# Ragismic microtemperaments

(Redirected from Deca temperament)

The ragisma is 4375/4374 with a monzo of |-1 -7 4 1>, the smallest 7-limit superparticular ratio. Since (10/9)^4=4375/4374 * 32/21, the minor tone 10/9 tends to be an interval of relatively low complexity in temperaments tempering out the ragisma, though when looking at microtemperaments the word "relatively" should be emphasized. Even so mitonic uses it as a generator, which ennealimmal and enneadecal can do also, and amity reaches it in three generators. We also have 7/6 = 4375/4374 * (27/25)^2, so 27/25 also tends to relatively low complexity, with the same caveat about "relatively"; however 27/25 is the period for ennealimmal.

Temperaments not discussed here include flattone, hystrix, sensi, unidec, quartonic, catakleismic, modus, pontiac, vishnu, and vulture.

# Ennealimmal

Ennealimmal temperament tempers out the two smallest 7-limit superparticular commas, 2401/2400 and 4375/4374, leading to a temperament of unusual efficiency. It also tempers out the ennealimmal comma, |1 -27 18>, which leads to the identification of (27/25)^9 with the octave, and gives ennealimmal a period of 1/9 octave. While 27/25 is a 5-limit interval, two periods equates to 7/6 because of identification by 4375/4374, and this represents 7/6 with such accuracy (a fifth of a cent flat) that there is no realistic possibility of treating ennealimmal as anything other than 7-limit. Its wedgie is <<18 27 18 1 -22 -34||.

Aside from 10/9 which has already been mentioned, possible generators include 36/35, 21/20, 6/5, 7/5 and the neutral thirds pair 49/40 and 60/49, all of which have their own interesting advantages. Possible tunings are 441, 612, or 3600 EDOs, though its hardly likely anyone could tell the difference.

If 1/9 of an octave is too small of a period for you, you could try generator-period pairs of [3, 5], [5/3, 3], [6/5, 4/3], [4/3, 8/5] or [10/9, 4/3] (for example.) In particular, people fond of the idea of "tritaves" as analogous to octaves might consider the 28 or 43 note MOS with generator an approximate 5/3 within 3; for instance as given by 451/970 of a "tritave". Tetrads have a low enough complexity that (for example) there are nine 1-3/2-7/4-5/2 tetrads in the 28 notes to the tritave MOS, which is equivalent in average step size to a 17 2/3 to the octave MOS.

valid range: [26.667, 66.667] (45bcd to 18bcd)

nice range: [48.920, 49.179]

strict range: [48.920, 49.179]

Commas: 2401/2400, 4375/4374

POTE generators: ~36/35 = 49.0205; ~10/9 = 182.354; ~6/5 = 315.687; ~49/40 = 350.980

Map: [<9 1 1 2|, <0 2 3 2|]

Wedgie: <<18 27 18 1 -22 -34||

EDOs: 27, 45, 72, 99, 171, 270, 441, 612, 3600

## Hemiennealimmal

Commas: 2401/2400, 4375/4374, 3025/3024

valid range: [13.333, 22.222] (90bcd, 54c)

nice range: [17.304, 17.985]

strict range: [17.304, 17.985]

POTE generator: ~99/98 = 17.6219

Map: [<18 0 -1 22 48|, <0 2 3 2 1|]

EDOs: 72, 198, 270, 342, 612, 954, 1566

### 13-limit

Commas: 676/675, 1001/1000, 1716/1715, 3025/3024

valid range: [16.667, 22.222] (72 to 54cf)

nice range: [17.304, 18.309]

strict range: [17.304, 18.309]

POTE generator ~99/98 = 17.7504

Map: [<18 0 -1 22 48 -19|, <0 2 3 2 1 6|]

EDOs: 72, 198, 270

### Semihemiennealimmal

Commas: 2401/2400, 4375/4374, 3025/3024, 4225/4224

POTE generator: ~39/32 = 342.139

Map: [<18 0 -1 22 48 88|, <0 4 6 4 2 -3|]

EDOs: 126, 144, 270, 684, 954

## Semiennealimmal

Commas: 2401/2400, 4375/4374, 4000/3993

POTE generator: ~140/121 = 250.3367

Map: [<9 3 4 14 18|, <0 6 9 6 7|]

