@@ Line 1: / Line 1: @@
 {{interwiki
+| en = Schismatic family
 | de = Schismatische Temperaturen
-| en =
 | es =
 | ja =
@@ Line 20: / Line 20: @@
 {{Mapping|legend=1| 1 0 15 | 0 1 -8 }}
+: mapping generators: ~2, ~3
-: Mapping generators: ~2, ~3
 [[Optimal tuning]]s:
-* [[CTE]]: ~2 = 1\1, ~3/2 = 701.7187
+* [[CTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.7187{{c}}
-* [[POTE]]: ~2 = 1\1, ~3/2 = 701.7359
+* [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.7359{{c}}
 [[Tuning ranges]]:
 * 5-odd-limit [[diamond monotone]]: ~3/2 = [685.714, 705.882] (4\7 to 10\17)
 * 5-odd-limit [[diamond tradeoff]]: ~3/2 = [701.711, 701.955] (1/8-comma to untempered)
-* 5-odd-limit diamond monotone and tradeoff: ~3/2 = [701.711, 701.955]
 {{Optimal ET sequence|legend=1| 12, 29, 41, 53, 118, 171, 289, 460, 749, 3456bc, 4205bc, 4954bc, 5703bbc, 6452bbcc }}
-[[Badness]]: 0.004259
+[[Badness]] (Smith): 0.004259
 === Overview to extensions ===
@@ Line 67: / Line 65: @@
 {{Mapping|legend=1| 1 0 15 25 | 0 1 -8 -14 }}
-: Mapping generators: ~2, ~3
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~3/2 = 702.085{{c}}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 702.085
 [[Minimax tuning]]:
 * [[7-odd-limit]]: ~3/2 = {{monzo| 2/3 1/15 0 -1/15 }}
 : {{monzo list| 1 0 0 0 | 5/3 1/15 0 -1/15 | 5/3 -8/15 0 8/15 | 5/3 -14/15 0 14/15 }}
-: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/3
+: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/3
 * [[9-odd-limit]]: ~3/2 = {{monzo| 9/16 1/8 0 -1/16 }}
 : {{monzo list| 1 0 0 0 | 25/16 1/8 0 -1/16 | 5/2 -1 0 1/2 | 25/8 -7/4 0 7/8 }}
-: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/7
+: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/7
 [[Tuning ranges]]:
@@ Line 85: / Line 81: @@
 {{Optimal ET sequence|legend=1| 12, 29, 41, 53, 94, 241c, 335cd, 576ccd }}
-[[Badness]]: 0.021644
+[[Badness]] (Smith): 0.021644
 === Cassandra ===
@@ Line 96: / Line 92: @@
 Mapping: {{mapping| 1 0 15 25 -33 | 0 1 -8 -14 23 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.157
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 702.157{{c}}
 Minimax tuning:
@@ Line 106: / Line 102: @@
 * 11-odd-limit diamond tradeoff: ~3/2 = [701.711, 702.915]
-{{Optimal ET sequence|legend=1| 41, 53, 94, 229c, 323c, 417cce }}
+{{Optimal ET sequence|legend=0| 41, 53, 94, 229c, 323c, 417cce }}
-Badness: 0.027396
+Badness (Smith): 0.027396
 ==== 13-limit ====
@@ Line 117: / Line 113: @@
 Mapping: {{mapping| 1 0 15 25 -33 -28 | 0 1 -8 -14 23 20 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.113
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 702.113{{c}}
 Minimax tuning:
@@ Line 128: / Line 124: @@
 * 15-odd-limit diamond tradeoff: ~3/2 = [701.676, 703.597]
-{{Optimal ET sequence|legend=1| 41, 53, 94, 429ccdeef, 523ccdeef }}
+{{Optimal ET sequence|legend=0| 41, 53, 94, 429ccdeef, 523ccdeef }}
-Badness: 0.020676
+Badness (Sintel): 0.020676
 ===== Cassie =====
@@ Line 139: / Line 135: @@
 Mapping: {{mapping| 1 0 15 25 -33 -28 -7 | 0 1 -8 -14 23 20 7 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.092
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 702.092{{c}}
-{{Optimal ET sequence|legend=1| 41, 53, 94g }}
+{{Optimal ET sequence|legend=0| 41, 53, 94g }}
-Badness: 0.023270
+Badness (Smith): 0.023270
 ====== 19-limit ======
@@ Line 152: / Line 148: @@
 Mapping: {{mapping| 1 0 15 25 -33 -28 -7 9 | 0 1 -8 -14 23 20 7 -3 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.079
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 702.079{{c}}
-{{Optimal ET sequence|legend=1| 41, 53, 94g }}
+{{Optimal ET sequence|legend=0| 41, 53, 94g }}
-Badness: 0.018189
+Badness (Smith): 0.018189
 ===== Cassandric =====
@@ Line 165: / Line 161: @@
 Mapping: {{mapping| 1 0 15 25 -33 -28 77 | 0 1 -8 -14 23 20 -46 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.097
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 702.097{{c}}
-{{Optimal ET sequence|legend=1| 41g, 53, 94, 241ce, 335cde }}
+{{Optimal ET sequence|legend=0| 41g, 53, 94, 241ce, 335cde }}
-Badness: 0.023167
+Badness (Smith): 0.023167
 ====== 19-limit ======
@@ Line 179: / Line 175: @@
 Optimal tunings:
-* ~2 = 1200.2910, ~3/2 = -702.2681 ([[WE]])
+* WE: ~2 = 1200.2910{{c}}, ~3/2 = 702.2681{{c}}
-* ~2 = 1\1, ~3/2 = 702.0967 ([[CWE]])
+* CWE: ~2 = 1200.000{{c}}, ~3/2 = 702.0967{{c}}
-* ~2 = 1\1, ~3/2 = 702.0978 ([[POTE]])
+* POTE: ~2 = 1200.000{{c}}, ~3/2 = 702.0978{{c}}
 {{Optimal ET sequence|legend=1| 41g, 53, 94, 241ceh, 335cdehh }}
-Badness: 0.017635
+Badness (Smith): 0.017635
 ====== 23-limit ======
@@ Line 195: / Line 191: @@
 Optimal tunings:
-* ~2 = 1200.2970, ~3/2 = 702.2697 ([[WE]])
+* WE: ~2 = 1200.2970{{c}}, ~3/2 = 702.2697{{c}}
-* ~2 = 1\1, ~3/2 = 702.0943 ([[CWE]])
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.0943{{c}}
-* ~2 = 1\1, ~3/2 = 702.0960 ([[POTE]])
+* POTE: ~2 = 1200.0000{{c}}, ~3/2 = 702.0960{{c}}
-{{Optimal ET sequence|legend=1| 41g, 53, 94 }} <!-- fumica's calculator doesn't generate non-GPV ETs -->
