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Chromatic Modes

🔗Keenan Pepper <mtpepper@prodigy.net>

10/8/2000 3:13:22 PM

Every good music student knows the names of the 7 modes of the diatonic
scale:

C-D-E-F#-G-A-B-C "Lydian"
C-D-E-F-G-A-B-C "Ionian"
C-D-E-F-G-A-Bb-C "Mixolydian"
C-D-Eb-F-G-A-Bb-C "Dorian"
C-D-Eb-F-G-Ab-Bb-C "Aeolian"
C-Db-Eb-F-G-Ab-Bb-C "Phrygian"
C-Db-Eb-F-Gb-Ab-Bb-C "Locrian"

Has anyone come up with names for the 12 modes of the chromatic scale yet?

C-C#-D-D#-E-E#-F#-G-G#-A-A#-B-C
C-C#-D-D#-E-F-F#-G-G#-A-A#-B-C
C-C#-D-D#-E-F-F#-G-G#-A-Bb-B-C
C-C#-D-Eb-E-F-F#-G-G#-A-Bb-B-C
C-C#-D-Eb-E-F-F#-G-Ab-A-Bb-B-C
C-Db-D-Eb-E-F-F#-G-Ab-A-Bb-B-C
C-Db-D-Eb-E-F-Gb-G-Ab-A-Bb-B-C
C-Db-D-Eb-E-F-Gb-G-Ab-A-Bb-Cb-C
C-Db-D-Eb-Fb-F-Gb-G-Ab-A-Bb-Cb-C
C-Db-D-Eb-Fb-F-Gb-G-Ab-Bbb-Bb-Cb-C
C-Db-Ebb-Eb-Fb-F-Gb-G-Ab-Bbb-Bb-Cb-C
C-Db-Ebb-Eb-Fb-F-Gb-Abb-Ab-Bbb-Bb-Cb-C

Keenan P.

🔗M. Edward Borasky <znmeb@teleport.com>

10/8/2000 3:27:48 PM

> -----Original Message-----
> From: Keenan Pepper [mailto:mtpepper@prodigy.net]
> Sent: Sunday, October 08, 2000 3:13 PM
> To: tuning@egroups.com
> Subject: [tuning] Chromatic Modes
>
>
> Every good music student knows the names of the 7 modes of the diatonic
> scale:
>
> C-D-E-F#-G-A-B-C "Lydian"
> C-D-E-F-G-A-B-C "Ionian"
> C-D-E-F-G-A-Bb-C "Mixolydian"
> C-D-Eb-F-G-A-Bb-C "Dorian"
> C-D-Eb-F-G-Ab-Bb-C "Aeolian"
> C-Db-Eb-F-G-Ab-Bb-C "Phrygian"
> C-Db-Eb-F-Gb-Ab-Bb-C "Locrian"

I don't know about music students, but Appalachian dulcimer players do :-)

> Has anyone come up with names for the 12 modes of the chromatic scale yet?
>
> C-C#-D-D#-E-E#-F#-G-G#-A-A#-B-C
> C-C#-D-D#-E-F-F#-G-G#-A-A#-B-C
> C-C#-D-D#-E-F-F#-G-G#-A-Bb-B-C
> C-C#-D-Eb-E-F-F#-G-G#-A-Bb-B-C
> C-C#-D-Eb-E-F-F#-G-Ab-A-Bb-B-C
> C-Db-D-Eb-E-F-F#-G-Ab-A-Bb-B-C
> C-Db-D-Eb-E-F-Gb-G-Ab-A-Bb-B-C
> C-Db-D-Eb-E-F-Gb-G-Ab-A-Bb-Cb-C
> C-Db-D-Eb-Fb-F-Gb-G-Ab-A-Bb-Cb-C
> C-Db-D-Eb-Fb-F-Gb-G-Ab-Bbb-Bb-Cb-C
> C-Db-Ebb-Eb-Fb-F-Gb-G-Ab-Bbb-Bb-Cb-C
> C-Db-Ebb-Eb-Fb-F-Gb-Abb-Ab-Bbb-Bb-Cb-C

What intervals do these scales represent?

🔗Keenan Pepper <mtpepper@prodigy.net>

10/10/2000 2:17:51 PM

> What intervals do these scales represent?

Oh, sorry. I meant "in any meantone between 7-eq to 12-eq," but I forgot to
write it. Something like 19-eq or 26-eq allows the differences to be heard
clearly. I was assuming that chromatic semitones were always smaller that
diatonic semitones, which is obviously false without that condition.
If no one has names for the modes I'll make some up myself.

Keenan P.

