Breedsmic temperaments: Difference between revisions

This page discusses miscellaneous rank-2 temperaments tempering out the [[breedsma]], {{monzo|-5 -1 -2 4}} = 2401/2400. This is the amount by which two 49/40 intervals exceed 3/2, and by which two 60/49 intervals fall short. Either of these represent a neutral third interval which is highly characteristic of breedsmic tempering; any tuning system (12EDO, for example) which does not possess a neutral third cannot be tempering out the breedsma.

The breedsma is also the amount by which four stacked [[10/7]] intervals exceed 25/6: 10000/2401 × 2401/2400 = 10000/2400 = 25/6, which is two octaves above the classic chromatic semitone, [[25/24]]. We might note also that 49/40 × 10/7 = 7/4 and 49/40 × (10/7)² = 5/2, relationships which will be significant in any breedsmic temperament. As a consequence of these facts, the 49/40~60/49 neutral third and the 7/5 and 10/7 intervals tend to have relatively low complexity in a breedsmic system.

* ''[[Decimal]]'' → [[Dicot family #Decimal|Dicot family]] ({25/24, 49/48})

* ''[[Beatles]]'' → [[Archytas clan #Beatles|Archytas clan]] ({64/63, 686/675})

* [[Squares]] → [[Meantone family #Squares|Meantone family]] ({81/80, 2401/2400})

* [[Myna]] → [[Starling temperaments #Myna|Starling temperaments]] ({126/125, 1728/1715})

* [[Miracle]] → [[Gamelismic clan #Miracle|Gamelismic clan]] ({225/224, 1029/1024})

* ''[[Octacot]]'' → [[Tetracot family #Octacot|Tetracot family]] ({245/243, 2401/2400})

* ''[[Greenwood]]'' → [[Greenwoodmic temperaments #Greenwood|Greenwoodmic temperaments]] ({405/392, 1323/1280})

* ''[[Quasitemp]]'' → [[Keemic temperaments #Quasitemp|Keemic temperaments]] ({875/864, 2401/2400})

* ''[[Quadrasruta]]'' → [[Diaschismic family #Quadrasruta|Diaschismic family]] ({2048/2025, 2401/2400})

* ''[[Quadrimage]]'' → [[Magic family #Quadrimage|Magic family]] ({2401/2400, 3125/3072})

* ''[[Hemiwürschmidt]]'' → [[Würschmidt family #Hemiwürschmidt|Würschmidt family]] and [[Hemimean clan #Hemiwürschmidt|hemimean clan]] ({2401/2400, 3136/3125})

* [[Ennealimmal]] → [[Ragismic microtemperaments #Ennealimmal|Ragismic microtemperaments]] ({2401/2400, 4375/4374})

* ''[[Quadritikleismic]]'' → [[Kleismic family #Quadritikleismic|Kleismic family]] ({2401/2400, 15625/15552})

* [[Harry]] → [[Gravity family #Harry|Gravity family]] ({2401/2400, 19683/19600})

* ''[[Sesquiquartififths]]'' → [[Schismatic family #Sesquiquartififths|Schismatic family]] ({2401/2400, 32805/32768})

* ''[[Neptune]]'' → [[Gammic family #Neptune|Gammic family]] ({2401/2400, 48828125/48771072})

* ''[[Eagle]]'' → [[Vulture family #Eagle|Vulture family]] ({2401/2400, 10485760000/10460353203})

Hemififths tempers out [[5120/5103]], the hemifamity comma, and [[10976/10935]], hemimage. It has a neutral third as a generator, with [[99edo|99EDO]] and [[140edo|140EDO]] providing good tunings, and [[239edo|239EDO]] an even better one; and other possible tunings are 160^(1/25), giving just 5s, the 7- and 9-odd-limit minimax tuning, or 14^(1/13), giving just 7s. It may be called the 41&58 temperament. It requires 25 generator steps to get to the class for the harmonic 5, whereas the 7 is half as complex, and hence hemififths makes for a good no-fives temperament, to which the 17 and 24 note MOS are suited. The full force of this highly accurate temperament can be found using the 41 note MOS or even the 34 note 2MOS{{clarify}}.

By adding [[243/242]] (which also means 441/440, 540/539 and 896/891) to the commas, hemififths extends to a less accurate 11-limit version, but one where 11/4 is only five generator steps. 99EDO is an excellent tuning; one which loses little of the accuracy of the 7-limit but improves the 11-limit a bit. Now adding [[144/143]] brings in the 13-limit with less accuracy yet, but with very low complexity, as the generator can be taken to be [[16/13]]. 99 remains a good tuning choice.