+{{Optimal ET sequence|legend=0| 41g, 53, 94 }}
-Badness: 0.015072
+Badness (Smith): 0.015072
 ===== Cassander =====
@@ Line 210: / Line 206: @@
 Mapping: {{mapping| 1 0 15 25 -33 -28 -72 | 0 1 -8 -14 23 20 48 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.144
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 702.144{{c}}
-{{Optimal ET sequence|legend=1| 41, 53g, 94 }}
+{{Optimal ET sequence|legend=0| 41, 53g, 94 }}
-Badness: 0.022454
+Badness (Smith): 0.022454
 ====== 19-limit ======
@@ Line 223: / Line 219: @@
 Mapping: {{mapping| 1 0 15 25 -33 -28 -72 9 | 0 1 -8 -14 23 20 48 -3 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.135
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 702.135{{c}}
-{{Optimal ET sequence|legend=1| 41, 53g, 94 }}
+{{Optimal ET sequence|legend=0| 41, 53g, 94 }}
-Badness: 0.017576
+Badness (Smith): 0.017576
 === Andromeda ===
@@ Line 236: / Line 232: @@
 Mapping: {{mapping| 1 0 15 25 32 | 0 1 -8 -14 -18 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.321
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 702.321{{c}}
 Minimax tuning:
@@ Line 246: / Line 242: @@
 * 11-odd-limit diamond tradeoff: ~3/2 = [701.711, 704.377]
-{{Optimal ET sequence|legend=1| 12, 29, 41, 217ce, 258ce }}
+{{Optimal ET sequence|legend=0| 12, 29, 41, 217ce, 258ce }}
-Badness: 0.023556
+Badness (Smith): 0.023556
 ==== 13-limit ====
@@ Line 257: / Line 253: @@
 Mapping: {{mapping| 1 0 15 25 32 37 | 0 1 -8 -14 -18 -21 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.559
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 702.559{{c}}
 Minimax tuning:
@@ Line 268: / Line 264: @@
 * 15-odd-limit diamond tradeoff: ~3/2 = [701.676, 704.377]
-{{Optimal ET sequence|legend=1| 12f, 29, 41, 152cdf, 193cdf, 234cdf }}
+{{Optimal ET sequence|legend=0| 12f, 29, 41, 152cdf, 193cdf, 234cdf }}
-Badness: 0.020749
+Badness (Smith): 0.020749
 ===== 17-limit =====
@@ Line 279: / Line 275: @@
 Mapping: {{mapping| 1 0 15 25 32 37 -7 | 0 1 -8 -14 -18 -21 7 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.312
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 702.312{{c}}
-{{Optimal ET sequence|legend=1| 12f, 29, 41 }}
+{{Optimal ET sequence|legend=0| 12f, 29, 41 }}
-Badness: 0.023406
+Badness (Smith): 0.023406
 ====== 19-limit ======
@@ Line 292: / Line 288: @@
 Mapping: {{mapping| 1 0 15 25 32 37 -7 9 | 0 1 -8 -14 -18 -21 7 -3 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.357
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 702.357{{c}}
-{{Optimal ET sequence|legend=1| 12f, 29, 41 }}
+{{Optimal ET sequence|legend=0| 12f, 29, 41 }}
-Badness: 0.019154
+Badness (Smith): 0.019154
 ===== Schisicosiennic =====
@@ Line 305: / Line 301: @@
 Mapping: {{mapping| 1 0 15 25 32 37 58 | 0 1 -8 -14 -18 -21 -34 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.725
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 702.725{{c}}
-{{Optimal ET sequence|legend=1| 12fg, 29g, 41, 70cd, 111cd }}
+{{Optimal ET sequence|legend=0| 12fg, 29g, 41, 70cd, 111cd }}
-Badness: 0.021758
+Badness (Smith): 0.021758
 ====== 19-limit ======
@@ Line 318: / Line 314: @@
 Mapping: {{mapping| 1 0 15 25 32 37 58 9 | 0 1 -8 -14 -18 -21 -34 -3 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.753
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 702.753{{c}}
-{{Optimal ET sequence|legend=1| 12fg, 29g, 41, 70cd, 111cdh, 181ccddh }}
+{{Optimal ET sequence|legend=0| 12fg, 29g, 41, 70cd, 111cdh, 181ccddh }}
-Badness: 0.017902
+Badness (Smith): 0.017902
 ===== Schisicosiennoid =====
@@ Line 331: / Line 327: @@
 Mapping: {{mapping| 1 0 15 25 32 37 12 | 0 1 -8 -14 -18 -21 -5 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.717
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 702.717{{c}}
-{{Optimal ET sequence|legend=1| 12f, 29g, 41g, 70cdgg }}
+{{Optimal ET sequence|legend=0| 12f, 29g, 41g, 70cdgg }}
-Badness: 0.020895
+Badness (Smith): 0.020895
 ====== 19-limit ======
@@ Line 344: / Line 340: @@
 Mapping: {{mapping| 1 0 15 25 32 37 12 9 | 0 1 -8 -14 -18 -21 -5 -3 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.716
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 702.716{{c}}
 {{Optimal ET sequence|legend=1| 12f, 29g, 41g, 70cdgg }}
-Badness: 0.016773
+Badness (Smith): 0.016773
 === Helenus ===
@@ Line 357: / Line 353: @@
 Mapping: {{mapping| 1 0 15 25 51 | 0 1 -8 -14 -30 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 701.725
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.725{{c}}
 Minimax tuning:
@@ Line 363: / Line 359: @@
 : unchanged-interval (eigenmonzo) basis: 2.11/9
-{{Optimal ET sequence|legend=1| 12, 41e, 53, 118d, 171de }}
+{{Optimal ET sequence|legend=0| 12, 41e, 53, 118d, 171de }}
-Badness: 0.035637
+Badness (Smith): 0.035637
 ==== 13-limit ====
@@ Line 374: / Line 370: @@
 Mapping: {{mapping| 1 0 15 25 51 56 | 0 1 -8 -14 -30 -33 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 701.747
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.747{{c}}
 Minimax tuning:
@@ Line 380: / Line 376: @@
 : unchanged-interval (eigenmonzo) basis: 2.11/9