EDOs: 72, 369, 441

### 13-limit

Commas: 1575/1573, 2080/2079, 2401/2400, 4375/4374

POTE generator: ~140/121 = 250.3375

Map: [<9 3 4 14 18 -8|, <0 6 9 6 7 22|]

EDOs: 72, 441

Commas: 2401/2400, 4375/4374, 234375/234256

POTE generator: ~77/75 = 45.595

Map: [<9 1 1 12 -7|, <0 8 12 8 23|]

EDOs: 342, 1053, 1395, 1737, 4869d, 6606cd

## Ennealimnic

Commas: 243/242, 441/440, 4375/4356

valid range: [44.444, 53.333] (27e to 45e)

nice range: [48.920, 52.592]

strict range: [48.920, 52.592]

POTE generator: ~36/35 = 49.395

Map: [<9 1 1 12 -2|, <0 2 3 2 5|]

EDOs: 72, 171, 243

### 13-limit

Commas: 243/242, 364/363, 441/440, 625/624

valid range: [48.485, 50.000] (99ef to 72)

nice range: [48.825, 52.592]

strict range: [48.825, 50.000]

POTE generator: ~36/35 = 49.341

Map: [<9 1 1 12 -2 -33|, <0 2 3 2 5 10|]

EDOs: 72, 171, 243

#### 17-limit

Commas: 243/242, 364/363, 375/374, 441/440, 595/594

valid range: [48.485, 50.000] (99ef to 72)

nice range: [46.363, 52.592]

strict range: [48.485, 50.000]

POTE generator: ~36/35 = 49.335

Map: [<9 1 1 12 -2 -33 -3|, <0 2 3 2 5 10 6|]

EDOs: 72, 171, 243

### Ennealim

Commas: 169/168, 243/242, 325/324, 441/440

POTE generator: ~36/35 = 49.708

Map: [<9 1 1 12 -2 20|, <0 2 3 2 5 2|]

EDOs: 27e, 45ef, 72, 315ff, 387cff, 459cdfff

## Ennealiminal

Commas: 385/384, 1375/1372, 4375/4374

POTE generator: ~36/35 = 49.504

Map: [<9 1 1 12 51|, <0 2 3 2 -3|]

EDOs: 27, 45, 72, 171e, 243e, 315e

### 13-limit

Commas: 169/168, 325/324, 385/384, 1375/1372

POTE generator: ~36/35 = 49.486

Map: [<9 1 1 12 51 20|, <0 2 3 2 -3 2|]

EDOs: 27, 45f, 72, 171ef, 243ef

## Trinealimmal

Commas: 2401/2400, 4375/4374, 2097152/2096325

POTE generator: ~6/5 = 315.644

Map: [<27 1 0 34 177|, <0 2 3 2 -4|]

EDOs: 27, 243, 270, 783, 1053, 1323, 10854bcde

# Gamera

Commas: 4375/4374, 589824/588245

POTE generator ~8/7 = 230.336

Map: [<1 6 10 3|, <0 -23 -40 -1|]

EDOs: 26, 73, 99, 224, 323, 422, 735

## Hemigamera

Commas: 3025/3024, 4375/4374, 202397184/201768035

POTE generator: ~8/7 = 230.337

Map: [<2 12 20 6 5|, <0 -23 -40 -1 5|]

EDOs: 26, 198, 224, 422, 646, 1068d

### 13-limit

Commas: 1716/1715 2080/2079 2200/2197 3025/3024

Map: [<2 12 20 6 5 17|, <0 -23 -40 -1 5 -25|]

EDOs: 26, 198, 224, 422, 646f, 1068df

# Supermajor

The generator for supermajor temperament is a supermajor third, 9/7, tuned about 0.0002 cents flat. 37 of these give (2^15)/3, 46 give (2^19)/5, and 75 give (2^30)/7, leading to a wedgie of <<37 46 75 -13 15 45||. This is clearly quite a complex temperament; it makes up for it, to the extent it does, with extreme accuracy: 1106 or 1277 can be used as tunings, leading to accuracy even greater than that of ennealimmal. The 80 note MOS is presumably the place to start, and if that isn't enough notes for you, there's always the 171 note MOS.

