Sensi extensions: Difference between revisions

[[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 ({{nowrap|{126/125, 176/175}}}), since {{nowrap|126/125 {{=}} (176/175)(441/440)}}. On the other, [[sensamagic]] strongly suggests tempering out [[385/384]], leading to undecimal sensamagic ({{nowrap|{245/243, 385/384}}}), since {{nowrap|245/243 {{=}} (385/384)(896/891)}}. Taking either path for sensi leads us to one of the following entries:  

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

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]].