Semaphoresmic clan: Difference between revisions

The '''semaphoresmic clan''' (or '''semaphore family''') [[tempering out|tempers out]] the slendro diesis, or semaphoresma, [[49/48]], a triprime comma with factors of 2, 3 and 7.  

: sval mapping generators: ~2, ~7/4

 

: [[gencom]]: [2 7/6; 49/48]

* [[CTE]]: ~2 = 1\1, ~7/4 = 952.2948

* [[POTE]]: ~2 = 1\1, ~7/4 = 949.615

The second comma of the comma list defines which 7-limit family member we are looking at.  

Godzilla adds [[81/80]]. Immunity adds [[2240/2187]]. Superpelog adds [[135/128]]. Beep adds [[21/20]]. Baba adds [[16/15]]. These all use the same nominal generator as semaphore, though some of them are of very low accuracy.  

Decimal adds [[25/24]], splitting 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. Blacksmith adds [[28/27]], splitting the octave in five. Spell adds [[3125/3072]], splitting the hemitwelfth in five. Hemiripple adds 6561/6250, splitting the hemifourth in five. Finally, mabila adds 28672/28125 and splits an interval of two octaves plus a hemifourth in five.  

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

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

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

Considered below are godzilla, superpelog, negri, nuke, mabila, and hemiripple.

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]]. [[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.

* [[CTE]]: ~2 = 1\1, ~7/4 = 948.7959

* [[POTE]]: ~2 = 1\1, ~7/4 = 947.365

[[Badness]]: 0.026747

=== 11-limit ===

Optimal tunings:

* CTE: ~2 = 1\1, ~7/4 = 947.4563

* POTE: ~2 = 1\1, ~7/4 = 945.973

{{Optimal ET sequence|legend=1| 14c, 19, 33cd }}

Badness: 0.028947

Optimal tunings:

* CTE: ~2 = 1\1, ~7/4 = 947.8877

* POTE: ~2 = 1\1, ~7/4 = 946.397

{{Optimal ET sequence|legend=1| 14cf, 19, 33cdff }}

Badness: 0.022503

* CTE: ~2 = 1\1, ~7/4 = 948.2089

* POTE: ~2 = 1\1, ~7/4 = 945.958

{{Optimal ET sequence|legend=1| 14c, 19e, 33cdee, 52cdeee }}

Badness: 0.028510

* CTE: ~2 = 1\1, ~7/4 = 949.6160

* POTE: ~2 = 1\1, ~7/4 = 948.921

{{Optimal ET sequence|legend=1| 19e, 24, 43de }}

Badness: 0.039647

* CTE: ~2 = 1\1, ~7/4 = 949.5255

* POTE: ~2 = 1\1, ~7/4 = 948.835

{{Optimal ET sequence|legend=1| 19e, 24, 43de }}

Badness: 0.025676

Optimal tunings:

* CTE: ~2 = 1\1, ~7/4 = 949.0311

* POTE: ~2 = 1\1, ~7/4 = 948.827

{{Optimal ET sequence|legend=1| 5, 19, 24 }}

Badness: 0.035673

Optimal tunings:

* CTE: ~2 = 1\1, ~7/4 = 949.0670

* POTE: ~2 = 1\1, ~7/4 = 948.802

{{Optimal ET sequence|legend=1| 5, 19, 24 }}

Badness: 0.026703

: ''For the 5-limit version of this temperament see [[High badness temperaments #Hogzilla]].''

* [[CTE]]: ~2 = 1\1, ~7/4 = 947.0969

[[Badness]]: 0.0791

 

[[Optimal tuning]]s:

* [[CTE]]: ~2 = 1\1, ~7/4 = 939.0297

* [[POTE]]: ~2 = 1\1, ~7/4 = 940.048

[[Badness]]: 0.058216

* CTE: ~2 = 1\1, ~7/4 = 938.4673

* POTE: ~2 = 1\1, ~7/4 = 940.041

{{Optimal ET sequence|legend=1| 9, 14c, 23de, 37bcde }}

Badness: 0.028535

: ''[http://micro.soonlabel.com/MOS/20120418-9mos-mindaugas.mp3 Mindaugas Rex Lithuaniae]'' by [[Chris Vaisvil]] ([http://chrisvaisvil.com/?p=2267 blog]) (superpelog[9] in 23edo tuning)

* [[POTE]]: ~2 = 1\1, ~7/4 = 973.296

 

{{Multival|legend=1| 2 -2 1 -8 -4 8 }}

[[Badness]]: 0.044321

* POTE: ~2 = 1\1, ~7/4 = 978.164

{{Optimal ET sequence|legend=1| 5, 11b, 16bc, 27bbcc }}

Badness: 0.036538

Negri tempers out the [[negri comma]] in the 5-limit, [[49/48]] and [[225/224]] in the 7-limit. It can be extended naturally to the 2.3.5.7.13 subgroup by adding [[91/90]] to the comma list; this will be discussed below under the title of negra.  