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

10/10/2000 2:15:07 PM

Hi Keenan.

You 12-out-of-19 scale is Yasser's basic scale. Have you read Yasser's book?
It's pretty crazy, but some of these modes would at least get some mention.

Paul.

🔗D.Stearns <STEARNS@CAPECOD.NET>

10/10/2000 6:43:01 PM

Paul H. Erlich wrote,

> You 12-out-of-19 scale is Yasser's basic scale. Have you read
Yasser's book? It's pretty crazy, but some of these modes would at
least get some mention.

Here's the Silver, Equal, and Golden, 5s7L and 7s5L. I put the first
rotations in a sLsLL and LsLss tetrachordal arrangement.

The 12-tone 5s & 7L:

0 74 192 266 385 504 577 696 770 889 962 1081 1200
0 119 192 311 430 504 623 815 815 889 1008 1126 1200
0 74 192 311 385 504 696 770 770 889 1008 1081 1200
0 119 238 311 430 623 696 815 815 934 1008 1126 1200
0 119 192 311 504 577 696 815 815 889 1008 1081 1200
0 74 192 385 458 577 696 770 770 889 962 1081 1200
0 119 311 385 504 623 696 815 815 889 1008 1126 1200
0 192 266 385 504 577 696 770 770 889 1008 1081 1200
0 74 192 311 385 504 577 696 696 815 889 1008 1200
0 119 238 311 430 504 623 742 742 815 934 1126 1200
0 119 192 311 385 504 623 696 696 815 1008 1081 1200

0 63 189 253 379 505 568 695 758 884 947 1074 1200
0 126 189 316 442 505 632 821 821 884 1011 1137 1200
0 63 189 316 379 505 695 758 758 884 1011 1074 1200
0 126 253 316 442 632 695 821 821 947 1011 1137 1200
0 126 189 316 505 568 695 821 821 884 1011 1074 1200
0 63 189 379 442 568 695 758 758 884 947 1074 1200
0 126 316 379 505 632 695 821 821 884 1011 1137 1200
0 189 253 379 505 568 695 758 758 884 1011 1074 1200
0 63 189 316 379 505 568 695 695 821 884 1011 1200
0 126 253 316 442 505 632 758 758 821 947 1137 1200
0 126 189 316 379 505 632 695 695 821 1011 1074 1200

0 55 187 242 374 506 561 694 748 881 935 1068 1200
0 132 187 319 452 506 639 826 826 881 1013 1145 1200
0 55 187 319 374 506 694 748 748 881 1013 1068 1200
0 132 265 319 452 639 694 826 826 958 1013 1145 1200
0 132 187 319 506 561 694 826 826 881 1013 1068 1200
0 55 187 374 429 561 694 748 748 881 935 1068 1200
0 132 319 374 506 639 694 826 826 881 1013 1145 1200
0 187 242 374 506 561 694 748 748 881 1013 1068 1200
0 55 187 319 374 506 561 694 694 826 881 1013 1200
0 132 265 319 452 506 639 771 771 826 958 1145 1200
0 132 187 319 374 506 639 694 694 826 1013 1068 1200

The 12-tone 7s & 5L:

0 129 208 337 416 496 625 704 833 912 1041 1120 1200
0 80 208 288 367 496 575 784 784 912 992 1071 1200
0 129 208 288 416 496 704 833 833 912 992 1120 1200
0 80 159 288 367 575 704 784 784 863 992 1071 1200
0 80 208 288 496 625 704 784 784 912 992 1120 1200
0 129 208 416 545 625 704 833 833 912 1041 1120 1200
0 80 288 416 496 575 704 784 784 912 992 1071 1200
0 208 337 416 496 625 704 833 833 912 992 1120 1200
0 129 208 288 416 496 625 704 704 784 912 992 1200
0 80 159 288 367 496 575 655 655 784 863 1071 1200
0 80 208 288 416 496 575 704 704 784 992 1120 1200

0 141 212 353 424 494 635 706 847 918 1059 1129 1200
0 71 212 282 353 494 565 776 776 918 988 1059 1200
0 141 212 282 424 494 706 847 847 918 988 1129 1200
0 71 141 282 353 565 706 776 776 847 988 1059 1200
0 71 212 282 494 635 706 776 776 918 988 1129 1200
0 141 212 424 565 635 706 847 847 918 1059 1129 1200
0 71 282 424 494 565 706 776 776 918 988 1059 1200
0 212 353 424 494 635 706 847 847 918 988 1129 1200
0 141 212 282 424 494 635 706 706 776 918 988 1200
0 71 141 282 353 494 565 635 635 776 847 1059 1200
0 71 212 282 424 494 565 706 706 776 988 1129 1200

