Some warped egresses

http://www.io.com/~hmiller/midi/egress/

I've been playing with retunings of _This Way to the Egress_ in different
7-limit temperaments. One thing I'm wondering is if it would be better to
use the same JI mapping for all the retunings, or try to find a different
one for each temperament. Since the original version is 14-ET, it could be
mapped to JI in different ways. Here's the one I've been using for the
Superpelog and Miracle warpings (in MIDICONV tuning format):

! 14 notes of 7-limit JI
coords 4
two 1.0
three 1.584962501
five 2.321928095
seven 2.807354922
notes 14
0 0 0 0 0 ! A# 5/4
1 -2 1 -1 1 ! B
2 0 -2 -1 2 ! B#
3 2 0 -2 1 ! C 7/5
4 1 1 -1 0 ! C# 3/2
5 3 -2 -1 1 ! D
6 1 -1 -2 2 ! D#
7 0 0 -1 1 ! E 7/4
8 2 -3 -1 2 ! E#
9 4 -1 -2 1 ! F
10 3 0 -1 0 ! F# 1/1
11 5 -3 -1 1 ! G
12 3 -2 -2 2 ! G#
13 2 -1 -1 1 ! A 7/6
14 1 0 0 0 ! A# 5/4

The basic harmony of the piece is an alternation between F# A# C# E and A C
E F# chords, which I'm interpreting as 4:5:6:7 and 1/(7:6:5:4) chords in
all the retunings. But it's not obvious what mapping to use for the other
notes, and I might want to adjust them to keep the number of generators
down to a reasonable number. So for the Orwell version, I changed the
tuning of B and G:

1 4 -1 -1 0 ! B
11 7 -1 -2 0 ! G

and the Pajara version changed the tuning of E# and F:

8 -2 1 -2 2 ! E#
9 1 -2 0 1 ! F

On the other hand, it might make it harder to directly compare temperaments
if they're mapped differently. But it seems like it'd be easier to find
mappings that work with each temperament individually than to try to find
one mapping that will work for everything.

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I think I've found a couple of good JI approximations for retuning _Egress_. The first one is a nice symmetrical looking one with lots of consonances, which looks like it'd work nicely with any of the pelog-type approximations, and would also work as 14 consecutive steps of meantone, Fb-B.

http://www.io.com/~hmiller/midi/egress/egress-jimajor.mid

0 0 0 0 0 ! Bb 5/4 -2 0 1 0
1 -2 1 -1 1 ! B
2 4 -1 -1 0 ! Cb
3 2 0 -2 1 ! C 7/5 0 0 -1 1 Ab Eb Bb
4 1 1 -1 0 ! Db 3/2 -1 1 0 0
5 3 -2 -1 1 ! D D A E B
6 2 -1 0 0 ! Eb Fb Cb Gb Db
7 0 0 -1 1 ! E 7/4 -2 0 0 1
8 6 -2 -1 0 ! Fb F C G
9 4 -1 -2 1 ! F
10 3 0 -1 0 ! Gb 1/1 1 0 0 0
11 1 1 -2 1 ! G
12 4 -2 0 0 ! Ab
13 2 -1 -1 1 ! A 7/6 -1 -1 0 1
14 1 0 0 0 ! Bb 5/4 -2 0 1 0

Does anyone know of any better 14-note block of JI that might be useful for this purpose? I haven't done any kind of systematic searches, but I've tried a number of possibilities, and I haven't found a better one. I think I'll want to use this one as the foundation for the Warped Egress page, with slight modifications for particular temperaments if necessary.

Since 14-ET is highly ambiguous, I've also been looking for a minor key version that's consistent with the _Egress_ harmony and melody. This is the best I've come up with thus far:

http://www.io.com/~hmiller/midi/egress/egress-jiminor.mid

0 0 0 0 0 ! A 6/5 1 1 -1 0
1 -1 1 1 -1 ! Bb
2 1 -2 1 0 ! B G# D#
3 0 -1 2 -1 ! C 10/7 1 0 1 -1 F C
4 -2 0 1 0 ! C# 3/2 -1 1 0 0
5 0 2 0 -1 ! Db B F# C#
6 -1 -2 2 0 ! D# Ab Eb Bb
7 1 0 1 -1 ! Eb 12/7 2 1 0 -1
8 -1 1 0 0 ! E A E
9 2 -2 2 -1 ! F Gb Db
10 0 -1 1 0 ! F# 1/1 1 0 0 0
11 2 1 0 -1 ! Gb
12 1 -3 2 0 ! G#
13 3 -1 1 -1 ! Ab 8/7 3 0 0 -1
14 1 0 0 0 ! A 6/5 1 1 -1 0

