Musical Scale Generator

[BLUMENKOHL 1,068]

http://techblog.bozho.net/?p=1523

But what does that have to do with programming? Computers can generate an almost infinite amount of musical scales that follow the rules of the scales already proven to be good. Why limit ourselves to 7-tone scales out of 12 tones, when we can divide the octave into 24 parts and make a scale of 15 tones? In fact, some composers and instrument makers, the most notable being Harry Partch, have experimented with such an approach, and music has been written in such “new” scales (although not everyone would call it “pleasant”). But with computers we can test new scales in seconds, and write music in them (or let the computer write it) in minutes. In fact, I see this as one way for advancing the musical landscape with the help of computers (algorithmic composition aside).

That’s why I wrote a scale generator. It takes a few input parameters – the fundamental frequency, on which you want to base the scale (by default C=262.626); the size of the scale (by default 7); the size of the ‘chromatic scale’ out of which the scale will be drawn (by default 12); and the final parameter specifies whether to use equal temperament or not.

The process, in a few sentences: it starts by calculating the overtones (harmonics), skipping the 7th (for reasons I don’t fully understand). Then transposes all of them into the same octave (it does so, by calculating the ratio from a given harmonic to its tonic (the closest power-of-two multiple of the fundamental frequency), and then using that ratio calculates the frequency from the fundamental frequency itself. It does that until the “chromatic scale size” parameter value is reached. Then it finds the perfect interval (perfect fifth in case of heptatonic (diatonic) scale), i.e. the one with ratio 3/2. If equal temperament is enabled, the previous chromatic scale is replaced with an equal-tempered one. Then the algorithm makes a “circle” from the tones in the chromatic scale (the circle of fifths is one example), based on the perfect interval, and starting from the tone before the fundamental frequency, enumerates N number of tones, where N is the size of the scale. This is the newly formed scale. Note that starting from each note in the scale we just obtained (and continuing in the next octave when we run out of tones) would yield a completely different scale (this is the difference between C-major and a A-minor – they use the same notes)

http://computoser.com