Sensi: Difference between revisions

Line 12:

| Mapping = 1; 7 9 13 10

| Pergen = (P8, ccP5/7)

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

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

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

| Odd limit 2 = (2.3.5.7.13) 21 | Mistuning 2 = 11.1 | 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}}, which is taken in the [[7-limit]] to represent a sharpened [[9/7]]. The most important equivalence in sensi (i.e. [[tempering out]] the comma [[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, and [[5/4]] is divided into three parts, each identified with [[15/14]]. Furthermore, since the supermajor third is tempered so sharply, it makes sense to have it represent both 9/7 and [[13/10]], which means [[91/90]] is tempered out in the 2.3.5.7.13 [[subgroup]]. There the 15/14 interval also represents [[14/13]] and [[13/12]], which results in [[169/168]] and [[196/195]] being tempered out.

@@ Line 12: / Line 12: @@
 | Mapping = 1; 7 9 13 10
 | Pergen = (P8, ccP5/7)
-| Odd limit 1 = 7 | Mistuning 1 = 7.5c | Complexity 1 = 19
+| Odd limit 1 = 7 | Mistuning 1 = 7.5 | Complexity 1 = 19
-| Odd limit 2 = (2.3.5.7.13) 21 | Mistuning 2 = 11.1c | Complexity 2 = 27
+| Odd limit 2 = (2.3.5.7.13) 21 | Mistuning 2 = 11.1 | 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}}, which is taken in the [[7-limit]] to represent a sharpened [[9/7]]. The most important equivalence in sensi (i.e. [[tempering out]] the comma [[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, and [[5/4]] is divided into three parts, each identified with [[15/14]]. Furthermore, since the supermajor third is tempered so sharply, it makes sense to have it represent both 9/7 and [[13/10]], which means [[91/90]] is tempered out in the 2.3.5.7.13 [[subgroup]]. There the 15/14 interval also represents [[14/13]] and [[13/12]], which results in [[169/168]] and [[196/195]] being tempered out.