Porcusmine: Difference between revisions
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'''Porcusmine''' is a | '''Porcusmine''' is a [[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. It is not [[chiral]] and it has [[maximum variety]] 3 for certain tunings only (otherwise it has maximum variety 4 in general). [[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 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 [[User:CellularAutomaton|cellularAutomaton]], who discovered it as a detempering of porcupine | "Porcusmine" is a name given by [[User:CellularAutomaton|cellularAutomaton]], who discovered it as a detempering of porcupine. 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. It was also later called the [[Pinetone #Pinetone diminished octatonic|Pinetone diminished octatonic]] when independently discovered by [[Lillian Hearne]]. Similar Porcupine[8] detemperings have also been [[Kite Guitar translations by Kite Giedraitis #Couples Therapy .28Jacob Barton.2C microtonal.29|discussed]] by [[Kite Giedraitis]] as well as by Lillian Hearne. | ||
== Modes == | == 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 [[ | 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 [[diminished (temperament)|diminshed]] ([[4L 4s]]), which has only 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 [[User:Ayceman|Alexandru Ianu]]'s names. Below are the modes arranged in cyclic order: | ||
{| class="wikitable" | {| class="wikitable" | ||
!Modes in cyclic order | ! Modes in cyclic order | ||
|- | |- | ||
|LMLMLMLs | | LMLMLMLs | ||
Porcusmine Octopus | Porcusmine Octopus | ||
| Line 17: | Line 18: | ||
Octzothic | Octzothic | ||
|- | |- | ||
|MLMLMLsL | | MLMLMLsL | ||
Porcusmine Mantis | Porcusmine Mantis | ||
| Line 24: | Line 25: | ||
Mandagothic | Mandagothic | ||
|- | |- | ||
|LMLMLsLM | | LMLMLsLM | ||
Porcusmine Dolphin | Porcusmine Dolphin | ||
| Line 31: | Line 32: | ||
Dolkhanic | Dolkhanic | ||
|- | |- | ||
|MLMLsLML | | MLMLsLML | ||
Porcusmine Crab | Porcusmine Crab | ||
| Line 38: | Line 39: | ||
Crablexian | Crablexian | ||
|- | |- | ||
|LMLsLMLM | | LMLsLMLM | ||
Porcusmine Tuna | Porcusmine Tuna | ||
| Line 45: | Line 46: | ||
Tunivecan | Tunivecan | ||
|- | |- | ||
|MLsLMLML | | MLsLMLML | ||
Porcusmine Salmon | Porcusmine Salmon | ||
| Line 52: | Line 53: | ||
Salmenacan | Salmenacan | ||
|- | |- | ||
|LsLMLMLM | | LsLMLMLM | ||
Porcusmine Starfish | Porcusmine Starfish | ||
| Line 59: | Line 60: | ||
Starevarine | Starevarine | ||
|- | |- | ||
|sLMLMLML | | sLMLMLML | ||
Porcusmine Whale | Porcusmine Whale | ||
| Line 69: | Line 70: | ||
== Tunings == | == Tunings == | ||
Porcusmine is MV3 when L+s=M+M, as reflected in the table below. | Porcusmine is MV3 when L+s=M+M, as reflected in the table below. | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
|+Porcusmine tunings | |+Porcusmine tunings | ||
!Tuning | ! Tuning | ||
!L:M:s | ! L:M:s | ||
!Good JI approximations | ! Good JI approximations | ||
!Other notes | ! Other notes | ||
