No-threes subgroup temperaments: Difference between revisions

* Jubilic ([[50/49]]) → [[Jubilismic clan #Jubilic|Jubilismic clan]]

* Didacus ([[3136/3125]]) → [[Hemimean clan #Didacus|Hemimean clan]]

* Mercy ([[823543/819200]]) → [[Quince clan #Mercy|Quince clan]]

* Llywelyn a.k.a. shoe ([[4194304/4117715]]) → [[Llywelynsmic clan #Llywelyn a.k.a. shoe|Llywelynsmic clan]]

* Sidewalk ([[823543/800000]]) → [[2023/2000 #Sidewalk]]

In rainy, three generators make an [[8/7]]; five generators make a [[5/4]]. It is the no-3's [[restriction]] of [[tertiaseptal]] (and [[valentine]]), notable theoretically as it equates ([[2/1]])/([[5/4]])³ (128/125, the lesser diesis) with ([[2/1]])/([[8/7]])⁵ (the 2.7-subgroup [[cloudy comma]], which is similar to the 2.5-subgroup lesser diesis in that tempering it out tunes the 8/7 about 8.8{{cent}} sharp, while tempering out 128/125 similarly sharpens the 5/4 by about 13.7{{cent}}). By tempering out their difference, stacked 5's and stacked 7's become easier to navigate, using the general-purpose diesis to simplify clusters.

[[Comma list]]: [[2100875/2097152]]

 

{{Mapping|legend=3| 1 0 2 3 | 0 0 5 -3 }}

[[Optimal tuning]]s:  

* [[CWE]]: ~2 = 1200.0000{{c}}, ~256/245 = 77.2093{{c}}

{{Optimal ET sequence|legend=1| 15, 16, 31, 109, 140, 171, 373, 544, 1259, 1803d }}

[[Badness]] (Sintel): 0.156

=== Augment ===

Augment is related to [[augmented]], but for 2.5.7 instead of 2.3.5.

 

 

 

 

 

 

 

==== 2.5.7.11 subgroup ====

Comma list: 56/55, 128/125

Subgroup-val mapping: {{mapping| 3 7 0 2 | 0 0 1 1 }}

Gencom mapping: {{mapping| 3 0 7 0 2 | 0 0 0 1 1 }}

Optimal tunings:  

* WE: ~5/4 = 398.9239{{c}}, ~7/4 = 969.1106{{c}}

* CWE: ~5/4 = 400.0000{{c}}, ~7/4 = 968.4397{{c}}

{{Optimal ET sequence|legend=0| 3, 6, 15, 21 }}

=== Frostburn ===

Frostburn is the common [[restriction]] of [[magic family #Quadrimage|quadrimage]] and [[subgroup temperaments #Baldy|baldy]].  

[[Subgroup]]: 2.5.7

[[Comma list]]: 78125/76832

: mapping generators: ~2, ~28/25

[[Optimal tuning]]s:  

* [[WE]]: ~2 = 1200.3462{{c}}, ~28/25 = 204.3386{{c}}

: [[error map]]: {{val| +0.346 -2.630 +2.189 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~28/25 = 204.2027{{c}}

: error map: {{val| 0.000 -3.125 +1.755 }}

{{Optimal ET sequence|legend=1| 6, 29, 35, 41, 47 }}

==== 2.5.7.11 subgroup ====

Subgroup: 2.5.7.11

Comma list: 245/242, 625/616

Subgroup-val mapping: {{mapping| 1 3 4 5 | 0 -4 -7 -9 }}

Optimal tunings:  

* WE: ~2 = 1200.6817{{c}}, ~28/25 = 205.0734{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~28/25 = 204.8199{{c}}

{{Optimal ET sequence|legend=0| 6, 23de, 29, 35, 41 }}

Badness (Sintel): 0.463

{{Main| Mabilic and trismegistus }}

{{See also| Chromatic pairs #Mabilic }}

Mabilic is the no-3 [[restriction]] of [[mavila family #Armodue|armodue]], [[mabila family #Semabila|semabila]], and [[magic family #Trismegistus|trismegistus]]. It is the 7 & 9 temperament in the [[2.5.7 subgroup]], and tempers out [[1071875/1048576]], the mabilisma.

