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'''Porcusmine''' is a [[Maximum variety|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''' 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, although the scale has also been [[Kite_Guitar_Translations_by_Kite_Giedraitis#Couples_Therapy_.28Jacob_Barton.2C_microtonal.29|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.
"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 ==
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"
! 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 ==
Porcusmine is MV3 when L+s=M+M, as reflected in the table below.
 
{| class="wikitable sortable"
|+Porcusmine tunings
! Tuning
! L:M:s
! Good JI approximations
! Other notes
|-
| JI (5-limit AGS interpretation)
| 2.581:1.885:1
| just 3/2, 6/5, 5/4, 9/8, and 10/9
|
|-
| 19edo
| 3:2:1
| excellent pental thirds, fairly good 3-limit
| MV3
|-
| 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
| excellent 10/9, 7/6, 6/5, and 7/5; fairly good 9/7 and 3/2
| MV3
|-
| 27edo
| 5:2:1
| excellent 5:6:7; fairly good 7/4, 11/9, and 3/2
|
|-
| 30edo
| 5:3:1
| excellent 15/14, 9/8, 6/5, and 9/7; fairly good 15/8, 7/4, and 11/8
| MV3
|-
| 31edo
| 5:3:2
| excellent 15/14 or 16/15, 7/6, 5/4, and 7/5; fairly good 6/5, 9/7, 3/2
| meantone fifths
|-
| 31edo
| 6:2:1
| excellent 7/4, 7/6, 11/9, 5/4, 7/5; fairly good 6/5, 3/2, and 11/8
| single meantone fifth
|-
| 33edo
| 5:4:1
| excellent 10/9; fairly good 11/6 and 11/8
|
|-
| 34edo
| 5:4:2
| very close to 5-limit just tuning
| gentle fifths
|-
| 34edo
| 6:3:1
| excellent 6/5; fairly good 9/8, 11/9, and 14/11
|
|-
| 41edo
| 6:5:2
| excellent 3-limit; good 7-limit; fairly good 5-limit
|
|}
 
== 5-limit AGS interpretation ==
Porcusmine can be interpreted as a member of an [[AGS]] series AGS(9/5, 50/27), which is [[constant structure]] at 5, 6, 7, 8, 15, 23, 38, 61, and 99 notes. It is noteworthy for an AGS series to retain constant structure to this size.
 
In this AGS interpretation, Whothic is the "root mode" of Porcusmine. The 5-limit tuning of Whothic generated by AGS(9/5, 50/27) is:
 
1/1 25/24 125/108 5/4 25/18 3/2 5/3 9/5 2/1
 
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:19edo]]
[[Category:23edo]]
[[Category:26edo]]
[[Category:27edo]]
[[Category:31edo]]
[[Category:34edo]]
[[Category:Just intonation scales]]
[[Category:5-limit]]
[[Category:GO scales]]
[[Category:Rank-3 scales]]
[[Category:Scales]]
Retrieved from "https://en.xen.wiki/w/Porcusmine"