asbru

From: Gene Ward Smith (2003-07-13)
Subject: Asbru

Asbru is a mutated version of bifrost. Bifrost has two major thirds
worse than those of 12-et, Asbru deals with this at the expense of the
fifths and the 14/11 thirds. It was created by an rms optimization
against the target major thirds of Bifrost; this did not completely
determine the values, so a second optimization was done for the fifths.

Asbru has three 12-et major thirds, 400 cents, six nice 3.29 cent
sharp major thirds, and three thirds sharper than 14/11 by precisely
the same 3.29 cents. In the minor third department, it has
two 12-et minor thirds, 300 cents, six minor thirds flat by 5.24
cents, two minor thirds sharper than 13/11 by a mere 0.39 cents, and
two subminor thirds sharper than 7/6 by 12.33 cents. Tuning optimists
may prefer to regard the last as a 20/17 third.

In the fifths department, we have eight of 12-ets excellent fifths,
two fifths sharp by 8.44 cents, and two fifths flat by 12.35 cents. It
should be noted that 12.35 cents is still less of an error than the
13.69 cents the 400 cent thirds are off by, and quite a bit less than
the 15.64 cents the 300 cent thirds are off by.

Asbru has a major tetrad on the fourth scale degree and minor tetrads
on the first (sort of, at any rate) and sixth degrees.

Here are the triads:

1: [420.796166, 289.601917, 710.398083]
2: [389.601917, 310.398083, 700.000000]
3: [389.601917, 310.398083, 700.000000]
4: [400.000000, 289.601917, 689.601917]
5: [389.601917, 300.000000, 689.601917]
6: [420.796167, 279.203833, 700.000000]
7: [389.601917, 310.398083, 700.000000]
8: [400.000000, 310.398083, 710.398083]
9: [389.601917, 310.398083, 700.000000]
10 [389.601917, 310.398083, 700.000000]
11 [420.796167, 279.203833, 700.000000]
12 [400.000000, 300.000000, 700.000000]

Here is Asbru:

! asbru.scl
Modified bifrost
12
!
89.601917
200.000000
310.398083
400.000000
510.398083
589.601917
700.000000
800.000000
900.000000
1010.398083
1089.601917
1200.000000

From: Gene Ward Smith (2003-07-13)
Subject: Asbru

Asbru is a mutated version of bifrost. Bifrost has two major thirds
worse than those of 12-et, Asbru deals with this at the expense of the
fifths and the 14/11 thirds. It was created by an rms optimization
against the target major thirds of Bifrost; this did not completely
determine the values, so a second optimization was done for the fifths.

Asbru has three 12-et major thirds, 400 cents, six nice 3.29 cent
sharp major thirds, and three thirds sharper than 14/11 by precisely
the same 3.29 cents. In the minor third department, it has
two 12-et minor thirds, 300 cents, six minor thirds flat by 5.24
cents, two minor thirds sharper than 13/11 by a mere 0.39 cents, and
two subminor thirds sharper than 7/6 by 12.33 cents. Tuning optimists
may prefer to regard the last as a 20/17 third.

In the fifths department, we have eight of 12-ets excellent fifths,
two fifths sharp by 8.44 cents, and two fifths flat by 12.35 cents. It
should be noted that 12.35 cents is still less of an error than the
13.69 cents the 400 cent thirds are off by, and quite a bit less than
the 15.64 cents the 300 cent thirds are off by.

Asbru has a major tetrad on the fourth scale degree and minor tetrads
on the first (sort of, at any rate) and sixth degrees.

Here are the triads:

1: [420.796166, 289.601917, 710.398083]
2: [389.601917, 310.398083, 700.000000]
3: [389.601917, 310.398083, 700.000000]
4: [400.000000, 289.601917, 689.601917]
5: [389.601917, 300.000000, 689.601917]
6: [420.796167, 279.203833, 700.000000]
7: [389.601917, 310.398083, 700.000000]
8: [400.000000, 310.398083, 710.398083]
9: [389.601917, 310.398083, 700.000000]
10 [389.601917, 310.398083, 700.000000]
11 [420.796167, 279.203833, 700.000000]
12 [400.000000, 300.000000, 700.000000]

Here is Asbru:

! asbru.scl
Modified bifrost
12
!
89.601917
200.000000
310.398083
400.000000
510.398083
589.601917
700.000000
800.000000
900.000000
1010.398083
1089.601917
1200.000000