[[Comma list]]: 1071875/1048576

{{Mapping|legend=2| 1 1 5 | 0 3 -5 }}

: mapping generators: ~2, ~175/128

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1201.2543{{c}}, ~175/128 = 527.7872{{c}}

: [[error map]]: {{val| +1.254 -1.698 -1.491 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~175/128 = 527.2041{{c}}

: error map: {{val| 0.000 -4.701 -4.846 }}

{{Optimal ET sequence|legend=1| 7, 9, 16, 25, 41, 66, 305ccdd, 371ccddd }}

[[Badness]] (Sintel): 1.70

{{See also| Chromatic pairs #Huntington }}

Huntington may be described as the 10 & 37 temperament in the 2.5.7.13 subgroup.  

[[Comma list]]: 40960000/40353607

{{Mapping|legend=2| 1 -4 0 | 0 9 4 }}

: mapping generators: ~2, ~80/49

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1199.5781{{c}}, ~80/49 = 842.6730{{c}}

: [[error map]]: {{val| -0.422 -0.569 +1.866 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~80/49 = 842.9136{{c}}

: error map: {{val| 0.000 -0.091 +2.828 }}

{{Optimal ET sequence|legend=0| 7c, 10, 27, 37, 84, 121 }}

Badness (Sintel): 1.87

Subgroup: 2.5.7.13

Subgroup-val mapping: {{mapping| 1 -4 0 3 | 0 9 4 1 }}

Gencom mapping: {{mapping| 1 0 -4 0 0 3 | 0 0 9 4 0 1 }}

: mapping generators: ~2, ~13/8

Optimal tunings:  

* CWE: ~2 = 1200.0000{{c}}, ~13/8 = 842.9447{{c}}

{{Optimal ET sequence|legend=0| 7c, 10, 17, 27, 37, 84, 121, 279df, 400ddf }}

Badness (Sintel): 0.319

{{See also| Chromatic pairs #Silver }}

Silver can be described as the 10 & 37 temperament in the 2.5.7.13.17 subgroup.  

Comma list: 170/169, 640/637, 5525/5488

Subgroup-val mapping: {{mapping| 1 -4 0 3 9 | 0 9 4 1 -7 }}

Gencom mapping: {{mapping| 1 0 -4 0 0 3 9 | 0 0 9 4 0 1 -7 }}

Optimal tunings:  

* WE: ~2 = 1200.0932{{c}}, ~13/8 = 842.7764{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~13/8 = 842.7143{{c}}

{{Optimal ET sequence|legend=0| 10, 27, 37, 47, 84, 131, 178g }}

Badness (Sintel): 0.504

=== Ostara ===

Ostara is a temperament that is derived from 93 & 524 solar calendar leap rule scale, interpreted in general no-3's 19-limit. It is a weak extension of the unnamed 2.5.7-subgroup 28 & 31 temperament, which tempers out 8589934592/8544921875.

Subgroup: 2.5.7.11

Comma list: 8589934592/8544921875, 30691800524/30517578125

Subgroup-val mapping: {{mapping| 1 1 20 -49 | 0 3 -39 119 }}

Optimal tunings:  

* WE: ~2 = 1199.9115{{c}}, ~5120/3773 = 528.9650{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~5120/3773 = 529.0037{{c}}

{{Optimal ET sequence|legend=0| 93, 245e, 338, 955c, 1386c }}

Badness (Sintel): 11.7

==== 2.5.7.11.13 subgroup ====

Comma list: 1001/1000, 34420736/34328125, 5670699008/5661858125

Subgroup-val mapping: {{mapping| 1 1 20 -49 35 | 0 3 -39 119 -71 }}

Optimal tunings:  

* WE: ~2 = 1199.9194{{c}}, ~1664/1225 = 528.9681{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~1664/1225 = 529.0036{{c}}

