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A better option?

🔗Mario Pizarro <piagui@...>

3/8/2011 11:10:03 AM

Mike,

I think this option is better than the previous one thanks to the -4 cents tone frequency differences with respect to the tet values. Probably Cmaj, Eb maj, Emaj, F#maj, Amaj, Bb maj sounds differ from their corresponding tet triads. Would you please analyze the information given below and inform me about it?. The figures at the bottom makes clear the point, here I used (") instead of the minus sign.

Thanks Mike

Mario

March 08

TWELVE TONE SCALE WITH P AND K PIAGUI SEMITONE FACTORS

P =
(8/9)*2^(1/4) =
1.05707299111

K =
(9/8)^(1/2) =
1.06066017178

(P*K)^(1/2) =
1.05886506238

TET

CENTS
CENT
MAJOR
MINOR

DIFF.
FIFTHS
THIRDS
THIRDS

C ?
1
1 =
0
0
699.0225
396.09
302.93

D ?
x (P*K)^(1/2) =
1.121195220 =
198.04
-2
699.0226
401.95
297.07

Eb?
x (P*K)^(1/2) =
1.187194446 =
297.07
-3
699.0228
401.95
297.07

E ?
x (P*K)^(1/2) =
1.257078722 =
396.09
-4
701.9560
401.95
300.01

F ?
x K =
1.333333333 =
498.04
-2
701.9555
399.02
302.94

F#?
x K =
1.414213562 =
600
0
699.0224
396.09
302.93

G ?
x (P*K)^(1/2) =
1.497461332 =
699.02
-1
699.0225
399.02
300.00

Ab?
x (P*K)^(1/2) =
1.585609486 =
798.05
-2
699.0225
401.95
297.07

A ?
x (P*K)^(1/2) =
1.678946488 =
897.07
-3
699.0226
401.95
297.07

Bb?
x (P*K)^(1/2) =
1.777777777 =
996.09
-4
701.9545
401.95
300.00

B ?
x K =
1.885618083 =
1098.05
-2
701.9550
399.02
302.94

2C?
x K =
2 =
1200
0
699.0224
396.09
302.93

CENTS

2.117730124 =
1299.02

2.242390440 =
1398.05

2.374388893 =
1497.07

2.514157444 =
1596.09

2.666666666 =
1698.04

2.828427124 =
1800.00

2.994922663 =
1899.02

DIFF.UNITS

MAJOR TRIADS

C ?
0, "4, "1

C#?
"1, "2, "2

D ?
"2, 0, "3

Eb?
"3, "1, "4

E ?
"4, "2, "2

F ?
"2, "3, 0

F#?
0, "4, "1

G ?
"1, "2, "2

Ab?
"2, 0, "3

A ?
"3, "1, "4

Bb?
"4, "2, "2

B ?
"2, "3, 0

2C?
0, "4, "1