FOUR, ALL THE MUSIC IS MICROTONAL

FOUR ALL THE MUSIC IS MICROTONAL TD 1187

) Where is the 12 ? 1192, 1194, 1201
) Musical writing
) Harmonics (Carl Lumma) 1188
) Just listen (Marion) 1188
) More than 12
) Sound Spectrum
continuum (Hstick) 1205
) Cross-cultural (J. Reinhard) 1198, 1203
) Piano's Tuning
) Microtonal Architecture (J. Szanto) 1197
- Myriad of both tunings and styles (J. Reinhard) 1201

Where is the 12 ?

Question: How many DIFFERENT intervals are there in the 7-Pythagoric Scale ?

Answer : 12 , Why ?

All the possibilities that are in the seven pyth modes may be counted one by
one, nevertheless there is another, more appropriate, analytical way.

The seven notes come from a row of (in this case) perfect fifths having in
between six different intervals that can go up and other six that can go
dwon. Total 12.
Twelve different intervals.
It goes up with positive exponents and goes down with negative ones.
To any row of fifths I call it a Pythagoric Structure.
The octaved (reduced) intervals that come from the positive exponents form
"Harmonic intervals" and the others, the negative exponents, are "Enharmonic
Intervals".

Starting from F, by fifths, we have the structure F, C, G, D, A, E, B.
The HARMONIC intervals are : (From F) 3/2 raised to +1 , 3/2 raised to +2,
3/2 raised to +3 ... and 3/2 raised to +6, that octaved they are 3/2, 9/8,
27/16 .... and 729/512.
The ENHARMONIC intervals are : (From B) 3/2 raised to -1, 3/2 raised to -2,
3/2 raised to -3 ... and 3/2 raised to -6, that octaved they are 4/3, 16/9,
32/27 ... and 1024/729.




Eduardo

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