{{Optimal ET sequence|legend=0| 93, 245e, 338, 431, 1386c }}

Badness (Sintel): 3.42

Subgroup: 2.5.7.11.13.17

Comma list: 1001/1000, 32768/32725, 147968/147875, 537824/537251

Subgroup-val mapping: {{mapping| 1 1 20 -49 35 42 | 0 3 -39 119 -71 -86 }}

Optimal tunings:  

* CWE: ~2 = 1200.0000{{c}}, ~1664/1225 = 529.0046{{c}}

{{Optimal ET sequence|legend=0| 93, 338, 431, 955c, 1386cg }}

Badness (Sintel): 1.99

Subgroup: 2.5.7.11.13.17.19

Comma list: 1001/1000, 2128/2125, 3328/3325, 16807/16796, 147968/147875

Subgroup-val mapping: {{mapping| 1 1 20 -49 35 42 21 | 0 3 -39 119 -71 -86 -38 }}

Optimal tunings:  

* CWE: ~2 = 1200.0000{{c}}, ~19/14 = 529.0045{{c}}

Badness (Sintel): 1.29

Bastille is described as the 2.5.7-subgroup 1407 & 1789 temperament, and named after an [[Wikipedia: Storming of the Bastille|eponymous historical event]] which took place on July 14, 1789 (14/07/1789). Extensions discussed elsewhere include [[The Jacobins #Double bastille|double bastille]].

[[Comma list]]: {{monzo| 1426 -596 -15 }}

: mapping generators: ~2, ~{{monzo| -380 159 4 }}

* [[WE]]: ~2 = 1199.9911{{c}}, ~{{monzo| -380 159 4 }} = 505.7532{{c}}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~{{monzo| -380 159 4 }} = 505.7570{{c}}

: error map: {{val| 0.000 +0.041 +0.018 }}

{{Optimal ET sequence|legend=1| 382, 1025, 1407, 14452, 15859c, 17266c, …, 27115cd }}

[[Badness]] (Sintel): 7.18 × 10³

{{Todo|inline=1| review | comment = Devise the permanent name for this temperament; determine its status with respect to its extensions linked below. }}

{{See also| Wizardharry clan #Naiad | Werckismic temperaments #Seminaiad }}

This temperament can be described as the 21 & 29 & 37 temperament in no-threes subgroups. It expands [[Subgroup temperaments #Tridec|tridec]] and [[Subgroup temperaments #Naiadec|naiadec]].

[[Subgroup]]: 2.5.7.11

[[Comma list]]: 5021863/5000000

: mapping generators: ~2, ~5, ~77/50

[[Optimal tuning]]s:  

* [[WE]]: ~2 = 1200.0805{{c}}, ~5/4 = 386.6593{{c}}, ~77/50 = 745.4622{{c}}

: [[error map]]: {{val| +0.080 +0.507 -1.318 -0.643 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~5/4 = 386.7404{{c}}, ~77/50 = 745.4102{{c}}

: error map: {{val| 0.000 +0.427 -0.445 -0.808 }}

{{Optimal ET sequence|legend=1| 16, 21, 29, 37, 87, 103, 124, 161, 227, 264, 388, 425, 652e, 689e, 1077de }}

[[Badness]] (Sintel): 1.86

==== 2.5.7.11.13 subgroup ====

Comma list: 847/845, 1001/1000

 

Optimal tunings:  

* WE: ~2 = 1200.0343{{c}}, ~5/4 = 386.6098{{c}}, ~20/13 = 745.4658{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 386.6458{{c}}, ~20/13 = 745.4431{{c}}

{{Optimal ET sequence|legend=0| 16, 21, 29, 37, 87, 103, 124, 161, 227, 264, 565e, 689e }}

==== 2.5.7.11.13.17 subgroup ====

Comma list: 170/169, 221/220, 847/845

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

Optimal tunings:  

* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 387.1074{{c}}, ~17/11 = 745.0940{{c}}

{{Optimal ET sequence|legend=0| 16, 21, 29g, 37, 66g, 87g, 124g }}

Badness (Sintel): 0.438

Temperaments discussed elsewhere include:

* Jacobin superfamily ([[6656/6655]]) → [[The Jacobins]]

Wizz, the 6 & 16 temperament in the 2.5.11 subgroup, tempers out [[15625/15488]], and is the common [[restriction]] of [[astrology]] and [[wizard]].  

