Semaphoresmic clan: Difference between revisions

(7 intermediate revisions by the same user not shown)

Line 13:

[[Comma list]]: 49/48

: mapping generators: ~2, ~7/4

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These all use the same nominal generator as semaphore, though some of them are of very low accuracy.

Decimal adds [[25/24]]. Anguirus adds [[2048/2025]]. Those split the octave in two. Negri adds [[225/224]], splitting the hemifourth in two. Triforce adds [[128/125]], splitting the octave in three. Keemun adds [[126/125]], splitting the hemitwelfth in three. Nautilus adds [[250/243]], splitting the hemifourth in three. Nuke is like nautilus, but adds 3584/3375 instead. Hemidim adds [[648/625]] with a 1/4-octave period. ~~Blackwood~~ adds [[28/27]], ~~with a 1/5-octave period~~. Spell adds [[3125/3072]], splitting the hemitwelfth in five. Hemiripple adds 6561/6250, splitting the hemifourth in five. ~~Finally, semabila~~ adds 28672/28125 and splits an interval of two octaves plus a hemifourth in five.

Decimal adds [[25/24]]. Anguirus adds [[2048/2025]]. Those split the octave in two. Negri adds [[225/224]], splitting the hemifourth in two. Triforce adds [[128/125]], splitting the octave in three. Keemun adds [[126/125]], splitting the hemitwelfth in three. Nautilus adds [[250/243]], splitting the hemifourth in three. Nuke is like nautilus, but adds 3584/3375 instead. Hemidim adds [[648/625]] with a 1/4-octave period. Rhinoceros adds [[4375/4374]], splitting the hemifourth in four. Spell adds [[3125/3072]], splitting the hemitwelfth in five. Hemiripple adds 6561/6250, splitting the hemifourth in five. Semabila adds 28672/28125 and splits an interval of two octaves plus a hemifourth in five. Finally, blackwood adds [[28/27]], reducing intervals of 3 and 7 to the same chain of 1/5-octave periods.

Discussed elsewhere are

* ''[[Beep]]'' (+21/20) → [[Bug family #Beep|Bug family]]

* ''[[Immunity]]'' (+2240/2187) → [[Immunity family #Septimal immunity|Immunity family]]

* ''[[Nessus]]'' (+10/9) → [[Very low accuracy temperaments #Nessus|Very low accuracy temperaments]]

* ''[[Malacoda]]'' (+15/14) → [[Very low accuracy temperaments #Malacoda|Very low accuracy temperaments]]

* [[Beep]] (+21/20) → [[Bug family #Beep|Bug family]]

* ''[[Immunity]]'' (+2240/2187) → [[Immunity family #Septimal immunity|Immunity family]]

* [[Decimal]] (+25/24) → [[Dicot family #Decimal|Dicot family]]

* ''[[Anguirus]]'' (+2048/2025) → [[Diaschismic family #Anguirus|Diaschismic family]]

Line 55:

* ''[[Nautilus]]'' (+250/243) → [[Porcupine family #Nautilus|Porcupine family]]

* ''[[Hemidim]]'' (+648/625) → [[Diminished family #Hemidim|Diminished family]]

* [[~~Blackwood~~]] (+28/27) → [[~~Limmic temperaments~~ #~~Blackwood~~|~~Limmic temperaments~~]]

* ''[[Rhinoceros]]'' (+4375/4374) → [[Unicorn family #Rhinoceros|Unicorn family]]

* ''[[Spell]]'' (+3125/3072) → [[Hemimean clan #Spell|Hemimean clan]]

* ''[[Hemiripple]]'' (+6561/6250) → [[Ripple family #Hemiripple|Ripple family]]

* ''[[Semabila]]'' (+28672/28125) → [[Mabila family #Mabila|Mabila family]]

* [[Blackwood]] (+28/27) → [[Blackwood family #Blackwood|Blackwood family]]

Considered below are godzilla, helayo, superpelog, baba, negri, and nuke.