-{{Optimal ET sequence|legend=1| 12f, 41ef, 53, 118d, 171de }}
+{{Optimal ET sequence|legend=0| 12f, 41ef, 53, 118d, 171de }}
-Badness: 0.026284
+Badness (Smith): 0.026284
 ==== 17-limit ====
@@ Line 391: / Line 387: @@
 Mapping: {{mapping| 1 0 15 25 51 56 -7 | 0 1 -8 -14 -30 -33 7 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 701.680
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.680{{c}}
-{{Optimal ET sequence|legend=1| 12f, 41ef, 53, 65d, 118dg }}
+{{Optimal ET sequence|legend=0| 12f, 41ef, 53, 65d, 118dg }}
-Badness: 0.023732
+Badness (Smith): 0.023732
 ==== 19-limit ====
@@ Line 404: / Line 400: @@
 Mapping: {{mapping| 1 0 15 25 51 56 -7 9 | 0 1 -8 -14 -30 -33 7 -3 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 701.705
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.705{{c}}
 {{Optimal ET sequence|legend=1| 12f, 41ef, 53, 65d, 118dg }}
-Badness: 0.019411
+Badness (Smith): 0.019411
 === Hemigari ===
@@ Line 416: / Line 412: @@
 Mapping: {{mapping| 1 0 15 25 9 | 0 2 -16 -28 -7 }}
+: mapping generators: ~2, ~110/63
-: Mapping generators: ~2, ~110/63
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~110/63 = 951.082{{c}}
-Optimal tuning (POTE): ~2 = 1\1, ~110/63 = 951.082 (~63/55 = 248.918)
+{{Optimal ET sequence|legend=0| 29, 53, 82e, 135e, 188ce }}
-{{Optimal ET sequence|legend=1| 29, 53, 82e, 135e, 188ce }}
+Badness (Smith): 0.050681
-Badness: 0.050681
 ==== 13-limit ====
@@ Line 432: / Line 427: @@
 Mapping: {{mapping| 1 0 15 25 9 14 | 0 2 -16 -28 -7 -13 }}
-Optimal tuning (POTE): ~2 = 1\1, ~26/15 = 951.082 (~15/13 = 248.918)
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~26/15 = 951.082{{c}}
-{{Optimal ET sequence|legend=1| 29, 53, 82e, 135ef, 188cef }}
+{{Optimal ET sequence|legend=0| 29, 53, 82e, 135ef, 188cef }}
-Badness: 0.027464
+Badness (Smith): 0.027464
 === Karadeniz ===
@@ Line 446: / Line 441: @@
 Mapping: {{mapping| 1 1 7 11 2 | 0 2 -16 -28 5 }}
+: mapping generators: ~2, ~11/9
-: Mapping generators: ~2, ~11/9
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/9 = 350.994{{c}}
-Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 350.994
+{{Optimal ET sequence|legend=0| 41, 106, 147 }}
-{{Optimal ET sequence|legend=1| 41, 106, 147 }}
+Badness (Smith): 0.041562
-Badness: 0.041562
 ==== 13-limit ====
@@ Line 462: / Line 456: @@
 Mapping: {{mapping| 1 1 7 11 2 -8 | 0 2 -16 -28 5 40 }}
-Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 351.014
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/9 = 351.014{{c}}
-{{Optimal ET sequence|legend=1| 41, 106, 147 }}
+{{Optimal ET sequence|legend=0| 41, 106, 147 }}
-Badness: 0.042564
+Badness (Smith): 0.042564
 === Sanjaab ===
@@ Line 474: / Line 468: @@
 Mapping: {{mapping| 1 2 -1 -3 0 | 0 -3 24 42 25 }}
 : mapping generators: ~2, ~11/10
-Optimal tuning (POTE): ~2 = 1\1, ~11/10 = 165.974
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/10 = 165.974{{c}}
 {{Optimal ET sequence|legend=1| 29, 65d, 94, 441cde, 535cde, 629cde }}
-Badness: 0.058040
+Badness (Smith): 0.058040
 ==== 13-limit ====
@@ Line 490: / Line 483: @@
 Mapping: {{mapping| 1 2 -1 -3 0 -1 | 0 -3 24 42 25 34 }}
-Optimal tuning (POTE): ~2 = 1\1, ~11/10 = 165.963
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/10 = 165.963{{c}}
-{{Optimal ET sequence|legend=1| 29, 65d, 94 }}
+{{Optimal ET sequence|legend=0| 29, 65d, 94 }}
-Badness: 0.033849
+Badness (Smith): 0.033849
 == Schism ==
@@ Line 512: / Line 505: @@
 {{Mapping|legend=1| 1 0 15 -59 | 0 1 -8 39 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 701.757
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~3/2 = 701.757{{c}}
 [[Minimax tuning]]:
 * [[7-odd-limit]]: ~3/2 = {{monzo| 27/47 0 -1/47 1/47 }}
 : [{{monzo| 1 0 0 0 }}, {{monzo| 74/47 0 -1/47 1/47 }}, {{monzo| 113/47 0 8/47 -8/47 }}, {{monzo| 113/47 0 -39/47 39/47 }}]
-: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/5
+: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/5
 * [[9-odd-limit]]: ~3/2 = {{monzo| 1/2 1/5 -1/10 }}
 : [{{monzo| 1 0 0 0 }}, {{monzo| 3/2 1/5 -1/10 0 }}, {{monzo| 3 -8/5 4/5 0 }}, {{monzo| -1/2 39/5 -39/10 0 }}]
-: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/5
+: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/5
 [[Tuning ranges]]:
 * 7- and 9-odd-limit [[diamond monotone]]: ~3/2 = [701.538, 701.886] (38\65 to 31\53)
 * 7- and 9-odd-limit [[diamond tradeoff]]: ~3/2 = [701.711, 701.955]
-* 7- and 9-odd-limit diamond monotone and tradeoff: ~3/2 = [701.711, 701.886]
 {{Optimal ET sequence|legend=1| 53, 118, 171, 1592c, 1763c, 1934c, 2105c, 2276cd, 2447cd, 2618cd, 2789cd, 2960cd, 3131bcd }}
-[[Badness]]: 0.014133
+[[Badness]] (Smith): 0.014133
 === Helenoid ===
-The helenoid temperament ({{nowrap|53 &amp; 118}}) is closely related to the helenus temperament, but with the ragisma rather than the [[225/224|marvel comma]] tempered out.
+The helenoid temperament ({{nowrap| 53 & 118 }}) is closely related to the helenus temperament, but with the ragisma rather than the [[225/224|marvel comma]] tempered out.
