mir8

From: Gene Ward Smith (2004-07-14)
Subject: An eight note miracle scale

Here is a 7-limit JI scale I've just mentioned on tuning-math:

1--15/14--6/5--9/7--7/5--3/2--8/5--12/7

It has two major and one minor tetrads, plus another minor triad which
does not complete to a tetrad. Also, it has a supermajor and a
subminor triad.

Tempering by 225/224 adds an additional major triad and a "magic"
augmented triad. In miracle, the chain of secors is 0,1,5,6,7,8,13,14;
which in 72-et leads to steps of size 7,12,7,9,7,7,7,16; irregular but
not extreme in terms of evenness. 

I have a feeling this might have been discussed before, but I can't
find it in the Scala archives, and it certainly could be useful for
people composing in miracle; it is in the range of scales which can be
understood as such, you can transpose in Blackjack for fans of
Blackjack, and it has enough harmonic resources to harmonize its own
notes.

! mir8.scl
tet3a in 72-et
8
!
116.666667
316.666667
433.333333
583.333333
700.000000
816.666667
933.333333
1200.00000

! tet3a.scl
Eight notes, two major one minor tetrad
8
!
15/14
6/5
9/7
7/5
3/2
8/5
12/7
2

From: Gene Ward Smith (2004-07-14)
Subject: An eight note miracle scale

Here is a 7-limit JI scale I've just mentioned on tuning-math:

1--15/14--6/5--9/7--7/5--3/2--8/5--12/7

It has two major and one minor tetrads, plus another minor triad which
does not complete to a tetrad. Also, it has a supermajor and a
subminor triad.

Tempering by 225/224 adds an additional major triad and a "magic"
augmented triad. In miracle, the chain of secors is 0,1,5,6,7,8,13,14;
which in 72-et leads to steps of size 7,12,7,9,7,7,7,16; irregular but
not extreme in terms of evenness. 

I have a feeling this might have been discussed before, but I can't
find it in the Scala archives, and it certainly could be useful for
people composing in miracle; it is in the range of scales which can be
understood as such, you can transpose in Blackjack for fans of
Blackjack, and it has enough harmonic resources to harmonize its own
notes.

! mir8.scl
tet3a in 72-et
8
!
116.666667
316.666667
433.333333
583.333333
700.000000
816.666667
933.333333
1200.00000

! tet3a.scl
Eight notes, two major one minor tetrad
8
!
15/14
6/5
9/7
7/5
3/2
8/5
12/7
2