Interseptimal interval: Difference between revisions
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In the theory of [[Margo Schulter]], '''interseptimal''' is a category of intervals which occupy regions intermediate between two septimal ratios such as [[8/7]] and [[7/6]], or [[12/7]] and [[7/4]]. There are four interseptimal regions given below, with approximate cents ranges from Schulter's article [http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt Regions of the Interval Spectrum]: | In the theory of [[Margo Schulter]], '''interseptimal''' is a category of intervals which occupy regions intermediate between two septimal ratios such as [[8/7]] and [[7/6]], or [[12/7]] and [[7/4]]. There are four interseptimal regions given below, with approximate cents ranges from Schulter's article [http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt Regions of the Interval Spectrum]: | ||
* | * Maj2–min3 – intermediate between [[8/7]] and [[7/6]] – 240¢–260¢ | ||
* | * Maj3–4 – intermediate between [[9/7]] and [[21/16]] – 440¢–468¢ | ||
* | * 5–min6 – intermediate between [[32/21]] and [[14/9]] – 732¢–760¢ | ||
* | * Maj6–min7 – intermediate between [[12/7]] and [[7/4]] – 940¢–960¢ | ||
Interseptimal intervals are well-represented in [[24edo]] at 250¢, 450¢, 750¢ and 950¢. They also appear in [[19edo]] and [[29edo]]. | Interseptimal intervals are well-represented in [[24edo]] at 250¢, 450¢, 750¢ and 950¢. They also appear in [[19edo]] and [[29edo]]. | ||
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As they fall in ambiguous zones between simpler categories, they are inevitably xenharmonic. This also makes them difficult to name: do we classify a 250-cent interval as a second, a third, both, or neither? One option is to give each region a distinct name (analogous to using the word ''tritone'' rather than diminished fifth or augmented fourth). Possible names that could be used are: | As they fall in ambiguous zones between simpler categories, they are inevitably xenharmonic. This also makes them difficult to name: do we classify a 250-cent interval as a second, a third, both, or neither? One option is to give each region a distinct name (analogous to using the word ''tritone'' rather than diminished fifth or augmented fourth). Possible names that could be used are: | ||
* | * 240¢–260¢ – '''semifourth''' – an interval of this size is around half the size of a perfect fourth. | ||
* | * 440¢–468¢ – '''semisixth''' – an interval of this size is around half the size of a major sixth. | ||
** | ** The term '''naiadic''' (from ''naiad'', a kind of ancient Greek water spirit) refers to the 440c–464c region by [[Zhea Erose]], who uses it frequently. | ||
* | * 732¢–760¢ – '''semitenth''' – an interval of this size is around half the size of a minor tenth (i. e., an octave plus a minor third). Another possible name is sesquifourth (since this is also about one and a half times the size of a perfect fourth). | ||
* | ** The term '''cocytic''' was proposed by [[Inthar]], and is carried on with by [[Flora Canou]]<ref>Flora Canou criticizes ''semisixth'' and ''semitenth'' as they fail to make clear whether the interval to be split is major or minor, and prefers ''naiadic'' and ''cocytic''.</ref>. | ||
* 940¢–960¢ – '''semitwelfth''' – an interval of this size is around half the size of a perfect twelfth (i.e. a compound perfect fifth, or tritave). All even [[edt]]s have a semitwelfth of approximately 951 cents, analogous to the 600 cent tritone shared by all even edos. | |||
This makes notating these intervals very easy as long as we have an agreed-upon symbol for "semi". | This makes notating these intervals very easy as long as we have an agreed-upon symbol for "semi". | ||
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Some interseptimal intervals in all four ranges, both just and tempered, are listed below. | Some interseptimal intervals in all four ranges, both just and tempered, are listed below. | ||
=== | === Maj2–min3 – 240-260¢ === | ||
{| class="wikitable center-1 right-2" | {| class="wikitable center-1 right-2" | ||
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|} | |} | ||
=== | === Maj3–4 – 440-468¢ === | ||
{| class="wikitable center-1 right-2" | {| class="wikitable center-1 right-2" | ||
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|} | |} | ||
=== | === 5–min6 – 732-760¢ === | ||
{| class="wikitable center-1 right-2" | {| class="wikitable center-1 right-2" | ||
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|} | |} | ||
=== | === Maj6–min7 – 940-960¢ === | ||
{| class="wikitable center-1 right-2" | {| class="wikitable center-1 right-2" | ||
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* [[Gentle region]] | * [[Gentle region]] | ||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
== Notes == | |||
[[Category:Interseptimal| ]] <!-- main article --> | [[Category:Interseptimal| ]] <!-- main article --> | ||
[[Category:Interval category]] | [[Category:Interval category]] | ||