Subgroup: 2.3.5.7

[[Mapping]]: [{{val| 1 1 -5 -1 }}, {{val| 0 2 25 13 }}]

{{Multival|legend=1| 2 25 13 35 15 -40 }}

[[POTE generator]]: ~49/40 = 351.477

* [[7-odd-limit|7-]] and [[9-odd-limit]] minimax: ~49/40 = {{monzo|1/5 0 1/25}}

: [{{monzo|1 0 0 0}}, {{monzo|7/5 0 2/25 0}}, {{monzo|0 0 1 0}}, {{monzo|8/5 0 13/25 0}}]

: Eigenmonzos: 2, 5

{{Val list|legend=1| 41, 58, 99, 239, 338 }}

[[Badness]]: 0.022243

Mapping: [{{val| 1 1 -5 -1 2 }}, {{val| 0 2 25 13 5 }}]

POTE generator: ~11/9 = 351.521

Optimal GPV sequence: {{Val list| 17c, 41, 58, 99e }}

Badness: 0.023498

Mapping: [{{val| 1 1 -5 -1 2 4 }}, {{val| 0 2 25 13 5 -1 }}]

POTE generator: ~11/9 = 351.573

Optimal GPV sequence: {{Val list| 17c, 41, 58, 99ef, 157eff }}

Badness: 0.019090

Mapping: [{{val| 2 0 -35 -15 -47 }}, {{val| 0 2 25 13 34 }}]

POTE generator: ~49/40 = 351.505

Optimal GPV sequence: {{Val list| 58, 140, 198 }}

Badness: 0.042487

Mapping: [{{val| 2 0 -35 -15 -47 -37 }}, {{val| 0 2 25 13 34 28 }}]

POTE generator: ~49/40 = 351.502

Optimal GPV sequence: {{Val list| 58, 140, 198, 536f }}

Badness: 0.021188

This has been logged as ''semihemififths'' in Graham Breed's temperament finder, but ''quadrafifths'' arguably makes more sense.  

Mapping: [{{val| 1 1 -5 -1 8 }}, {{val| 0 4 50 26 -31 }}]

POTE generator: ~243/220 = 175.7378

Optimal GPV sequence: {{Val list| 41, 157, 198, 239, 676b, 915be }}

Badness: 0.040170

Mapping: [{{val| 1 1 -5 -1 8 10 }}, {{val| 0 4 50 26 -31 -43 }}]

POTE generator: ~72/65 = 175.7470

Optimal GPV sequence: {{Val list| 41, 157, 198, 437f, 635bcff }}

Badness: 0.031144

Aside from the breedsma, tertiaseptal tempers out [[65625/65536]], the horwell comma, [[703125/702464]], the meter, and [[2100875/2097152]], the rainy comma. It can be described as the 31&171 temperament, and 256/245, 1029/1024 less than 21/20, serves as its generator. Three of these fall short of 8/7 by 2100875/2097152, and the generator can be taken as 1/3 of an 8/7 flattened by a fraction of a cent. [[171edo|171EDO]] makes for an excellent tuning. The 15 or 16 note MOS can be used to explore no-threes harmony, and the 31 note MOS gives plenty of room for those as well.

Subgroup: 2.3.5.7

[[Mapping]]: [{{val| 1 3 2 3 }}, {{val| 0 -22 5 -3 }}]

[[POTE generator]]: ~256/245 = 77.191

{{Val list|legend=1| 31, 109, 140, 171 }}

Mapping: [{{val| 1 3 2 3 7 }}, {{val| 0 -22 5 -3 -55 }}]

POTE generator: ~256/245 = 77.227

Optimal GPV sequence: {{Val list| 31, 109e, 140e, 171, 202 }}

Mapping: [{{val| 1 3 2 3 7 1 }}, {{val| 0 -22 5 -3 -55 42 }}]

POTE generator: ~117/112 = 77.203

Optimal GPV sequence: {{Val list| 31, 109e, 140e, 171 }}

Mapping: [{{val| 1 3 2 3 7 1 1 }}, {{val| 0 -22 5 -3 -55 42 48 }}]

POTE generator: ~68/65 = 77.201

Optimal GPV sequence: {{Val list| 31, 109eg, 140e, 171 }}

Mapping: [{{val| 1 3 2 3 5 }}, {{val| 0 -22 5 -3 -24 }}]