Commas: 4375/4374, 52734375/52706752

POTE generator: ~9/7 = 435.082

Map: [<1 15 19 30|, <0 -37 -46 -75|]

EDOs: 11, 80, 171, 764, 1106, 1277, 3660, 4937, 6214

## Semisupermajor

Commas: 3025/3024, 4375/4374, 35156250/35153041

POTE generator: ~9/7 = 435.082

Map: [<2 30 38 60 41|, <0 -37 -46 -75 -47|]

EDOs: 80, 342, 764, 1106, 1448, 2554, 4002f, 6556cf

Enndedecal temperament tempers out the enneadeca, |-14 -19 19>, and as a consequence has a period of 1/19 octave. This is because the enneadeca is the amount by which nineteen just minor thirds fall short of an octave. If to this we add 4375/4374 we get the 7-limit temperament we are considering here, but note should be taken of the fact that it makes for a reasonable 5-limit microtemperament also, where the generator can be 25/24, 27/25, 10/9, 5/4 or 3/2. To this we may add possible 7-limit generators such as 225/224, 15/14 or 9/7. Since enneadecal tempers out 703125/702464, the amount by which 81/80 falls short of three stacked 225/224, we can equate the 225/224 generator with (81/80)^(1/3). This is the interval needed to adjust the 1/3 comma meantone flat fifths and major thirds of 19edo up to just ones. 171edo is a good tuning for either the 5 or 7 limits, and 494edo shows how to extend the temperament to the 11 or 13 limit, where it is accurate but very complex. Fans of near-perfect fifths may want to use 665edo for a tuning.

Commas: 4375/4374, 703125/702464

POTE generator: ~3/2 = 701.880

Map: [<19 0 14 -37|, <0 1 1 3|]

Generators: 28/27, 3

EDOs: 19, 152, 171, 665, 836, 1007, 2185

Commas: 3025/3024, 4375/4374, 234375/234256

POTE generator: ~3/2 = 701.881

Map: [<38 0 28 -74 11|, <0 1 1 3 2|]

EDOs: 152, 342, 494, 836, 1178, 2014

### 13-limit

Commas: 3025/3024, 4096/4095, 4375/4374, 31250/31213

POTE generator: ~3/2 = 701.986

Map: [<38 0 28 -74 11 502|, <0 1 1 3 2 -6|]

EDOs: 152, 342, 494, 836

# Deca

Commas: 4375/4374, 165288374272/164794921875

POTE generator: ~460992/390625 = 284.423

Map: [<10 4 2 9|, <0 5 6 11|]

EDOs: 80, 190, 270, 1270, 1540, 1810, 2080

## 11-limit

Commas: 3025/3024, 4375/4374, 422576/421875

POTE generator: ~33/28 = 284.418

Map: [<10 4 2 9 18|, <0 5 6 11 7|]

EDOs: 80, 190, 270, 1000, 1270

## 13-limit

Commas: 1001/1000, 3025/3024, 4225/4224, 4375/4374

POTE generator: ~33/28 = 284.398

Map: [<10 4 2 9 18 37|, <0 5 6 11 7 0|]

EDOs: 80, 190, 270, 730, 1000

# Mitonic

Commas: 4375/4374, 2100875/2097152

POTE generator: ~10/9 = 182.458

Map: [<1 16 32 -15|, <0 -17 -35 21|]

EDOs: 46, 125, 171

# Abigail

Commas: 4375/4374, 2147483648/2144153025

POTE generator: 208.899

Map: [<2 7 13 -1|, <0 -11 -24 19|]

Wedgie: <<22 48 -38 25 -122 -223||

EDOs: 46, 132, 178, 224, 270, 494, 764, 1034, 1798

## 11-limit

Comma: 3025/3024, 4375/4374, 20614528/20588575

POTE generator: 208.901

Map: [<2 7 13 -1 1|, <0 -11 -24 19 17|]

EDOs: 46, 132, 178, 224, 270, 494, 764

## 13-limit

Commas: 1716/1715, 2080/2079, 3025/3024, 4096/4095

POTE generator: 208.903

Map: [<2 7 13 -1 1 -2|, <0 -11 -24 19 17 27|]

EDOs: 46, 178, 224, 270, 494, 764, 1258

# Semidimi

The generator of semidimi temperament is a semi-diminished fourth interval tuned between 162/125 and 35/27. It tempers out 5-limit |-12 -73 55> and 7-limit 3955078125/3954653486, as well as 4375/4374.

