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ported ennealimmal over as all the 5-limit extensions here are extensions of ennealimmal
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{{Optimal ET sequence|legend=1| 54, 63, 72, 135, 342, 477, 1089, 1566 }}
{{Optimal ET sequence|legend=1| 54, 63, 72, 135, 342, 477, 1089, 1566 }}


== Undecentic ==
== Ennealimmal ==
{{Main| Ennealimmal }}
 
Ennealimmal 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 [[ennealimma]], {{monzo| 1 -27 18 }}, which leads to the identification of (27/25)<sup>9</sup> with the [[octave]], and gives ennealimmal a [[period]] of 1/9 octave. Its [[pergen]] is (P8/9, P5/2). While 27/25 is a 5-limit interval, a stack of 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.
 
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 49/40~60/49, all of which have their own interesting advantages. Possible tunings are 441-, 612-, or 3600edo, 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 "[[tritave]]s" 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.
 
Ennealimmal extensions discussed elsewhere include [[Compton family #Omicronbeta|omicronbeta]], [[Tritrizo clan #Undecentic|undecentic]], [[Tritrizo clan #Schisennealimmal|schisennealimmal]], and [[Tritrizo clan #Lunennealimmal|lunennealimmal]].
 
7-limit ennealimmal's S-expression-based comma list is {[[4375/4374|S25/S27]], [[2401/2400|S49]]}. Interestingly, the [[landscape comma]] is equal to [[2401/2400|S49]]/([[4375/4374|S25/S27]]) while the [[wizma]] is equal to [[2401/2400|S49]]*[[4375/4374|S25/S27]].
 
''For the 5-limit temperament, see [[Ennealimma#Ennealimmal]].''
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 2401/2400, 4375/4374
 
{{Mapping|legend=1| 9 1 1 12 | 0 2 3 2 }}
 
{{Multival|legend=1| 18 27 18 1 -22 -34 }}
 
: mapping generators: ~27/25, ~5/3
 
[[Optimal tuning]] ([[POTE]]): ~27/25 = 1\9, ~5/3 = 884.3129 (~36/35 = 49.0205)
 
[[Tuning ranges]]:
* 7-odd-limit [[diamond monotone]]: ~36/35 = [26.667, 66.667] (1\45 to 1\18)
* 9-odd-limit diamond monotone: ~36/35 = [44.444, 53.333] (1\27 to 2\45)
* 7- and 9-odd-limit [[diamond tradeoff]]: ~36/35 = [48.920, 49.179]
* 7- and 9-odd-limit diamond monotone and tradeoff: ~36/35 = [48.920, 49.179]
 
{{Optimal ET sequence|legend=1| 27, 45, 72, 99, 171, 441, 612 }}
 
[[Badness]]: 0.003610
 
=== 11-limit ===
The ennealimmal temperament can be described as 99e &amp; 171e, which tempers out [[5632/5625]] (vishdel comma) and [[19712/19683]] (symbiotic comma).
 
Subgroup: 2.3.5.7.11
 
Comma list: 2401/2400, 4375/4374, 5632/5625
 
Mapping: {{mapping| 9 1 1 12 -75 | 0 2 3 2 16 }}
 
Optimal tuning (POTE): ~27/25 = 1\9, ~5/3 = 884.4679 (~36/35 = 48.8654)
 
{{Optimal ET sequence|legend=1| 99e, 171e, 270, 909, 1179, 1449c, 1719c }}
 
Badness: 0.027332
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 1001/1000, 1716/1715, 4096/4095, 4375/4374
 
Mapping: {{mapping| 9 1 1 12 -75 93 | 0 2 3 2 16 -9 }}
 
Optimal tuning (POTE): ~27/25 = 1\9, ~5/3 = 884.4304 (~36/35 = 48.9030)
 
{{Optimal ET sequence|legend=1| 99e, 171e, 270 }}
 
Badness: 0.029404
 
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 715/714, 1001/1000, 1716/1715, 4096/4095, 4375/4374
 