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Line 70:

Comma list: 49/48, 729/704

~~Subgroup-val mapping:~~ {{~~mapping~~| 1 0 2 -6 | 0 2 1 12 }}

Optimal tunings:

Line 84:

Line 85:

Comma list: 49/48, 77/76, 729/704

~~Subgroup-val mapping:~~ {{~~mapping~~| 1 0 2 -6 -6 | 0 2 1 12 13 }}

Optimal tunings:

Line 127:

Line 128:

Comma list: 49/48, 81/80, 91/90

~~Subgroup-val mapping:~~ {{~~mapping~~| 1 0 -4 2 -5 | 0 2 8 1 11 }}

Optimal tunings:

Line 142:

Line 143:

Comma list: 45/44, 49/48, 81/80

~~Mapping:~~ {{~~mapping~~| 1 0 -4 2 -6 | 0 2 8 1 12 }}

Optimal tunings:

Line 161:

Line 162:

Comma list: 45/44, 49/48, 78/77, 81/80

~~Mapping:~~ {{~~mapping~~| 1 0 -4 2 -6 -5 | 0 2 8 1 12 11 }}

Optimal tunings:

Line 180:

Line 181:

Comma list: 33/32, 49/48, 55/54

~~Mapping:~~ {{~~mapping~~| 1 0 -4 2 5 | 0 2 8 1 -2 }}

Optimal tunings:

Line 195:

Line 196:

Comma list: 33/32, 49/48, 55/54, 91/90

~~Mapping:~~ {{~~mapping~~| 1 0 -4 2 5 -5 | 0 2 8 1 -2 11 }}

Optimal tunings:

Line 210:

Line 211:

Comma list: 49/48, 77/75, 81/80

~~Mapping:~~ {{~~mapping~~| 1 0 -4 2 -10 | 0 2 8 1 17 }}

Optimal tunings:

Line 225:

Line 226:

Comma list: 49/48, 66/65, 77/75, 81/80

~~Mapping:~~ {{~~mapping~~| 1 0 -4 2 -10 -5 | 0 2 8 1 17 11 }}

Optimal tunings:

Line 240:

Line 241:

Comma list: 49/48, 56/55, 81/80

~~Mapping:~~ {{~~mapping~~| 1 0 -4 2 9 | 0 2 8 1 -7 }}

Optimal tunings:

Line 255:

Line 256:

Comma list: 49/48, 56/55, 81/80, 91/90

~~Mapping:~~ {{~~mapping~~| 1 0 -4 2 9 -5 | 0 2 8 1 -7 11 }}

Optimal tunings:

Line 315:

Line 316:

Comma list: 33/32, 45/44, 49/48

~~Mapping:~~ {{~~mapping~~| 1 0 7 2 5 | 0 2 -6 1 -2 }}

Optimal tunings:

Line 352:

Line 353:

Comma list: 16/15, 22/21, 49/45

~~Mapping:~~ {{~~mapping~~| 1 0 4 2 1 | 0 2 -2 1 3 }}

Optimal tunings:

Line 390:

Line 391:

Comma list: 49/48, 65/64, 91/90

~~Subgroup-val mapping:~~ {{~~mapping~~| 1 2 2 3 4 | 0 -4 3 -2 -3 }}

~~Gencom mapping:~~ {{~~mapping~~| 1 2 2 3 0 4 | 0 -4 3 -2 0 -3 }}

Optimal tunings:

Line 407:

Line 408:

Comma list: 45/44, 49/48, 56/55

~~Mapping:~~ {{~~mapping~~| 1 2 2 3 4 | 0 -4 3 -2 -5 }}

Optimal tunings:

Line 422:

Line 423:

Comma list: 45/44, 49/48, 56/55, 78/77

~~Mapping:~~ {{~~mapping~~| 1 2 2 3 4 4 | 0 -4 3 -2 -5 -3 }}

Optimal tunings:

Line 437:

Line 438:

Comma list: 49/48, 100/99, 225/224

~~Mapping:~~ {{~~mapping~~| 1 2 2 3 2 | 0 -4 3 -2 14 }}

Optimal tunings:

Line 452:

Line 453:

Comma list: 49/48, 65/64, 91/90, 875/858

~~Mapping:~~ {{~~mapping~~| 1 2 2 3 2 4 | 0 -4 3 -2 14 -3 }}

Optimal tunings:

Line 467:

Line 468:

Comma list: 33/32, 49/48, 77/75

~~Mapping:~~ {{~~mapping~~| 1 2 2 3 3 | 0 -4 3 -2 4 }}

Optimal tunings:

Line 482:

Line 483:

Comma list: 33/32, 49/48, 65/64, 91/90

~~Mapping:~~ {{~~mapping~~| 1 2 2 3 3 4 | 0 -4 3 -2 4 -3 }}

Optimal tunings:

Line 497:

Line 498:

Comma list: 49/48, 55/54, 225/224

~~Mapping:~~ {{~~mapping~~| 1 2 2 3 5 | 0 -4 3 -2 -15 }}

Optimal tunings:

Line 512:

Line 513:

Comma list: 49/48, 55/54, 65/64, 91/90

~~Mapping:~~ {{~~mapping~~| 1 2 2 3 5 4 | 0 -4 3 -2 -15 -3 }}

Optimal tunings:

Line 529:

Line 530:

Comma list: 49/48, 121/120, 225/224

~~Mapping:~~ {{~~mapping~~| 1 -2 5 1 3 | 0 8 -6 4 1 }}

: mapping generators: ~2, ~11/8

Line 546:

Line 547:

Comma list: 49/48, 65/64, 91/90, 121/120

~~Mapping:~~ {{~~mapping~~| 1 -2 5 1 3 1 | 0 8 -6 4 1 6 }}

Optimal tunings:

Line 561:

Line 562:

Comma list: 49/48, 65/64, 91/90, 121/120, 154/153

~~Mapping:~~ {{~~mapping~~| 1 -2 5 1 3 1 9 | 0 8 -6 4 1 6 -11 }}

Optimal tunings:

Line 576:

Line 577:

Comma list: 49/48, 65/64, 77/76, 91/90, 121/120, 154/153

~~Mapping:~~ {{~~mapping~~| 1 -2 5 1 3 1 9 2 | 0 8 -6 4 1 6 -11 5 }}

Optimal tunings:

Line 610:

Line 611:

Comma list: 49/48, 77/75, 512/495

~~Mapping:~~ {{~~mapping~~| 1 2 2 3 3 | 0 -6 5 -3 7 }}

Optimal tunings:

Line 625:

Line 626:

Comma list: 49/48, 66/65, 77/75, 448/429

~~Mapping:~~ {{~~mapping~~| 1 2 2 3 3 4 | 0 -6 5 -3 7 -4 }}

Optimal tunings:

Line 635:

Line 636:

Badness (Sintel): 2.01

[[Category:Semaphoresmic clan| ]]

[[Category:Temperament clans]]

[[Category:~~Semaphoresmic clan| ]] <!~~-~~- main article -->~~

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

~~[[Category:Rank~~ 2]]

