Sensi: Difference between revisions

Line 3:

| en = Sensi

}}

'''Sensi''' is a [[rank-2 temperament|rank-2]] [[regular temperament]] ~~in the 2.3.5.7.13 [[subgroup]]~~ [[generator|generated]] by an extremely sharp major third of between ~~440~~ and ~~446~~{{cent}} ~~which~~ represents ~~both~~ [[9/7]] and [[13/10]], ~~such that~~ two of these thirds stack to a major sixth which approximates [[5/3~~]], which cannot occur in [[12edo~~]]. ~~This results in~~ [[91/90]], [[~~126~~/~~125~~]], ~~and~~ [[~~245~~/~~243~~]] ~~being~~ tempered ~~out~~, ~~making~~ it an [[~~extension~~]] ~~of both~~ [[~~sensipent~~]] ~~and~~ [[~~BPS~~]].

'''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]].

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)~~. 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~~.

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 and 11-note [[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).

See [[Sensipent family #Sensi]] for more technical data, and [[Sensi extensions]] for extensions of sensi that include the [[11/1|11th harmonic]].

== ~~Intervals~~ ==

== Theory ==

=== Sensi vs. sentry vs. sensipent ===

It is worth noting that sensi distinguishes itself from other structures based around 245/243 (whose basic form in the 2.9/7.5/3 subgroup is known as [[sentry]]) by virtue of its minor third (6/5) being ''flattened'' from just rather than sharpened. This results in the supermajor third being sharpened even more than is typical, so much so that it is tuned [[interseptimal]]ly and may not fulfill all the functions that [[~]]9/7 is intended to have.

One way around this is to eschew the generator's interpretation as 9/7 altogether, and focus on the [[5-limit]] part of sensi, which is known as [[sensipent]] (whose comma is [[78732/78125]]). From there, an interpretation of the generator as [[31/24]]~[[40/31]] is apparent. Beyond the 2.3.5.31 subgroup, more accurate interpretations (in comparison to sensi) of sensipent's extended harmony are given by [[sensible]] (adding primes 11, 17, and 23) and [[sendai]] (adding 23 and 29).

=== Interval chain ===

In the following table, odd harmonics and subharmonics 1–21 are in '''bold'''.

Line 105:

Line 114:

<nowiki/>* In 2.3.5.7.13 CWE tuning

=== In Sensi[8] ===

=== Intervals of 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{{c}}). See [[3L 5s #Modes]] (resp. [[5L 3s #Modes]]) to see which modes have which qualities for each interval size.

@@ Line 3: / Line 3: @@
 | en = Sensi
 }}
-'''Sensi''' is a [[rank-2 temperament|rank-2]] [[regular temperament]] in the 2.3.5.7.13 [[subgroup]] [[generator|generated]] by an extremely sharp major third of between 440 and 446{{cent}} which represents both [[9/7]] and [[13/10]], such that two of these thirds stack to a major sixth which approximates [[5/3]], which cannot occur in [[12edo]]. This results in [[91/90]], [[126/125]], and [[245/243]] being tempered out, making it an [[extension]] of both [[sensipent]] and [[BPS]].
+'''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]].
-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). 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.
+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 and 11-note [[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).
 See [[Sensipent family #Sensi]] for more technical data, and [[Sensi extensions]] for extensions of sensi that include the [[11/1|11th harmonic]].
-== Intervals ==
+== Theory ==
+=== Sensi vs. sentry vs. sensipent ===
+{{Main| Sensipent }}
+It is worth noting that sensi distinguishes itself from other structures based around 245/243 (whose basic form in the 2.9/7.5/3 subgroup is known as [[sentry]]) by virtue of its minor third (6/5) being ''flattened'' from just rather than sharpened. This results in the supermajor third being sharpened even more than is typical, so much so that it is tuned [[interseptimal]]ly and may not fulfill all the functions that [[~]]9/7 is intended to have.
+One way around this is to eschew the generator's interpretation as 9/7 altogether, and focus on the [[5-limit]] part of sensi, which is known as [[sensipent]] (whose comma is [[78732/78125]]). From there, an interpretation of the generator as [[31/24]]~[[40/31]] is apparent. Beyond the 2.3.5.31 subgroup, more accurate interpretations (in comparison to sensi) of sensipent's extended harmony are given by [[sensible]] (adding primes 11, 17, and 23) and [[sendai]] (adding 23 and 29).
 === Interval chain ===
 In the following table, odd harmonics and subharmonics 1–21 are in '''bold'''.
@@ Line 105: / Line 114: @@
 <nowiki/>* In 2.3.5.7.13 CWE tuning
-=== In Sensi[8] ===
+=== Intervals of Sensi[8] ===
 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.