Mapping: {{mapping| 9 1 1 12 -75 93 -3 | 0 2 3 2 16 -9 6 }}
 
Optimal tuning (POTE): ~27/25 = 1\9, ~5/3 = 884.4304 (~36/35 = 48.9030)
 
{{Optimal ET sequence|legend=1| 99e, 171e, 270 }}
 
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 715/714, 1001/1000, 1216/1215, 1716/1715, 4096/4095, 4375/4374
 
Mapping: {{mapping| 9 1 1 12 -75 93 -3 -48 | 0 2 3 2 16 -9 6 13 }}
 
Optimal tuning (POTE): ~27/25 = 1\9, ~5/3 = 884.4304 (~36/35 = 48.9030)
 
{{Optimal ET sequence|legend=1| 99e, 171e, 270 }}
 
==== Ennealimmalis ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 2080/2079, 2401/2400, 4375/4374, 5632/5625
 
Mapping: {{mapping| 9 1 1 12 -75 -106 | 0 2 3 2 16 21 }}
 
Optimal tuning (CTE): ~27/25 = 1\9, ~5/3 = 884.4560 (~36/35 = 48.8773)
 
{{Optimal ET sequence|legend=1| 99ef, 171ef, 270, 639, 909, 1179, 2088bce }}
 
Badness: 0.022068
 
=== Ennealimmia ===
The ennealimmia temperament is an alternative extension and can be described as 99 & 171, which tempers out [[131072/130977]] (olympia).
 
Subgroup: 2.3.5.7.11
 
Comma list: 2401/2400, 4375/4374, 131072/130977
 
Mapping: {{mapping| 9 1 1 12 124 | 0 2 3 2 -14 }}
 
Optimal tuning (POTE): ~27/25 = 1\9, ~5/3 = 884.4089 (~36/35 = 48.9244)
 
{{Optimal ET sequence|legend=1| 99, 171, 270, 711, 981, 1251, 2232e }}
 
Badness: 0.026463
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 2080/2079, 2401/2400, 4096/4095, 4375/4374
 
Mapping: {{mapping| 9 1 1 12 124 93 | 0 2 3 2 -14 -9 }}
 
Optimal tuning (POTE): ~27/25 = 1\9, ~5/3 = 884.3997 (~36/35 = 48.9336)
 
{{Optimal ET sequence|legend=1| 99, 171, 270, 711, 981, 1692e, 2673e }}
 
Badness: 0.016607
 
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 936/935, 2080/2079, 2401/2400, 4096/4095, 4375/4374
 
Mapping: {{mapping| 9 1 1 12 124 93 -3 | 0 2 3 2 -14 -9 6 }}
 
Optimal tuning (POTE): ~27/25 = 1\9, ~5/3 = 884.3997 (~36/35 = 48.9336)
 
{{Optimal ET sequence|legend=1| 99, 171, 270 }}
 
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 936/935, 1216/1215, 2080/2079, 2401/2400, 4096/4095, 4375/4374
 
Mapping: {{mapping| 9 1 1 12 124 93 -3 -48 | 0 2 3 2 -14 -9 6 13 }}
 
Optimal tuning (POTE): ~27/25 = 1\9, ~5/3 = 884.3997 (~36/35 = 48.9336)
 
{{Optimal ET sequence|legend=1| 99, 171, 270 }}
 
=== Ennealimnic ===
Ennealimnic (72 &amp; 171) equates 11/9 with 27/22, 49/40, and 60/49 as a neutral third interval.
 