 Subgroup: 2.3.5.7.11
@@ Line 540: / Line 532: @@
 Mapping: {{mapping| 1 0 15 -59 51 | 0 1 -8 39 -30 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 701.722
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.722{{c}}
 Minimax tuning:
@@ Line 546: / Line 538: @@
 : unchanged-interval (eigenmonzo) basis: 2.11/7
-{{Optimal ET sequence|legend=1| 53, 118, 289e, 407de }}
+{{Optimal ET sequence|legend=0| 53, 118, 289e, 407de }}
-Badness: 0.038863
+Badness (Smith): 0.038863
 ==== 13-limit ====
@@ Line 557: / Line 549: @@
 Mapping: {{mapping| 1 0 15 -59 51 56 | 0 1 -8 39 -30 -33 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 701.745
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.745{{c}}
 Minimax tuning:
@@ Line 563: / Line 555: @@
 : unchanged-interval (eigenmonzo) basis: 2.13/7
-{{Optimal ET sequence|legend=1| 53, 118, 171e }}
+{{Optimal ET sequence|legend=0| 53, 118, 171e }}
-Badness: 0.033677
+Badness (Smith): 0.033677
 ===== 17-limit =====
@@ Line 574: / Line 566: @@
 Mapping: {{mapping| 1 0 15 -59 51 56 -91 | 0 1 -8 39 -30 -33 60 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 701.742
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.742{{c}}
 Minimax tuning:
@@ Line 580: / Line 572: @@
 : unchanged-interval (eigenmonzo) basis: 2.17/13
-{{Optimal ET sequence|legend=1| 53, 118, 171e, 289ef, 460eef }}
+{{Optimal ET sequence|legend=0| 53, 118, 171e, 289ef, 460eef }}
-Badness: 0.028891
+Badness (Smith): 0.028891
 ==== Helena ====
@@ Line 591: / Line 583: @@
 Mapping: {{mapping| 1 0 15 -59 51 -28 | 0 1 -8 39 -30 20 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 701.740
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.740{{c}}
-{{Optimal ET sequence|legend=1| 53, 118f, 171ef }}
+{{Optimal ET sequence|legend=0| 53, 118f, 171ef }}
-Badness: 0.036281
+Badness (Smith): 0.036281
 ===== 17-limit =====
@@ Line 604: / Line 596: @@
 Mapping: {{mapping| 1 0 15 -59 51 -28 -91 | 0 1 -8 39 -30 20 60 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 701.730
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.730{{c}}
-{{Optimal ET sequence|legend=1| 53, 118f, 171ef, 289eff }}
+{{Optimal ET sequence|legend=0| 53, 118f, 171ef, 289eff }}
-Badness: 0.030688
+Badness (Smith): 0.030688
 ===== 19-limit =====
@@ Line 617: / Line 609: @@
 Mapping: {{mapping| 1 0 15 -59 51 -28 -91 9 | 0 1 -8 39 -30 20 60 -3 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 701.729
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.729{{c}}
-{{Optimal ET sequence|legend=1| 53, 118f, 171ef, 289effh }}
+{{Optimal ET sequence|legend=0| 53, 118f, 171ef, 289effh }}
-Badness: 0.021892
+Badness (Smith): 0.021892
 === Ponta ===
-The ponta temperament ({{nowrap|53 &amp; 171}}) tempers out the [[540/539|swetisma]] and the ragisma.
+The ponta temperament ({{nowrap| 53 & 171 }}) tempers out the [[540/539|swetisma]] and the ragisma.
 Subgroup: 2.3.5.7.11
@@ Line 632: / Line 624: @@
 Mapping: {{mapping| 1 0 15 -59 135 | 0 1 -8 39 -83 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 701.783
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.783{{c}}
 Minimax tuning:
@@ Line 638: / Line 630: @@
 : unchanged-interval (eigenmonzo) basis: 2.11/7
-{{Optimal ET sequence|legend=1| 53, 171, 224, 1291cde, 1515cde, 1739cddee, 1963cddee, 2187ccddee }}
+{{Optimal ET sequence|legend=0| 53, 171, 224, 1291cde, 1515cde, 1739cddee, 1963cddee, 2187ccddee }}
-Badness: 0.048692
+Badness (Smith): 0.048692
 ==== 13-limit ====
@@ Line 649: / Line 641: @@
 Mapping: {{mapping| 1 0 15 -59 135 56 | 0 1 -8 39 -83 -33 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 701.784
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.784{{c}}
 Minimax tuning:
 * 13 and 15-odd-limit: ~3/2 = {{monzo| 36/61 0 0 1/122 -1/122 }}
-: Unchanged-interval (eigenmonzo) basis: 2.11/7
+: unchanged-interval (eigenmonzo) basis: 2.11/7
-{{Optimal ET sequence|legend=1| 53, 171, 224 }}
+{{Optimal ET sequence|legend=0| 53, 171, 224 }}
-Badness: 0.023616
+Badness (Smith): 0.023616
 ==== 17-limit ====
@@ Line 666: / Line 658: @@
 Mapping: {{mapping| 1 0 15 -59 135 56 -91 | 0 1 -8 39 -83 -33 60 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 701.777
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.777{{c}}
 Minimax tuning:
 * 17-odd-limit: ~3/2 = {{monzo| 83/143 0 0 0 -1/143 0 1/143 }}
-: Unchanged-interval (eigenmonzo) basis: 2.17/11
+: unchanged-interval (eigenmonzo) basis: 2.17/11
-{{Optimal ET sequence|legend=1| 53, 171, 224, 395e, 619eg }}
+{{Optimal ET sequence|legend=0| 53, 171, 224, 395e, 619eg }}
-Badness: 0.022853
+Badness (Smith): 0.022853
 === Pontic ===
-The pontic temperament ({{nowrap|118 &amp; 171}}) tempers out the [[441/440|werckisma]] and the ragisma.
+The pontic temperament ({{nowrap| 118 & 171 }}) tempers out the [[441/440|werckisma]] and the ragisma.
 Subgroup: 2.3.5.7.11
@@ Line 685: / Line 677: @@
 Mapping: {{mapping| 1 0 15 -59 -136 | 0 1 -8 39 88 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 701.724
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.724{{c}}
 Minimax tuning:
@@ Line 691: / Line 683: @@
 : unchanged-interval (eigenmonzo) basis: 2.11
-{{Optimal ET sequence|legend=1| 53e, 118, 289, 407d, 696d }}
+{{Optimal ET sequence|legend=0| 53e, 118, 289, 407d, 696d }}
-Badness: 0.049573
+Badness (Smith): 0.049573
 ==== 13-limit ====
@@ Line 702: / Line 694: @@
 Mapping: {{mapping| 1 0 15 -59 -136 56 | 0 1 -8 39 88 -33 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 701.738
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.738{{c}}
 Minimax tuning:
@@ Line 708: / Line 700: @@
 : unchanged-interval (eigenmonzo) basis: 2.13/11
-{{Optimal ET sequence|legend=1| 53e, 118, 171, 289f, 460ef }}
+{{Optimal ET sequence|legend=0| 53e, 118, 171, 289f, 460ef }}
-Badness: 0.045308
+Badness (Smith): 0.045308
 ===== 17-limit =====
@@ Line 719: / Line 711: @@
 Mapping: {{mapping| 1 0 15 -59 -136 56 -91 | 0 1 -8 39 88 -33 60 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 701.740
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.740{{c}}
 Minimax tuning:
 * 17-odd-limit: ~3/2 = {{monzo| 71/121 0 0 0 1/121 -1/121 }}
-: Unchanged-interval (eigenmonzo) basis: 2.13/11
+: unchanged-interval (eigenmonzo) basis: 2.13/11
-{{Optimal ET sequence|legend=1| 53e, 118, 171, 289f, 460ef }}
+{{Optimal ET sequence|legend=0| 53e, 118, 171, 289f, 460ef }}
-Badness: 0.029618
+Badness (Smith): 0.029618
 ==== Pontoid ====
@@ Line 736: / Line 728: @@
 Mapping: {{mapping| 1 0 15 -59 -136 -215 | 0 1 -8 39 88 138 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 701.735
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.735{{c}}
-{{Optimal ET sequence|legend=1| 53ef, 118f, 171, 289, 460e, 749def }}
+{{Optimal ET sequence|legend=0| 53ef, 118f, 171, 289, 460e, 749def }}
-Badness: 0.050188
+Badness (Smith): 0.050188
 ===== 17-limit =====
@@ Line 749: / Line 741: @@
 Mapping: {{mapping| 1 0 15 -59 -136 -215 -91 | 0 1 -8 39 88 138 60 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 701.735
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.735{{c}}
-{{Optimal ET sequence|legend=1| 53ef, 118f, 171, 289, 460e, 749defg }}
+{{Optimal ET sequence|legend=0| 53ef, 118f, 171, 289, 460e, 749defg }}
-Badness: 0.029383
+Badness (Smith): 0.029383
 === Bipont ===
-The bipont temperament ({{nowrap|118 &amp; 224}}) has a period of half octave and tempers out the [[3025/3024|lehmerisma (3025/3024)]] and the [[9801/9800|kalisma (9801/9800)]].
