Interval span: Difference between revisions

Cmloegcmluin (talk | contribs)
I think it's less confusing to say "different" here, since the linear span meaning is not really a broadening of the interval span meaning
Dummy index (talk | contribs)
+link
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The '''span''' of an interval is a technical term referring to the size of an interval, typically in some logarithmic unit such as cents, octaves, or something else. The [[JIP]] can give the span of any just interval, whereas within regular temperaments, this is typically given by a [[tuning map]].
The '''span''' of an interval is a technical term referring to the [[Interval size measure|size of an interval]], typically in some logarithmic unit such as cents, octaves, or something else. The [[JIP]] can give the span of any just interval, whereas within regular temperaments, this is typically given by a [[tuning map]].


The span of some comma can be thought of as a very simple metric to measure the usefulness of the temperament vanishing that comma. This is because the formula for the [[TE simple badness|simple badness]], which is the product of the best-case tuning error and the complexity of the temperament, happens to reduce to the span of the comma in the situation where there is only one comma tempered out.
The span of some comma can be thought of as a very simple metric to measure the usefulness of the temperament vanishing that comma. This is because the formula for the [[TE simple badness|simple badness]], which is the product of the best-case tuning error and the complexity of the temperament, happens to reduce to the span of the comma in the situation where there is only one comma tempered out.