0 152 215 367 430 493 644 707 859 922 1074 1137 1200
0 63 215 278 341 493 556 770 770 922 985 1048 1200
0 152 215 278 430 493 707 859 859 922 985 1137 1200
0 63 126 278 341 556 707 770 770 833 985 1048 1200
0 63 215 278 493 644 707 770 770 922 985 1137 1200
0 152 215 430 582 644 707 859 859 922 1074 1137 1200
0 63 278 430 493 556 707 770 770 922 985 1048 1200
0 215 367 430 493 644 707 859 859 922 985 1137 1200
0 152 215 278 430 493 644 707 707 770 922 985 1200
0 63 126 278 341 493 556 618 618 770 833 1048 1200
0 63 215 278 430 493 556 707 707 770 985 1137 1200

So if one calls these "scales", then their single generator
two-stepsize MOS scales without Myhill's property... right?

--Dan Stearns

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

10/10/2000 3:36:23 PM

Dan wrote,

>So if one calls these "scales", then their single generator
>two-stepsize MOS scales without Myhill's property... right?

That's impossible. Any non-Myhill scale must have more than a single
generator. Look again at your scales.

🔗Jon Wild <wild@fas.harvard.edu>

10/10/2000 3:51:28 PM

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:

> Any non-Myhill scale must have more than a single generator.

I don't think so - the 7-note scale I mentioned before, generated by
taking the fraction (phi+1)/(3phi+2) of an octave six times, has got
three sizes of seconds.

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

10/10/2000 3:43:21 PM

I wrote,

>> Any non-Myhill scale must have more than a single generator.

Jon wrote,

>I don't think so - the 7-note scale I mentioned before, generated by
>taking the fraction (phi+1)/(3phi+2) of an octave six times, has got
>three sizes of seconds.

Oops, I meant any two-step-size non-Myhill scale has got to have more than a
single generator.

(Dan wrote: "So if one calls these "scales", then their single generator
two-stepsize MOS scales without Myhill's property... right?")

🔗D.Stearns <STEARNS@CAPECOD.NET>

10/10/2000 6:58:51 PM

Paul H. Erlich wrote,

> That's impossible. Any non-Myhill scale must have more than a single
generator. Look again at your scales.

Wait a minute, didn't you write "MOS scales, though, have
Myhill's property -- every generic interval size (except the unison)
comes in _exactly_ two specific sizes"... these 12-tone scales are all
two-stepsize single generator scales with as many as 4 different
interval sizes in some cases; see the "11ths" for example.

--Dan Stearns

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

10/10/2000 3:52:54 PM

Dan wrote,

>Wait a minute, didn't you write "MOS scales, though, have
>Myhill's property -- every generic interval size (except the unison)
>comes in _exactly_ two specific sizes"... these 12-tone scales are all
>two-stepsize single generator scales with as many as 4 different
>interval sizes in some cases; see the "11ths" for example.

You made an error -- even the 2nds come in three different sizes in the
scales you typed.

🔗D.Stearns <STEARNS@CAPECOD.NET>

10/10/2000 7:14:12 PM

I wrote,

> Wait a minute,

Wait a minute indeed! All a blunder on my part... the 12-tone scales I
posted earlier contained an obvious error that I totally went to sleep
on. My fault -- sorry!

Here's that whole post again as intended.

Here's the Silver, Equal, and Golden, 5s7L and 7s5L. I put the first
rotations in a sLsLL and LsLss tetrachordal arrangement.

The 12-tone 5s & 7L:

0 74 192 266 385 504 577 696 770 889 962 1081 1200
0 119 192 311 430 504 623 696 815 889 1008 1126 1200
0 74 192 311 385 504 577 696 770 889 1008 1081 1200
0 119 238 311 430 504 623 696 815 934 1008 1126 1200
0 119 192 311 385 504 577 696 815 889 1008 1081 1200
0 74 192 266 385 458 577 696 770 889 962 1081 1200
0 119 192 311 385 504 623 696 815 889 1008 1126 1200
0 74 192 266 385 504 577 696 770 889 1008 1081 1200
0 119 192 311 430 504 623 696 815 934 1008 1126 1200
0 74 192 311 385 504 577 696 815 889 1008 1081 1200
0 119 238 311 430 504 623 742 815 934 1008 1126 1200