POTE generator: ~22/21 = 77.173

Optimal GPV sequence: {{Val list| 31, 109, 140, 171e, 311e }}

Mapping: [{{val| 1 3 2 3 5 1 }}, {{val| 0 -22 5 -3 -24 42 }}]

POTE generator: ~22/21 = 77.158

Optimal GPV sequence: {{Val list| 31, 109, 140, 311e, 451ee }}

Mapping: [{{val| 1 3 2 3 5 1 1 }}, {{val| 0 -22 5 -3 -24 42 48 }}]

POTE generator: ~22/21 = 77.162

Optimal GPV sequence: {{Val list| 31, 109g, 140, 311e, 451ee }}

Mapping: [{{val|1 3 2 3 -4}}, {{val|0 -22 5 -3 116}}]

POTE generator: ~256/245 = 77.169

Optimal GPV sequence: {{Val list| 140, 171, 311, 1695c, 2006bcd, 2317bcd, 2628bccde, 2939bccde, 3250bccde }}

Mapping: [{{val|1 3 2 3 -4 1}}, {{val|0 -22 5 -3 116 42}}]

POTE generator: ~117/112 = 77.168

Optimal GPV sequence: {{Val list| 140, 171, 311, 1073, 1384cf, 1695cf, 2006bcdf }}

Mapping: [{{val|1 3 2 3 -4 1 1}}, {{val|0 -22 5 -3 116 42 48}}]

POTE generator: ~68/65 = 77.169

Optimal GPV sequence: {{Val list| 140, 171, 311 }}

Mapping: [{{val|1 3 2 3 -4 1 1 11}}, {{val|0 -22 5 -3 116 42 48 -105}}]

POTE generator: ~68/65 = 77.169

Optimal GPV sequence: {{Val list| 140, 171, 311, 1384cfgg, 1695cfgg, 2006bcdfgg }}

Mapping: [{{val|1 3 2 3 -4 1 1 11 -3}}, {{val|0 -22 5 -3 116 42 48 -105 117}}]

POTE generator: ~23/22 = 77.168

Optimal GPV sequence: {{Val list| 140, 311, 762g, 1073g, 1384cfgg }}

Mapping: [{{val|1 3 2 3 -4 1 1 11 -3 1}}, {{val|0 -22 5 -3 116 42 48 -105 117 60}}]

POTE generator: ~23/22 = 77.167

Optimal GPV sequence: {{Val list| 140, 311, 762g, 1073g, 1384cfggj }}

Mapping: [{{val|1 3 2 3 -4 1 1 11 -3 1 11}}, {{val|0 -22 5 -3 116 42 48 -105 117 60 -94}}]

POTE generator: ~23/22 = 77.169

Optimal GPV sequence: {{Val list| 140, 171, 311 }}

Mapping: [{{val|1 3 2 3 -4 1 1 11 -3 1 11 0}}, {{val|0 -22 5 -3 116 42 48 -105 117 60 -94 81}}]

POTE generator: ~23/22 = 77.170

Optimal GPV sequence: {{Val list| 140, 171, 311 }}

Mapping: [{{val|1 3 2 3 -4 1 1 11 -3 1 11 0 6}}, {{val|0 -22 5 -3 116 42 48 -105 117 60 -94 81 -10}}]

POTE generator: ~23/22 = 77.169

Optimal GPV sequence: {{Val list| 140, 171, 311 }}

Mapping: [{{val| 1 3 2 3 6 }}, {{val| 0 -44 10 -6 -79 }}]

POTE generator: ~45/44 = 38.596

Optimal GPV sequence: {{Val list| 31, 280, 311, 342 }}

Mapping: [{{val| 1 3 2 3 6 1 }}, {{val| 0 -44 10 -6 -79 84 }}]

POTE generator: ~45/44 = 38.588

Optimal GPV sequence: {{Val list| 31, 280, 311, 964f, 1275f, 1586cff }}

Mapping: [{{val| 1 3 2 3 6 1 1 }}, {{val| 0 -44 10 -6 -79 84 96 }}]

POTE generator: ~45/44 = 38.589

Optimal GPV sequence: {{Val list| 31, 280, 311, 653f, 964f }}

Mapping: [{{val|2 6 4 6 1}}, {{val|0 -22 5 -3 46}}]

POTE generator: ~256/245 = 77.193

Optimal GPV sequence: {{Val list| 62e, 140, 202, 342 }}

In addition to 2401/2400, quasiorwell tempers out 29360128/29296875 = {{monzo|22 -1 -10 1}}. It has a generator 1024/875, which is 6144/6125 more than 7/6. It may be described as the 31&270 temperament, and as one might expect, 61\270 makes for an excellent tuning choice. Other possibilities are (7/2)^1/8, giving just 7s, or 384^1/38, giving pure fifths.

