If there are 12 semi-tones in an octave and those are each 100 cents apart, and the octave is 1200 semi-tones apart, am I right in assuming splitting that octave into 8 semi-tones is simple? Would it be 150 cents between notes, or is the math more complicated than that?

Thank you.

EDIT: I'm aware that this will sound very odd and unconventional. It is for experimental purposes of composing in the randomly generated musical forms of the video game Dwarf Fortress, and will be using primitive self-constructed instruments for the purpose.

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    The math is as simple as you say, but if you call these intervals "semi-tones" you will confuse everybody! Whether they would form a useful musical scale is a different question - this scale certainly isn't going to sound anything like conventional western music. – user19146 Apr 13 '17 at 16:14
  • That's the idea! Attempting to compose in the randomly generated musical forms of a video game. What should they be called if not semi tones? – stumpbeard Apr 13 '17 at 16:16
  • Are you trying to invent a totally new scale? If so then you set the rules and you can have 8 semitones in your octave which are 150 cents wide. You won't be able to play in your new scale with most standard instruments. – badjohn Apr 13 '17 at 16:16
  • On the name, why the semi? Its use in standard scales is somewhat historical. A totally new word might be better e.g. step? – badjohn Apr 13 '17 at 16:19
  • @badjohn I'm just unfamiliar with correct vernacular is all. – stumpbeard Apr 13 '17 at 16:24

Your math is correct, assuming you want an equally tempered system. As it turns out, the mathematics for intervals within an octave are a bit more complex than just "every half step is 100 cents," but it's pretty good. And since you're basically creating an unfamiliar new scale system, I would say this equally tempered approach, with tones 150 cents apart, is exactly what you're looking for.

With that said, I agree that you should stay away from "semitone." One solution may be to call it a dodrantitone, dodrant- literally meaning "three-quarters." It's an archaic prefix, but it's one option. Strangely, the 3/4 slot is pretty empty in this table of prefixes. (Note: a silly error resulted in me originally saying sesqui-, for "one and a half.")

And maybe in the future you can edit your original question with a sound sample, I'd love to hear it!

Edit: Other options for "strange" scale collections, if that's your goal, can be found in Messiaen's Modes of Limited Transposition.

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  • As Richard implies, you need not stick to equal intervals. This is a relatively new system in western music (in a sense in which Bach is new). Look up just and equal tempered scales. If you want an effect that might be an alternative human music then you are probably heading in the wrong direction. If you want something that sounds alien or robotic then maybe you are heading the right way. If you want to go really alien, why even retain the octave? If you are giving the perfect 4th and 5th, the octave could go as well. – badjohn Apr 13 '17 at 16:40
  • Good point about equal temperament. It's going to sound weird at best anyway, so I don't believe et will go much in its favour. Good answer, as ever +1. – Tim Apr 13 '17 at 16:44
  • A lot of really fantastic information here. I appreciate the guidance from everyone in pointing me in the direction of making a more "listenable" piece, if that's the direction that I end up going in. – stumpbeard Apr 13 '17 at 16:47
  • Sesqui is alive and well in mathematics. – badjohn Apr 13 '17 at 16:49

If you want to go even more odd, don't use a logarithm scale. All of the standard scales work on the basis that equal intervals mean an equal ratio of frequencies rather than an equal frequency gap. So, 1000Hz, 1100Hx, 1210Hz, 1331Hz, etc would be equally spaced notes (though not in the current standard scales). This is what I mean by logarithmic. Have your notes an equal number of Hz apart: 1000Hz, 1100Hz, 1200Hz, etc. Interpreted by the current rules, these would be decreasing intervals but who knows how alien ears work (if they perceive sound at all) and it might be natural to them. This should sound very, very weird to our ears.

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