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 Forum index » How-tos » Micro Tuning
Useful properties of prime number tunings
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Dovdimus Prime



Joined: Jul 26, 2004
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Location: Bristol, UK
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PostPosted: Tue Jun 15, 2010 3:12 pm    Post subject: Useful properties of prime number tunings Reply with quote  Mark this post and the followings unread

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

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seraph
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Joined: Jun 21, 2003
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PostPosted: Tue Jun 15, 2010 3:49 pm    Post subject: Reply with quote  Mark this post and the followings unread

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?

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Dovdimus Prime



Joined: Jul 26, 2004
Posts: 664
Location: Bristol, UK
Audio files: 6

PostPosted: Mon Jul 05, 2010 4:34 am    Post subject: Reply with quote  Mark this post and the followings unread

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

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xjscott



Joined: Apr 25, 2007
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Location: Appalachia

PostPosted: Sun Jul 18, 2010 6:53 am    Post subject: Reply with quote  Mark this post and the followings unread

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?
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