Comma: |-12 -73 55>

POTE generator: ~162/125 = 449.127

Map: [<1 36 48|, <0 -55 -73|]

Wedgie: <<55 73 -12||

EDOs: 171, 863, 1034, 1205, 1376, 1547, 1718, 4983, 6701, 8419

## 7-limit

Commas: 4375/4374, 3955078125/3954653486

POTE generator: ~35/27 = 449.127

Map: [<1 36 48 61|, <0 -55 -73 -93|]

Wedgie: <<55 73 93 -12 -7 11||

EDOs: 171, 863, 1034, 1205, 1376, 1547, 1718, 4983, 6701, 8419

# Brahmagupta

Commas: 4375/4374, 70368744177664/70338939985125

POTE generator: ~27/20 = 519.716

Map: [<7 2 -8 53|, <0 3 8 -11|]

Wedgie: <<21 56 -77 40 -181 -336||

EDOs: 217, 224, 441, 1106, 1547

## 11-limit

Commas: 4000/3993, 4375/4374, 131072/130977

POTE generator: ~27/20 = 519.704

Map: [<7 2 -8 53 3|, <0 3 8 -11 7|]

EDOs: 217, 224, 441, 665, 1771ee

## 13-limit

Commas: 1575/1573, 2080/2079, 4096/4095, 4375/4374

POTE generator: ~27/20 = 519.706

Map: [<7 2 -8 53 3 35|, <0 3 8 -11 7 -3|]

EDOs: 217, 224, 441, 665, 1771eef

# Quasithird

Comma: |55 -64 20>

POTE generator: ~1594323/1280000 = 380.395

Map: [<4 0 -11|, <0 5 16|]

Wedgie: <<20 64 55||

EDOs: 164, 224, 388, 612, 836, 1000, 1448, 1612, 2224, 2836

## 7-limit

Commas: 4375/4374, 1153470752371588581/1152921504606846976

POTE generator: ~5103/4096 = 380.388

Map: [<4 0 -11 48|, <0 5 16 -29|]

Wedgie: <<20 64 -116 55 -240 -449||

EDOs: 164, 224, 388, 612, 1448, 2060

## 11-limit

Commas: 3025/3024, 4375/4374, 4296700485/4294967296

POTE generator: ~5103/4096 = 380.387

Map: [<4 0 -11 48 43|, <0 5 16 -29 -23|]

EDOs: 164, 224, 388, 612, 836, 1448

## 13-limit

Commas: 2200/2197, 3025/3024, 4375/4374, 468512/468195

POTE generator: ~5103/4096 = 380.385

Map: [<4 0 -11 48 43 11|, <0 5 16 -29 -23 3|]

EDOs: 164, 224, 388, 612, 836, 1448f, 2284f

# Semidimfourth

Comma: |7 41 -31>

POTE generator: ~162/125 = 448.449

Map: [<1 21 28|, <0 -31 -41|]

Wedgie: <<31 41 -7||

EDOs: 91, 99, 190, 289, 388, 487, 677, 875, 966

## 7-limit

Commas: 4375/4374, 235298/234375

POTE generator: ~35/27 = 448.457

Map: [<1 21 28 36|, <0 -31 -41 -53|]

Wedgie: <<31 41 53 -7 -3 8||

EDOs: 91, 99, 289, 388, 875, 1263d, 1651d

## Neusec

Commas: 3025/3024, 4375/4374, 235298/234375

POTE generator: ~12/11 = 151.547

Map: [<2 11 15 19 15|, <0 -31 -41 -53 -32|]

EDOs: 190, 388

### 13-limit

Commas: 847/845, 1001/1000, 3025/3024, 4375/4374

POTE generator: ~12/11 = 151.545

Map: [<2 11 15 19 15 17|, <0 -31 -41 -53 -32 -38|]

EDOs: 190, 198, 388

# Acrokleismic

Commas: 4375/4374, 2202927104/2197265625

POTE generator: ~6/5 = 315.557

Map: [<1 10 11 27|, <0 -32 -33 -92|]