Subgroup: 2.3.5.7.11
 
Comma list: 243/242, 441/440, 4375/4356
 
Mapping: {{mapping| 9 1 1 12 -2 | 0 2 3 2 5 }}
 
Optimal tuning (POTE): ~27/25 = 1\9, ~5/3 = 883.9386 (~36/35 = 49.3948)
 
Tuning ranges:
* 11-odd-limit diamond monotone: ~36/35 = [44.444, 53.333] (1\27 to 2\45)
* 11-odd-limit diamond tradeoff: ~36/35 = [48.920, 52.592]
* 11-odd-limit diamond monotone and tradeoff: ~36/35 = [48.920, 52.592]
 
{{Optimal ET sequence|legend=1| 72, 171, 243 }}
 
Badness: 0.020347
 
See also: [[Chords of ennealimnic]]
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 243/242, 364/363, 441/440, 625/624
 
Mapping: {{mapping| 9 1 1 12 -2 -33 | 0 2 3 2 5 10 }}
 
Optimal tuning (POTE): ~27/25 = 1\9, ~5/3 = 883.9920 (~36/35 = 49.3414)
 
Tuning ranges:
* 13- and 15-odd-limit diamond monotone: ~36/35 = [48.485, 50.000] (4\99 to 3\72)
* 13- and 15-odd-limit diamond tradeoff: ~36/35 = [48.825, 52.592]
* 13- and 15-odd-limit diamond monotone and tradeoff: ~36/35 = [48.825, 50.000]
 
{{Optimal ET sequence|legend=1| 72, 171, 243 }}
 
Badness: 0.023250
 
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 243/242, 364/363, 375/374, 441/440, 595/594
 
Mapping: {{mapping| 9 1 1 12 -2 -33 -3 | 0 2 3 2 5 10 6 }}
 
Optimal tuning (POTE): ~27/25 = 1\9, ~5/3 = 883.9981 (~36/35 = 49.3353)
 
Tuning ranges:
* 17-odd-limit diamond monotone: ~36/35 = [48.485, 50.000] (4\99 to 3\72)
* 17-odd-limit diamond tradeoff: ~36/35 = [46.363, 52.592]
* 17-odd-limit diamond monotone and tradeoff: ~36/35 = [48.485, 50.000]
 
{{Optimal ET sequence|legend=1| 72, 171, 243 }}
 
Badness: 0.014602
 
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 243/242, 364/363, 375/374, 441/440, 513/512, 595/594
 
Mapping: {{mapping| 9 1 1 12 -2 -33 -3 78  | 0 2 3 2 5 10 6 -6 }}
 
{{Optimal ET sequence|legend=1| 72, 171, 243 }}
 
==== Ennealim ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 169/168, 243/242, 325/324, 441/440
 
Mapping: {{mapping| 9 1 1 12 -2 20 | 0 2 3 2 5 2 }}
 
Optimal tuning (POTE): ~13/12 = 1\9, ~5/3 = 883.6257 (~36/35 = 49.7076)
 
{{Optimal ET sequence|legend=1| 27e, 45ef, 72 }}
 
Badness: 0.020697
 
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 169/168, 221/220, 243/242, 325/324, 441/440
 
Mapping: {{mapping| 9 1 1 12 -2 20 -3 | 0 2 3 2 5 2 6 }}
 
Optimal tuning (POTE): ~13/12 = 1\9, ~5/3 = 883.6257 (~36/35 = 49.7076)
 
{{Optimal ET sequence|legend=1| 27eg, 45efg, 72 }}
 
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 169/168, 221/220, 243/242, 325/324, 441/440
 
Mapping: {{mapping| 9 1 1 12 -2 20 -3 25 | 0 2 3 2 5 2 6 2 }}
 
Optimal tuning (POTE): ~13/12 = 1\9, ~5/3 = 883.6257 (~36/35 = 49.7076)
 
{{Optimal ET sequence|legend=1| 27eg, 45efg, 72 }}
 
=== Ennealiminal ===
Subgroup: 2.3.5.7.11
 
Comma list: 385/384, 1375/1372, 4375/4374
 
Mapping: {{mapping| 9 1 1 12 51 | 0 2 3 2 -3 }}
 
Optimal tuning (POTE): ~27/25 = 1\9, ~5/3 = 883.8298 (~36/35 = 49.5036)
 
{{Optimal ET sequence|legend=1| 27, 45, 72, 171e, 243e, 315e }}
 
Badness: 0.031123
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 169/168, 325/324, 385/384, 1375/1372
 