[[Subgroup]]: 2.5.11

[[Comma list]]: 15625/15488

{{Mapping|legend=3| 2 0 4 0 5 | 0 0 1 0 3 }}

: mapping generators: ~125/88, ~5/4

[[Optimal tuning]]s:  

* [[CWE]]: ~125/88 = 600.0000{{c}}, ~5/4 = 383.9977{{c}}

: error map: {{val| 0.000 -2.316 +0.675 }}

{{Optimal ET sequence|legend=1| 6, 16, 22, 28, 50, 122, 172, 222, 394c }}

[[Badness]] (Sintel): 0.266

[[Subgroup]]: 2.5.11

[[Comma list]]: 33275/32768

{{Mapping|legend=2| 1 0 5 | 0 3 -2 }}

[[Optimal tuning]]s:

* [[CWE]]: ~2 = 1200.0000{{c}}, ~55/32 = 927.7384{{c}}

: error map: {{val| 0.000 -3.099 -6.975 }}

{{Optimal ET sequence|legend=1| 9, 13, 22, 97e, 119e, 141e, 163e, 304ceee }}

[[Badness]] (Sintel): 0.564

This temperament has a structure very similar to [[mavila]] but is somewhat more accurate because the generator is a flat [[11/8]] rather than a sharp [[4/3]]. The major third is still ~[[5/4]], but the minor third is now ~[[64/55]] instead of ~[[6/5]].

[[Subgroup]]: 2.5.11

[[Comma list]]: 1331/1280

{{Mapping|legend=2| 1 1 3 | 0 3 1 }}

: mapping generators: ~2, ~11/8

* [[WE]]: ~2 = 1203.0339{{c}}, ~11/8 = 528.4296{{c}}

: [[error map]]: {{val| +3.034 +2.009 -13.787 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~11/8 = 528.1575{{c}}

: error map: {{val| 0.000 -1.841 -23.160 }}

{{Optimal ET sequence|legend=1| 7, 9, 16, 25, 41e, 66ee }}

[[Badness]] (Sintel): 0.718

=== Sephiroth ===

Sephiroth is the common [[restriction]] of [[muggles]] and [[submerged]].  

[[Subgroup]]: 2.5.11

[[Comma list]]: 34375/32768

{{Mapping|legend=2| 1 0 15 | 0 1 -5 }}

{{Mapping|legend=3| 1 0 0 0 15 | 0 0 1 0 -5 }}

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1203.3290{{c}}, ~5/4 = 373.6097{{c}}

: [[error map]]: {{val| +3.329 -6.046 -2.722 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~5/4 = 372.1586{{c}}

: error map: {{val| 0.000 -14.155 -12.111 }}

{{Optimal ET sequence|legend=0| 3, 10, 13, 16, 29, 132cceee }}

[[Badness]] (Sintel): 1.85

Comma list: 65/64, 6875/6656

 

Subgroup-val mapping: {{mapping| 1 0 15 6 | 0 1 -5 -1 }}

Gencom mapping: {{mapping| 1 0 0 0 15 6 | 0 0 1 0 -5 -1 }}

Optimal tunings:  

* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 372.1519{{c}}

{{Optimal ET sequence|legend=0| 3, 10, 13, 16, 29, 132cceeeff }}

 

==== 2.5.11.13.17 subgroup ====

Subgroup: 2.5.11.13.17

 

