Porwell temperaments: Difference between revisions

This is a collection of [[regular temperament|temperaments]] that [[tempering out|tempers out]] the porwell comma, {{monzo| 11 1 -3 -2 }} ([[6144/6125]]), and includes hendecatonic, hemischis, twothirdtonic, nessafof, septisuperfourth, whoops, and polypyth.  

* ''[[Armodue]]'' (+36/35) → [[Pelogic family #Armodue|Pelogic family]]

* [[Porcupine]] (+64/63) → [[Porcupine family #Porcupine|Porcupine family]]

* [[Mohajira]] (+81/80) → [[Meantone family #Mohajira|Meantone family]]

* [[Valentine]] (+126/125) → [[Starling temperaments #Valentine|Starling temperaments]]

* [[Orwell]] (+225/224) → [[Semicomma family #Orwell|Semicomma family]]

* [[Shrutar]] (+245/243) → [[Diaschismic family #Shrutar|Diaschismic family]]

* ''[[Quinkee]]'' (+1029/1000) → [[Cloudy clan #Quinkee|Cloudy clan]]

* ''[[Hemiwürschmidt]]'' (+2401/2400 or 3136/3125) → [[Hemimean clan #Hemiwürschmidt|Hemimean clan]]

* ''[[Hemikleismic]]'' (+4000/3969) → [[Kleismic family #Hemikleismic|Kleismic family]]

* [[Amity]] (+4375/4374 or 5120/5103) → [[Amity family #Septimal amity|Amity family]]

* ''[[Freivald]]'' (+6272/6075) → [[Passion family #Freivald|Passion family]]

* ''[[Grendel]]'' (+16875/16807) → [[Mirkwai clan #Grendel|Mirkwai clan]]

* ''[[Hemischis]]'' (+19683/19600) → [[Schismatic family #Hemischis|Schismatic family]]

* ''[[Bison]]'' (+78732/78125) → [[Sensipent family #Bison|Sensipent family]]

* ''[[Hemimabila]]'' (+117649/116640) → [[Mabila family #Hemimabila|Mabila family]]

* ''[[Septisuperfourth]]'' (+118098/117649) → [[Escapade family #Septisuperfourth|Escapade family]]

* ''[[Alphatrident]]'' (+14348907/14336000) → [[Alphatricot family #Alphatrident|Alphatricot family]]

* ''[[Hemimaquila]]'' (+{{monzo| -5 10 5 -8 }}) → [[Maquila family #Hemimaquila|Maquila family]]

* ''[[Decimaleap]]'' (+{{monzo| 15 -18 1 4 }}) → [[Quintaleap family #Decimaleap|Quintaleap family]]

* ''[[Twilight]]'' (+{{monzo| 19 -22 2 4 }}) → [[Undim family #Twilight|Undim family]]

{{see also|11th-octave temperaments}}

 

[[Subgroup]]: 2.3.5.7

{{Mapping|legend=1| 11 0 43 -4 | 0 1 -1 2 }}

[[Optimal tuning]] ([[POTE]]): ~16/15 = 1\11, ~3/2 = 703.054

{{Mapping|legend=1| 11 0 43 -4 38 | 0 1 -1 2 0 }}

Optimal tuning (POTE): ~16/15 = 1\11, ~3/2 = 702.636

{{Optimal ET sequence|legend=0| 22, 55, 77, 99, 176e, 275e }}

{{Mapping|legend=1| 11 0 43 -4 38 93 | 0 1 -1 2 0 -3 }}

Optimal tuning (POTE): ~16/15 = 1\11, ~3/2 = 702.291

{{Optimal ET sequence|legend=0| 22, 55, 77, 99, 176e }}

{{Mapping|legend=1| 11 0 43 -4 38 93 45 | 0 1 -1 2 0 -3 0 }}

Optimal tuning (POTE): ~16/15 = 1\11, ~3/2 = 702.301

{{Optimal ET sequence|legend=0| 22, 55, 77, 99, 176eg }}

{{Mapping|legend=1| 11 0 43 -4 73 | 0 1 -1 2 -2 }}

Optimal tuning (POTE): ~16/15 = 1\11, ~3/2 = 703.686

{{Optimal ET sequence|legend=0| 22, 77e, 99e, 121, 220e }}

{{Mapping|legend=1| 11 0 43 -4 73 128 | 0 1 -1 2 -2 -5 }}

Optimal tuning (POTE): ~16/15 = 1\11, ~3/2 = 703.888

{{Optimal ET sequence|legend=0| 22, 77eff, 99ef, 121, 341bdeeff }}

{{Mapping|legend=1| 11 0 43 -4 73 128 45 | 0 1 -1 2 -2 -5 0 }}

Optimal tuning (POTE): ~16/15 = 1\11, ~3/2 = 703.877

{{Optimal ET sequence|legend=0| 22, 77eff, 99ef, 121, 220efg, 341bdeeffgg }}

{{Mapping|legend=1| 22 0 86 -8 111 | 0 1 -1 2 -1 }}

: Mapping generators: ~33/32, ~3

 

