Sensi: Difference between revisions

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'''Sensi''' is a [[rank-2 temperament|rank-2]] [[regular temperament]] that is [[generator|generated]] by an extremely sharp major third of between 442 and 445{{cent}}. In the [[7-limit]], this interval represents [[9/7]], and by the most important equivalence in sensi (i.e. [[tempering out]] [[245/243]]), two of these thirds stack to a major sixth which approximates [[5/3]]. The next comma to be tempered out is [[126/125]], through which three of these major sixths approximate [[7/6]], two octaves up. The [[6/1|6th harmonic]] is therefore split into seven. Furthermore, since the supermajor third is tempered so sharply, it makes sense to have it represent both 9/7 and [[13/10]], which results in [[91/90]] being tempered out in the 2.3.5.7.13 [[subgroup]].

The structure whereby 5/3 is split into two supermajor thirds is obviously xenharmonic as this cannot occur in [[12edo]]. But particularly, as the simplest [[EDO]]s with similar structures are [[8edo]] and [[11edo]] (whence the 8-note ([[3L 5s]]/checkertonic) and 11-note ([[8L 3s]]/flanatonic) [[MOS scale]]s), sensi has a very xenmelodic character compared to many other ways of organizing the 7-limit (such as [[superpyth]], which is based on the familiar [[chain of fifths]], and even [[porcupine]], which is fundamentally heptatonic).

The structure whereby 5/3 is split into two supermajor thirds is obviously xenharmonic as this cannot occur in [[12edo]]. But particularly, as the simplest [[EDO]]s with similar structures are [[8edo]] and [[11edo]] (whence the 8-note ([[3L 5s]], checkertonic) and 11-note ([[8L 3s]], flanatonic) [[MOS scale]]s), sensi has a very xenmelodic character compared to many other ways of organizing the 7-limit (such as [[superpyth]], which is based on the familiar [[chain of fifths]], and even [[porcupine]], which is fundamentally heptatonic).

Equal temperaments that support sensi include [[19edo]] (generator 7\19; [[soft]] checkertonic), [[27edo]] (generator 10\27; [[supersoft]] checkertonic), and [[46edo]] (generator 17\46; {{nowrap| L/s {{=}} 7/5 }}, more optimized for sensi temperament).

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 '''Sensi''' is a [[rank-2 temperament|rank-2]] [[regular temperament]] that is [[generator|generated]] by an extremely sharp major third of between 442 and 445{{cent}}. In the [[7-limit]], this interval represents [[9/7]], and by the most important equivalence in sensi (i.e. [[tempering out]] [[245/243]]), two of these thirds stack to a major sixth which approximates [[5/3]]. The next comma to be tempered out is [[126/125]], through which three of these major sixths approximate [[7/6]], two octaves up. The [[6/1|6th harmonic]] is therefore split into seven. Furthermore, since the supermajor third is tempered so sharply, it makes sense to have it represent both 9/7 and [[13/10]], which results in [[91/90]] being tempered out in the 2.3.5.7.13 [[subgroup]].
-The structure whereby 5/3 is split into two supermajor thirds is obviously xenharmonic as this cannot occur in [[12edo]]. But particularly, as the simplest [[EDO]]s with similar structures are [[8edo]] and [[11edo]] (whence the 8-note ([[3L 5s]]/checkertonic) and 11-note ([[8L 3s]]/flanatonic) [[MOS scale]]s), sensi has a very xenmelodic character compared to many other ways of organizing the 7-limit (such as [[superpyth]], which is based on the familiar [[chain of fifths]], and even [[porcupine]], which is fundamentally heptatonic).
+The structure whereby 5/3 is split into two supermajor thirds is obviously xenharmonic as this cannot occur in [[12edo]]. But particularly, as the simplest [[EDO]]s with similar structures are [[8edo]] and [[11edo]] (whence the 8-note ([[3L 5s]], checkertonic) and 11-note ([[8L 3s]], flanatonic) [[MOS scale]]s), sensi has a very xenmelodic character compared to many other ways of organizing the 7-limit (such as [[superpyth]], which is based on the familiar [[chain of fifths]], and even [[porcupine]], which is fundamentally heptatonic).
 Equal temperaments that support sensi include [[19edo]] (generator 7\19; [[soft]] checkertonic), [[27edo]] (generator 10\27; [[supersoft]] checkertonic), and [[46edo]] (generator 17\46; {{nowrap| L/s {{=}} 7/5 }}, more optimized for sensi temperament).