7-limit: Difference between revisions

+subsets, supersets, relation to odd limits and harmonic/subharmonic modes
Move the property of infinity to the parent page
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{{Prime limit navigation|7}}
{{Prime limit navigation|7}}
{{Wikipedia|7-limit tuning}}
{{Wikipedia|7-limit tuning}}
The '''7-limit''' or 7-prime-limit consists of [[just intonation|rational intervals]] where 7 is the highest allowable [[prime]] factor, so that every such interval may be written as a [[ratio]] of integers which are products of 2, 3, 5 and 7. This is an infinite set and still infinite even if we restrict consideration to a single octave. Some examples within the octave include [[7/4]], [[7/5]], [[7/6]], [[9/7]], [[15/14]], [[21/16]], [[21/20]], [[35/27]], [[49/36]], and so on. The 7-limit is the fourth prime limit and is a superset of the [[5-limit]] and a subset of the [[11-limit]].  
The '''7-limit''' or 7-prime-limit consists of [[just intonation|rational intervals]] where 7 is the highest allowable [[prime]] factor, so that every such interval may be written as a [[ratio]] of integers which are products of 2, 3, 5 and 7. The 7-limit is the fourth prime limit and is a superset of the [[5-limit]] and a subset of the [[11-limit]]. Some examples of 7-limit intervals include [[7/4]], [[7/5]], [[7/6]], [[9/7]], [[15/14]], [[21/16]], [[21/20]], [[35/27]], [[49/36]], and so on.  


These things are contained by the 7-limit, but not the 5-limit:  
These things are contained by the 7-limit, but not the 5-limit: