Sensi: Difference between revisions

Line 12:

| Mapping = 1; 7 9 13 10

| Pergen = (P8, ccP5/7)

| Odd limit 1 = 7 | Mistuning 1 = ~~???~~ | Complexity 1 = 19

| Odd limit 1 = 7 | Mistuning 1 = 7.5c | Complexity 1 = 19

| Odd limit 2 = (2.3.5.7.13) 21 | Mistuning 2 = ~~???~~ | Complexity 2 = 27

| Odd limit 2 = (2.3.5.7.13) 21 | Mistuning 2 = 11.1c | Complexity 2 = 27

}}

'''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]].

'''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}}, which is taken in the [[7-limit]] to represent a sharpened [[9/7]]. The most important equivalence in sensi (i.e. [[tempering out]] [[245/243]]) is known as ''sensamagic'', by which two of these thirds stack to a major sixth which approximates [[5/3]]. Sensi then makes the additional tempering of [[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).

@@ Line 12: / Line 12: @@
 | Mapping = 1; 7 9 13 10
 | Pergen = (P8, ccP5/7)
-| Odd limit 1 = 7 | Mistuning 1 = ??? | Complexity 1 = 19
+| Odd limit 1 = 7 | Mistuning 1 = 7.5c | Complexity 1 = 19
-| Odd limit 2 = (2.3.5.7.13) 21 | Mistuning 2 = ??? | Complexity 2 = 27
+| Odd limit 2 = (2.3.5.7.13) 21 | Mistuning 2 = 11.1c | Complexity 2 = 27
 }}
-'''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]].
+'''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}}, which is taken in the [[7-limit]] to represent a sharpened [[9/7]]. The most important equivalence in sensi (i.e. [[tempering out]] [[245/243]]) is known as ''sensamagic'', by which two of these thirds stack to a major sixth which approximates [[5/3]]. Sensi then makes the additional tempering of [[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).