Comma list: 65/64, 170/169, 221/220

Subgroup-val mapping: {{mapping| 1 0 15 6 11 | 0 1 -5 -1 -3 }}

Gencom mapping: {{mapping| 1 0 0 0 15 6 11 | 0 0 1 0 -5 -1 -3 }}

Optimal tunings:  

* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 371.6773{{c}}

{{Optimal ET sequence|legend=0| 3, 10, 13, 16, 29g, 129ccceeffgggg }}

=== Trader ===

[[Subgroup]]: 2.5.13

[[Comma list]]: 26/25

{{Mapping|legend=2| 1 2 3 | 0 1 2 }}

* [[WE]]: ~2 = 1198.0216{{c}}, ~5/4 = 410.2152{{c}}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~5/4 = 408.9029{{c}}

{{Optimal ET sequence|legend=1| 3, 20c, 23c, 26c }}

=== Superquintal ===

{{Mapping|legend=2| 1 -2 0 | 0 7 6 }}

 

: [[error map]]: {{val| -0.408 -1.098 +3.244 }}

: error map: {{val| 0.000 -0.673 +4.307 }}

 

 

 

* 21-23-commatic → [[21st-octave temperaments #21-23-commatic|21st-octave temperaments]]

 

 

Amaranthine is the high-accuracy 2.7.11-subgroup strong [[restriction]] of [[Gamelismic clan #11-limit 3|undecimal mothra]].

 

 

 

 

 

 

 

 

 

 

 

: error map: {{val| 0.000 -6.079 +11.429 }}

{{Optimal ET sequence|legend=1| 6, 9, 15, 36, 51e, 66e }}

[[Badness]] (Sintel): 0.475

{{See also| Chromatic pairs #Score }}

 

 

 

{{Mapping|legend=2| 1 1 3 1 | 0 4 1 6 }}

 

{{Mapping|legend=3| 1 0 0 1 3 1 | 0 0 0 4 1 6 }}

 

 

 

 

=== Bossier ===

 

 

[[Subgroup]]: 2.7.11

 

 

 

 

 

 

 

==== 2.7.11.13 subgroup ====

 

Subgroup-val mapping: {{mapping| 1 0 1 3 | 0 8 7 2 }}

Gencom mapping: {{mapping|| 1 0 0 0 1 3 | 0 0 0 8 7 2 }}

Optimal tunings:  

* WE: ~2 = 1199.8668{{c}}, ~14/11 = 421.2623{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~14/11 = 421.2874{{c}}

{{Optimal ET sequence|legend=0| 17, 20, 37, 57, 94, 225 }}

=== Voltage ===

Voltage is the 3 & 7 temperament in the 2.7.13 subgroup. Among the notable tunings is pure-7 tuning, 7^1/4 of 842.2065{{c}}, which is also the CTC (constrained Tenney–Chebyshevian) tuning.

[[Subgroup]]: 2.7.13

[[Comma list]]: 28672/28561

{{Mapping|legend=3| 1 0 0 0 0 3 | 0 0 0 4 0 1 }}

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1199.7827{{c}}, ~13/8 = 842.1707{{c}}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~13/8 = 842.2568{{c}}

: error map: {{val| 0.000 +0.201 +1.729 }}

{{Optimal ET sequence|legend=1| 3, 7, 10, 27, 37, 47, 57, 104, 463f, 567f, 671ff, 775ff }}

[[Badness]] (Sintel): 0.115

{{Mapping|legend=2| 1 2 3 | 0 3 4 }}

* [[WE]]: ~2 = 1200.1379{{c}}, ~17/14 = 324.3440{{c}}

* [[CWE]]: ~2 = 1200.000{{c}}, ~17/14 = 324.3738{{c}}

{{Optimal ET sequence|legend=1| 4, 7, 11, 26, 37 }}

{{Mapping|legend=2| 1 0 1 | 0 10 11 }}

* [[WE]]: ~2 = 1199.9723{{c}}, ~17/14 = 336.8586{{c}}

* [[CWE]]: ~2 = 1200.000{{c}}, ~17/14 = 336.8621{{c}}

{{Optimal ET sequence|legend=1| 7, 18dg, 25, 32, 57, 488, 545, 602, 659, 716, 773, 830, 887, 1717g }}