Mapping: {{mapping| 9 1 1 12 51 20 | 0 2 3 2 -3 2 }}
 
Optimal tuning (POTE): ~13/12 = 1\9, ~5/3 = 883.8476 (~36/35 = 49.4857)
 
{{Optimal ET sequence|legend=1| 27, 45f, 72, 171ef, 243eff }}
 
Badness: 0.030325
 
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 169/168, 221/220, 325/324, 385/384, 1375/1372
 
Mapping: {{mapping| 9 1 1 12 51 20 50 | 0 2 3 2 -3 2 -2 }}
 
Optimal tuning (POTE): ~13/12 = 1\9, ~5/3 = 883.8476 (~36/35 = 49.4857)
 
{{Optimal ET sequence|legend=1| 27, 45f, 72 }}
 
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 153/152, 169/168, 221/220, 325/324, 385/384, 1375/1372
 
Mapping: {{mapping| 9 1 1 12 51 20 50 25 | 0 2 3 2 -3 2 -2 2 }}
 
Optimal tuning (POTE): ~13/12 = 1\9, ~5/3 = 883.8476 (~36/35 = 49.4857)
 
{{Optimal ET sequence|legend=1| 27, 45f, 72 }}
 
=== Hemiennealimmal ===
Hemiennealimmal (72 &amp; 198) has a period of 1/18 octave and tempers out the four smallest superparticular commas of the 11-limit JI, 2401/2400, 3025/3024, 4375/4374, and 9801/9800. Tempering out [[9801/9800]] leads to an octave split into two equal parts. Notably, every one of these commas is part of one or more known infinite comma families; see directly below.
 
Its S-expression-based comma list is {([[3025/3024|S22/S24 = S55 = S25/S27 * S99]],) [[4375/4374|S25/S27]], [[2401/2400|S49]], [[9801/9800|S33/S35 = S99]]}.
 
Subgroup: 2.3.5.7.11
 
Comma list: 2401/2400, 3025/3024, 4375/4374
 
Mapping: {{mapping| 18 0 -1 22 48 | 0 2 3 2 1 }}
 
: mapping generators: ~80/77, ~400/231
 
Optimal tuning (POTE): ~80/77 = 1\18, ~400/231 = 950.9553
 
Tuning ranges:
* 11-odd-limit diamond monotone: ~99/98 = [13.333, 22.222] (1\90 to 1\54)
* 11-odd-limit diamond tradeoff: ~99/98 = [17.304, 17.985]
* 11-odd-limit diamond monotone and tradeoff: ~99/98 = [17.304, 17.985]
 
{{Optimal ET sequence|legend=1| 72, 198, 270, 342, 612, 954, 1566 }}
 
Badness: 0.006283
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 676/675, 1001/1000, 1716/1715, 3025/3024
 
Mapping: {{mapping| 18 0 -1 22 48 -19 | 0 2 3 2 1 6 }}
 
Optimal tuning (POTE): ~27/26 = 1\18, ~26/15 = 951.0837
 
Tuning ranges:
* 13-odd-limit diamond monotone: ~99/98 = [16.667, 22.222] (1\72 to 1\54)
* 15-odd-limit diamond monotone: ~99/98 = [16.667, 19.048] (1\72 to 2\126)
* 13-odd-limit diamond tradeoff: ~99/98 = [17.304, 18.309]
* 15-odd-limit diamond tradeoff: ~99/98 = [17.304, 18.926]
* 13-odd-limit diamond monotone and tradeoff: ~99/98 = [17.304, 18.309]
* 15-odd-limit diamond monotone and tradeoff: ~99/98 = [17.304, 18.926]
 
{{Optimal ET sequence|legend=1| 72, 198, 270 }}
 
Badness: 0.012505
 
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 676/675, 715/714, 1001/1000, 1716/1715, 3025/3024
 
Mapping: {{mapping| 18 0 -1 22 48 -19 -12 | 0 2 3 2 1 6 6 }}
 
Optimal tuning (POTE): ~27/26 = 1\18, ~26/15 = 951.0837
 
{{Optimal ET sequence|legend=1| 72, 198g, 270 }}
 
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 676/675, 715/714, 1001/1000, 1331/1330, 1716/1715, 3025/3024
 
