL size: 5, diff. 4.9354 cents
approximate superset of DIV_FIFTH4.SCL size: 5, diff. 4.1142 cents (2)
approximate superset of EFG333.SCL size: 4, diff. 3.9100 cents (2)
approximate superset of EFG335.SCL size: 6, diff. 4.9354 cents (2)
approximate superset of EFG3355.SCL size: 9, diff. 4.9354 cents (2)
approximate superset of EFG3377.SCL size: 9, diff. 4.1142 cents
approximate superset of EFG33777A.SCL size: 10, diff. 4.1142 cents
approximate superset of EFG355.SCL size: 6, diff. 4.9354 cents (2)
approximate superset of ENH_MOD.SCL size: 7, diff. 3.9100 cents (2)
approximate superset of ERLICH11.SCL size: 10, diff. 4.9354 cents (2)
approximate superset of ERLICH11S1.SCL size: 10, diff. 4.9354 cents (2)
approximate superset of FAREY3.SCL size: 5, diff. 2.9804 cents (2)
approximate superset of FAREY4.SCL size: 9, diff. 2.9804 cents (2)
approximate superset of FOKKER_12T.SCL size: 12, diff. 2.2988 cents (2)
approximate superset of FOKKER_12T2.SCL size: 12, diff. 2.2951 cents (2)
approximate superset of GAMELAN_OM.SCL size: 12, diff. 4.9354 cents (2)
approximate superset of GANN_GHOST.SCL size: 8, diff. 4.1142 cents (2)
approximate superset of GRADY7.SCL size: 12, diff. 4.9354 cents (2)
approximate superset of GRADY7T.SCL size: 12, diff. 2.6151 cents (2)
approximate superset of HAHN_7.SCL size: 12, diff. 2.9804 cents (2)
approximate superset of HANDBLUE.SCL size: 12, diff. 4.9354 cents (2)
approximate superset of HARM3.SCL size: 3, diff. 2.9804 cents
approximate superset of HARM6.SCL size: 6, diff. 3.9100 cents (2)
approximate superset of HARRISON_5.SCL size: 5, diff. 4.9354 cents (2)
approximate superset of HARRISON_5_1.SCL size: 5, diff. 2.9804 cents (2)
approximate superset of HARRISON_5_4.SCL size: 5, diff. 4.9354 cents (2)
approximate superset of HARRISON_JOY.SCL size: 6, diff. 4.9354 cents (2)
approximate superset of HARRISON_MID.SCL size: 7, diff. 3.9100 cents (2)
approximate superset of HARRISON_MIN.SCL size: 5, diff. 1.9550 cents (2)
approximate superset of HARRISON_MIX2.SCL size: 5, diff. 4.9354 cents (2)
approximate superset of HARRISON_MIX3.SCL size: 5, diff. 2.9804 cents (2)
approximate superset of HARRISON_MIX4.SCL size: 5, diff. 2.9804 cents
approximate superset of HELMHOLTZ.SCL size: 7, diff. 4.9354 cents
approximate superset of HEXANY10.SCL size: 6, diff. 4.9354 cents (2)
approximate superset of HEXANY11.SCL size: 6, diff. 4.1142 cents (2)
approximate superset of HEXANY15.SCL size: 5, diff. 2.9804 cents
approximate superset of HEXANY16.SCL size: 5, diff. 3.9100 cents (2)
approximate superset of HEXANY18.SCL size: 5, diff. 4.3185 cents
approximate superset of HEXANY19.SCL size: 5, diff. 2.9804 cents
approximate superset of HEXANY20.SCL size: 6, diff. 4.9354 cents (2)
approximate superset of HEXANY23.SCL size: 5, diff. 1.9550 cents (2)
approximate superset of HEXANY24.SCL size: 5, diff. 2.9804 cents (2)
approximate superset of HEXANY25.SCL size: 5, diff. 2.1592 cents (2)
approximate superset of HEXANY26.SCL size: 5, diff. 3.9100 cents (2)
approximate superset of HEXANY49.SCL size: 6, diff. 4.3185 cents
approximate superset of HEXANY9.SCL size: 6, diff. 3.1847 cents (2)
approximate superset of HEXANY_FLANK.SCL size: 12, diff. 3.1847 cents (2)
approximate superset of HEXANY_UNION.SCL size: 19, diff. 3.1847 cents (2)
approximate superset of HIRAJOSHI2.SCL size: 5, diff. 3.9100 cents (2)
approximate superset of HYPOD_CHROM2.SCL size: 7, diff. 4.9354 cents (2)
approximate superset of HYPOD_CHROM2INV.SCL size: 7, diff. 4.9354 cents (2)
approximate superset of INDIAN-DK.SCL size: 9, diff. 3.9100 cents (2)
approximate superset of INDIAN-RAJA.SCL size: 6, diff. 4.9354 cents (2)
approximate superset of JI_12A.SCL size: 12, diff. 4.9354 cents (2)
approximate superset of KRING1.SCL size: 7, diff. 2.9804 cents (2)
approximate superset of KRING2.SCL size: 7, diff. 2.1592 cents
approximate superset of KRING3.SCL size: 7, diff. 1.0254 cents (2)
