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 |
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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. | ||