Yahoo Tuning Groups Ultimate Backup tuning MTT-24-like Fokker block

I said yesterday that a version of MTT-24 I posted was a Fokker block, but it isn't, quite. Below I give a Fokker block as similar as possible to MTT-24, and which seems like a decent scale to me.

! mttfokker.scl
!
MTT-24-like Fokker block in POTE parapyth tuning
! two chains of fifths 7/6 apart
24
!
58.33846
126.99416
185.33261
207.71262
266.05107
288.43108
393.04523
415.42523
473.76369
496.14369
554.48215
623.13785
681.47631
703.85631
762.19476
784.57477
889.18892
911.56892
969.90738
992.28738
1050.62584
1119.28154
1177.62000
1200.00000
!
!! mttfokkertrans.scl
!!
!2.3.7 transversal of mttfokker
!! 49/48: -9 to 14; 531441/524288 0 or 12
! 24
!!
! 28/27
! 2187/2048
! 567/512
! 9/8
! 7/6
! 32/27
! 5103/4096
! 81/64
! 21/16
! 4/3
! 112/81
! 729/512
! 189/128
! 3/2
! 14/9
! 128/81
! 1701/1024
! 27/16
! 7/4
! 16/9
! 448/243
! 243/128
! 63/32
! 2/1

🔗Mike Battaglia <battaglia01@...>

Margo's technique for generating scales is basically a generalization of
the Euler genus to temperaments, right? They're just rectangles on the
lattice, which may or may not be epimorphic.

The interesting thing about these scales, in regular temperament terms, is
that Margo seems to like rank-3 scales which are twice-over epimorphic. For
instance we can say that a scale which is "doubly epimorphic" has a val for
which there are two notes in the scale that map to every integer under the
val. You could probably have triply epimorphic scales as well. So maybe we
should call them Margo blocks (or Schulter blocks) and then note that Euler
genera are just these as applied to the JI lattice.

These scales are useful because if you think of the val as a central
organizing principle for the intervals in the scale, dividing them into
seconds, thirds, fourths, etc (or more generally, mapping-1, mapping-2,
mapping-3, etc intervals), it can be useful to have scales where there are
-deliberately- more than one of each type of interval being mapped to - but
the same amount for every interval type, and this appears to be what
Margo's intuitive approach for rank-3 scales is.

This is just a clever way of saying that her 24-note rank-3 scales tend to
have two things mapping to 0\12, 1\12, 2\12, 3\12, etc, so they're all
(probably) doubly epimorphic under some 12-note val.

(I note that I have no idea what the difference between an Euler genus and
a Euler-Fokker genus is.)

-Mike

On Thu, Nov 1, 2012 at 11:25 AM, genewardsmith
<genewardsmith@...>wrote:

> **
>
>
> I said yesterday that a version of MTT-24 I posted was a Fokker block, but
> it isn't, quite. Below I give a Fokker block as similar as possible to
> MTT-24, and which seems like a decent scale to me.
>
> ! mttfokker.scl
> !
> MTT-24-like Fokker block in POTE parapyth tuning
> ! two chains of fifths 7/6 apart
> 24
> !
> 58.33846
> 126.99416
> 185.33261
> 207.71262
> 266.05107
> 288.43108
> 393.04523
> 415.42523
> 473.76369
> 496.14369
> 554.48215
> 623.13785
> 681.47631
> 703.85631
> 762.19476
> 784.57477
> 889.18892
> 911.56892
> 969.90738
> 992.28738
> 1050.62584
> 1119.28154
> 1177.62000
> 1200.00000
> !
> !! mttfokkertrans.scl
> !!
> !2.3.7 transversal of mttfokker
> !! 49/48: -9 to 14; 531441/524288 0 or 12
> ! 24
> !!
> ! 28/27
> ! 2187/2048
> ! 567/512
> ! 9/8
> ! 7/6
> ! 32/27
> ! 5103/4096
> ! 81/64
> ! 21/16
> ! 4/3
> ! 112/81
> ! 729/512
> ! 189/128
> ! 3/2
> ! 14/9
> ! 128/81
> ! 1701/1024
> ! 27/16
> ! 7/4
> ! 16/9
> ! 448/243
> ! 243/128
> ! 63/32
> ! 2/1
>
>
>

🔗Chris Vaisvil <chrisvaisvil@...>

ok, here is my performance with this tuning. I rather like the tuning.

