TV show Red Dwarf.
Holly. “Among his achievements was the invention of Hol Rock, where he decimalised music, having ten notes instead of eight.”
I’ve always wondered how it was that the ten notes that Holly sang in the show didn’t sound too bad as a scale. Just recently I got wondering if music really could be decimalised.
Think for instance of a melodic minor, when we add the two different notes on descent to the eight notes on ascent we get a ten note scale.
Also cast your mind back to the times before Bach’s “well tempered clavier”, when keyboards had a range of tunings.
In a “well-tempered” instrument, the frequencies and wavelengths are selected using a constant exponential/logarithmic constant. But what if a constant linear constant was used instead? Then what would be a tone at the bottom of the scale would become a semitone at the top. Double it all for the next octave.
Like pre-Bach tunings this would be inappropriate for some keys – the instrument would be tuned to say the key of C and be able to play keys between say A and E but not outside that range. It’s no worse than some ethnic music, traditional music from the country Georgia for instance doesn’t contain octaves.
An octave on a well-tempered scale contains 6 tones (so why call it an octave) separating 7 notes. Above A440 these are
The equivalent in decimalised music would be (6 tones in the octave, 8 tones in the decimalised equivalent):
440, 495, 550, 605, 660, 715, 770, 825, 880 Hz.
which is a close enough match for:
A, B, C#, ?, E, ?, G, G#, A.
where only the question marks are closer to quarter tones. This looks startlingly like an A major scale, with only the additional G and quarter tones.
And as I say, this works with any octave and also at octave boundaries where a tone becomes a semitone without any change in frequency interval.
Not sure whether it should be called decimal or nonimal.
Looks like something that should be explored in modern music. Something like the modes of Bartok but slightly more extreme.