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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]].
'''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]].


It can be seen as implying a rank-2 tuning which is [[generator|generated]] by an extremely sharp major third of about 443 cents 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 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.


See [[Sensipent family #Sensi]] for more technical data. For full 13-limit extensions of sensi, see [[Sensi extensions]].
See [[Sensipent family #Sensi]] for more technical data. For full 13-limit extensions of sensi, see [[Sensi extensions]].
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{| class="wikitable right-1 right-2 sortable"
{| class="wikitable right-1 right-2 sortable"
|-
! #
! #
! Cents{{asterisk}}
! Cents<sup>*</sup>
! class="unsortable" | Approximate Ratios<sup>&dagger;</sup>
! class="unsortable" |Approximate Ratios<sup>†</sup>
|-
|-
| 0
| 0
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|}
|}


: <sup>*</sup> in 2.3.5.7.13 CTE tuning
<nowiki />* In 2.3.5.7.13 CTE tuning
: <sup>†</sup> 2.3.5.7.13 ratio interpretations
 
&dagger; 2.3.5.7.13 Ratio interpretations


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


{| class="wikitable right-2 right-3 right-4 sortable "
{| class="wikitable right-2 right-3 right-4 sortable"
|-
|-
! class="unsortable" | Degree
! class="unsortable" | Degree
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! Size in [[46edo]]
! Size in [[46edo]]
! class="unsortable" | Approximate ratios
! class="unsortable" | Approximate ratios
! #Generators up
! &#35;Generators up
|-
|-
| unison
| unison
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Other otonal chords approximated in the 8-note MOS include:
Other otonal chords approximated in the 8-note MOS include:


* root - maj. sen7th - maj. sen8th ≈ 7:12:13
* Root - maj. sen7th - maj. sen8th ≈ 7:12:13
* root - maj. sen2nd - maj. sen5th ≈ 9:10:13
* Root - maj. sen2nd - maj. sen5th ≈ 9:10:13
* root - min. sen3rd - dim. sen6th ≈ 6:7:9
* Root - min. sen3rd - dim. sen6th ≈ 6:7:9
* root - perf. sen4th - dim. sen6th ≈ 10:13:15 (ultramajor triad)
* Root - perf. sen4th - dim. sen6th ≈ 10:13:15 (ultramajor triad)
* root - perf. sen4th - maj. sen7th ≈ 7:9:13
* Root - perf. sen4th - maj. sen7th ≈ 7:9:13
* root - perf. sen4th - maj. sen5th - maj. sen7th ≈ 7:9:10:13
* Root - perf. sen4th - maj. sen5th - maj. sen7th ≈ 7:9:10:13
* root - perf. sen4th - min. sen7th ≈ 10:13:18
* Root - perf. sen4th - min. sen7th ≈ 10:13:18
* root - perf. sen4th - min. sen5th - min. sen7th ≈ 10:13:14:18
* Root - perf. sen4th - min. sen5th - min. sen7th ≈ 10:13:14:18
* root - min. sen7th - min. sen3rd (+ octave) ≈ 3:5:7
* Root - min. sen7th - min. sen3rd (+ octave) ≈ 3:5:7
* root - min. sen7th - min. sen2nd (+ octave) ≈ 6:10:13
* Root - min. sen7th - min. sen2nd (+ octave) ≈ 6:10:13
* root - dim. sen6th - min. sen7th ≈ 6:9:10
* Root - dim. sen6th - min. sen7th ≈ 6:9:10
* root - dim. sen6th - min. sen2nd (+octave) ≈ 6:9:13
* Root - dim. sen6th - min. sen2nd (+octave) ≈ 6:9:13


== Scales ==
== Scales ==
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{| class="wikitable center-all left-4"
{| class="wikitable center-all left-4"
|-
|-
! Edo<br>Generators
! Edo<br />Generators
! [[Eigenmonzo|Eigenmonzo<br>(Unchanged-interval)]]<nowiki>*</nowiki>
! [[Eigenmonzo|Eigenmonzo<br />(Unchanged-interval)]]{{asterisk}}
! Generator (¢)
! Generator (¢)
! Comments
! Comments
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|
|
|}
|}
<nowiki>*</nowiki> besides the octave
<nowiki />* Besides the octave


== Visualizations ==
== Visualizations ==
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; [[Budjarn Lambeth]]
; [[Budjarn Lambeth]]
* [https://www.youtube.com/watch?v=qc0CkUKj7t4 Music in Sensi Temperament (+ Tempered Octaves) - Mar 2024]
* [https://www.youtube.com/watch?v=qc0CkUKj7t4 Music in Sensi Temperament (+ Tempered Octaves) &ndash; Mar 2024]


[[Category:Temperaments]]
[[Category:Temperaments]]
[[Category:Sensi| ]] <!-- main article -->
[[Category:Sensi| ]] <!-- Main article -->
[[Category:Sensipent family]]
[[Category:Sensipent family]]
[[Category:Sensamagic clan]]
[[Category:Sensamagic clan]]
Retrieved from "https://en.xen.wiki/w/Sensi"