{{Optimal ET sequence|legend=0| 22, 154, 176, 198 }}

[[Subgroup]]: 2.3.5.7

{{Mapping|legend=1| 1 3 2 4 | 0 -13 3 -11 }}

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~15/14 = 130.401

Mapping: {{mapping| 1 3 2 4 4 | 0 -13 3 -11 -5 }}

Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 130.430

Mapping: {{mapping| 1 3 2 4 4 5 | 0 -13 3 -11 -5 -12 }}

Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 130.409

 

[[Subgroup]]: 2.3.5.7

{{Mapping|legend=1| 1 -2 1 3 | 0 19 7 -1 }}

: Mapping generators: ~2, ~8/7

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~8/7 = 226.4834

Mapping: {{mapping| 1 -2 1 3 1 | 0 19 7 -1 13 }}

Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 226.4856

Mapping: {{mapping| 1 -2 1 3 1 2 | 0 19 7 -1 13 9 }}

Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 226.4794

 

Cryptically named by [[Petr Pařízek]] in 2011<ref name="petr's short post">[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101089.html Yahoo! Tuning Group | ''Some more unclassified temperaments'']</ref>, nessafof adds the [[landscape comma]] and has a third-octave period. The name actually refers to the fact that it has a neutral-second generator, and that a semi-augmented fourth, stacked 5 times, makes 5/1<ref name="petr's long post"/>.  

: Mapping generators: ~63/50, ~35/32

:''For the 5-limit version, see [[High badness temperaments #Untriton]].''

 

[[Subgroup]]: 2.3.5.7

{{Mapping|legend=1| 1 6 -7 19 | 0 -9 19 -33 }}

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~45/32 = 588.782

Mapping: {{mapping| 1 6 -7 19 1 | 0 -9 19 -33 5 }}

Optimal tuning (POTE): ~2 = 1\1, ~45/32 = 588.811

Mapping: {{mapping| 1 6 -7 19 1 -12 | 0 -9 19 -33 5 32 }}

Optimal tuning (POTE): ~2 = 1\1, ~45/32 = 588.788

Mapping: {{mapping| 1 6 -7 19 -25 | 0 -9 19 -33 58 }}

Optimal tuning (POTE): ~2 = 1\1, ~45/32 = 588.800

Mapping: {{mapping| 1 6 -7 19 -25 -12 | 0 -9 19 -33 58 32 }}

Optimal tuning (POTE): ~2 = 1\1, ~45/32 = 588.796

:''For the 5-limit version, see [[Very high accuracy temperaments #Whoosh]].''

 

[[Subgroup]]: 2.3.5.7

{{Mapping|legend=1| 1 17 14 -7 | 0 -33 -25 21 }}

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~441/320 = 560.519

Mapping: {{mapping| 1 17 14 -7 10 | 0 -33 -25 21 -14 }}

Optimal tuning (POTE): ~2 = 1\1, ~242/175 = 560.519

:''For the 5-limit version, see [[High badness temperaments #Leapday]].''

Polypyth (46 &amp; 121) tempers out the same 5-limit comma as the [[Hemifamity temperaments #Leapday|leapday temperament]] (29 &amp; 46), but with the porwell (6144/6125) rather than the hemifamity (5120/5103) tempered out.

[[Subgroup]]: 2.3.5.7

{{Mapping|legend=1| 1 0 -31 52 | 0 1 21 -31 }}

 

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 704.174

Mapping: {{mapping| 1 0 -31 52 59 | 0 1 21 -31 -35 }}

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.177

Mapping: {{mapping| 1 0 -31 52 59 64 | 0 1 21 -31 -35 -38 }}

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.168

Mapping: {{mapping| 1 0 -31 52 59 64 39 | 0 1 21 -31 -35 -38 -22 }}

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.168

The icositritonic temperament (46 &amp; 161) has a period of 1/23 octave, so six period represents [[6/5]] and nine period represents [[21/16]].

[[Subgroup]]: 2.3.5.7

{{Mapping|legend=1| 23 0 17 101 | 0 1 1 -1 }}

[[Optimal tuning]] ([[POTE]]): ~1323/1280 = 1\23, ~64/63 = 29.3586

{{Optimal ET sequence|legend=1| 46, 115, 161, 207, 368c }}

Mapping: {{mapping| 23 0 17 101 116 | 0 1 1 -1 -1 }}

Optimal tuning (POTE): ~33/32 = 1\23, ~64/63 = 29.3980

{{Optimal ET sequence|legend=1| 46, 115, 161, 207, 368c }}

Mapping: {{mapping| 23 0 17 101 116 158 | 0 1 1 -1 -1 -2 }}

Optimal tuning (POTE): ~33/32 = 1\23, ~64/63 = 29.2830

Mapping: {{mapping| 23 0 17 101 116 158 94 | 0 1 1 -1 -1 -2 0 }}

Optimal tuning (POTE): ~33/32 = 1\23, ~64/63 = 29.2800

Mapping: {{mapping| 23 0 17 101 116 158 94 207 | 0 1 1 -1 -1 -2 0 -3 }}

Optimal tuning (POTE): ~33/32 = 1\23, ~64/63 = 29.3760

Mapping: {{mapping| 23 0 17 101 116 158 94 207 104 | 0 1 1 -1 -1 -2 0 -3 0 }}

Optimal tuning (POTE): ~33/32 = 1\23, ~64/63 = 29.3471

The ''countermiracle'' temperament (31 &amp; 145) tempers out the trimyna, 50421/50000 and the [[quince comma]], 823543/819200.

