Yes it's just based on the number of semitones in the octave.
I explored the same idea with other numbers per octave, in Tune Smithy - you can set it to show centisteps (that's Margo Schulter's name for them). So e.g. 1700 centisteps to an octave for musicians working in 17 equal temperament, 3100 centisteps to an octave if working in 31-et and so on.
The idea hasn't caught on, it seems it is generally more convenient to use the same reference for all scales, I suppose historically 12-et came first and so now we are used to using cents. But there isn't really any special reason to use 1200 except for the convenience for 12 tone scales. Also world wide though there are many different systems with other numbers of notes per octave, there are perhaps more tunings based on 12 notes per octave in one way than another than any other number, so it makes sense to stick with it too, and internationally it means anyone from any musical culture knows what you mean when you say an interval is, say, 386 cents.
Here are a couple of links for the Tune Smithy notation:
Window 161 - Tune Smithy
Scale Notations - Tune Smithy
I also explored the idea of using other number bases - in Tune Smithy you can set it to use e.g. 500 centisteps to an octave and also show the numbers in base 5 notation so then 500 means 125 steps per octave in decimal notation.
Scale Notations - Alternative Cents Notations (with alternative bases) - Tune Smithy
I explored the same idea with other numbers per octave, in Tune Smithy - you can set it to show centisteps (that's Margo Schulter's name for them). So e.g. 1700 centisteps to an octave for musicians working in 17 equal temperament, 3100 centisteps to an octave if working in 31-et and so on.
The idea hasn't caught on, it seems it is generally more convenient to use the same reference for all scales, I suppose historically 12-et came first and so now we are used to using cents. But there isn't really any special reason to use 1200 except for the convenience for 12 tone scales. Also world wide though there are many different systems with other numbers of notes per octave, there are perhaps more tunings based on 12 notes per octave in one way than another than any other number, so it makes sense to stick with it too, and internationally it means anyone from any musical culture knows what you mean when you say an interval is, say, 386 cents.
Here are a couple of links for the Tune Smithy notation:
Window 161 - Tune Smithy
Scale Notations - Tune Smithy
I also explored the idea of using other number bases - in Tune Smithy you can set it to use e.g. 500 centisteps to an octave and also show the numbers in base 5 notation so then 500 means 125 steps per octave in decimal notation.
Scale Notations - Alternative Cents Notations (with alternative bases) - Tune Smithy
About the Author
Robert Walker
Writer of articles on Mars and Space issues - Software Developer of Tune Smithy, Bounce Metronome etc.Studied at Wolfson College, Oxford
Lives in Isle of Mull
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