|- | |- | ||
|JI (5-limit AGS interpretation) | | JI (5-limit AGS interpretation) | ||
|2.581:1.885:1 | | 2.581:1.885:1 | ||
|just 3/2, 6/5, 5/4, 9/8, and 10/9 | | just 3/2, 6/5, 5/4, 9/8, and 10/9 | ||
| | | | ||
|- | |- | ||
|19edo | | 19edo | ||
|3:2:1 | | 3:2:1 | ||
|excellent pental thirds, fairly good 3-limit | | excellent pental thirds, fairly good 3-limit | ||
|MV3 | | MV3 | ||
|- | |- | ||
|23edo | | 23edo | ||
|4:2:1 | | 4:2:1 | ||
|excellent 6/5 and 9/8, fairly good 7/5 | | excellent 6/5 and 9/8, fairly good 7/5 | ||
| | | | ||
|- | |- | ||
|26edo | | 26edo | ||
|4:3:1 | | 4:3:1 | ||
|excellent 10/9, 11/8, and 7/4; fairly good 5/4 and 3/2 | | excellent 10/9, 11/8, and 7/4; fairly good 5/4 and 3/2 | ||
| | | | ||
|- | |- | ||
|27edo | | 27edo | ||
|4:3:2 | | 4:3:2 | ||
|excellent 10/9, 7/6, 6/5, and 7/5; fairly good 9/7 and 3/2 | | excellent 10/9, 7/6, 6/5, and 7/5; fairly good 9/7 and 3/2 | ||
|MV3 | | MV3 | ||
|- | |- | ||
|27edo | | 27edo | ||
|5:2:1 | | 5:2:1 | ||
|excellent 5:6:7; fairly good 7/4, 11/9, and 3/2 | | excellent 5:6:7; fairly good 7/4, 11/9, and 3/2 | ||
| | | | ||
|- | |- | ||
|30edo | | 30edo | ||
|5:3:1 | | 5:3:1 | ||
|excellent 15/14, 9/8, 6/5, and 9/7; fairly good 15/8, 7/4, and 11/8 | | excellent 15/14, 9/8, 6/5, and 9/7; fairly good 15/8, 7/4, and 11/8 | ||
|MV3 | | MV3 | ||
|- | |- | ||
|31edo | | 31edo | ||
|5:3:2 | | 5:3:2 | ||
|excellent 15/14 or 16/15, 7/6, 5/4, and 7/5; fairly good 6/5, 9/7, 3/2 | | excellent 15/14 or 16/15, 7/6, 5/4, and 7/5; fairly good 6/5, 9/7, 3/2 | ||
|meantone fifths | | meantone fifths | ||
|- | |- | ||
|31edo | | 31edo | ||
|6:2:1 | | 6:2:1 | ||
|excellent 7/4, 7/6, 11/9, 5/4, 7/5; fairly good 6/5, 3/2, and 11/8 | | excellent 7/4, 7/6, 11/9, 5/4, 7/5; fairly good 6/5, 3/2, and 11/8 | ||
|single meantone fifth | | single meantone fifth | ||
|- | |- | ||
|33edo | | 33edo | ||
|5:4:1 | | 5:4:1 | ||
|excellent 10/9; fairly good 11/6 and 11/8 | | excellent 10/9; fairly good 11/6 and 11/8 | ||
| | | | ||
|- | |- | ||
|34edo | | 34edo | ||
|5:4:2 | | 5:4:2 | ||
|very close to 5-limit just tuning | | very close to 5-limit just tuning | ||
|gentle fifths | | gentle fifths | ||
|- | |- | ||
|34edo | | 34edo | ||
|6:3:1 | | 6:3:1 | ||
|excellent 6/5; fairly good 9/8, 11/9, and 14/11 | | excellent 6/5; fairly good 9/8, 11/9, and 14/11 | ||
| | | | ||
|- | |- | ||
|41edo | | 41edo | ||
|6:5:2 | | 6:5:2 | ||
|excellent 3-limit; good 7-limit; fairly good 5-limit | | excellent 3-limit; good 7-limit; fairly good 5-limit | ||
| | | | ||
|} | |} | ||
| Line 150: | Line 152: | ||
In this tuning, the interval 25/18 occurs frequently, and the scale could be more consonant by tempering out [[126/125]] to equate this interval with 7/5. | In this tuning, the interval 25/18 occurs frequently, and the scale could be more consonant by tempering out [[126/125]] to equate this interval with 7/5. | ||
[[Category:8-tone scales]] | [[Category:8-tone scales]] | ||
[[Category:19edo]] | [[Category:19edo]] | ||