Sensi: Difference between revisions

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'''Sensi''', in this article, is the [[Rank-2 temperament|rank-2]] [[regular temperament]] for the 2.3.5.7.13 [[subgroup]] defined by [[tempering out]] [[~~245~~/~~243~~]], [[126/125]], and [[91/90]]. See [[sensipent]] for alternative extensions of 5-limit sensi.

'''Sensi''', in this article, is the [[Rank-2 temperament|rank-2]] [[regular temperament]] for the 2.3.5.7.13 [[subgroup]] defined by [[tempering out]] [[91/90]], [[126/125]], and [[245/243]]. See [[sensipent]] for alternative extensions of 5-limit sensi.

It can be seen as implying a rank-2 tuning which is [[generator|generated]] by an extremely sharp major third of 440–~~445~~{{c}} which represents both [[9/7]] and [[13/10]]. It is so named because the generator is a "semisixth": two generators make a major sixth which approximates [[5/3]], which cannot occur in [[12edo]]. Equal temperaments that support sensi include [[19edo]] (generator 7\19; [[soft]] [[sensoid]]), [[27edo]] (generator 10\27; [[supersoft]] sensoid), and [[46edo]] (generator 17\46; L/s = 7/5, more optimized for sensi temperament). More obscure but significantly more accurate interpretations of its generator are given by [[sensible]] and especially [[sensipent]]'s extension to the 2.3.5.31 subgroup.

It can be seen as implying a rank-2 tuning which is [[generator|generated]] by an extremely sharp major third of between 440–446{{cent}} which represents both [[9/7]] and [[13/10]]. It is so named because the generator is a "semisixth": two generators make a major sixth which approximates [[5/3]], which cannot occur in [[12edo]]. Equal temperaments that support sensi include [[19edo]] (generator 7\19; [[soft]] [[sensoid]]), [[27edo]] (generator 10\27; [[supersoft]] sensoid), and [[46edo]] (generator 17\46; {{nowrap|L/s {{=}} 7/5}}, more optimized for sensi temperament). More obscure but significantly more accurate interpretations of its generator are given by [[sensible]] and especially [[sensipent]]'s extension to the 2.3.5.31 subgroup.

See [[Sensipent family #Sensi]] for more technical data. For full 13-limit extensions of sensi, see [[Sensi extensions]].

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=== In Sensi[8] ===

Sensi[8] is a [[mos scale]] with a [[3L 5s]] pattern (or [[5L 3s]] in extreme cases where the generator is larger than 450{{~~cent~~}}). See [[3L 5s #Modes]] (resp. [[5L 3s #Modes]]) to see which modes have which qualities for each interval size.

Sensi[8] is a [[mos scale]] with a [[3L 5s]] pattern (or [[5L 3s]] in extreme cases where the generator is larger than 450{{c}}). See [[3L 5s#Modes]] (resp. [[5L 3s#Modes]]) to see which modes have which qualities for each interval size.

Sortable table of Sensi[8]'s major and minor intervals in various sensi tunings:

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One of the most common consonant triads in sensi is the 6:10:13 triad, which spans 3 generators. Sensi[8] has five 6:10:13 triads, four 7:9:13 triads, three 5:6:7:9 tetrads and one 5:6:7:9:13 pentad. Having many diminished triads, it is similar to the 12edo diminished scale in some ways. Sensi is interesting mainly because it gives new 13-limit interpretations to fairly familiar (in the sense of extended meantone-like) intervals. Restricted to the 8-note MOS, it is essentially a [[non-over-1 temperament]].

Melodically, sensi[8] sounds fairly familiar because many intervals are either 5-limit or have familiar categorical interpretations, being represented in the meantone tuning [[19edo]]. For example, the small step of about 130 ~~cents~~ categorizes pretty well as a large semitone (except at places in the scale where two of them make a flat subminor third); the large step is a small whole tone representing 10/9.

Melodically, sensi[8] sounds fairly familiar because many intervals are either 5-limit or have familiar categorical interpretations, being represented in the meantone tuning [[19edo]]. For example, the small step of about 130{{c}} categorizes pretty well as a large semitone (except at places in the scale where two of them make a flat subminor third); the large step is a small whole tone representing 10/9.