Wedgie: <<32 33 92 -22 56 121||

EDOs: 19, 251, 270

## 11-limit

Commas: 4375/4374, 41503/41472, 172032/171875

POTE generator: ~6/5 = 315.558

Map: [<1 10 11 27 -16|, <0 -32 -33 -92 74|]

EDOs: 19, 251, 270, 829, 1099, 1369, 1639

### 13-limit

Commas: 676/675, 1001/1000, 4375/4374, 10985/10976

POTE generator: ~6/5 = 315.557

Map: [<1 10 11 27 -16 25|, <0 -32 -33 -92 74 -81|]

EDOs: 19, 251, 270

## Counteracro

Commas: 4375/4374, 5632/5625, 117649/117612

POTE generator: ~6/5 = 315.553

Map: [<1 10 11 27 55|, <0 -32 -33 -92 -196|]

EDOs: 270, 1061e, 1331c, 1601c, 1871bc, 4012bcde

### 13-limit

Commas: 676/675, 1716/1715, 4225/4224, 4375/4374

POTE generator: ~6/5 = 315.554

Map: [<1 10 11 27 55 25|, <0 -32 -33 -92 -196 -81|]

EDOs: 270, 1331c, 1601c, 1871bcf, 2141bcf

# Seniority

Commas: 4375/4374, 201768035/201326592

POTE generator: ~3087/2560 = 322.804

Map: [<1 11 19 2|, <0 -35 -62 3|]

Wedgie: <<35 62 -3 17 -103 -181||

EDOs: 26, 145, 171, 2710d

# Orga

Commas: 4375/4374, 54975581388800/54936068900769

POTE generator: ~8/7 = 231.104

Map: [<2 21 36 5|, <0 -29 -51 1|]

Wedgie: <<58 102 -2 27 -166 -291||

EDOs: 26, 244, 270, 836, 1106, 1376, 2482

## 11-limit

Commas: 3025/3024, 4375/4374, 5767168/5764801

POTE generator: ~8/7 = 231.103

Map: [<2 21 36 5 2|, <0 -29 -51 1 8|]

EDOs: 26, 244, 270, 566, 836, 1106

## 13-limit

Commas: 1716/1715, 2080/2079, 3025/3024, 15379/15360

POTE generator: ~8/7 = 231.103

Map: [<2 21 36 5 2 24|, <0 -29 -51 1 8 -27|]

EDOs: 26, 244, 270, 566, 836f, 1106f

# Quatracot

Commas: 4375/4374, 1483154296875/1473173782528

POTE generator: ~448/405 = 176.805

Map: [<2 7 7 23|, <0 -13 -8 -59|]

Wedgie: <<26 16 118 -35 114 229||

EDOs: 190, 224, 414, 638, 1052c, 1690bc

## 11-limit

Commas: 3025/3024, 4375/4374, 1265625/1261568

POTE generator: ~448/405 = 176.806

Map: [<2 7 7 23 19|, <0 -13 -8 -59 -41|]

EDOs: 190, 224, 414, 638, 1052c

## 13-limit

Commas: 625/624, 729/728, 1575/1573, 2200/2197

POTE generator: ~448/405 = 176.804

Map: [<2 7 7 23 19 13|, <0 -13 -8 -59 -41 -19|]

EDOs: 190, 224, 414, 638, 1690bc, 2328bcde

# Octoid

Commas: 4375/4374, 16875/16807

valid range: [578.571, 600.000] (56bcd to 8d)

nice range: [582.512, 584.359]

strict range: [582.512, 584.359]

POTE generator: ~7/5 = 583.940

Map: [<8 1 3 3|, <0 3 4 5|]

Generators: 49/45, 7/5

EDOs: 72, 152, 224

## 11-limit

Commas: 540/539, 1375/1372, 4000/3993

valid range: [581.250, 586.364] (64cd, 88bcde)

nice range: [582.512, 585.084]

strict range: [582.512, 585.084]

POTE generator: ~7/5 = 583.692

Map: [<8 1 3 3 16|, <0 3 4 5 3|]

EDOs: 72, 152, 224

### 13-limit

Commas: 540/539, 1375/1372, 4000/3993, 625/624

POTE generator: ~7/5 = 583.905

Map: [<8 1 3 3 16 -21|, <0 3 4 5 3 13|]

