Prime interval: Difference between revisions

+link to highly composite interval
don't expect people to know what "unity" means.
 
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For example, the [[2/1|octave]] is a prime interval whereas the intervals [[5/3]] or even [[1/1]] are not. In traditional ratio notation, the prime intervals are [[2/1]], [[3/1]], [[5/1]], [[7/1]], [[11/1]] etc.
For example, the [[2/1|octave]] is a prime interval whereas the intervals [[5/3]] or even [[1/1]] are not. In traditional ratio notation, the prime intervals are [[2/1]], [[3/1]], [[5/1]], [[7/1]], [[11/1]] etc.


The [[monzo]] notation of each prime interval consists of all-zeros except for a single unity entry: (2: {{monzo| 1 }}, 3: {{monzo| 0 1 }}, 5: {{monzo| 0 0 1 }}, 7: {{monzo| 0 0 0 1 }}, 11: {{monzo| 0 0 0 0 1 }}, …)
The [[monzo]] notation of each prime interval consists of all-zeros except for a single entry equal to 1: (2: {{monzo| 1 }}, 3: {{monzo| 0 1 }}, 5: {{monzo| 0 0 1 }}, 7: {{monzo| 0 0 0 1 }}, 11: {{monzo| 0 0 0 0 1 }}, …)


The opposite of a prime interval is a [[highly composite interval]].  
The opposite of a prime interval is a [[highly composite interval]].