Adding 3025/3024 extends to the 11-limit and gives {{multival| 38 -3 8 64 …}} for the initial wedgie, and as expected, 270 remains an excellent tuning.

Subgroup: 2.3.5.7

[[Mapping]]: [{{val|1 31 0 9}}, {{val|0 -38 3 -8}}]

[[POTE generator]]: ~1024/875 = 271.107

{{Val list|legend=1| 31, 177, 208, 239, 270, 571, 841, 1111 }}

Mapping: [{{val|1 31 0 9 53}}, {{val|0 -38 3 -8 -64}}]

POTE generator: ~90/77 = 271.111

Optimal GPV sequence: {{Val list| 31, 208, 239, 270 }}

Mapping: [{{val|1 31 0 9 53 -59}}, {{val|0 -38 3 -8 -64 81}}]

POTE generator: ~90/77 = 271.107

Optimal GPV sequence: {{Val list| 31, 239, 270, 571, 841, 1111 }}

Subgroup: 2.3.5.7

[[Mapping]]: [{{val|1 3 12 8}}, {{val|0 -6 -41 -22}}]

[[POTE generator]]: ~189/160 = 283.280

{{Val list|legend=1| 72, 161, 233, 305 }}

Mapping: [{{val|1 3 12 8 7}}, {{val|0 -6 -41 -22 -15}}]

POTE generator: ~33/28 = 283.276

Optimal GPV sequence: {{Val list| 72, 161, 233, 305 }}

Mapping: [{{val|1 3 12 8 7 7}}, {{val|0 -6 -41 -22 -15 -14}}]

POTE generator: ~13/11 = 283.294

Optimal GPV sequence: {{Val list| 72, 161f, 233f }}

The generator for emmthird temperament is the hemimage third, sharper than 5/4 by the hemimage comma, 10976/10935.

Subgroup: 2.3.5.7

[[Mapping]]: [{{val|1 -3 -17 -8}}, {{val|0 14 59 33}}]

[[POTE generator]]: ~2744/2187 = 392.988

{{Val list|legend=1| 58, 113, 171, 742, 913, 1084, 1255, 2681d, 3936d }}

Mapping: [{{val|1 -3 -17 -8 -8}}, {{val|0 14 59 33 35}}]

POTE generator: ~1372/1089 = 392.991

Optimal GPV sequence: {{Val list| 58, 113, 171 }}

Mapping: [{{val|1 -3 -17 -8 -8 -13}}, {{val|0 14 59 33 35 51}}]

POTE generator: ~180/143 = 392.989

Optimal GPV sequence: {{Val list| 58, 113, 171 }}

Mapping: [{{val|1 -3 -17 -8 -8 -13 9}}, {{val|0 14 59 33 35 51 -15}}]

POTE generator: ~64/51 = 392.985

Optimal GPV sequence: {{Val list| 58, 113, 171 }}

The generator for quinmite is quasi-tempered minor third 25/21, flatter than 6/5 by the starling comma, 126/125. It is also generated by 1/5 of minor tenth 12/5, and its name is a play on the words "quintans" (Latin for "one fifth") and "minor tenth".

Subgroup: 2.3.5.7

[[Mapping]]: [{{val|1 -7 -5 -3}}, {{val|0 34 29 23}}]

[[POTE generator]]: ~25/21 = 302.997

{{Val list|legend=1| 95, 99, 202, 301, 400, 701, 1101c, 1802c, 2903cc }}

The generator for unthirds temperament is undecimal major third, 14/11.

Subgroup: 2.3.5.7

[[Mapping]]: [{{val|1 -13 -14 -9}}, {{val|0 42 47 34}}]

[[POTE generator]]: ~3969/3125 = 416.717

{{Val list|legend=1| 72, 167, 239, 311, 694, 1005c }}

Mapping: [{{val|1 -13 -14 -9 -8}}, {{val|0 42 47 34 33}}]

POTE generator: ~14/11 = 416.718

Optimal GPV sequence: {{Val list| 72, 167, 239, 311, 1316c }}

Mapping: [{{val|1 -13 -14 -9 -9 -47}}, {{val|0 42 47 34 33 146}}]

POTE generator: ~14/11 = 416.716

Optimal GPV sequence: {{Val list| 72, 311, 694, 1005c, 1699cd }}

This temperament has a generator of neutral third (0.2 cents flat of [[49/40]]) and tempers out the [[garischisma]].

