Porcusmine
Porcusmine is a max-variety-3, generator-offset scale with step pattern 4L 3M 1s. It is equivalent to the porcupine (7L 1s) mos with 4 of the large steps made bigger and the other 3 made smaller, or to the smitonic (4L 3s) with an extra-small step added. Porcusmine is not chiral. 19edo is the smallest edo to support a non-degenerate porcusmine.
Porcusmine can be tuned as a 5-limit JI scale or a tempered version thereof, where L represents 10/9, M represents 27/25, and s represents 25/24.
"Porcusmine" is a name given by cellularAutomaton, who discovered it as a detempering of porcupine, although the scale has also been discussed by Kite Giedraitis and possibly others. The name is a portmanteau of "porcupine" and "smitonic", since its step sizes are intermediate between those of the 8-note porcupine and 7-note smitonic mosses.
Modes
Porcusmine has 8 modes. Names are provided based on porcupine (tuning-neutral) and smitonic (for tunings where s is small), as well as a unique portmanteau name. When M and s are close, the scale approaches diminshed (4L 4s), which has two distinct modes and is therefore not useful for naming. The porcupine mode names refer to William Lynch's names, and the smitonic mode names refer to Alexandru Ianu's names. Below are the modes arranged in cyclic order:
| Modes in cyclic order |
|---|
| LMLMLMLs
Porcusmine Octopus Porcusmine Sothic Ascending Octzothic |
| MLMLMLsL
Porcusmine Mantis Porcusmine Dagothic Mandagothic |
| LMLMLsLM
Porcusmine Dolphin Porcusmine Lorkhanic Dolkhanic |
| MLMLsLML
Porcusmine Crab Porcusmine Almalexian Crablexian |
| LMLsLMLM
Porcusmine Tuna Porcusmine Vivecan Tunivecan |
| MLsLMLML
Porcusmine Salmon Porcusmine Kagrenacan Salmenacan |
| LsLMLMLM
Porcusmine Starfish Porcusmine Nerevarine Starevarine |
| sLMLMLML
Porcusmine Whale Porcusmine Sothic Descending Whothic |
Tunings
| Tuning | L:M:s | Good JI approximations | Other notes |
|---|---|---|---|
| JI (5-limit interpretation) | 2.581:1.885:1 | just 3/2, 4/3, 6/5, 5/4, 9/8, and 16/9 | |
| 19edo | 3:2:1 | excellent pental thirds, fairly good 3-limit | |
| 23edo | 4:2:1 | excellent 6/5 and 9/8, fairly good 7/5 | |
| 26edo | 4:3:1 | excellent 10/9, 11/8, and 7/4; fairly good 5/4 and 3/2 | |
| 27edo | 4:3:2 | ||
| 27edo | 5:2:1 | ||
| 30edo | 5:3:1 | ||
| 31edo | 5:3:2 | ||
| 31edo | 6:2:1 | ||
| 33edo | 5:4:1 | ||
| 34edo | 5:4:2 | very close to 5-limit just tuning | offers slightly sharp fifths which some people prefer |
| 34edo | 6:3:1 | ||
| 35edo | 5:4:3 | ||
| 35edo | 6:3:2 | ||
| 35edo | 7:2:1 |