Semaphoresmic clan: Difference between revisions
Document semaphore as a 2.3.5.7.13-subgroup temp |
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{{Mapping|legend=2| 1 0 2 | 0 2 1 }} | {{Mapping|legend=2| 1 0 2 | 0 2 1 }} | ||
{{Mapping|legend=3| 1 0 0 2 | 0 2 0 1 }} | {{Mapping|legend=3| 1 0 0 2 | 0 2 0 1 }} | ||
: | : mapping generators: ~2, ~7/4 | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
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These all use the same nominal generator as semaphore, though some of them are of very low accuracy. | 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. | 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 | Discussed elsewhere are | ||
* ''[[Nessus]]'' (+10/9) → [[Very low accuracy temperaments #Nessus|Very low accuracy temperaments]] | * ''[[Nessus]]'' (+10/9) → [[Very low accuracy temperaments #Nessus|Very low accuracy temperaments]] | ||
* ''[[Malacoda]]'' (+15/14) → [[Very low accuracy temperaments #Malacoda|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]] | * [[Decimal]] (+25/24) → [[Dicot family #Decimal|Dicot family]] | ||
* ''[[Anguirus]]'' (+2048/2025) → [[Diaschismic family #Anguirus|Diaschismic family]] | * ''[[Anguirus]]'' (+2048/2025) → [[Diaschismic family #Anguirus|Diaschismic family]] | ||
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* [[Keemun]] (+126/125) → [[Kleismic family #Keemun|Kleismic family]] | * [[Keemun]] (+126/125) → [[Kleismic family #Keemun|Kleismic family]] | ||
* ''[[Nautilus]]'' (+250/243) → [[Porcupine family #Nautilus|Porcupine family]] | * ''[[Nautilus]]'' (+250/243) → [[Porcupine family #Nautilus|Porcupine family]] | ||
* ''[[Hemidim]]'' (+648/625) → [[ | * ''[[Hemidim]]'' (+648/625) → [[Diminished family #Hemidim|Diminished family]] | ||
* [[ | * ''[[Rhinoceros]]'' (+4375/4374) → [[Unicorn family #Rhinoceros|Unicorn family]] | ||
* ''[[Spell]]'' (+3125/3072) → [[Hemimean clan #Spell|Hemimean clan]] | * ''[[Spell]]'' (+3125/3072) → [[Hemimean clan #Spell|Hemimean clan]] | ||
* ''[[Hemiripple]]'' (+6561/6250) → [[Ripple family #Hemiripple|Ripple family]] | * ''[[Hemiripple]]'' (+6561/6250) → [[Ripple family #Hemiripple|Ripple family]] | ||
* ''[[Semabila]]'' (+28672/28125) → [[Mabila family #Mabila|Mabila 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. | Considered below are godzilla, helayo, superpelog, baba, negri, and nuke. | ||
=== Semaerophore === | |||
Named by [[CompactStar]] in 2023, this extension tempers out [[729/704]]. It is the no-5 [[restriction]] of undecimal godzilla. | |||
Subgroup: 2.3.7.11 | |||
Comma list: 49/48, 729/704 | |||
Subgroup-val mapping: {{mapping| 1 0 2 -6 | 0 2 1 12 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1204.9027{{c}}, ~7/4 = 948.7772{{c}} | |||
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 945.4959{{c}} | |||
{{Optimal ET sequence|legend=0| 14, 33d, 47de }} | |||
Badness (Sintel): 1.27 | |||
==== 2.3.7.11.19 subgroup ==== | |||
Subgroup: 2.3.7.11.19 | |||
Comma list: 49/48, 77/76, 729/704 | |||
Subgroup-val mapping: {{mapping| 1 0 2 -6 -6 | 0 2 1 12 13 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1204.9645{{c}}, ~7/4 = 948.5749{{c}} | |||
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 945.2236{{c}} | |||
{{Optimal ET sequence|legend=0| 14, 33d, 47deh }} | |||
Badness (Sintel): 1.08 | |||
== Godzilla == | == Godzilla == | ||
{{Main| Semaphore and godzilla }} | {{Main| Semaphore and godzilla }} | ||
Godzilla tempers out [[81/80]], equating [[9/8]] and [[10/9]], so it finds the prime 5 at a stack of four fifths, as does any temperament in the [[meantone family]]. Like many entries of this clan, godzilla can be extended naturally to the 2.3.5.7.13 subgroup by identifying the hemifourth as ~15/13, tempering out [[91/90]]. [[19edo]] is close to being the optimal generator tuning; hence it can be more or less equated with taking 4\19 as a generator. [[Mos scale]]s are of 5, 9, or 14 notes. | Godzilla tempers out [[81/80]], equating [[9/8]] and [[10/9]], so it finds the prime 5 at a stack of four fifths, as does any temperament in the [[meantone family]]. Like many entries of this clan, godzilla can be extended naturally to the 2.3.5.7.13 subgroup by identifying the hemifourth as ~15/13, tempering out [[91/90]] and [[105/104]]. [[19edo]] is close to being the optimal generator tuning; hence it can be more or less equated with taking 4\19 as a generator. [[Mos scale]]s are of 5, 9, or 14 notes. | ||