approximate superset of KRING4.SCL size: 7, diff. 2.9804 cents
approximate superset of KRING6.SCL size: 7, diff. 1.9550 cents (2)
approximate superset of KROUSSEAU.SCL size: 12, diff. 4.1142 cents (2)
approximate superset of LUMMA.SCL size: 12, diff. 2.1592 cents (2)
approximate superset of LUMMADEC1.SCL size: 10, diff. 4.8387 cents
approximate superset of LUMMAK.SCL size: 12, diff. 1.5636 cents (2)
approximate superset of MAGIC.SCL size: 12, diff. 3.8016 cents (2)
approximate superset of MALCOLM_ME.SCL size: 7, diff. 4.9354 cents (2)
approximate superset of MINOR_5.SCL size: 5, diff. 3.9100 cents (2)
approximate superset of NEUTR_DIAT.SCL size: 7, diff. 3.9100 cents (2)
approximate superset of OCTONY_MIN.SCL size: 8, diff. 4.9354 cents (2)
approximate superset of PELOG_ALV.SCL size: 7, diff. 4.1142 cents (2)
approximate superset of PIPEDUM7_9.SCL size: 9, diff. 4.9354 cents
approximate superset of POOLE.SCL size: 7, diff. 3.9100 cents (2)
approximate superset of PRIME_5.SCL size: 5, diff. 3.9100 cents (2)
approximate superset of PS-ENH.SCL size: 7, diff. 4.9354 cents
approximate superset of PTOLEMY.SCL size: 7, diff. 4.9354 cents (2)
approximate superset of PTOLEMY_MALAK.SCL size: 7, diff. 3.9100 cents (2)
approximate superset of PTOLEMY_META.SCL size: 7, diff. 3.9100 cents (2)
approximate superset of PYGMIE.SCL size: 5, diff. 4.1142 cents
approximate superset of SCOTTJ.SCL size: 4, diff. 3.9100 cents (2)
approximate superset of SEV-ELEV.SCL size: 12, diff. 4.9354 cents (2)
approximate superset of SLENDRO5_1.SCL size: 5, diff. 2.1592 cents (2)
approximate superset of SLENDRO5_2.SCL size: 5, diff. 2.1592 cents
approximate superset of SLENDRO5_4.SCL size: 5, diff. 3.9100 cents (2)
approximate superset of SLENDRO_7_1.SCL size: 5, diff. 4.3185 cents
approximate superset of SLENDRO_7_2.SCL size: 5, diff. 4.1142 cents (2)
approximate superset of SLENDRO_7_3.SCL size: 5, diff. 3.9100 cents (2)
approximate superset of SLENDRO_7_4.SCL size: 5, diff. 4.1142 cents (2)
approximate superset of SLENDRO_7_5.SCL size: 5, diff. 4.5228 cents (2)
approximate superset of SLENDRO_A1.SCL size: 5, diff. 2.1592 cents
approximate superset of SLENDRO_A2.SCL size: 5, diff. 4.3185 cents
approximate superset of SLENDRO_ALV.SCL size: 5, diff. 3.9100 cents (2)
approximate superset of SLENDRO_M.SCL size: 5, diff. 2.1592 cents
approximate superset of SLENDRO_PB.SCL size: 5, diff. 2.6666 cents
approximate superset of SLENDRO_PC.SCL size: 5, diff. 2.6666 cents
approximate superset of SLENDRO_S1.SCL size: 5, diff. 4.1142 cents
approximate superset of SPON_TERP.SCL size: 5, diff. 2.5921 cents
approximate superset of STELTRI1.SCL size: 6, diff. 4.9354 cents (2)
approximate superset of SUPER_6.SCL size: 6, diff. 3.9100 cents (2)
approximate superset of TRIANG11.SCL size: 15, diff. 3.9100 cents (2)
approximate superset of TRITRIAD10.SCL size: 7, diff. 3.9100 cents (2)
approximate superset of TRITRIAD18.SCL size: 7, diff. 4.5471 cents (2)
approximate superset of TRITRIAD3C.SCL size: 7, diff. 1.6423 cents (2)
approximate superset of TRITRIAD68.SCL size: 7, diff. 3.9100 cents (2)
approximate superset of TRITRIAD68I.SCL size: 7, diff. 4.1142 cents (2)
approximate superset of TRITRIAD69.SCL size: 7, diff. 3.9100 cents (2)
approximate superset of TURKISH.SCL size: 7, diff. 4.9354 cents (2)
approximate superset of WAUCHOPE.SCL size: 8, diff. 2.9804 cents (2)
approximate superset of ZALZAL.SCL size: 7, diff. 4.5471 cents (2)
approximate superset of ZARLINO.SCL size: 7, diff. 4.9354 cents (2)
approximate superset of ZESSTER_C.SCL size: 8, diff. 4.1142 cents (2)
superset of ARIST_CHROM3.SCL size: 7
superset of ARIST_DIATDOR.SCL size: 7
superset of ARIST_DIATRED.SCL size: 7
superset of BREED4-3.SCL size: 7 (2)
superset of BREED7-3.SCL size: 10 (2)
superset of MOHAJIRA.SCL size: 7
superset of MOHA_BAYA.SCL size: 7 (2)
superset of MUSAQA.SCL size: 7 (2)
superset of RAST_MOHA.SCL size: 7 (2)
superset of XENAKIS_SCHROM.SCL size: 7