Mapping: {{mapping| 18 0 -1 22 48 -19 -12 48 105 | 0 2 3 2 1 6 6 -2 }}
 
Optimal tuning (POTE): ~27/26 = 1\18, ~26/15 = 951.0837
 
{{Optimal ET sequence|legend=1| 72, 198g, 270 }}
 
==== Semihemiennealimmal ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 2401/2400, 3025/3024, 4225/4224, 4375/4374
 
Mapping: {{mapping| 18 0 -1 22 48 88 | 0 4 6 4 2 -3 }}
 
: mapping generators: ~80/77, ~1053/800
 
Optimal tuning (POTE): ~80/77 = 1\18, ~1053/800 = 475.4727
 
{{Optimal ET sequence|legend=1| 126, 144, 270, 684, 954 }}
 
Badness: 0.013104
 
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 2401/2400, 2431/2430, 3025/3024, 4225/4224, 4375/4374
 
Mapping: {{mapping| 18 0 -1 22 48 88 -119 | 0 4 6 4 2 -3 27 }}
 
: mapping generators: ~80/77, ~1053/800
 
Optimal tuning (POTE): ~80/77 = 1\18, ~1053/800 = 475.4727
 
{{Optimal ET sequence|legend=1| 270, 684, 954 }}
 
Badness: 0.013104
 
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 2401/2400, 2431/2430, 2926/2925, 3025/3024, 4225/4224, 4375/4374
 
Mapping: {{mapping| 18 0 -1 22 48 88 -119 -2 | 0 4 6 4 2 -3 27 11 }}
 
: mapping generators: ~80/77, ~1053/800
 
Optimal tuning (POTE): ~80/77 = 1\18, ~1053/800 = 475.4727
 
{{Optimal ET sequence|legend=1| 270, 684h, 954h, 1224 }}
 
Badness: 0.013104
 
=== Semiennealimmal ===
Semiennealimmal tempers out [[4000/3993]], and uses a ~140/121 semifourth generator. Notably, however, two generator steps do not reach ~4/3, despite that the name may suggest so. In fact, it splits the generator of ennealimmal into three.
 
Subgroup: 2.3.5.7.11
 
Comma list: 2401/2400, 4000/3993, 4375/4374
 
Mapping: {{mapping| 9 3 4 14 18 | 0 6 9 6 7 }}
 
: mapping generators: ~27/25, ~140/121
 
Optimal tuning (POTE): ~27/25 = 1\9, ~140/121 = 250.3367
 
{{Optimal ET sequence|legend=1| 72, 369, 441 }}
 
Badness: 0.034196
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 1575/1573, 2080/2079, 2401/2400, 4375/4374
 
Mapping: {{mapping| 9 3 4 14 18 -8 | 0 6 9 6 7 22 }}
 
Optimal tuning (POTE): ~27/25 = 1\9, ~140/121 = 250.3375
 
{{Optimal ET sequence|legend=1| 72, 297ef, 369f, 441 }}
 
Badness: 0.026122
 
=== Quadraennealimmal ===
Subgroup: 2.3.5.7.11
 
Comma list: 2401/2400, 4375/4374, 234375/234256
 
Mapping: {{mapping| 9 1 1 12 -7 | 0 8 12 8 23 }}
 
: mapping generators: ~27/25, ~25/22
 
Optimal tuning (POTE): ~27/25 = 1\9, ~25/22 = 221.0717
 
{{Optimal ET sequence|legend=1| 342, 1053, 1395, 1737, 4869dd, 6606cdd }}
 
Badness: 0.021320
 
=== Trinealimmal ===
Subgroup: 2.3.5.7.11
 
Comma list: 2401/2400, 4375/4374, 2097152/2096325
 
Mapping: {{mapping| 27 1 0 34 177 | 0 2 3 2 -4 }}
 
: mapping generators: ~2744/2673, ~2352/1375
 
Optimal tuning (POTE): ~2744/2673 = 1\27, ~2352/1375 = 928.8000
 
{{Optimal ET sequence|legend=1| 27, 243, 270, 783, 1053, 1323 }}
 
Badness: 0.029812
 
=== Rhodium ===
{{Main| Rhodium }}
Rhodium splits the ennealimmal period in five parts and thereby features a period of 9 × 5 = 45, thus the name is given after the 45th element.
 
