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}). 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: | [[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) | |||
* '''Sensus''' (19e & 27e) | * '''Sensor''' (19 & 27) – Tempering out 126/125, 245/243, 385/384 | ||
* '''Sensus''' (19e & 27e)– Tempering out 126/125, 176/175, 245/243 | |||
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]]. | 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: | In addition, there are some low-complexity low-accuracy entries: | ||
* '''Sensis''' (19 & 27e) | * '''Sensis''' (19 & 27e) – Tempering out 56/55, 100/99, 245/243 | ||
* '''Sensa''' (19e & 27) | * '''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 has the effect of slicing the octave in two, and 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]]. | ||
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{| class="wikitable right-1 right-2" | {| class="wikitable right-1 right-2" | ||
|- | |- | ||
! rowspan=2 | # | ! rowspan=2 | # | ||
! rowspan=2 | Cents | ! rowspan=2 | Cents* | ||
! colspan=5 | Approximate Ratios | ! colspan=5 | Approximate Ratios | ||
|- | |- | ||
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| | | | ||
|} | |} | ||
<nowiki />* In 2.3.5.7.13.17/11 subgroup CTE tuning | |||
== Tuning spectra == | == Tuning spectra == | ||
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{| class="wikitable center-1 center-2" | {| class="wikitable center-1 center-2" | ||
|- | |- | ||
! [[Eigenmonzo|Eigenmonzo<br>(Unchanged-interval]]) | ! [[Eigenmonzo|Eigenmonzo<br />(Unchanged-interval]]) | ||
! Generator (¢) | ! Generator (¢) | ||
! Comments | ! Comments | ||
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{| class="wikitable center-1 center-2" | {| class="wikitable center-1 center-2" | ||
|- | |- | ||
! Eigenmonzo<br>(Unchanged-interval) | ! Eigenmonzo<br />(Unchanged-interval) | ||
! Generator (¢) | ! Generator (¢) | ||
! Comments | ! Comments | ||
| Line 508: | Line 508: | ||
{| class="wikitable center-1 center-2" | {| class="wikitable center-1 center-2" | ||
|- | |- | ||
! Eigenmonzo<br>(Unchanged-interval) | ! Eigenmonzo<br />(Unchanged-interval) | ||
! Generator (¢) | ! Generator (¢) | ||
! Comments | ! Comments | ||
| Line 612: | Line 612: | ||
{| class="wikitable center-1 center-2" | {| class="wikitable center-1 center-2" | ||
|- | |- | ||
! Eigenmonzo<br>(Unchanged-interval) | ! Eigenmonzo<br />(Unchanged-interval) | ||
! Generator (¢) | ! Generator (¢) | ||
! Comments | ! Comments | ||