Sensi extensions: Difference between revisions

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[[Sensi]] has multiple competing [[extension]]s to the [[11-limit]]. The simplest [[7-limit]] [[comma]]s of sensi are [[126/125|starling (126/125)]] and [[245/243|sensamagic (245/243)]], and it can be viewed as the merge of the two corresponding [[rank-3 temperament]]s. These rank-3 temperaments are associated with distinct paths to the 11-limit. On one hand, [[starling]] strongly suggests tempering out [[176/175]], leading to thrush ({126/125, 176/175}). ~~Note:~~ 126/125 = (176/175)(441/440). On the other, [[sensamagic]] strongly suggests tempering out [[385/384]], leading to undecimal sensamagic ({245/243, 385/384}). ~~Note:~~ 245/243 = (385/384)(896/891). Taking either path for sensi leads us to the following entries:

[[Sensi]] has multiple competing [[extension]]s to the [[11-limit]]. The simplest [[7-limit]] [[comma]]s of sensi are [[126/125|starling (126/125)]] and [[245/243|sensamagic (245/243)]], and it can be viewed as the merge of the two corresponding [[rank-3 temperament]]s. These rank-3 temperaments are associated with distinct paths to the 11-limit. On one hand, [[starling]] strongly suggests tempering out [[176/175]], leading to thrush ({126/125, 176/175}). Notice the factorization 126/125 = (176/175)(441/440). On the other, [[sensamagic]] strongly suggests tempering out [[385/384]], leading to undecimal sensamagic ({245/243, 385/384}). Notice the factorization 245/243 = (385/384)(896/891). Taking either path for sensi leads us to one of the following entries:

* '''Sensor''' (19 & 27) – tempering out 126/125, 245/243, 385/384

* '''Sensus''' (19e & 27e) – tempering out 126/125, 176/175, 245/243

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The two unite in [[46edo|46et]], where both 176/175 and 385/384, as well as their sum, [[121/120]], are tempered out. They can be extended to the 13- and 17-limit naturally by adding [[91/90]] and [[154/153]] to the comma list in this order. Then the generator represents [[9/7]], [[13/10]], and [[22/17]].

In addition, ~~here~~ are some low-complexity low-accuracy entries:

In addition, there are some low-complexity low-accuracy entries:

* '''Sensis''' (19 & 27e) – tempering out 56/55, 100/99, 245/243

* '''Sensa''' (19e & 27) – tempering out 55/54, 77/75, 99/98

Another possible path which relates a sense of compromise is to temper out [[121/120]], leading to bisensi. This ~~temperament~~ is supported by [[38edo|38df]], 46, and [[54edo|54c]].

Another possible path which relates a sense of compromise is to temper out [[121/120]], leading to bisensi. This has the effect of slicing the octave in two, and is supported by [[38edo|38df]], 46, and [[54edo|54c]].

== Interval chain ==

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-[[Sensi]] has multiple competing [[extension]]s to the [[11-limit]]. The simplest [[7-limit]] [[comma]]s of sensi are [[126/125|starling (126/125)]] and [[245/243|sensamagic (245/243)]], and it can be viewed as the merge of the two corresponding [[rank-3 temperament]]s. These rank-3 temperaments are associated with distinct paths to the 11-limit. On one hand, [[starling]] strongly suggests tempering out [[176/175]], leading to thrush ({126/125, 176/175}). Note: 126/125 = (176/175)(441/440). On the other, [[sensamagic]] strongly suggests tempering out [[385/384]], leading to undecimal sensamagic ({245/243, 385/384}). Note: 245/243 = (385/384)(896/891). Taking either path for sensi leads us to the following entries:
+[[Sensi]] has multiple competing [[extension]]s to the [[11-limit]]. The simplest [[7-limit]] [[comma]]s of sensi are [[126/125|starling (126/125)]] and [[245/243|sensamagic (245/243)]], and it can be viewed as the merge of the two corresponding [[rank-3 temperament]]s. These rank-3 temperaments are associated with distinct paths to the 11-limit. On one hand, [[starling]] strongly suggests tempering out [[176/175]], leading to thrush ({126/125, 176/175}). Notice the factorization 126/125 = (176/175)(441/440). On the other, [[sensamagic]] strongly suggests tempering out [[385/384]], leading to undecimal sensamagic ({245/243, 385/384}). Notice the factorization 245/243 = (385/384)(896/891). Taking either path for sensi leads us to one of the following entries:
 * '''Sensor''' (19 &amp; 27) – tempering out 126/125, 245/243, 385/384
 * '''Sensus''' (19e &amp; 27e) – tempering out 126/125, 176/175, 245/243
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 The two unite in [[46edo|46et]], where both 176/175 and 385/384, as well as their sum, [[121/120]], are tempered out. They can be extended to the 13- and 17-limit naturally by adding [[91/90]] and [[154/153]] to the comma list in this order. Then the generator represents [[9/7]], [[13/10]], and [[22/17]].
-In addition, here are some low-complexity low-accuracy entries:
+In addition, there are some low-complexity low-accuracy entries:
 * '''Sensis''' (19 &amp; 27e) – tempering out 56/55, 100/99, 245/243
 * '''Sensa''' (19e &amp; 27) – tempering out 55/54, 77/75, 99/98
-Another possible path which relates a sense of compromise is to temper out [[121/120]], leading to bisensi. This temperament is supported by [[38edo|38df]], 46, and [[54edo|54c]].
+Another possible path which relates a sense of compromise is to temper out [[121/120]], leading to bisensi. This has the effect of slicing the octave in two, and is supported by [[38edo|38df]], 46, and [[54edo|54c]].
 == Interval chain ==