@@ Line 13: / Line 13: @@
 [[Comma list]]: 49/48
-{{Mapping|legend=2| 1 0 2 | 0 2 1 }}
+{{Mapping|legend=3| 1 0 2 | 0 2 1 }}
-{{Mapping|legend=3| 1 0 0 2 | 0 2 0 1 }}
+{{Mapping|legend=5| 1 0 0 2 | 0 2 0 1 }}
 : mapping generators: ~2, ~7/4
@@ Line 42: / Line 42: @@
 These all use the same nominal generator as semaphore, though some of them are of very low accuracy.
-Decimal adds [[25/24]]. Anguirus adds [[2048/2025]]. Those split the octave in two. Negri adds [[225/224]], splitting the hemifourth in two. Triforce adds [[128/125]], splitting the octave in three. Keemun adds [[126/125]], splitting the hemitwelfth in three. Nautilus adds [[250/243]], splitting the hemifourth in three. Nuke is like nautilus, but adds 3584/3375 instead. Hemidim adds [[648/625]] with a 1/4-octave period. Blackwood adds [[28/27]], with a 1/5-octave period. Spell adds [[3125/3072]], splitting the hemitwelfth in five. Hemiripple adds 6561/6250, splitting the hemifourth in five. Finally, semabila adds 28672/28125 and splits an interval of two octaves plus a hemifourth in five.
+Decimal adds [[25/24]]. Anguirus adds [[2048/2025]]. Those split the octave in two. Negri adds [[225/224]], splitting the hemifourth in two. Triforce adds [[128/125]], splitting the octave in three. Keemun adds [[126/125]], splitting the hemitwelfth in three. Nautilus adds [[250/243]], splitting the hemifourth in three. Nuke is like nautilus, but adds 3584/3375 instead. Hemidim adds [[648/625]] with a 1/4-octave period. Rhinoceros adds [[4375/4374]], splitting the hemifourth in four. Spell adds [[3125/3072]], splitting the hemitwelfth in five. Hemiripple adds 6561/6250, splitting the hemifourth in five. Semabila adds 28672/28125 and splits an interval of two octaves plus a hemifourth in five. Finally, blackwood adds [[28/27]], reducing intervals of 3 and 7 to the same chain of 1/5-octave periods.
 Discussed elsewhere are
-* ''[[Beep]]'' (+21/20) → [[Bug family #Beep|Bug family]]
-* ''[[Immunity]]'' (+2240/2187) → [[Immunity family #Septimal immunity|Immunity family]]
 * ''[[Nessus]]'' (+10/9) → [[Very low accuracy temperaments #Nessus|Very low accuracy temperaments]]
 * ''[[Malacoda]]'' (+15/14) → [[Very low accuracy temperaments #Malacoda|Very low accuracy temperaments]]
+* [[Beep]] (+21/20) → [[Bug family #Beep|Bug family]]
+* ''[[Immunity]]'' (+2240/2187) → [[Immunity family #Septimal immunity|Immunity family]]
 * [[Decimal]] (+25/24) → [[Dicot family #Decimal|Dicot family]]
 * ''[[Anguirus]]'' (+2048/2025) → [[Diaschismic family #Anguirus|Diaschismic family]]
@@ Line 55: / Line 55: @@
 * ''[[Nautilus]]'' (+250/243) → [[Porcupine family #Nautilus|Porcupine family]]
 * ''[[Hemidim]]'' (+648/625) → [[Diminished family #Hemidim|Diminished family]]
-* [[Blackwood]] (+28/27) → [[Limmic temperaments #Blackwood|Limmic temperaments]]
+* ''[[Rhinoceros]]'' (+4375/4374) → [[Unicorn family #Rhinoceros|Unicorn family]]
 * ''[[Spell]]'' (+3125/3072) → [[Hemimean clan #Spell|Hemimean clan]]