Subgroup: 2.3.5.7

[[Mapping]]: [{{val|1 1 19 11}}, {{val|0 2 -57 -28}}]

{{Multival|legend=1|2 -57 -28 -95 -50 95}}

[[POTE generator]]: ~49/40 = 351.113

{{Val list|legend=1| 41, 188, 229, 270, 1121, 1391, 1661, 1931, 2201, 6333bbcc }}

Mapping: [{{val|1 1 19 11 -10}}, {{val|0 2 -57 -28 46}}]

POTE generator: ~49/40 = 351.115

Optimal GPV sequence: {{Val list| 41, 188, 229, 270, 581, 851, 1121, 1972, 3093b, 4214b }}

Mapping: [{{val|1 1 19 11 -10 -20}}, {{val|0 2 -57 -28 46 81}}]

POTE generator: ~49/40 = 351.117

Optimal GPV sequence: {{Val list| 41, 229, 270, 581, 851, 2283b, 3134b }}

== Amicable ==

 

 

While it extends well into 2.3.5.7.13/11, there are multiple reasonable places for the prime 11 and 13 in the interval chain. Amical (311 & 410) does this with no compromise of accuracy, but is enormously complex. Amorous (212 & 311) has the new primes placed on the same side of the interval chain so blends smarter with the other harmonics. Pseudoamical (99 & 113) and pseudoamorous (14cf & 99ef) are the corresponding low-complexity interpretations. Floral (198 & 212) shares the semioctave period and the ~21/20 generator with harry, but in a complementary style, including a characteristic flat 11. Finally, humorous (198 & 311) is one of the best extensions out there and it splits the generator in two.

 

 

 

 

 

 

 

 

=== Amical ===

Subgroup: 2.3.5.7.11

 

 

 

 

 

Badness: 0.100668

 

==== 13-limit ====

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Badness: 0.056583

Subgroup: 2.3.5.7.11.13

Comma list: 243/242, 364/363, 441/440, 1875/1859

Mapping: [{{val| 1 3 6 5 7 10 }}, {{val| 0 -20 -52 -31 -50 -89 }}]

 

 

 

 

 

 

 

 

 

 

 

 

 

Optimal GPV sequence: {{val list| 198, 410 }}

 

 

 

 

 

 

Optimal GPV sequence: {{val list| 85c, 113, 198, 311, 509, 820 }}

 

 

 

Comma list: 2080/2079, 2200/2197, 2401/2400, 3025/3024

 

Mapping: [{{val| 1 3 6 5 3 6 }}, {{val| 0 -40 -104 -62 13 -65 }}]

 

 

Optimal GPV sequence: {{val list| 85c, 113, 198, 311, 509, 820f }}

 

Subgroup: 2.3.5.7

[[Mapping]]: [{{val| 1 -1 6 4 }}, {{val| 0 26 -37 -12 }}]

[[POTE generator]]: ~15/14 = 119.297

{{Val list|legend=1| 10, 151, 161, 171, 3581bcdd, 3752bcdd, 3923bcdd, 4094bcdd, 4265bccdd, 4436bccdd, 4607bccdd }}

Mapping: [{{val| 1 -1 6 4 -3 }}, {{val| 0 26 -37 -12 65 }}]

POTE generator: ~15/14 = 119.279

Optimal GPV sequence: {{Val list| 10, 151, 161, 171, 332 }}

Mapping: [{{val| 1 -1 6 4 -3 4 }}, {{val| 0 26 -37 -12 65 -3 }}]

POTE generator: ~15/14 = 119.281

Optimal GPV sequence: {{Val list| 10, 151, 161, 171, 332, 835eeff }}

Mapping: [{{val| 1 -1 6 4 -3 4 2 }}, {{val| 0 26 -37 -12 65 -3 21 }}]

POTE generator: ~15/14 = 119.281

Optimal GPV sequence: {{Val list| 10, 151, 161, 171, 332, 503ef, 835eeff }}

{{see also| Ragismic microtemperaments #Parakleismic }}

Subgroup: 2.3.5.7

[[Mapping]]: [{{val| 1 31 34 26 }}, {{val| 0 -52 -56 -41 }}]

