Useful properties of prime number tunings

[Dovdimus Prime]

Hi chaps

I enjoy working with 19tET a lot, but one of the things I miss from working with 12tET are its yummy symmetric properties, i.e. the ambiguous properties of scales such as whole tone and chords like augmented triads.

Prime number tunings have the property that any interval can be used to generate all the tones (much as the cycle of fifths can generate all the tones in 12tET), but this is not a property I consider useful from the compositional standpoint.

Just wondering if any of you consider there are any properties of prime number tunings that come in handy when writing music.

Interested to know what you think!

Ta

Dovder

[seraph]

what do you mean by "prime number tunings"?
the division of an octave into a number of equal steps like 7, 11, 13tET? or something like prime limit?

[Dovdimus Prime]

Hi Carlo

I mean the former. I have been working with 17tET and 19tET a fair bit.

I would also be interested in talking about tonality in microtonal tunings, but I'm interested to see if anyone's got anything to say about the mathematical properties just now.

Cheers

Dovder

[xjscott]

That's an interesting point. When you have a p-tET scale, since p, being prime, is not divisible by any other number than itself, it means that any other interval, repeated, is not going to line up with the repeat interval of the scale (octave in the case of a tET), and so any ascending or descending sequence of such intervals is going to wrap around in a spiral pattern, hitting all the notes of the scale.

Have you exploited this property in any compositions you'd like to share?