EDOs: 72, 224

### Octopus

Commas: 169/168, 325/324, 364/363, 540/539

POTE generator: ~7/5 = 583.892

Map: [<8 1 3 3 16 14|, <0 3 4 5 3 4|]

EDOs: 72, 152, 224f

# Amity

Main article: Amity

The generator for amity temperament is the acute minor third, which means an ordinary 6/5 minor third raised by an 81/80 comma to 243/200, and from this it derives its name. Aside from the ragisma it tempers out the 5-limit amity comma, 1600000/1594323, 5120/5103 and 6144/6125. It can also be described as the 46&53 temperament, or by its wedgie, <<5 13 -17 9 -41 -76||. 99edo is a good tuning for amity, with generator 28/99, and MOS of 11, 18, 25, 32, 46 or 53 notes are available. If you are looking for a different kind of neutral third this could be the temperament for you.

In the 5-limit amity is a genuine microtemperament, with 58/205 being a possible tuning. Another good choice is (64/5)^(1/13), which gives pure major thirds.

Comma: 1600000/1594323

POTE generator: ~243/200 = 339.519

Map: [<1 3 6|, <0 -5 -13|]

EDOs: 7, 39, 46, 53, 152, 205, 463, 668, 873

## 7-limit

Commas: 4375/4374, 5120/5103

POTE generator: ~128/105 = 339.432

Map: [<1 3 6 -2|, <0 -5 -13 17|]

Wedgie: <<5 13 -17 9 -41 -76||

EDOs: 7, 39, 46, 53, 99, 251, 350

## 11-limit

Commas: 540/539, 4375/4374, 5120/5103

POTE generator: ~128/105 = 339.464

Map: [<1 3 6 -2 21|, <0 -5 -13 17 -62|]

EDOs: 53, 99e, 152, 555de, 707de, 859bde

### 13-limit

Commas: 352/351, 540/539, 625/624, 847/845

POTE generator: ~128/105 = 339.481

Map: [<1 3 6 -2 21 17|, <0 -5 -13 17 -62 -47|]

EDOS: 53, 99ef, 152f, 205

## Hitchcock

Commas: 121/120, 176/175, 2200/2187

POTE generator: ~11/9 = 339.340

Map: [<1 3 6 -2 6|, <0 -5 -13 17 -9|]

EDOs: 7, 39, 46, 53, 99

### 13-limit

Commas: 121/120, 169/168, 176/175, 325/324

POTE generator: ~11/9 = 339.419

Map: [<1 3 6 -2 6 2|, <0 -5 -13 17 -9 6|]

EDOs: 7, 39, 46, 53, 99

## Hemiamity

Commas: 3025/3024, 4375/4374, 5120/5103

POTE generator: ~64/55 = 339.493

Map: [<2 1 -1 13 13|, <0 5 13 -17 -14|]

EDOs: 14cde, 46, 106, 152, 198, 350

# Parakleismic

In the 5-limit, parakleismic is an undoubted microtemperament, tempering out the parakleisma, |8 14 -13>, with the 118edo tuning giving errors well under a cent. It has a generator a very slightly (half a cent or less) flat 6/5, 13 of which give 32/3, and 14 give 64/5. However while 118 no longer has better than a cent of accuracy in the 7 or 11 limits, it is a decent temperament there nonetheless, and this allows an extension, with the 7-limit wedgie being <<13 14 35 -8 19 42|| and adding 3136/3125 and 4375/4374, and the 11-limit wedgie <<13 14 35 -36 ...|| adding 385/384. For the 7-limit 99edo may be preferred, but in the 11-limit it is best to stick with 118.

