Pursuing clarity through openness, part 8: integer-ratio intervals against a logarithmic scale

While integer-ratio intervals generally sound better than irrational intervals, the sensation of pitch is roughly logarithmic. Ascending octaves on a piano sound like they each rise about the same amount, but the frequency doubles from one to the next.

To accommodate this, when adapting harmonic series to a playable interface, whether on-screen or physical, the spacing between the buttons or touch-pads or whatever represents notes should diminish moving from lower to higher harmonics. The distance between the 1st and 2nd harmonics should be the same as the distance between the 2nd and 4th, between the 4th and 8th, and between the 8th and 16th. Depending upon how many harmonics you include, it may not be possible to have them all on-screen or within reach simultaneously, and the higher ones will present increasingly smaller targets.

The problem of smaller targets can be alleviated by using multiple harmonic series, which is what harmonic structures are all about. It can also be alleviated by removing harmonics that are irrelevant to a particular purpose, leaving a sparse structure that might be termed a lattice. This filtering is another case where prime factors can be useful.

A perk of using a logarithmic scale for pitch is that it allows having multiple harmonic series that are copies of a template, all with exactly the same dimensions. These duplicate series can be moved up or down-scale without distorting the correlation between their position and the frequencies they produce. Even better, everything at the same position along that scale will have the same pitch.

I'm rather fond of the notion of a physical instrument interface patterned generally on the shape of the saguaro cactus, which has branches that emerge almost horizontally from the main stem and then turn sharply upwards. Vertical pieces each representing a single harmonic series could be mounted on a central post so they would slide up/down through slots, or pivot on a parallelogram linkage, the idea being that the higher they were positioned the higher the frequencies they would generate, again using a logarithmic frequency scale.

There is one more major topic to cover, and probably some loose ends to tie up, but I think I'll be taking a break before proceeding with the next installment.

Part 9: crafting voice by shifting amplitude among harmonics over time