Manuel

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

/tuning/topicId_23116.html#23116

> For Dave Keenan I did a "fuzzy" scale comparison with two
> Miracle scales. The maximum difference has been set to 5 cents.
> This doesn't say how close the scales actually are, only that
> the corresponding tones for both are inside a small hypercube
> if you know what I mean. The results for the two have been
> combined to save bandwidth.
>
> <snip - really long list of approximated scales>

Whew!

And Joe Pehrson thinks *one* lifetime is enough
to explore MIRACLE!!

-monz
http://www.monz.org
"All roads lead to n^0"

--- In tuning@y..., <manuel.op.de.coul@e...> wrote:
>
> For Dave Keenan I did a "fuzzy" scale comparison with two Miracle
> scales. The maximum difference has been set to 5 cents. This doesn't
> say how close the scales actually are, only that the corresponding
> tones for both are inside a small hypercube if you know what I mean.
...

Thanks heaps Manuel. You're a miracle worker :-)

Some crude statistics from that:
Canasta (Miracle-31) is an approximate superset of about 160 scales. A
basket indeed.
But 31 is still a lot of notes, so it's possibly more significant that
Blackjack (Miracle-21) is an approximate superset of about 36 scales.

I'm afraid I'm not sure what you mean about the approximation. I
assume you mean you are only looking at the difference between
corresponding pitches, not the corresponding "11-limit consonant"
intervals. Comparing pitches is less strict than comparing all
intervals but more strict than comparing only "consononant" intervals.
Why "hypercube", why not simply "range". Does this refer only to
rational scales, where the dimensions are the primes?

In any case, this sure narrows the search, so that more detailed
comparison with these scales could be undertaken.

-- Dave Keenan

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:

/tuning/topicId_23116.html#23154

> Canasta (Miracle-31) is an approximate superset of about
> 160 scales. A basket indeed.

Well, then fate has spoken. Now I *have* to devote my
composing time to Canasta, since I'm already a basket case. :)

> But 31 is still a lot of notes, so it's possibly more
> significant that Blackjack (Miracle-21) is an approximate
> superset of about 36 scales.

I'm scared to ask this, for fear of the deluge of incomprehensible
math that's bound to ensue, but... actually how would one
measure this kind of thing? I can envision all sorts of
crisscrossing scales of importance based on whether any
given scale is a subset or a superset of another. .....?

-monz
http://www.monz.org
"All roads lead to n^0"

--- In tuning@y..., "monz" <joemonz@y...> wrote:

/tuning/topicId_23116.html#23166

> I'm scared to ask this, for fear of the deluge of incomprehensible
> math that's bound to ensue, but... actually how would one
> measure this kind of thing? I can envision all sorts of
> crisscrossing scales of importance based on whether any
> given scale is a subset or a superset of another. .....?

Wow, I just realized on rereading this that "scales of importance"
was a terrible choice of words.

Let's try "crisscrossing measurements of levels of importance".

-monz
http://www.monz.org
"All roads lead to n^0"

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

/tuning/topicId_23116.html#23116

>
> For Dave Keenan I did a "fuzzy" scale comparison with two Miracle
> scales. The maximum difference has been set to 5 cents. This doesn't
> say how close the scales actually are, only that the corresponding
> tones for both are inside a small hypercube if you know what I mean.
> The results for the two have been combined to save bandwidth.
>
> (1) = only Miracle-21
> (2) = only Miracle-31
> = both

Wow... this is cool. Thanks Manuel!! Saved it immediately.

________ ______ ______
Joseph Pehrson

Dave wrote:

>I'm afraid I'm not sure what you mean about the approximation. I
>assume you mean you are only looking at the difference between
>corresponding pitches, not the corresponding "11-limit consonant"
>intervals.

Yes.

>Why "hypercube", why not simply "range". Does this refer only to
>rational scales, where the dimensions are the primes?

No, the hypercube comes from imagining the scale itself as a vector,
i.e. each pitch is a vector component; nothing to do with ratio space.
So if you have two scales of the same size which are approximately
equal, the vector endpoints are within a hypercube with the size
equal to the maximum difference for each pitch. That's all.

Manuel