+The bipont temperament ({{nowrap| 118 & 224 }}) has a period of half octave and tempers out the [[3025/3024|lehmerisma (3025/3024)]] and the [[9801/9800|kalisma (9801/9800)]].
 Subgroup: 2.3.5.7.11
@@ Line 763: / Line 755: @@
 Mapping: {{mapping| 2 0 30 -118 -85 | 0 1 -8 39 29 }}
+: mapping generators: ~99/70, ~3
-: Mapping generators: ~99/70, ~3
+Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~3/2 = 701.757{{c}}
-Optimal tuning (POTE): ~99/70 = 1\2, ~3/2 = 701.757
-{{Optimal ET sequence|legend=1| 106, 118, 224, 342, 1592c, 1934ce, 2276cde, 2618cde, 2960cde }}
+{{Optimal ET sequence|legend=0| 106, 118, 224, 342, 1592c, 1934ce, 2276cde, 2618cde, 2960cde }}
-Badness: 0.014629
+Badness (Smith): 0.014629
 ==== 13-limit ====
@@ Line 779: / Line 770: @@
 Mapping: {{mapping| 2 0 30 -118 -85 112 | 0 1 -8 39 29 -33 }}
-Mapping generators: ~99/70, ~3
+Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~3/2 = 701.773{{c}}
-Optimal tuning (POTE): ~99/70 = 1\2, ~3/2 = 701.773
+{{Optimal ET sequence|legend=0| 106, 118, 224, 566f, 790f }}
-{{Optimal ET sequence|legend=1| 106, 118, 224, 566f, 790f }}
+Badness (Smith): 0.030172
-Badness: 0.030172
 ===== 17-limit =====
@@ Line 794: / Line 783: @@
 Mapping: {{mapping| 2 0 30 -118 -85 112 -182 | 0 1 -8 39 29 -33 60 }}
-Optimal tuning (POTE): ~99/70 = 1\2, ~3/2 = 701.765
+Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~3/2 = 701.765{{c}}
-{{Optimal ET sequence|legend=1| 106g, 118, 224, 342, 566f }}
+{{Optimal ET sequence|legend=0| 106g, 118, 224, 342, 566f }}
-Badness: 0.027051
+Badness (Smith): 0.027051
 ==== Counterbipont ====
@@ Line 807: / Line 796: @@
 Mapping: {{mapping| 2 0 30 -118 -85 -243 | 0 1 -8 39 29 79 }}
-Optimal tuning (POTE): ~99/70 = 1\2, ~3/2 = 701.769
+Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~3/2 = 701.769{{c}}
-{{Optimal ET sequence|legend=1| 106f, 118f, 224, 342f, 566, 1356cf, 1922cff }}
+{{Optimal ET sequence|legend=0| 106f, 118f, 224, 342f, 566, 1356cf, 1922cff }}
-Badness: 0.025547
+Badness (Smith): 0.025547
 ===== 17-limit =====
@@ Line 820: / Line 809: @@
 Mapping: {{mapping| 2 0 30 -118 -85 -243 -182 | 0 1 -8 39 29 79 60 }}
-Optimal tuning (POTE): ~99/70 = 1\2, ~3/2 = 701.764
+Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~3/2 = 701.764{{c}}
-{{Optimal ET sequence|legend=1| 106fg, 118f, 224, 342f, 566, 908fg, 1474cffgg }}
+{{Optimal ET sequence|legend=0| 106fg, 118f, 224, 342f, 566, 908fg, 1474cffgg }}
-Badness: 0.025251
+Badness (Smith): 0.025251
 ===== 19-limit =====
@@ Line 833: / Line 822: @@
 Mapping: {{mapping| 2 0 30 -118 -85 -243 -182 -169 | 0 1 -8 39 29 79 60 56 }}
-Optimal tuning (POTE): ~99/70 = 1\2, ~3/2 = 701.761
+Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~3/2 = 701.761{{c}}
-{{Optimal ET sequence|legend=1| 106fgh, 118f, 224, 342f, 566h, 908fgh }}
+{{Optimal ET sequence|legend=0| 106fgh, 118f, 224, 342f, 566h, 908fgh }}
-Badness: 0.022267
+Badness (Smith): 0.022267
 ==== Quadrapont ====
@@ Line 845: / Line 834: @@
 Mapping: {{mapping| 4 0 60 -236 -170 -131 | 0 1 -8 39 29 23 }}
+: mapping generators: ~208/175, ~3
-: Mapping generators: ~208/175, ~3
+Optimal tuning (POTE): ~208/175 = 300.000{{c}}, ~3/2 = 701.756{{c}}
-Optimal tuning (POTE): ~208/175 = 1\4, ~3/2 = 701.756
-{{Optimal ET sequence|legend=1| 224, 460, 684, 2276cde, 2960cde, 3644bccddee }}
+{{Optimal ET sequence|legend=0| 224, 460, 684, 2276cde, 2960cde, 3644bccddee }}
-Badness: 0.021025
+Badness (Smith): 0.021025
 == Grackle ==
@@ Line 862: / Line 850: @@
 {{Mapping|legend=1| 1 0 15 44 | 0 1 -8 -26 }}
+: mapping generators: ~2, ~3
-: Mapping generators: ~2, ~3
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~3/2 = 701.239{{c}}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 701.239
 [[Minimax tuning]]:
@@ Line 873: / Line 860: @@
 {{Optimal ET sequence|legend=1| 12, 53d, 65, 77, 166c, 243c }}
-[[Badness]]: 0.070407
+[[Badness]] (Smith): 0.070407
 === 11-limit ===
@@ Line 882: / Line 869: @@
 Mapping: {{mapping| 1 0 15 44 70 | 0 1 -8 -26 -42 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 701.172
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.172{{c}}
-{{Optimal ET sequence|legend=1| 12, 53dee, 65e, 77, 89, 166c, 255c }}
+{{Optimal ET sequence|legend=0| 12, 53dee, 65e, 77, 89, 166c, 255c }}
-Badness: 0.048887
+Badness (Smith): 0.048887
 ==== 13-limit ====
@@ Line 895: / Line 882: @@
 Mapping: {{mapping| 1 0 15 44 70 75 | 0 1 -8 -26 -42 -45 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 701.226
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.226{{c}}
-{{Optimal ET sequence|legend=1| 12f, 53deeff, 65ef, 77, 166cf, 243cf }}
+{{Optimal ET sequence|legend=0| 12f, 53deeff, 65ef, 77, 166cf, 243cf }}
-Badness: 0.037859
+Badness (Smith): 0.037859
 ===== 17-limit =====
@@ Line 908: / Line 895: @@
 Mapping: {{mapping| 1 0 15 44 70 75 -7 | 0 1 -8 -26 -42 -45 7 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 701.206
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.206{{c}}
-{{Optimal ET sequence|legend=1| 12f, 53deeff, 65ef, 77, 89f, 166cf }}
+{{Optimal ET sequence|legend=0| 12f, 53deeff, 65ef, 77, 89f, 166cf }}
-Badness: 0.029864
+Badness (Smith): 0.029864