0 63 189 253 379 505 568 695 758 884 947 1074 1200
0 126 189 316 442 505 632 695 821 884 1011 1137 1200
0 63 189 316 379 505 568 695 758 884 1011 1074 1200
0 126 253 316 442 505 632 695 821 947 1011 1137 1200
0 126 189 316 379 505 568 695 821 884 1011 1074 1200
0 63 189 253 379 442 568 695 758 884 947 1074 1200
0 126 189 316 379 505 632 695 821 884 1011 1137 1200
0 63 189 253 379 505 568 695 758 884 1011 1074 1200
0 126 189 316 442 505 632 695 821 947 1011 1137 1200
0 63 189 316 379 505 568 695 821 884 1011 1074 1200
0 126 253 316 442 505 632 758 821 947 1011 1137 1200

0 55 187 242 374 506 561 694 748 881 935 1068 1200
0 132 187 319 452 506 639 694 826 881 1013 1145 1200
0 55 187 319 374 506 561 694 748 881 1013 1068 1200
0 132 265 319 452 506 639 694 826 958 1013 1145 1200
0 132 187 319 374 506 561 694 826 881 1013 1068 1200
0 55 187 242 374 429 561 694 748 881 935 1068 1200
0 132 187 319 374 506 639 694 826 881 1013 1145 1200
0 55 187 242 374 506 561 694 748 881 1013 1068 1200
0 132 187 319 452 506 639 694 826 958 1013 1145 1200
0 55 187 319 374 506 561 694 826 881 1013 1068 1200
0 132 265 319 452 506 639 771 826 958 1013 1145 1200

The 12-tone 7s & 5L:

0 129 208 337 416 496 625 704 833 912 1041 1120 1200
0 80 208 288 367 496 575 704 784 912 992 1071 1200
0 129 208 288 416 496 625 704 833 912 992 1120 1200
0 80 159 288 367 496 575 704 784 863 992 1071 1200
0 80 208 288 416 496 625 704 784 912 992 1120 1200
0 129 208 337 416 545 625 704 833 912 1041 1120 1200
0 80 208 288 416 496 575 704 784 912 992 1071 1200
0 129 208 337 416 496 625 704 833 912 992 1120 1200
0 80 208 288 367 496 575 704 784 863 992 1071 1200
0 129 208 288 416 496 625 704 784 912 992 1120 1200
0 80 159 288 367 496 575 655 784 863 992 1071 1200

0 141 212 353 424 494 635 706 847 918 1059 1129 1200
0 71 212 282 353 494 565 706 776 918 988 1059 1200
0 141 212 282 424 494 635 706 847 918 988 1129 1200
0 71 141 282 353 494 565 706 776 847 988 1059 1200
0 71 212 282 424 494 635 706 776 918 988 1129 1200
0 141 212 353 424 565 635 706 847 918 1059 1129 1200
0 71 212 282 424 494 565 706 776 918 988 1059 1200
0 141 212 353 424 494 635 706 847 918 988 1129 1200
0 71 212 282 353 494 565 706 776 847 988 1059 1200
0 141 212 282 424 494 635 706 776 918 988 1129 1200
0 71 141 282 353 494 565 635 776 847 988 1059 1200

Again, my apologies to all for the confusion (Paul especially).

--Dan Stearns

🔗D.Stearns <STEARNS@CAPECOD.NET>

10/10/2000 7:20:16 PM

Hmm, I can't seem to get anything quite right today -- I omitted the
silver 7s5L from that last post <no more, I promise!>...

0 152 215 367 430 493 644 707 859 922 1074 1137 1200
0 63 215 278 341 493 556 707 770 922 985 1048 1200
0 152 215 278 430 493 644 707 859 922 985 1137 1200
0 63 126 278 341 493 556 707 770 833 985 1048 1200
0 63 215 278 430 493 644 707 770 922 985 1137 1200
0 152 215 367 430 582 644 707 859 922 1074 1137 1200
0 63 215 278 430 493 556 707 770 922 985 1048 1200
0 152 215 367 430 493 644 707 859 922 985 1137 1200
0 63 215 278 341 493 556 707 770 833 985 1048 1200
0 152 215 278 430 493 644 707 770 922 985 1137 1200
0 63 126 278 341 493 556 618 770 833 985 1048 1200

----- Original Message -----
From: D.Stearns <stearns@capecod.net>
To: <tuning@egroups.com>
Sent: Tuesday, October 10, 2000 7:14 PM
Subject: Re: [tuning] Chromatic Modes