[[Subgroup]]: 2.3.5.7

{{Mapping|legend=1| 1 4 3 3 | 0 -25 -7 -2 }}

: Mapping generators: ~2, ~343/320

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~343/320 = 115.9169

Mapping: {{mapping| 1 4 3 3 8 | 0 -25 -7 -2 -47 }}

Optimal tuning (POTE): ~2 = 1\1, ~77/72 = 115.9158

Mapping: {{mapping| 1 4 3 3 8 1 | 0 -25 -7 -2 -47 28 }}

Optimal tuning (POTE): ~2 = 1\1, ~77/72 = 115.8803

Mapping: {{mapping| 1 4 3 3 8 1 1 | 0 -25 -7 -2 -47 28 32 }}

Optimal tuning (POTE): ~2 = 1\1, ~77/72 = 115.8756

Mapping: {{mapping| 1 4 3 3 8 -2 | 0 -25 -7 -2 -47 59 }}

Optimal tuning (POTE): ~2 = 1\1, ~77/72 = 115.9335

Mapping: {{mapping| 1 4 3 3 8 -2 -2 | 0 -25 -7 -2 -47 59 63 }}

Optimal tuning (POTE): ~2 = 1\1, ~77/72 = 115.9391

Mapping: {{mapping| 1 4 3 3 8 15 0 -25 -7 -2 -47 -117 }}

Optimal tuning (POTE): ~2 = 1\1, ~77/72 = 115.8898

Mapping: {{mapping| 1 4 3 3 8 15 15 | 0 -25 -7 -2 -47 -117 -113 }}

Optimal tuning (POTE): ~2 = 1\1, ~77/72 = 115.8832

Mapping: {{mapping| 1 4 3 3 5 | 0 -25 -7 -2 -16 }}

Optimal tuning (POTE): ~2 = 1\1, ~343/320 = 115.9192

Mapping: {{mapping| 1 4 3 3 5 1 | 0 -25 -7 -2 -16 28 }}

Optimal tuning (POTE): ~2 = 1\1, ~273/256 = 115.8624

Mapping: {{mapping| 1 4 3 3 5 1 1 | 0 -25 -7 -2 -16 28 32 }}

Optimal tuning (POTE): ~2 = 1\1, ~91/85 = 115.8527

: ''For the 5-limit version, see [[Syntonic–chromatic equivalence continuum #Absurdity]].''

[[Subgroup]]: 2.3.5.7

{{Mapping|legend=1| 7 0 -17 64 | 0 1 3 -4 }}

 

[[Optimal tuning]] ([[POTE]]): ~972/875 = 1\7, ~3/2 = 700.5854 (or ~10/9 = 186.2997)

{{Mapping|legend=1| 7 0 -17 64 124 | 0 1 3 -4 -9 }}

Optimal tuning (POTE): ~495/448 = 1\7, ~3/2 = 700.6354 (or ~10/9 = 186.3497)

{{Mapping|legend=1| 7 0 -17 64 124 37 | 0 1 3 -4 -9 -1 }}

Optimal tuning (POTE): ~72/65 = 1\7, ~3/2 = 700.6291 (or ~10/9 = 186.3434)

{{Mapping|legend=1| 7 0 -17 64 124 37 -49 | 0 1 3 -4 -9 -1 7 }}

Optimal tuning (POTE): ~72/65 = 1\7, ~3/2 = 700.6524 (or ~10/9 = 186.3667)

{{Mapping|legend=1| 7 0 -17 64 124 37 -49 63 | 0 1 3 -4 -9 -1 7 -3 }}

Optimal tuning (POTE): ~21/19 = 1\7, ~3/2 = 700.6565 (or ~10/9 = 186.3708)

: ''For the 5-limit version, see [[High badness temperaments #Dodifo]].''

 

[[Subgroup]]: 2.3.5.7

{{Mapping|legend=1| 1 12 5 4 | 0 -35 -9 -4 }}

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~49/40 = 357.070

Mapping: {{mapping| 1 12 5 4 -1 | 0 -35 -9 -4 15 }}

Optimal tuning (POTE): ~2 = 1\1, ~49/40 = 357.048

Mapping: {{mapping| 1 12 5 4 -1 4 | 0 -35 -9 -4 15 -1 }}

Optimal tuning (POTE): ~2 = 1\1, ~16/13 = 357.049