Comma: 124440064/1220703125

POTE generator: ~6/5 = 315.240

Map: [<1 5 6|, <0 -13 -14|]

EDOs: 19, 61, 80, 99, 118, 453, 571, 689, 1496

## 7-limit

Commas: 3136/3125, 4375/4374

POTE generator: ~6/5 = 315.181

Map: [<1 5 6 12|, <0 -13 -14 -35|]

EDOs: 19, 80, 99, 217, 316, 415

## 11-limit

Commas: 385/384, 3136/3125, 4375/4374

POTE generator: ~6/5 = 315.251

Map: [<1 5 6 12 -6|, <0 -13 -14 -35 36|]

EDOs: 19, 99, 118

## Parkleismic

Commas: 176/175, 1375/1372, 2200/2187

POTE generator: ~6/5 = 315.060

Map: [<1 5 6 12 20|, <0 -13 -14 -35 -63|]

EDOs: 80, 179, 259cd

### 13-limit

Commas: 169/168, 176/175, 325/324, 1375/1372

POTE generator: ~6/5 = 315.075

Map: [<1 5 6 12 20 10|, <0 -13 -14 -35 -63 -24|]

EDOs: 15, 19, 80, 179

Commas: 540/539, 896/891, 3136/3125

POTE generator: ~6/5 = 315.096

Map: [<1 5 6 12 -1|, <0 -13 -14 -35 17|]

EDOs: 19, 80, 99e, 179e

### 13-limit

Commas: 169/168, 325/324, 540/539, 832/825

POTE generator: ~6/5 = 315.080

Map: [<1 5 6 12 -1 10|, <0 -13 -14 -35 17 -24|]

EDOs: 19, 80, 99e, 179e

## Semiparakleismic

Commas: 3025/3024, 3136/3125, 4375/4374

POTE generator: ~6/5 = 315.181

Map: [<2 10 12 24 19|, <0 -13 -14 -35 -23|]

EDOs: 80, 118, 198, 316, 514c, 830c

### 13-limit

Commas: 352/351, 1001/1000, 3025/3024, 4375/4374

POTE generator: ~6/5 = 315.1563

Map: [<2 10 12 24 19 -1|, <0 -13 -14 -35 -23 16|]

EDOs: 80, 118, 198

### Gentsemiparakleismic

Commas: 169/168, 325/324, 364/363, 3136/3125

POTE generator: ~6/5 = 315.1839

Map: [<2 10 12 24 19 20|, <0 -13 -14 -35 -23 -24|]

EDOs: 80, 118f, 198f

# Quincy

Commas: 4375/4374, 823543/819200

POTE generator: ~1728/1715 = 16.613

Map: [<1 2 2 3|, <0 -30 -49 -14|]

EDOs: 72, 217, 289

## 11-limit

Commas: 441/440, 4000/3993, 41503/41472

POTE generator: ~100/99 = 16.613

Map: [<1 2 2 3 4|, <0 -30 -49 -14 -39|]

EDOs: 72, 217, 289

## 13-limit

Commas: 364/363, 441/440, 676/675, 4375/4374

POTE generator: ~100/99 = 16.602

Map: [<1 2 2 3 4 5|, <0 -30 -49 -14 -39 -94|]

EDOs: 72, 145, 217, 289

## 17-limit

Commas: 364/363, 441/440, 595/594, 1001/1000, 1156/1155

POTE generator: ~100/99 = 16.602

Map: [<1 2 2 3 4 5 5|, <0 -30 -49 -14 -39 -94 -66|]

EDOs: 72, 145, 217, 289

## 19-limit

Commas: 343/342, 364/363, 441/440, 595/594, 676/675, 2601/2600

POTE generator: ~100/99 = 16.594

Map: [<1 2 2 3 4 5 5 4|, <0 -30 -49 -14 -39 -94 -66 18|]

EDOs: 72, 145, 217

# Chlorine

The name of chlorine temperament comes from Chlorine, the 17th element.

Chlorine microtemperament has a period of 1/17 octave. It tempers out the septendecima, |-52 -17 34>, by which 17 chromatic semitones (25/24) fall short of an octave. Possible tunings for chlorine are 289, 323, and 612 EDOs, though its hardly likely anyone could tell the difference. In the 7-limit, 289&323 temperament tempers out |-49 4 22 -3> as well as the ragisma.

Comma: |-52 -17 34>

POTE generators: ~25/24 = 70.5882, ~5/4 = 386.2687

Map: [<17 26 39|, <0 2 1|]

EDOs: 34, 289, 323, 612, 901

## 7-limit

Commas: 4375/4374, 193119049072265625/193091834023510016

POTE generators: ~25/24 = 70.5882, ~5/4 = 386.2936

Map: [<17 26 39 43|, <0 2 1 10|]

EDOs: 34d, 289, 323, 612, 935, 1547