Difference pitches re: Manuel's comments on meantone & Erv.

Prompted by Manuel's recent comments on beating and difference tones
I have been playing with some numbers and arrived at some odd results.
It seems that Harrison's concept, when applied, generates further
notes within the expected scales to very close values.
Maybe someone with less vested interest can interpret the significance
of these differences.


LucyTuning A Major chord. (All Values in Hz.)
A4 440 C#5 548.6224 E5 657.5411 A5 880
A3 220
A2 110

Difference pitches
A4 to C#5 108.6224 (� -1.3776) * 256 176.3328 (� - 0.1092)
A4 to E5 217.5411 (� -2.4589) * 64 157.3696 (�3 + 0.3571)
A4 to A5 440 (�)
C#5 to E5 108.9188 (� -1.1012)* 128 140.9536 (�3 - 0.5545)
C#5 to A5 331.3776 (� +2.6071)* 128 333.7088 (� + 4.9383)
E5 to A5 222.4589 (� +2.4589)* 64 157.3696 (�3 + 0.3571)
NOTES:
E4 328.7706; F3 176.4420; Eb3 157.0125; Db3 141.5081
F2 88.2210
F4 352.8839

LucyTuning A minor chord. (All Values in Hz.)
A4 440 C5 527.3539 E5 657.5411 A5 880
C3 131.8385
Difference pitches
A4 to C5 87.3539 (� -0.8671) * 128 110.9888 (� + 0.9888)
A4 to E5 217.5411 (� -2.4589) * 64 157.3696 (�3 + 0.3571)
A4 to A5 440 (�)
C5 to E5 130.1872 (� -1.6513) * 128 211.3626 (�3 - 0.1086)
C5 to A5 352.6461 (� -0.2378) * 512 121.7536 (� - 1.0760)
E5 to A5 222.4589 (� +2.4589) * 64 157.3696 (�3 + 0.3571)

NOTES:
Ab3 211.4712
B2 122.8296

So by playing A Major we generate A C# E plus approximations of Db Eb & F
So by playing A minor we generate A C E plus approximations of Ab B & F

which may partly explain why the Major bVIths (A C# E F) and
the Minor Ninths (A C E B) also always sound so consonant in this tuning.

lucy@hour.com
25 May 97.


Comments welcomed

http://www.wonderlandinorbit.com/projects/lullaby



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