 

 

 

 

 

 

 

 

* [[POTE]]: ~2 = 1\1, ~15/14 = 125.608

[[Badness]]: 0.026483

Sval mapping: {{mapping| 1 2 2 3 4 | 0 -4 3 -2 -3 }}

: gencom: [2 14/13; 49/48 65/64 91/90]

Optimal tunings:

* POTE: ~2 = 1\1, ~14/13 = 125.567

=== 11-limit ===

* POTE: ~2 = 1\1, ~15/14 = 126.474

{{Optimal ET sequence|legend=1| 9, 10, 19 }}

Badness: 0.026190

* POTE: ~2 = 1\1, ~14/13 = 126.431

{{Optimal ET sequence|legend=1| 9, 10, 19 }}

Badness: 0.017833

* POTE: ~2 = 1\1, ~15/14 = 124.767

{{Optimal ET sequence|legend=1| 19, 29, 48d, 77cdd }}

Badness: 0.038679

* POTE: ~2 = 1\1, ~14/13 = 124.716

{{Optimal ET sequence|legend=1| 19, 29, 48df, 77cddf }}

Badness: 0.024383

* POTE: ~2 = 1\1, ~15/14 = 127.039

{{Optimal ET sequence|legend=1| 9, 19e }}

Badness: 0.030617

* POTE: ~2 = 1\1, ~14/13 = 127.039

{{Optimal ET sequence|legend=1| 9, 19e }}

Badness: 0.020205

* POTE: ~2 = 1\1, ~15/14 = 124.539

{{Optimal ET sequence|legend=1| 10, 19e, 29, 77cddee }}

Badness: 0.035296

* POTE: ~2 = 1\1, ~14/13 = 124.545

{{Optimal ET sequence|legend=1| 10, 19e, 29, 77cddeef }}

Badness: 0.021559

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

* POTE: ~2 = 1\1, ~11/8 = 537.186

{{Optimal ET sequence|legend=1| 9, 20, 29, 38d, 67cdde }}

Badness: 0.041886

Mapping: {{mapping| 1 6 -1 5 4 7 | 0 -8 6 -4 -1 -6 }}

* POTE: ~2 = 1\1, ~11/8 = 537.208

{{Optimal ET sequence|legend=1| 9, 20, 29, 38df, 67cddef }}

Badness: 0.025192

Mapping: {{mapping| 1 6 -1 5 4 7 -2 | 0 -8 6 -4 -1 -6 11 }}

* POTE: ~2 = 1\1, ~11/8 = 537.230

{{Optimal ET sequence|legend=1| 9, 20g, 29g, 38df, 67cddefg }}

Badness: 0.021778

Mapping: {{mapping| 1 6 -1 5 4 7 -2 7 | 0 -8 6 -4 -1 -6 11 -5 }}

* POTE: ~2 = 1\1, ~11/8 = 537.214

{{Optimal ET sequence|legend=1| 9, 20g, 29g, 38df, 67cddefgh }}

Badness: 0.016828

* [[POTE]]: ~2 = 1\1, ~16/15 = 80.9538

{{Optimal ET sequence|legend=1| 14, 15, 44cd }}

[[Badness]]: 0.129339

* POTE: ~2 = 1\1, ~16/15 = 80.8171

{{Optimal ET sequence|legend=1| 14e, 15 }}

Badness: 0.069398

* POTE: ~2 = 1\1, ~16/15 = 81.0243

 

{{Optimal ET sequence|legend=1| 14e, 15, 44cdeff }}

 

 

 

 

[[Comma list]]: 49/48, 28672/28125

 

 

 

* POTE: ~2 = 1\1, ~75/56 = 529.667

 

 

 

 

Comma list: 49/48, 56/55, 1350/1331

 

 

* POTE: ~2 = 1\1, ~15/11 = 529.729

 

{{Optimal ET sequence|legend=1| 9, 25e, 34 }}

 

 

 

 

 

* POTE: ~2 = 1\1, ~15/11 = 529.763

 

{{Optimal ET sequence|legend=1| 9, 25e, 34 }}

 

 

 

 

 

* POTE: ~2 = 1\1, ~15/11 = 529.695

 

 

 

 

 

 

* POTE: ~2 = 1\1, ~15/11 = 529.736

 

{{Optimal ET sequence|legend=1| 9, 25e, 34 }}

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

{{Optimal ET sequence|legend=1| 23de, 24, 47de, 71bdde }}

Badness: 0.046588

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