Undim family: Difference between revisions

Septimal undim tempers out the [[dimcomp comma]], mapping [[~]][[25/21]] to the 1/4-octave period. It can be described as {{nowrap| 12 & 140 }}, and is the unique temperament that tempers together the syntonic and septimal commas and equates it with a stack of three [[marvel comma]]s. A [[Pythagorean comma]] is then found as a stack of four marvel commas. In certain 7-limit adaptive-tuning practice, the marvel comma corresponds to a melodic unit called a [[kleisma #As an interval region|kleisma]], with three kleismas making a comma, so this temperament may be useful for modeling that. [[292edo]] makes for an excellent tuning.  

{{Mapping|legend=0| 4 0 41 81 128 | 0 1 -5 -11 -18 }}

{{Mapping|legend=0| 4 0 41 81 128 148 | 0 1 -5 -11 -18 -21 }}

Unlit tempers out 4375/4374, the [[ragisma]], and may be described as {{nowrap| 152 & 164 }}. This temperament is more faithful to the 5-limit optimal tuning, but comes with the cost of a much higher complexity. It was named by [[Flora Canou]] in 2021 for it is some sort of opposite of [[#Septimal undim|septimal undim]].  

{{Mapping|legend=0| 4 0 41 -160 -113 | 0 1 -5 27 20 }}

{{Mapping|legend=0| 4 0 41 -160 -113 -334 | 0 1 -5 27 20 55 }}

Twilight tempers out 6144/6125, the [[porwell comma]], and may be described as {{nowrap| 152 & 176 }}. It splits the period of undim into 1/8 of an octave, and has a [[ploidacot]] of octaploid monocot. It was named by [[Flora Canou]] in 2021 for it splits the period in halves to reconcile the different mappings of [[#Septimal undim|septimal undim]] and [[#Unlit|unlit]].  

{{Mapping|legend=0| 8 0 82 -79 15 | 0 1 -5 8 1 }}

{{Mapping|legend=0| 8 0 82 -79 15 -186 | 0 1 -5 8 1 17 }}

[[Category:Catalogs of rank-2 temperaments]]