For your price of admission you get:
mp3
midi
scoredature pdf
scala
a picture of Fokker street in Toowoomba, Australia.

http://chrisvaisvil.com/?p=2821

On Thu, Nov 1, 2012 at 11:25 AM, genewardsmith
<genewardsmith@sbcglobal.net>wrote:

🔗Margo Schulter <mschulter@...>

Hello, Mike and all.

You've certainly created a teachable moment for me, and I wonder
if I'm catching on at all to the meaning of a val from the
xenwiki pages and Joe Monzo's encyclopedia. etc.

If I understand correctly, the Parapyth mapping for any
tuning of this class (Peppermint, MET-24, O3, POTE) can
be expressed by a set of three vals for the period,
generator, and spacing, as one uses them to obtain
each prime -- 2.3.7.11.13. I didn't see a rank-3 example
on xenwiki, but thought I'd have a go at my possibly
imperfect idea of such a Parapyth mapping.

And I know that making mistakes is a way to learn.

Here's a first try:

<1 1 - 1 4 5]
<0 1 - 3 -1 -4]
<0 0 - 1 1 1]

Maybe a georgian would also be useful, although some might
consider it a bit odd: what a georgian does it show the
mapping of odd factors, here most notably including 9.
The georgian is named after George Secor, who is famous
for the near-just 4:5:6:7:9:11:13:15 ogdads of 29-HTT.

<1 1 - 1 2 4 5]
<0 1 - 3 2 -1 -4]
<0 0 - 1 0 1 1]

If this is correct, it's the mapping for Parapyth.

I have a little experience with simple Euler-Fokker groups,
so this could be a very interesting discussion!

Peace and love,

Margo

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, Margo Schulter <mschulter@...> wrote:

> If I understand correctly, the Parapyth mapping for any
> tuning of this class (Peppermint, MET-24, O3, POTE) can
> be expressed by a set of three vals for the period,
> generator, and spacing, as one uses them to obtain
> each prime -- 2.3.7.11.13.

There's nothing in parapyth which requires you to use period-generator-spacing, but you can certainly do it that way.

> Here's a first try:
>
> <1 1 - 1 4 5]
> <0 1 - 3 -1 -4]
> <0 0 - 1 1 1]

There's another of my goofy ideas called a "gencom", for list of generators followed by list of commas. In this case, we could use 2, 3/2, 28/27 as generators, and get [2 3/2 28/27; 352/351 364/363] for the "gencom". Using a mathematical technique called "pseudoinverse", this gives a "gencom mapping":

<1 1 0 1 4 6|
<0 1 0 3 -1 -4|
<0 0 0 1 1 1|

We seem not to be in entire agreement, but close. You have <1 1 0 1 3 5| for the first val, I got <1 1 0 1 4 6|.

🔗Mike Battaglia <battaglia01@...>

Well, I'm glad this idea was such a hit.

-Mike

On Thu, Nov 1, 2012 at 3:08 PM, Mike Battaglia <battaglia01@...> wrote:
>
> Margo's technique for generating scales is basically a generalization of the Euler genus to temperaments, right? They're just rectangles on the lattice, which may or may not be epimorphic.
>
> The interesting thing about these scales, in regular temperament terms, is that Margo seems to like rank-3 scales which are twice-over epimorphic. For instance we can say that a scale which is "doubly epimorphic" has a val for which there are two notes in the scale that map to every integer under the val. You could probably have triply epimorphic scales as well. So maybe we should call them Margo blocks (or Schulter blocks) and then note that Euler genera are just these as applied to the JI lattice.
>
> These scales are useful because if you think of the val as a central organizing principle for the intervals in the scale, dividing them into seconds, thirds, fourths, etc (or more generally, mapping-1, mapping-2, mapping-3, etc intervals), it can be useful to have scales where there are -deliberately- more than one of each type of interval being mapped to - but the same amount for every interval type, and this appears to be what Margo's intuitive approach for rank-3 scales is.
>
> This is just a clever way of saying that her 24-note rank-3 scales tend to have two things mapping to 0\12, 1\12, 2\12, 3\12, etc, so they're all (probably) doubly epimorphic under some 12-note val.
>
> (I note that I have no idea what the difference between an Euler genus and a Euler-Fokker genus is.)
>
> -Mike