=== 7-limit === | === 7-limit === | ||
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==== 2.3.5.7.13 subgroup ==== | ==== 2.3.5.7.13 subgroup ==== | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7.13 | ||
Comma list: 49/48, 81/80, 91/90 | Comma list: 49/48, 81/80, 91/90 | ||
Subgroup-val mapping: {{mapping| 1 0 -4 2 -5 | 0 2 8 1 11 }} | |||
Optimal tunings: | Optimal tunings: | ||
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== Helayo == | == Helayo == | ||
: ''For the 5-limit version of this temperament see [[ | : ''For the 5-limit version of this temperament see [[Syntonic–kleismic equivalence continuum #Hogzilla]].'' | ||
Helayo tempers out 3645/3584 and may be thought of as the opposite of godzilla with respect to 19edo. Like godzilla, 19edo's generator is close to the optimum. | Helayo tempers out 3645/3584 and may be thought of as the opposite of godzilla with respect to 19edo. Like godzilla, 19edo's generator is close to the optimum. | ||
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[[Badness]] (Sintel): 2.00 | [[Badness]] (Sintel): 2.00 | ||
Scales: [[Helayo14]], [[Helayo19]], [[Helayo24]] | |||
; Music | ; Music | ||
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: ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Negri (5-limit)]].'' | : ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Negri (5-limit)]].'' | ||
Negri tempers out the [[negri comma]] in the 5-limit, 49/48 and [[225/224]] in the 7-limit. It may be described as {{nowrap| 9 & 10 }}; its ploidacot is omega-tetracot. It can be extended naturally to the 2.3.5.7.13 subgroup by adding | Negri tempers out the [[negri comma]] in the 5-limit, 49/48 and [[225/224]] in the 7-limit. It may be described as {{nowrap| 9 & 10 }}; its ploidacot is omega-tetracot. It can be extended naturally to the 2.3.5.7.13 subgroup by adding 91/90 and/or 105/104 to the comma list; this will be discussed below under the title of negra. | ||
=== 7-limit === | === 7-limit === | ||
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Comma list: 49/48, 65/64, 91/90 | 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 }} | Gencom mapping: {{mapping| 1 2 2 3 0 4 | 0 -4 3 -2 0 -3 }} | ||
Optimal tunings: | Optimal tunings: | ||
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=== Wilsec === | === Wilsec === | ||
Wilsec splits the fifthward generator of negri in half for 11/8~15/11, tempering out [[121/120]]. Its ploidacot is gamma-octacot. | |||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
Comma list: 49/48, 121/120, 225/224 | Comma list: 49/48, 121/120, 225/224 | ||
Mapping: {{mapping| 1 | Mapping: {{mapping| 1 -2 5 1 3 | 0 8 -6 4 1 }} | ||
: mapping generators: ~2, ~ | : mapping generators: ~2, ~11/8 | ||
Optimal tunings: | Optimal tunings: | ||
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Comma list: 49/48, 65/64, 91/90, 121/120 | Comma list: 49/48, 65/64, 91/90, 121/120 | ||
Mapping: {{mapping| 1 | Mapping: {{mapping| 1 -2 5 1 3 1 | 0 8 -6 4 1 6 }} | ||
Optimal tunings: | Optimal tunings: | ||
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Comma list: 49/48, 65/64, 91/90, 121/120, 154/153 | Comma list: 49/48, 65/64, 91/90, 121/120, 154/153 | ||
Mapping: {{mapping| 1 | Mapping: {{mapping| 1 -2 5 1 3 1 9 | 0 8 -6 4 1 6 -11 }} | ||
Optimal tunings: | Optimal tunings: | ||
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Comma list: 49/48, 65/64, 77/76, 91/90, 121/120, 154/153 | Comma list: 49/48, 65/64, 77/76, 91/90, 121/120, 154/153 | ||
Mapping: {{mapping| 1 | Mapping: {{mapping| 1 -2 5 1 3 1 9 2 | 0 8 -6 4 1 6 -11 5 }} | ||
Optimal tunings: | Optimal tunings: | ||
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Badness (Sintel): 2.01 | Badness (Sintel): 2.01 | ||
[[Category:Semaphoresmic clan| ]] <!-- main article --> | |||
[[Category:Temperament clans]] | [[Category:Temperament clans]] | ||
[[Category: | [[Category:Catalogs of rank-2 temperaments]] | ||