The root-sen5th-sen8th chords in sensi[8] usually spell 5:7:9 (root-minor sen5th-minor sen8th) and 7:10:13 (root-major sen5th-major sen8th) chords (shown in the Anti-Dylathian mode QJKLMNOPQ = ssLssLsL):

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-'''Sensi''', in this article, is the [[Rank-2 temperament|rank-2]] [[regular temperament]] for the 2.3.5.7.13 [[subgroup]] defined by [[tempering out]] [[245/243]], [[126/125]], and [[91/90]]. See [[sensipent]] for alternative extensions of 5-limit sensi.
+'''Sensi''', in this article, is the [[Rank-2 temperament|rank-2]] [[regular temperament]] for the 2.3.5.7.13 [[subgroup]] defined by [[tempering out]] [[91/90]], [[126/125]], and [[245/243]]. See [[sensipent]] for alternative extensions of 5-limit sensi.
-It can be seen as implying a rank-2 tuning which is [[generator|generated]] by an extremely sharp major third of 440&ndash;445{{c}} which represents both [[9/7]] and [[13/10]]. It is so named because the generator is a "semisixth": two generators make a major sixth which approximates [[5/3]], which cannot occur in [[12edo]]. Equal temperaments that support sensi include [[19edo]] (generator 7\19; [[soft]] [[sensoid]]), [[27edo]] (generator 10\27; [[supersoft]] sensoid), and [[46edo]] (generator 17\46; L/s = 7/5, more optimized for sensi temperament). More obscure but significantly more accurate interpretations of its generator are given by [[sensible]] and especially [[sensipent]]'s extension to the 2.3.5.31 subgroup.
+It can be seen as implying a rank-2 tuning which is [[generator|generated]] by an extremely sharp major third of between 440&ndash;446{{cent}} which represents both [[9/7]] and [[13/10]]. It is so named because the generator is a "semisixth": two generators make a major sixth which approximates [[5/3]], which cannot occur in [[12edo]]. Equal temperaments that support sensi include [[19edo]] (generator 7\19; [[soft]] [[sensoid]]), [[27edo]] (generator 10\27; [[supersoft]] sensoid), and [[46edo]] (generator 17\46; {{nowrap|L/s {{=}} 7/5}}, more optimized for sensi temperament). More obscure but significantly more accurate interpretations of its generator are given by [[sensible]] and especially [[sensipent]]'s extension to the 2.3.5.31 subgroup.
 See [[Sensipent family #Sensi]] for more technical data. For full 13-limit extensions of sensi, see [[Sensi extensions]].
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 ! &#35;
 ! Cents*
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 === In Sensi[8] ===
-Sensi[8] is a [[mos scale]] with a [[3L 5s]] pattern (or [[5L 3s]] in extreme cases where the generator is larger than 450{{cent}}). See [[3L 5s #Modes]] (resp. [[5L 3s #Modes]]) to see which modes have which qualities for each interval size.
+Sensi[8] is a [[mos scale]] with a [[3L&nbsp;5s]] pattern (or [[5L&nbsp;3s]] in extreme cases where the generator is larger than 450{{c}}). See [[3L&nbsp;5s#Modes]] (resp. [[5L&nbsp;3s#Modes]]) to see which modes have which qualities for each interval size.
 Sortable table of Sensi[8]'s major and minor intervals in various sensi tunings:
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 One of the most common consonant triads in sensi is the 6:10:13 triad, which spans 3 generators. Sensi[8] has five 6:10:13 triads, four 7:9:13 triads, three 5:6:7:9 tetrads and one 5:6:7:9:13 pentad. Having many diminished triads, it is similar to the 12edo diminished scale in some ways. Sensi is interesting mainly because it gives new 13-limit interpretations to fairly familiar (in the sense of extended meantone-like) intervals. Restricted to the 8-note MOS, it is essentially a [[non-over-1 temperament]].
-Melodically, sensi[8] sounds fairly familiar because many intervals are either 5-limit or have familiar categorical interpretations, being represented in the meantone tuning [[19edo]]. For example, the small step of about 130 cents categorizes pretty well as a large semitone (except at places in the scale where two of them make a flat subminor third); the large step is a small whole tone representing 10/9.
+Melodically, sensi[8] sounds fairly familiar because many intervals are either 5-limit or have familiar categorical interpretations, being represented in the meantone tuning [[19edo]]. For example, the small step of about 130{{c}} categorizes pretty well as a large semitone (except at places in the scale where two of them make a flat subminor third); the large step is a small whole tone representing 10/9.
 The root-sen5th-sen8th chords in sensi[8] usually spell 5:7:9 (root-minor sen5th-minor sen8th) and 7:10:13 (root-major sen5th-major sen8th) chords (shown in the Anti-Dylathian mode QJKLMNOPQ = ssLssLsL):