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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | A '''prime interval''' or '''prime harmonic''' is a [[harmonic]] which as a [[ratio]] of frequencies is a [[prime number]]; that is, a number such as 2, 3, 5, 7, 11, … which is divisible only by itself and 1. |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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| : This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-06-30 09:19:10 UTC</tt>.<br>
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| : The original revision id was <tt>239487635</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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| <h4>Original Wikitext content:</h4>
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| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">A **prime interval** is a musical interval which as a ratio of frequencies is a [[prime numbers|prime number]]; that is, a number such as 2, 3, 5, 7, ... which is divisible only by itself and 1. Any musical interval in the [[Harmonic Limit|p-limit]] can be expressed in terms of a product of prime numbers less than or equal to p.
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| Question: Is 5/3 a prime interval?</pre></div>
| | Any interval of [[just intonation|just intonation (JI)]] can be expressed in terms of a product of prime intervals, allowing us to decompose a complex JI interval into simpler parts. A prime interval itself cannot be expressed by other prime intervals, so no prime intervals are redundant for reconstructing the entirety of JI. For those reasons and for the fact that prime intervals occur in [[harmonic series]], they form a very important [[basis]] (literally and mathematically) for JI. |
| <h4>Original HTML content:</h4>
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| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>prime interval</title></head><body>A <strong>prime interval</strong> is a musical interval which as a ratio of frequencies is a <a class="wiki_link" href="/prime%20numbers">prime number</a>; that is, a number such as 2, 3, 5, 7, ... which is divisible only by itself and 1. Any musical interval in the <a class="wiki_link" href="/Harmonic%20Limit">p-limit</a> can be expressed in terms of a product of prime numbers less than or equal to p.<br />
| | 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. |
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| Question: Is 5/3 a prime interval?</body></html></pre></div>
| | 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 }}, …) |
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| | The opposite of a prime interval is a [[highly composite interval]]. |
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| | == Individual pages == |
| | See [[:Category: Prime harmonics]]. |
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| | == See also == |
| | * [[Patent val]] |
| | * [[Harmonic limit]] |
| | * [[Prime harmonic series]] |
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| | [[Category:Terms]] |
| | [[Category:Prime]] |
| | [[Category:Harmonic]] |