 * ''[[Hemiripple]]'' (+6561/6250) → [[Ripple family #Hemiripple|Ripple family]]
 * ''[[Semabila]]'' (+28672/28125) → [[Mabila family #Mabila|Mabila family]]
+* [[Blackwood]] (+28/27) → [[Blackwood family #Blackwood|Blackwood family]]
 Considered below are godzilla, helayo, superpelog, baba, negri, and nuke.
@@ Line 69: / Line 70: @@
 Comma list: 49/48, 729/704
-Subgroup-val mapping: {{mapping| 1 0 2 -6 | 0 2 1 12 }}
+{{Mapping|legend=2| 1 0 2 -6 | 0 2 1 12 }}
 Optimal tunings:
@@ Line 84: / Line 85: @@
 Comma list: 49/48, 77/76, 729/704
-Subgroup-val mapping: {{mapping| 1 0 2 -6 -6 | 0 2 1 12 13 }}
+{{Mapping|legend=2| 1 0 2 -6 -6 | 0 2 1 12 13 }}
 Optimal tunings:
@@ Line 127: / Line 128: @@
 Comma list: 49/48, 81/80, 91/90
-Subgroup-val mapping: {{mapping| 1 0 -4 2 -5 | 0 2 8 1 11 }}
+{{Mapping|legend=2| 1 0 -4 2 -5 | 0 2 8 1 11 }}
 Optimal tunings:
@@ Line 142: / Line 143: @@
 Comma list: 45/44, 49/48, 81/80
-Mapping: {{mapping| 1 0 -4 2 -6 | 0 2 8 1 12 }}
+{{Mapping|legend=0| 1 0 -4 2 -6 | 0 2 8 1 12 }}
 Optimal tunings:
@@ Line 161: / Line 162: @@
 Comma list: 45/44, 49/48, 78/77, 81/80
-Mapping: {{mapping| 1 0 -4 2 -6 -5 | 0 2 8 1 12 11 }}
+{{Mapping|legend=0| 1 0 -4 2 -6 -5 | 0 2 8 1 12 11 }}
 Optimal tunings:
@@ Line 180: / Line 181: @@
 Comma list: 33/32, 49/48, 55/54
-Mapping: {{mapping| 1 0 -4 2 5 | 0 2 8 1 -2 }}
+{{Mapping|legend=0| 1 0 -4 2 5 | 0 2 8 1 -2 }}
 Optimal tunings:
@@ Line 195: / Line 196: @@
 Comma list: 33/32, 49/48, 55/54, 91/90
-Mapping: {{mapping| 1 0 -4 2 5 -5 | 0 2 8 1 -2 11 }}
+{{Mapping|legend=0| 1 0 -4 2 5 -5 | 0 2 8 1 -2 11 }}
 Optimal tunings:
@@ Line 210: / Line 211: @@
 Comma list: 49/48, 77/75, 81/80
-Mapping: {{mapping| 1 0 -4 2 -10 | 0 2 8 1 17 }}
+{{Mapping|legend=0| 1 0 -4 2 -10 | 0 2 8 1 17 }}
 Optimal tunings:
@@ Line 225: / Line 226: @@
 Comma list: 49/48, 66/65, 77/75, 81/80
-Mapping: {{mapping| 1 0 -4 2 -10 -5 | 0 2 8 1 17 11 }}
+{{Mapping|legend=0| 1 0 -4 2 -10 -5 | 0 2 8 1 17 11 }}
 Optimal tunings:
@@ Line 240: / Line 241: @@
 Comma list: 49/48, 56/55, 81/80
-Mapping: {{mapping| 1 0 -4 2 9 | 0 2 8 1 -7 }}
+{{Mapping|legend=0| 1 0 -4 2 9 | 0 2 8 1 -7 }}
 Optimal tunings:
@@ Line 255: / Line 256: @@
 Comma list: 49/48, 56/55, 81/80, 91/90
-Mapping: {{mapping| 1 0 -4 2 9 -5 | 0 2 8 1 -7 11 }}
+{{Mapping|legend=0| 1 0 -4 2 9 -5 | 0 2 8 1 -7 11 }}
 Optimal tunings:
@@ Line 315: / Line 316: @@
 Comma list: 33/32, 45/44, 49/48
-Mapping: {{mapping| 1 0 7 2 5 | 0 2 -6 1 -2 }}
+{{Mapping|legend=0| 1 0 7 2 5 | 0 2 -6 1 -2 }}
 Optimal tunings:
@@ Line 352: / Line 353: @@
 Comma list: 16/15, 22/21, 49/45
-Mapping: {{mapping| 1 0 4 2 1 | 0 2 -2 1 3 }}
+{{Mapping|legend=0| 1 0 4 2 1 | 0 2 -2 1 3 }}
 Optimal tunings:
@@ Line 390: / Line 391: @@
 Comma list: 49/48, 65/64, 91/90
-Subgroup-val mapping: {{mapping| 1 2 2 3 4 | 0 -4 3 -2 -3 }}
+{{Mapping|legend=2| 1 2 2 3 4 | 0 -4 3 -2 -3 }}
-Gencom mapping: {{mapping| 1 2 2 3 0 4 | 0 -4 3 -2 0 -3 }}
+{{Mapping|legend=4| 1 2 2 3 0 4 | 0 -4 3 -2 0 -3 }}
 Optimal tunings:
@@ Line 407: / Line 408: @@