Subgroup: 2.3.5.7.11
 
Comma list: 2401/2400, 4375/4374, 117440512/117406179
 
Mapping: {{mapping| 45 1 -1 56 226 | 0 2 3 2 -2 }}
 
: mapping generators: ~3072/3025, ~55/32
 
Optimal tunings:
* CTE: ~3072/3025 = 1\45, ~55/32 = 937.6658 (~385/384 = 4.3325)
* CWE: ~3072/3025 = 1\45, ~55/32 = 937.6630 (~385/384 = 4.3397)
 
Optimal ET sequence: {{Optimal ET sequence| 45, 225c, 270, 1125, 1395, 1665, 5265d }}
 
Badness: 0.0381
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 2401/2400, 4225/4224, 4375/4374, 6656/6655
 
Mapping: {{mapping| 45 1 -1 56 226 272 | 0 2 3 2 -2 -3 }}
 
Optimal tunings:
* CTE: ~66/65 = 1\45, ~55/32 = 937.6569 (~385/384 = 4.3236)
* CWE: ~66/65 = 1\45, ~55/32 = 937.6515 (~385/384 = 4.3182)
 
Optimal ET sequence: {{Optimal ET sequence| 45, 270, 855, 1125, 1395, 1665, 3060d, 4725df }}
 
Badness: 0.0226
 
=== Undecentic ===
Undecentic (99&amp;198) has a period of 1/99 octave.
Undecentic (99&amp;198) has a period of 1/99 octave.


Line 47: Line 554:
[[Badness]]: 0.058801
[[Badness]]: 0.058801


=== 13-limit ===
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 60: Line 567:
Badness: 0.042547
Badness: 0.042547


== Schisennealimmal ==
=== Schisennealimmal ===
Schisennealimmal (171&amp;342) has a period of 1/171 octave. [[171edo|171EDO]] and its multiples are members of both [[Schismatic family|schismic]] and [[Ragismic microtemperaments #Ennealimmal|ennealimmal]], and from this it derives its name.
Schisennealimmal (171&amp;342) has a period of 1/171 octave. [[171edo|171EDO]] and its multiples are members of both [[Schismatic family|schismic]] and [[Ragismic microtemperaments #Ennealimmal|ennealimmal]], and from this it derives its name.


Line 75: Line 582:
[[Badness]]: 0.031739
[[Badness]]: 0.031739


=== 13-limit ===
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 88: Line 595:
Badness: 0.054029
Badness: 0.054029


==== 17-limit ====
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Line 101: Line 608:
Badness: 0.031323
Badness: 0.031323


=== Schisennealimmic ===
==== Schisennealimmic ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 114: Line 621:
Badness: 0.046843
Badness: 0.046843


==== 17-limit ====
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Line 127: Line 634:
Badness: 0.030622
Badness: 0.030622


== Lunennealimmal ==
=== Lunennealimmal ===
Lunennealimmal (441&amp;882) has has a period of 1/441 octave. [[441edo|441EDO]] and its multiples are members of both [[Luna family|luna]] and [[Ragismic microtemperaments #Ennealimmal|ennealimmal]], and from this it derives its name.
Lunennealimmal (441&amp;882) has has a period of 1/441 octave. [[441edo|441EDO]] and its multiples are members of both [[Luna family|luna]] and [[Ragismic microtemperaments #Ennealimmal|ennealimmal]], and from this it derives its name.


Line 142: Line 649:
[[Badness]]: 0.091939
[[Badness]]: 0.091939


=== 13-limit ===
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 155: Line 662:
Badness: 0.042975
Badness: 0.042975


=== 17-limit ===
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


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