Cauldron
This is another version of the same basic idea, this time with two pure 9/7 major thirds and some other nice features.
Here is an analysis
0 C
[378.409788, 316.192659, 694.602447]
[291.903672, 402.698775, 694.602447]
The major triad is almost exactly a 19-equal major triad; the minor
triad has a minor third 2.69 cents sharper than a 13/11
1 C sharp
[435.084095, 275.711011, 710.795106]
[308.096329, 402.698777, 710.795106]
The major triad has a pure 9/7 major third
2 D
[378.409788, 316.192659, 694.602447]
[316.192660, 378.409787, 694.602447]
Another 19-et major triad, but the minor triad is also 19-equal
3 E flat
[402.698775, 308.096331, 710.795106]
[275.711010, 435.084096, 710.795106]
The major triad is close to 27-equal, the minor triad has a pure 9/7
and therefore a minor third just as sharp above 7/6 as the fifth:
8.84 cents
4 E
[402.698777, 291.903670, 694.602447]
[316.192659, 378.409788, 694.602447]
The minor triad is another 19-equal minor triad, meaning a flat fifth
and a nearly pure minor third
5 F
[378.409787, 316.192659, 694.602446]
[275.711011, 418.891435, 694.602446]
Still another 19-equal major triad, but the minor triad has another
subminor third sharp by 8.84 cents
6 F sharp
[435.084096, 267.614681, 702.698777]
[316.192659, 386.506118, 702.698777]
A pure 9/7 major third and a fifth only 3/4 of a cent sharp gives us
a really nice supermajor triad; the minor triad has a minor third 0.55
cents sharp and a major third 0.19 cents sharp
7 G
[378.409788, 316.192659, 694.602447]
[308.096331, 386.506116, 694.602447]
You guessed it--still another 19-equal major triad; the minor triad
has an essentially pure major third 0.19 cents sharp
8 A flat
[418.891435, 291.903672, 710.795107]
[291.903670, 418.891437, 710.795107]
The major triad has a 14/11 major third which is 1.38 cents sharp;
the minor triad has a minor third which is 2.69 cents above 13/11; the
two triads have corresponding major and minor thirds
9 A
[386.506118, 308.096329, 694.602447]
[316.192659, 378.409788, 694.602447]
Once again, the major and minor triads are 19-et; the circle of
fifths from F to F# is pretty well identical to 19-equal; from B flat to F
and F# to C# we have a 3/4-cent sharp fifth, and from C# to B flat we
have 8.84 cents sharp fifths
10 B flat
[386.506116, 316.192660, 702.698776]
[267.614681, 435.084095, 702.698776]
A nearly pure major triad, with major third sharp by 0.19 cents and
minor third sharp by 0.55 cents; the minor triad is a nearly perfect
subminor triad, with subminor third sharp by 0.74 cents and the
supermajor triad pure. Both F sharp and B flat have almost
pure triads
11 B
[418.891437, 275.711010, 694.602447] [316.192659, 378.409788,
694.602447]
The major triad has another 14/11 major third sharp by 1.38 cents;
the minor triad is another 19-equal minor triad
! cauldron.scl
Circulating temperament with two pure 9/7 thirds
12
!
70.313459
189.204894
291.903672
378.409788
505.397554
567.614682
694.602447
781.108565
883.807341
1002.698778
1073.012235
1200.000000