[[POTE generator]]: ~1296/875 = 678.810

{{Val list|legend=1| 76, 99, 274, 373, 472, 571, 1043, 1614 }}

Subgroup: 2.3.5.7

[[Mapping]]: [{{val| 1 19 0 6 }}, {{val| 0 -60 8 -11 }}]

[[POTE generator]]: ~57344/46875 = 348.301

{{Val list|legend=1| 31, 348, 379, 410, 441, 1354, 1795, 2236 }}

Subgroup: 2.3.5.7

[[Mapping]]: [{{val| 1 13 33 21 }}, {{val| 0 -32 -86 -51 }}]

[[POTE generator]]: ~2800/2187 = 428.066

{{Val list|legend=1| 157, 171, 1012, 1183, 1354, 1525, 1696, 6955dd }}

Subgroup: 2.3.5.7

[[Mapping]]: [{{val| 1 5 1 3 }}, {{val| 0 -18 7 -1 }}]

{{Multival|legend=1|18 -7 1 -53 -49 22}}

[[POTE generator]]: ~8/7 = 227.512

{{Val list|legend=1| 21, 37, 58, 153bc, 211bccd, 269bccd }}

Mapping: [{{val| 1 5 1 3 1 }}, {{val| 0 -18 7 -1 13 }}]

POTE generator: ~8/7 = 227.500

Optimal GPV sequence: {{Val list| 21, 37, 58, 153bce, 211bccdee, 269bccdee }}

Mapping: [{{val| 1 5 1 3 1 2 }}, {{val| 0 -18 7 -1 13 9 }}]

POTE generator: ~8/7 = 227.493

Optimal GPV sequence: {{Val list| 21, 37, 58, 153bcef, 211bccdeeff }}

Subgroup: 2.3.5.7

[[Mapping]]: [{{val| 1 19 8 10 }}, {{val| 0 -46 -15 -19 }}]

{{Multival|legend=1|46 15 19 -83 -99 2}}

[[POTE generator]]: ~125/96 = 454.310

{{Val list|legend=1| 37, 103, 140, 243, 383, 1009cd, 1392ccd }}

Mapping: [{{val| 1 19 8 10 8 }}, {{val| 0 -46 -15 -19 -12 }}]

POTE generator: ~100/77 = 454.318

Optimal GPV sequence: {{Val list| 37, 103, 140, 243e }}

Mapping: [{{val| 1 19 8 10 8 9 }}, {{val| 0 -46 -15 -19 -12 -14 }}]

POTE generator: ~13/10 = 454.316

Optimal GPV sequence: {{Val list| 37, 103, 140, 243e }}

In addition to 2401/2400, mintone tempers out 177147/175000 = {{monzo|-3 11 -5 -1}} in the 7-limit; 243/242, 441/440, and 43923/43750 in the 11-limit. It has a generator tuned around 49/44. It may be described as the 58&103 temperament, and as one might expect, 25\161 makes for an excellent tuning choice.

Subgroup: 2.3.5.7

[[Mapping]]: [{{val| 1 5 9 7 }}, {{val| 0 -22 -43 -27 }}]

[[POTE generator]]: ~10/9 = 186.343

{{Val list|legend=1| 45, 58, 103, 161, 586b, 747bc, 908bbc }}

Mapping: [{{val| 1 5 9 7 12 }}, {{val| 0 -22 -43 -27 -55 }}]

POTE generator: ~10/9 = 186.345

Optimal GPV sequence: {{Val list| 58, 103, 161, 425b, 586b, 747bc }}

Mapping: [{{val| 1 5 9 7 12 11 }}, {{val| 0 -22 -43 -27 -55 -47 }}]

POTE generator: ~10/9 = 186.347

Optimal GPV sequence: {{Val list| 58, 103, 161, 425b, 586bf }}

Mapping: [{{val| 1 5 9 7 12 11 3 }}, {{val| 0 -22 -43 -27 -55 -47 7 }}]

POTE generator: ~10/9 = 186.348

Optimal GPV sequence: {{Val list| 58, 103, 161, 425b, 586bf }}

{{see also| Sensipent family }}

Subgroup: 2.3.5.7

[[Mapping]]: [{{val| 1 13 17 13 }}, {{val| 0 -28 -36 -25 }}]

[[POTE generator]]: ~250/189 = 489.235

{{Val list|legend=1| 27, 76, 103, 130 }}

Mapping: [{{val| 1 13 17 13 32 }}, {{val| 0 -28 -36 -25 -70 }}]

POTE generator: ~250/189 = 489.252

Optimal GPV sequence: {{Val list| 103, 130, 233, 363, 493e, 856be }}