 Comma list: 45/44, 49/48, 56/55
-Mapping: {{mapping| 1 2 2 3 4 | 0 -4 3 -2 -5 }}
+{{Mapping|legend=0| 1 2 2 3 4 | 0 -4 3 -2 -5 }}
 Optimal tunings:
@@ Line 422: / Line 423: @@
 Comma list: 45/44, 49/48, 56/55, 78/77
-Mapping: {{mapping| 1 2 2 3 4 4 | 0 -4 3 -2 -5 -3 }}
+{{Mapping|legend=0| 1 2 2 3 4 4 | 0 -4 3 -2 -5 -3 }}
 Optimal tunings:
@@ Line 437: / Line 438: @@
 Comma list: 49/48, 100/99, 225/224
-Mapping: {{mapping| 1 2 2 3 2 | 0 -4 3 -2 14 }}
+{{Mapping|legend=0| 1 2 2 3 2 | 0 -4 3 -2 14 }}
 Optimal tunings:
@@ Line 452: / Line 453: @@
 Comma list: 49/48, 65/64, 91/90, 875/858
-Mapping: {{mapping| 1 2 2 3 2 4 | 0 -4 3 -2 14 -3 }}
+{{Mapping|legend=0| 1 2 2 3 2 4 | 0 -4 3 -2 14 -3 }}
 Optimal tunings:
@@ Line 467: / Line 468: @@
 Comma list: 33/32, 49/48, 77/75
-Mapping: {{mapping| 1 2 2 3 3 | 0 -4 3 -2 4 }}
+{{Mapping|legend=0| 1 2 2 3 3 | 0 -4 3 -2 4 }}
 Optimal tunings:
@@ Line 482: / Line 483: @@
 Comma list: 33/32, 49/48, 65/64, 91/90
-Mapping: {{mapping| 1 2 2 3 3 4 | 0 -4 3 -2 4 -3 }}
+{{Mapping|legend=0| 1 2 2 3 3 4 | 0 -4 3 -2 4 -3 }}
 Optimal tunings:
@@ Line 497: / Line 498: @@
 Comma list: 49/48, 55/54, 225/224
-Mapping: {{mapping| 1 2 2 3 5 | 0 -4 3 -2 -15 }}
+{{Mapping|legend=0| 1 2 2 3 5 | 0 -4 3 -2 -15 }}
 Optimal tunings:
@@ Line 512: / Line 513: @@
 Comma list: 49/48, 55/54, 65/64, 91/90
-Mapping: {{mapping| 1 2 2 3 5 4 | 0 -4 3 -2 -15 -3 }}
+{{Mapping|legend=0| 1 2 2 3 5 4 | 0 -4 3 -2 -15 -3 }}
 Optimal tunings:
@@ Line 529: / Line 530: @@
 Comma list: 49/48, 121/120, 225/224
-Mapping: {{mapping| 1 -2 5 1 3 | 0 8 -6 4 1 }}
+{{Mapping|legend=0| 1 -2 5 1 3 | 0 8 -6 4 1 }}
 : mapping generators: ~2, ~11/8
@@ Line 546: / Line 547: @@
 Comma list: 49/48, 65/64, 91/90, 121/120
-Mapping: {{mapping| 1 -2 5 1 3 1 | 0 8 -6 4 1 6 }}
+{{Mapping|legend=0| 1 -2 5 1 3 1 | 0 8 -6 4 1 6 }}
 Optimal tunings:
@@ Line 561: / Line 562: @@
 Comma list: 49/48, 65/64, 91/90, 121/120, 154/153
-Mapping: {{mapping| 1 -2 5 1 3 1 9 | 0 8 -6 4 1 6 -11 }}
+{{Mapping|legend=0| 1 -2 5 1 3 1 9 | 0 8 -6 4 1 6 -11 }}
 Optimal tunings:
@@ Line 576: / Line 577: @@
 Comma list: 49/48, 65/64, 77/76, 91/90, 121/120, 154/153
-Mapping: {{mapping| 1 -2 5 1 3 1 9 2 | 0 8 -6 4 1 6 -11 5 }}
+{{Mapping|legend=0| 1 -2 5 1 3 1 9 2 | 0 8 -6 4 1 6 -11 5 }}
 Optimal tunings:
@@ Line 610: / Line 611: @@
 Comma list: 49/48, 77/75, 512/495
-Mapping: {{mapping| 1 2 2 3 3 | 0 -6 5 -3 7 }}
+{{Mapping|legend=0| 1 2 2 3 3 | 0 -6 5 -3 7 }}
 Optimal tunings:
@@ Line 625: / Line 626: @@
 Comma list: 49/48, 66/65, 77/75, 448/429
-Mapping: {{mapping| 1 2 2 3 3 4 | 0 -6 5 -3 7 -4 }}
+{{Mapping|legend=0| 1 2 2 3 3 4 | 0 -6 5 -3 7 -4 }}
 Optimal tunings:
@@ Line 635: / Line 636: @@
 Badness (Sintel): 2.01
+[[Category:Semaphoresmic clan| ]] <!-- main article -->
 [[Category:Temperament clans]]
-[[Category:Semaphoresmic clan| ]] <!-- main article -->
+[[Category:Catalogs of rank-2 temperaments]]
-[[Category:Rank 2]]

Semaphoresmic clan: Difference between revisions

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