The Pentadecaphonic system - 4. Pentadecaphonic System properties

4. Pentadecaphonic system properties

-----------> frequency in [Hz]

The pentadecaphonic system has some interesting peculiarities (with reference to the figure above):

- the minor third of A (for example C5p for A4p) in the pentadecaphonic system is sharper than the minor third (i.e. C5d) in the dodecaphonic system and closer to the 'natural minor third'. In addition, a 'flatted' minor third (for example B4#p for A4p) can be used to create another 'minor triad'. The Consonance Analysis (see par. 1.) shows that, at least from G4p= 366 Hz and higher frequencies, the minor triad obtained with the 'flatted' minor third (i.e. G4p, H4#p, C5#p) has a consonant effect

- the major third of A of the dodecaphonic and pentadecaphonic systems are identical ( C#p = C#d , by construction): this could suggest that the major triads of the two systems are very similar.

- the forth of A in the pentadecaphonic system (i.e. D5p for A4p) is flatter than the dodecaphonic one (i.e. D5d for A4d), but still very close to the natural one.

- the fifth of A (for example F4p for A3p) in the pentadecaphonic system is sharper than the correspondent fifth (for example E4d for A3d) in the dodecadecaphonic system, but it is still very close to the natural note and the result in the major or minor triad is quite acceptable.

- the minor sixth of A (for example F5#p for A4p) is, by construction, identical to the minor sixth of A in the dodecaphonic system (i.e. F5d for A4d)

- the major sixth of A (for example G5p for A4p) is closer to the natural major sixth than the correspondent note in the dodecaphonic system (i.e. F5#d for A4d)

- in the Blues Scale some intermediate notes are played 'in the cracks' (called 'blue notes'):

- half-semitone between the minor third and the major third

- half-semitone between the sharp forth and the perfect fifth

- half-semitone between the minor seventh and major seventh

-----------> frequency in [Hz]

Example:

Dodecaphonic C Blues Scale			Pentadecaphonic C Blues Scale
Note	Freq. [Hz]	Blue Note	Note	Freq.[Hz]	Blue Note
C4d	262		C4p	264
D4#d	311	320	E4p	318	318
F4d	349		F4#p	349
F4#d	370	381	G4#p	384	384
G4d	392		H4p	402
A4#d	466	480	B4p	482	482
C5d	523		C5p	529
D5#d	622	640	E5p	637	637
F5d	698		F5#p	698
F5#d	740	762	G5#p	766	766
G5d	784		H5p	802
A5#d	932	960	B5p	965	965
C6d	1047		C6p	1059

The Blue Notes in the Blues Style cannot be played by 'equal tempered' instruments, but only by analogic instruments (i.e. violins and trumpets) and by the human voice. In the pentadecaphonic system, with reference to the C Blues Scale, the blue notes are very close to notes of the scale (i.e. Ep, G#p and Bp).

Play the pentadecaphonic C Blues Scale (flute tone, from C4 = 265 Hz to C5 = 529 Hz)

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