rainbow

From: Gene Ward Smith (2003-06-08)
Subject: Rainbow circulating temperament

Cauldron gives a genuine meantone spliced to some mictrononal thirds;
grail isn't a regular meantone but also has nice mictrotonal thirds. I
find, incidentally, that even with equal grail I miss the locked-in
effect in remote keys.

Cauldron, at 1/3-comma meantone, is a little too flat for my taste.
Another approach is to take nine 1/4-comma meantone fifths, and make
up the rest with three fifths of size (128/125)^(1/3) * 5^(1/4), or
710.265 cents. This gives us six pure 5/4 major thirds, two 12-equal
major thirds of 400 cents, two 413.7 cent thirds which might be
considered 14/11s 3.82 cents flat, and two of 9/7s of dubious
pedigree, 7.71 cents flat. We do, however, get a way of bridging
1/4-comma meantone around without jarring ourselves with a wolf fifth,
and 1/4-comma meantone is lovely; to my ear pretty much perfection in
the meantone department.

I continue the Celtic magic naming theme with rainbow, which sounds
better than pot or kettle.

! rainbow.scl
Circulating 1/4-comma meantone
12
!
76.048999
193.156857
296.578429
386.313713
503.421572
579.470571
696.578429
786.313713
889.735285
1006.843143
1082.892142
1200.000000

From: Gene Ward Smith (2003-06-08)
Subject: Rainbow circulating temperament

Cauldron gives a genuine meantone spliced to some mictrononal thirds;
grail isn't a regular meantone but also has nice mictrotonal thirds. I
find, incidentally, that even with equal grail I miss the locked-in
effect in remote keys.

Cauldron, at 1/3-comma meantone, is a little too flat for my taste.
Another approach is to take nine 1/4-comma meantone fifths, and make
up the rest with three fifths of size (128/125)^(1/3) * 5^(1/4), or
710.265 cents. This gives us six pure 5/4 major thirds, two 12-equal
major thirds of 400 cents, two 413.7 cent thirds which might be
considered 14/11s 3.82 cents flat, and two of 9/7s of dubious
pedigree, 7.71 cents flat. We do, however, get a way of bridging
1/4-comma meantone around without jarring ourselves with a wolf fifth,
and 1/4-comma meantone is lovely; to my ear pretty much perfection in
the meantone department.

I continue the Celtic magic naming theme with rainbow, which sounds
better than pot or kettle.

! rainbow.scl
Circulating 1/4-comma meantone
12
!
76.048999
193.156857
296.578429
386.313713
503.421572
579.470571
696.578429
786.313713
889.735285
1006.843143
1082.892142
1200.000000