--- In tuning-math@yahoogroups.com, Herman Miller <hmiller@I...>
wrote:
> I think I've found a couple of good JI approximations for retuning
> _Egress_. The first one is a nice symmetrical looking one with lots
of
> consonances, which looks like it'd work nicely with any of the
> pelog-type approximations, and would also work as 14 consecutive
steps
> of meantone, Fb-B.
>
> http://www.io.com/~hmiller/midi/egress/egress-jimajor.mid
>
> 0 0 0 0 0 ! Bb 5/4 -2 0 1 0
> 1 -2 1 -1 1 ! B
> 2 4 -1 -1 0 ! Cb
> 3 2 0 -2 1 ! C 7/5 0 0 -1 1 Ab Eb Bb
> 4 1 1 -1 0 ! Db 3/2 -1 1 0 0
> 5 3 -2 -1 1 ! D D A E B
> 6 2 -1 0 0 ! Eb Fb Cb Gb Db
> 7 0 0 -1 1 ! E 7/4 -2 0 0 1
> 8 6 -2 -1 0 ! Fb F C G
> 9 4 -1 -2 1 ! F
> 10 3 0 -1 0 ! Gb 1/1 1 0 0 0
> 11 1 1 -2 1 ! G
> 12 4 -2 0 0 ! Ab
> 13 2 -1 -1 1 ! A 7/6 -1 -1 0 1
> 14 1 0 0 0 ! Bb 5/4 -2 0 1 0
>
> Does anyone know of any better 14-note block of JI that might be
useful
> for this purpose?

Maybe not, but I did post one or two 14-note blocks once -- they're
in Scala. I would search the tuning list for "What's your favorite
number?", but it seems the yahoogroups search engine has suddenly
become near-useless as it only searches a very small number of posts
at a time.

>Maybe not, but I did post one or two 14-note blocks once -- they're
>in Scala. I would search the tuning list for "What's your favorite
>number?", but it seems the yahoogroups search engine has suddenly
>become near-useless as it only searches a very small number of posts
>at a time.

Also I remember it not enforcing "".

I don't find any tuning stuff with this on google.

-C.

--- In tuning-math@yahoogroups.com, Herman Miller <hmiller@I...> wrote:
> I think I've found a couple of good JI approximations for retuning
> _Egress_. The first one is a nice symmetrical looking one with lots of
> consonances, which looks like it'd work nicely with any of the
> pelog-type approximations, and would also work as 14 consecutive steps
> of meantone, Fb-B.
>
> http://www.io.com/~hmiller/midi/egress/egress-jimajor.mid
>
> 0 0 0 0 0 ! Bb 5/4 -2 0 1 0
> 1 -2 1 -1 1 ! B

This looks as if it should be 2 * 3^(-2) * 5 * 7^(-1) * 11 = 110/63,
but instead it's |-2 1 -2 1> = 21/20.

Gene Ward Smith wrote:

> --- In tuning-math@yahoogroups.com, Herman Miller <hmiller@I...> wrote:
> >>I think I've found a couple of good JI approximations for retuning >>_Egress_. The first one is a nice symmetrical looking one with lots of >>consonances, which looks like it'd work nicely with any of the >>pelog-type approximations, and would also work as 14 consecutive steps >>of meantone, Fb-B.
>>
>>http://www.io.com/~hmiller/midi/egress/egress-jimajor.mid
>>
>> 0 0 0 0 0 ! Bb 5/4 -2 0 1 0
>> 1 -2 1 -1 1 ! B
> > > This looks as if it should be 2 * 3^(-2) * 5 * 7^(-1) * 11 = 110/63,
> but instead it's |-2 1 -2 1> = 21/20.

The first column of MIDICONV tuning files is just the note number.

--- In tuning-math@yahoogroups.com, Herman Miller <hmiller@I...> wrote:

> The first column of MIDICONV tuning files is just the note number.

Why not tell us that?