 

[[Optimal tuning]]s:  

* [[WE]]: ~2 = 1199.6967{{c}}, ~64/53 = 323.1839{{c}}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~64/53 = 323.1959{{c}}

 

 

[[Badness]] (Sintel): 0.224

 

 

 

 

 

 

 

{{Optimal ET sequence|legend=1| 4, 9, 13, 30, 43, 73, 116e }}

[[Badness]] (Sintel): 0.175

 

 

 

 

 

 

{{Optimal ET sequence|legend=1| 6, 7, 13, 33, 46, 79, 125f, 204ef, 329eeff }}

 

 

{{See also | Chromatic pairs #Blackbirds }}

 

 

 

{{Mapping|legend=2| 4 0 1 | 0 1 1 }}

: mapping generators, ~13/11, ~11

[[Optimal tuning]]s:

* [[WE]]: ~13/11 = 299.9728{{c}}, ~11/8 = 546.6107{{c}}

: [[error map]]: {{val| -0.109 -5.033 +5.730 }}

* [[CWE]]: ~13/11 = 300.0000{{c}}, ~11/8 = 546.4664{{c}}

: error map: {{val| 0.000 -4.852 +5.939 }}

{{Optimal ET sequence|legend=1| 4, 12e, 16, 20, 24, 44, 68 }}

Yamablu, with a generator of ~26/17, is named for its tempering of the yama comma (209/208) and the blume comma (2057/2048), which also implies the blumeyer comma (2432/2431). It extends the 2.11.13-subgroup temperament tempering out 556573090931/549755813888. The [[Kite's Genchain mode numbering|13th Yamablu[13]]] scale is a linear-temperament version of [[Gjaeck]].  

 

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1200.4661{{c}}, ~26/17 = 737.3256{{c}}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~26/17 = 737.0014{{c}}

 

{{Optimal ET sequence|legend=1| 13, 44, 57, 70, 127, 197eh }}

 

 

 

 

[[Comma list]]: 2432/2431, 7086244/7054567, 33698267/33554432

 

{{Mapping|legend=2| 33 0 8 249 26 | 0 1 1 -1 1 }}

 

* [[CWE]]: ~247/242 = 36.3636{{c}}, ~11/8 = 550.4187{{c}}

 

 

 

Berylic tempers out the [[berylisma]] in the 2.11.37 subgroup, representing the fact that [[44/37]] is a {{w|continued fraction}} convergent to 2^1/4 the fourth root of 2. Beryllic is an example of a temperament which has an astronomically low [[badness]], being a very high-accuracy [[microtemperament]] with low-to-average [[complexity]] for the harmonics in its [[subgroup]]. This also makes it simultaneously supported by edo systems as low as [[16edo]] and up into the tens of thousands. The tradeoff with this temperament, not captured within the metric of badness, is that it is defined within an obscure subgroup, 2.11.37.

 

 

[[Comma list]]: 1874161/1874048

{{Mapping|legend=2| 4 0 7 | 0 1 1 }}

: mapping generators: ~44/37, ~11

[[Optimal tuning]]s:

: [[error map]]: {{val| +0.001 +0.007 -0.017 }}

: error map: {{val| 0.000 +0.006 -0.020 }}

 

 

[[Badness]] (Sintel): 0.00188

 

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1199.8817{{c}}, ~26/19 = 539.9150{{c}}

: [[error map]]: {{val| -0.118 -1.156 +1.825 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~26/19 = 539.9280{{c}}

: error map: {{val| 0.000 -0.960 +2.127 }}

 

{{Optimal ET sequence|legend=1| 9, 11, 20 }}

 

[[Badness]] (Sintel): 0.559

 

 

 

[[Optimal tuning]]s:

* [[CWE]]: ~2 = 1200.0000{{c}}, ~11/8 = 548.2193{{c}}, ~13/8 = 841.4707{{c}}