> I wrote,
>
>
> > Wait a minute,
>
> Wait a minute indeed! All a blunder on my part... the 12-tone scales
I
> posted earlier contained an obvious error that I totally went to
sleep
> on. My fault -- sorry!
>
> Here's that whole post again as intended.
>
> Here's the Silver, Equal, and Golden, 5s7L and 7s5L. I put the first
> rotations in a sLsLL and LsLss tetrachordal arrangement.
>
> The 12-tone 5s & 7L:
>
> 0 74 192 266 385 504 577 696 770 889 962 1081 1200
> 0 119 192 311 430 504 623 696 815 889 1008 1126 1200
> 0 74 192 311 385 504 577 696 770 889 1008 1081 1200
> 0 119 238 311 430 504 623 696 815 934 1008 1126 1200
> 0 119 192 311 385 504 577 696 815 889 1008 1081 1200
> 0 74 192 266 385 458 577 696 770 889 962 1081 1200
> 0 119 192 311 385 504 623 696 815 889 1008 1126 1200
> 0 74 192 266 385 504 577 696 770 889 1008 1081 1200
> 0 119 192 311 430 504 623 696 815 934 1008 1126 1200
> 0 74 192 311 385 504 577 696 815 889 1008 1081 1200
> 0 119 238 311 430 504 623 742 815 934 1008 1126 1200
>
> 0 63 189 253 379 505 568 695 758 884 947 1074 1200
> 0 126 189 316 442 505 632 695 821 884 1011 1137 1200
> 0 63 189 316 379 505 568 695 758 884 1011 1074 1200
> 0 126 253 316 442 505 632 695 821 947 1011 1137 1200
> 0 126 189 316 379 505 568 695 821 884 1011 1074 1200
> 0 63 189 253 379 442 568 695 758 884 947 1074 1200
> 0 126 189 316 379 505 632 695 821 884 1011 1137 1200
> 0 63 189 253 379 505 568 695 758 884 1011 1074 1200
> 0 126 189 316 442 505 632 695 821 947 1011 1137 1200
> 0 63 189 316 379 505 568 695 821 884 1011 1074 1200
> 0 126 253 316 442 505 632 758 821 947 1011 1137 1200
>
> 0 55 187 242 374 506 561 694 748 881 935 1068 1200
> 0 132 187 319 452 506 639 694 826 881 1013 1145 1200
> 0 55 187 319 374 506 561 694 748 881 1013 1068 1200
> 0 132 265 319 452 506 639 694 826 958 1013 1145 1200
> 0 132 187 319 374 506 561 694 826 881 1013 1068 1200
> 0 55 187 242 374 429 561 694 748 881 935 1068 1200
> 0 132 187 319 374 506 639 694 826 881 1013 1145 1200
> 0 55 187 242 374 506 561 694 748 881 1013 1068 1200
> 0 132 187 319 452 506 639 694 826 958 1013 1145 1200
> 0 55 187 319 374 506 561 694 826 881 1013 1068 1200
> 0 132 265 319 452 506 639 771 826 958 1013 1145 1200
>
> The 12-tone 7s & 5L:
>
> 0 129 208 337 416 496 625 704 833 912 1041 1120 1200
> 0 80 208 288 367 496 575 704 784 912 992 1071 1200
> 0 129 208 288 416 496 625 704 833 912 992 1120 1200
> 0 80 159 288 367 496 575 704 784 863 992 1071 1200
> 0 80 208 288 416 496 625 704 784 912 992 1120 1200
> 0 129 208 337 416 545 625 704 833 912 1041 1120 1200
> 0 80 208 288 416 496 575 704 784 912 992 1071 1200
> 0 129 208 337 416 496 625 704 833 912 992 1120 1200
> 0 80 208 288 367 496 575 704 784 863 992 1071 1200
> 0 129 208 288 416 496 625 704 784 912 992 1120 1200
> 0 80 159 288 367 496 575 655 784 863 992 1071 1200
>
> 0 141 212 353 424 494 635 706 847 918 1059 1129 1200
> 0 71 212 282 353 494 565 706 776 918 988 1059 1200
> 0 141 212 282 424 494 635 706 847 918 988 1129 1200
> 0 71 141 282 353 494 565 706 776 847 988 1059 1200
> 0 71 212 282 424 494 635 706 776 918 988 1129 1200
> 0 141 212 353 424 565 635 706 847 918 1059 1129 1200
> 0 71 212 282 424 494 565 706 776 918 988 1059 1200
> 0 141 212 353 424 494 635 706 847 918 988 1129 1200
> 0 71 212 282 353 494 565 706 776 847 988 1059 1200
> 0 141 212 282 424 494 635 706 776 918 988 1129 1200
> 0 71 141 282 353 494 565 635 776 847 988 1059 1200
>
> Again, my apologies to all for the confusion (Paul especially).
>
>
> --Dan Stearns
>