 ===== 19-limit =====
@@ Line 921: / Line 908: @@
 Mapping: {{mapping| 1 0 15 44 70 75 -7 9 | 0 1 -8 -26 -42 -45 7 -3 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 701.217
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.217{{c}}
-{{Optimal ET sequence|legend=1| 12f, 53deeff, 65ef, 77, 166cf }}
+{{Optimal ET sequence|legend=0| 12f, 53deeff, 65ef, 77, 166cf }}
-Badness: 0.023096
+Badness (Smith): 0.023096
 ==== Grackloid ====
@@ Line 934: / Line 921: @@
 Mapping: {{mapping| 1 0 15 44 70 -47 | 0 1 -8 -26 -42 32 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 701.217
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.217{{c}}
-{{Optimal ET sequence|legend=1| 12, 53deef, 65e, 77, 166c }}
+{{Optimal ET sequence|legend=0| 12, 53deef, 65e, 77, 166c }}
-Badness: 0.048511
+Badness (Smith): 0.048511
 === Grack ===
@@ Line 947: / Line 934: @@
 Mapping: {{mapping| 1 0 15 44 51 | 0 1 -8 -26 -30 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 701.401
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.401{{c}}
-{{Optimal ET sequence|legend=1| 12, 53d, 65, 77e, 142de }}
+{{Optimal ET sequence|legend=0| 12, 53d, 65, 77e, 142de }}
-Badness: 0.055908
+Badness (Smith): 0.055908
 ==== 13-limit ====
@@ Line 960: / Line 947: @@
 Mapping: {{mapping| 1 0 15 44 51 75 | 0 1 -8 -26 -30 -45 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 701.348
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.348{{c}}
-{{Optimal ET sequence|legend=1| 12f, 53dff, 65f, 77e }}
+{{Optimal ET sequence|legend=0| 12f, 53dff, 65f, 77e }}
-Badness: 0.044458
+Badness (Smith): 0.044458
 ==== Catahelenic ====
@@ Line 973: / Line 960: @@
 Mapping: {{mapping| 1 0 15 44 51 56 | 0 1 -8 -26 -30 -33 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 701.529
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.529{{c}}
-{{Optimal ET sequence|legend=1| 12f, 53df, 65 }}
+{{Optimal ET sequence|legend=0| 12f, 53df, 65 }}
-Badness: 0.048524
+Badness (Smith): 0.048524
 == Bischismic ==
@@ Line 985: / Line 972: @@
 {{Mapping|legend=1| 2 0 30 69 | 0 1 -8 -20 }}
+: mapping generators: ~567/400, ~3
-: Mapping generators: ~567/400, ~3
+[[Optimal tuning]] ([[CTE]]): ~567/400 = 600.0000{{c}}, ~3/2 = 701.5899{{c}}
-[[Optimal tuning]] ([[CTE]]): ~567/400 = 1\2, ~3/2 = 701.5899
 [[Minimax tuning]]:
@@ Line 996: / Line 982: @@
 {{Optimal ET sequence|legend=1| 12, 106d, 118, 130, 248, 378 }}
-[[Badness]]: 0.054744
+[[Badness]] (Smith): 0.054744
 === 11-limit ===
@@ Line 1,005: / Line 991: @@
 Mapping: {{mapping| 2 0 30 69 102 | 0 1 -8 -20 -30 }}
-Optimal tuning (CTE): ~99/70 = 1\2, ~3/2 = 701.6077
+Optimal tuning (CTE): ~99/70 = 600.0000{{c}}, ~3/2 = 701.6077{{c}}
-{{Optimal ET sequence|legend=1| 12, 106de, 118, 130, 248 }}
+{{Optimal ET sequence|legend=0| 12, 106de, 118, 130, 248 }}
-Badness: 0.028160
+Badness (Smith): 0.028160
 ==== 13-limit ====
@@ Line 1,018: / Line 1,004: @@
 Mapping: {{mapping| 2 0 30 69 102 -75 | 0 1 -8 -20 -30 26 }}
-Optimal tuning (CTE): ~99/70 = 1\2, ~3/2 = 701.5949
+Optimal tuning (CTE): ~99/70 = 600.0000{{c}}, ~3/2 = 701.5949{{c}}
-{{Optimal ET sequence|legend=1| 12, 106def, 118, 130, 248, 378 }}
+{{Optimal ET sequence|legend=0| 12, 106def, 118, 130, 248, 378 }}
-Badness: 0.028722
+Badness (Smith): 0.028722
 ===== 17-limit =====
@@ Line 1,031: / Line 1,017: @@
 Mapping: {{mapping| 2 0 30 69 102 -75 5 | 0 1 -8 -20 -30 26 1 }}
-Optimal tuning (CTE): ~99/70 = 1\2, ~3/2 = 701.5959
+Optimal tuning (CTE): ~99/70 = 600.0000{{c}}, ~3/2 = 701.5959{{c}}
-{{Optimal ET sequence|legend=1| 12, 106def, 118, 130, 248g }}
+{{Optimal ET sequence|legend=0| 12, 106def, 118, 130, 248g }}
-Badness: 0.029340
+Badness (Smith): 0.029340
 ==== Bischis ====
@@ Line 1,044: / Line 1,030: @@
 Mapping: {{mapping| 2 0 30 69 102 131 | 0 1 -8 -20 -30 -39 }}
-Optimal tuning (CTE): ~55/39 = 1\2, ~3/2 = 701.5708
+Optimal tuning (CTE): ~55/39 = 600.0000{{c}}, ~3/2 = 701.5708{{c}}
-{{Optimal ET sequence|legend=1| 12f, 106deff, 118f, 130 }}
+{{Optimal ET sequence|legend=0| 12f, 106deff, 118f, 130 }}
-Badness: 0.029321
+Badness (Smith): 0.029321
 ===== 17-limit =====
@@ Line 1,057: / Line 1,043: @@
 Mapping: {{mapping| 2 0 30 69 102 131 5 | 0 1 -8 -20 -30 -39 1 }}
-Optimal tuning (CTE): ~55/39 = 1\2, ~3/2 = 701.5717
+Optimal tuning (CTE): ~55/39 = 600.0000{{c}}, ~3/2 = 701.5717{{c}}
-{{Optimal ET sequence|legend=1| 12f, 106deff, 118f, 130, 248fg }}
+{{Optimal ET sequence|legend=0| 12f, 106deff, 118f, 130, 248fg }}
-Badness: 0.026894
+Badness (Smith): 0.026894
 == Kleischismic ==
@@ Line 1,069: / Line 1,055: @@
 {{Mapping|legend=1| 2 1 22 -15 | 0 2 -16 19 }}
+: mapping generators: ~1225/864, ~35/24
-: Mapping generators: ~1225/864, ~35/24
+[[Optimal tuning]] ([[POTE]]): ~1225/864 = 600.000{{c}}, ~35/24 = 650.920{{c}} (~36/35 = 50.920{{c}})
-[[Optimal tuning]] ([[POTE]]): ~1225/864 = 1\2, ~35/24 = 650.920 (~36/35 = 50.920)
 {{Optimal ET sequence|legend=1| 24, 70c, 94, 118, 212, 330, 542d, 872cd }}
-[[Badness]]: 0.110583
+[[Badness]] (Smith): 0.110583
 === 11-limit ===
@@ Line 1,085: / Line 1,070: @@
 Mapping: {{mapping| 2 1 22 -15 8 | 0 2 -16 19 -1 }}
-Optimal tuning (POTE): ~99/70 = 1\2, ~35/24 = 650.918 (~36/35 = 50.918)
+Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~35/24 = 650.918{{c}} (~36/35 = 50.918{{c}})
-{{Optimal ET sequence|legend=1| 24, 70c, 94, 118, 212, 330e, 542de }}
+{{Optimal ET sequence|legend=0| 24, 70c, 94, 118, 212, 330e, 542de }}
-Badness: 0.036749
+Badness (Smith): 0.036749
 ==== 13-limit ====
@@ Line 1,098: / Line 1,083: @@
 Mapping: {{mapping| 2 1 22 -15 8 15 | 0 2 -16 19 -1 -7 }}
-Optimal tuning (POTE): ~99/70 = 1\2, ~35/24 = 650.938 (~36/35 = 50.938)
+Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~35/24 = 650.938{{c}} (~36/35 = 50.938{{c}})
-{{Optimal ET sequence|legend=1| 24, 70c, 94, 118, 212f }}
+{{Optimal ET sequence|legend=0| 24, 70c, 94, 118, 212f }}
-Badness: 0.037640
+Badness (Smith): 0.037640
 ===== 17-limit =====
@@ Line 1,111: / Line 1,096: @@
 Mapping: {{mapping| 2 1 22 -15 8 15 6 | 0 2 -16 19 -1 -7 2 }}
-Optimal tuning (POTE): ~99/70 = 1\2, ~35/24 = 650.942 (~36/35 = 50.942)
+Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~35/24 = 650.942{{c}} (~36/35 = 50.942{{c}})
-{{Optimal ET sequence|legend=1| 24, 70c, 94, 118, 212fg }}
+{{Optimal ET sequence|legend=0| 24, 70c, 94, 118, 212fg }}
-Badness: 0.025615
+Badness (Smith): 0.025615
 ==== Kleischis ====
@@ Line 1,124: / Line 1,109: @@
 Mapping: {{mapping| 2 1 22 -15 8 -36 | 0 2 -16 19 -1 40 }}
-Optimal tuning (POTE): ~99/70 = 1\2, ~35/24 = 650.951 (~36/35 = 50.951)
+Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~35/24 = 650.951{{c}} (~36/35 = 50.951{{c}})
-{{Optimal ET sequence|legend=1| 24f, 70cf, 94, 118f, 212 }}
+{{Optimal ET sequence|legend=0| 24f, 70cf, 94, 118f, 212 }}
-Badness: 0.037607
+Badness (Smith): 0.037607
 ===== 17-limit =====
@@ Line 1,137: / Line 1,122: @@
 Mapping: {{mapping| 2 1 22 -15 8 -36 6 | 0 2 -16 19 -1 40 2 }}
-Optimal tuning (POTE): ~99/70 = 1\2, ~35/24 = 650.948 (~36/35 = 50.948)
+Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~35/24 = 650.948{{c}} (~36/35 = 50.948{{c}})
-{{Optimal ET sequence|legend=1| 24f, 70cf, 94, 118f, 212g }}
+{{Optimal ET sequence|legend=0| 24f, 70cf, 94, 118f, 212g }}
-Badness: 0.024734
+Badness (Smith): 0.024734
 == Hemischis ==
@@ Line 1,149: / Line 1,134: @@
 {{Mapping|legend=1| 1 0 15 -17 | 0 2 -16 25 }}
+: mapping generators: ~2, ~140/81
-: Mapping generators: ~2, ~140/81
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~140/81 = 950.797{{c}}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~140/81 = 950.797
 {{Optimal ET sequence|legend=1| 24, 53, 130, 183, 313 }}
-[[Badness]]: 0.045817
+[[Badness]] (Smith): 0.045817
 === 2.3.5.7.13.19.23 subgroup ===
@@ Line 1,165: / Line 1,149: @@
 Mapping: {{mapping| 1 0 15 -17 14 9 -24 | 0 2 -16 25 -13 -6 36 }}
-Optimal tuning (POTE): ~2 = 1\1, ~26/15 = 950.783
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~26/15 = 950.783{{c}}
-{{Optimal ET sequence|legend=1| 24i, 53, 130 }}
+{{Optimal ET sequence|legend=0| 24i, 53, 130 }}
 Badness (Sintel): 0.583
@@ Line 1,178: / Line 1,162: @@
 Mapping: {{mapping| 1 0 15 -17 51 | 0 2 -16 25 -60 }}
-Optimal tuning (POTE): ~2 = 1\1, ~140/81 = 950.801
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~140/81 = 950.801{{c}}
-{{Optimal ET sequence|legend=1| 24e, 53, 130, 183, 313 }}
+{{Optimal ET sequence|legend=0| 24e, 53, 130, 183, 313 }}
-Badness: 0.036289
+Badness (Smith): 0.036289
 === 13-limit ===
@@ Line 1,193: / Line 1,177: @@
 Mapping: {{mapping| 1 0 15 -17 51 14 | 0 2 -16 25 -60 -13 }}
-Optimal tuning (POTE): ~2 = 1\1, ~26/15 = 950.801
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~26/15 = 950.801{{c}}
-{{Optimal ET sequence|legend=1| 24e, 53, 130, 183, 313 }}
+{{Optimal ET sequence|legend=0| 24e, 53, 130, 183, 313 }}
-Badness: 0.020816
+Badness (Smith): 0.020816
 === 17-limit ===
@@ Line 1,206: / Line 1,190: @@
 Mapping: {{mapping| 1 0 15 -17 51 14 -49 | 0 2 -16 25 -60 -13 67 }}
-Optimal tuning (POTE): ~2 = 1\1, ~26/15 = 950.810
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~26/15 = 950.810{{c}}
-{{Optimal ET sequence|legend=1| 53, 130, 183, 496d }}
+{{Optimal ET sequence|legend=0| 53, 130, 183, 496d }}
-Badness: 0.021073
+Badness (Smith): 0.021073
 === 19-limit ===
@@ Line 1,219: / Line 1,203: @@
 Mapping: {{mapping| 1 0 15 -17 51 14 -49 9 | 0 2 -16 25 -60 -13 67 -6 }}
-Optimal tuning (POTE): ~2 = 1\1, ~26/15 = 950.809
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~26/15 = 950.809{{c}}
-{{Optimal ET sequence|legend=1| 53, 130, 183, 313h }}
+{{Optimal ET sequence|legend=0| 53, 130, 183, 313h }}
-Badness : 0.018262
+Badness (Smith): 0.018262
 === 23-limit ===
@@ Line 1,232: / Line 1,216: @@
 Mapping: {{mapping| 1 0 15 -17 51 14 -49 9 -24 | 0 2 -16 25 -60 -13 67 -6 36 }}
-Optimal tuning (POTE): ~2 = 1\1, ~26/15 = 950.807
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~26/15 = 950.807{{c}}
-{{Optimal ET sequence|legend=1| 53, 130, 183, 313h }}
+{{Optimal ET sequence|legend=0| 53, 130, 183, 313h }}
-Badness (Sintel): 0.014819
+Badness (Smith): 0.014819
 ; Music
@@ Line 1,242: / Line 1,226: @@
 == Squirrel ==
-The squirrel temperament ({{nowrap|29 &amp; 36}}) has a ~11/10 generator, three of which give the fourth (~4/3), and thirteen of which give 7/4 with octave reduction.
