Valinorsmic clan

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

The valinorsmic clan of rank-3 temperaments tempers out the valinorsma, 176/175, which equates 48/35 with 15/11 (rather than 11/8, which is what the keenanisma 385/384 does).

The second comma in the comma list determines how we extend the no-3 subgroup temperament to include the harmonic 3. Zeus adds 121/120 as well as 385/384, and shares the same lattice structure as no-3 valinorsmic. Julius, a.k.a. varda, adds 896/891, slicing the first generator in two with a semi-octave period. Nickel adds 36/35 as well as 45/44. Ares adds 64/63. Minerva adds 99/98. Thrush adds 126/125. These slice the last generator in two. Guanyin adds 540/539, slicing the first generator in three. Manwe adds 1331/1323, slicing the last generator in three. Clio adds 81/80, slicing the first generator in four. Lono adds 5120/5103, slicing the last generator in six. Mandos adds 243/242. Shrusus adds 245/243. These slice the last generator in five. Ulmo adds 2200/2187, slicing the last generator in seven. Finally, draco adds 19683/19600, slicing the last generator in nine. Most of these have neat extensions to the 13-limit via tempering out both 351/350 and 352/351.

Discussed elsewhere are:

Zeus (+121/120) → Porwell family and Biyatismic clan
Varda (+896/891) → Diaschismic rank-3 family
Nickel (+36/35 or 45/44) → Mint family
Ares (+64/63 or 100/99) → Archytas family
Minerva (+99/98) → Marvel family
Thrush (+126/125) → Starling family
Guanyin (+540/539) → Orwellismic family
Clio (+81/80) → Didymus rank-3 family
Lono (+5120/5103) → Hemifamity family
Mandos (+243/242) → Rastmic rank-3 clan
Shrusus (+245/243) → Sensamagic family
Ulmo (+2200/2187) → Ragismic family
Draco (+19683/19600) → Cataharry family

Considered below are manwe and augenic, besides the no-3 subgroup temperament. For the rank-4 valinorsmic temperament, see Rank-4 temperament #Valinorsmic (176/175).