+The squirrel temperament ({{nowrap| 29 & 36 }}) has a ~11/10 generator, three of which give the fourth (~4/3), and thirteen of which give 7/4 with octave reduction.
 [[Subgroup]]: 2.3.5.7
@@ Line 1,250: / Line 1,234: @@
 {{Mapping|legend=1| 1 2 -1 1 | 0 -3 24 13 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~160/147 = 166.140
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~160/147 = 166.140{{c}}
 {{Optimal ET sequence|legend=1| 29, 36, 65 }}
-[[Badness]]: 0.174705
+[[Badness]] (Smith): 0.174705
 === 11-limit ===
@@ Line 1,263: / Line 1,247: @@
 Mapping: {{mapping| 1 2 -1 1 0 | 0 -3 24 13 25 }}
-Optimal tuning (POTE): ~2 = 1\1, ~11/10 = 166.097
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/10 = 166.097{{c}}
-{{Optimal ET sequence|legend=1| 29, 36, 65 }}
+{{Optimal ET sequence|legend=0| 29, 36, 65 }}
-Badness: 0.068310
+Badness (Smith): 0.068310
 === 13-limit ===
@@ Line 1,276: / Line 1,260: @@
 Mapping: {{mapping| 1 2 -1 1 0 3 | 0 -3 24 13 25 5 }}
-Optimal tuning (POTE): ~2 = 1\1, ~11/10 = 166.054
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/10 = 166.054{{c}}
-{{Optimal ET sequence|legend=1| 29, 36, 65f, 94df, 159df }}
+{{Optimal ET sequence|legend=0| 29, 36, 65f, 94df, 159df }}
-Badness: 0.043750
+Badness (Smith): 0.043750
 == Tertiaschis ==
-The tertiaschis temperament ({{nowrap|94 &amp; 159}}) has a ~11/10 generator, sharing the same 2.3.5.11 subgroup with [[#Squirrel]], but tempers out 1071875/1062882 for prime 7.
+The tertiaschis temperament ({{nowrap| 94 & 159 }}) has a ~11/10 generator, sharing the same 2.3.5.11 subgroup with [[#Squirrel]], but tempers out 1071875/1062882 for prime 7.
 [[Subgroup]]: 2.3.5.7
@@ Line 1,291: / Line 1,275: @@
 {{Mapping|legend=1| 1 2 -1 10 | 0 -3 24 -52 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~192/175 = 166.019
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~192/175 = 166.019{{c}}
 {{Optimal ET sequence|legend=1| 65, 94, 159, 253, 412cd }}
-[[Badness]]: 0.211859
+[[Badness]] (Smith): 0.211859
 === 11-limit ===
@@ Line 1,304: / Line 1,288: @@
 Mapping: {{mapping| 1 2 -1 10 0 | 0 -3 24 -52 25 }}
-Optimal tuning (POTE): ~2 = 1\1, ~11/10 = 166.017
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/10 = 166.017{{c}}
-{{Optimal ET sequence|legend=1| 65, 94, 159, 253, 412cd }}
+{{Optimal ET sequence|legend=0| 65, 94, 159, 253, 412cd }}
-Badness: 0.061336
+Badness (Smith): 0.061336
 === 13-limit ===
@@ Line 1,317: / Line 1,301: @@
 Mapping: {{mapping| 1 2 -1 10 0 12 | 0 -3 24 -52 25 -60 }}
-Optimal tuning (POTE): ~2 = 1\1, ~11/10 = 166.016
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/10 = 166.016{{c}}
-{{Optimal ET sequence|legend=1| 65f, 94, 159, 253, 412cdf, 665ccdef }}
+{{Optimal ET sequence|legend=0| 65f, 94, 159, 253, 412cdf, 665ccdef }}
-Badness: 0.036700
+Badness (Smith): 0.036700
 === 17-limit ===
@@ Line 1,330: / Line 1,314: @@
 Mapping: {{mapping| 1 2 -1 10 0 12 -2 | 0 -3 24 -52 25 -60 44 }}
-Optimal tuning (POTE): ~2 = 1\1, ~11/10 = 166.012
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/10 = 166.012{{c}}
 {{Optimal ET sequence|legend=1| 65f, 94, 159, 253 }}
-Badness: 0.026504
+Badness (Smith): 0.026504
 == Countertertiaschis ==
-The countertertiaschis temperament ({{nowrap|159 &amp; 224}}) has a ~11/10 generator, sharing the same 2.3.5.11 subgroup with [[#Squirrel]], but tempers out 244140625/243045684 for prime 7.
+The countertertiaschis temperament ({{nowrap| 159 & 224 }}) has a ~11/10 generator, sharing the same 2.3.5.11 subgroup with [[#Squirrel]], but tempers out 244140625/243045684 for prime 7.
 [[Subgroup]]: 2.3.5.7
@@ Line 1,345: / Line 1,329: @@
 {{Mapping|legend=1| 1 2 -1 -12 | 0 -3 24 107 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~625/567 = 166.0621
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~625/567 = 166.0621{{c}}
 {{Optimal ET sequence|legend=1| 65d, 159, 224, 383, 607 }}
-[[Badness]]: 0.188043
+[[Badness]] (Smith): 0.188043
 === 11-limit ===
@@ Line 1,358: / Line 1,342: @@
 Mapping: {{mapping| 1 2 -1 -12 0 | 0 -3 24 107 25 }}
-Optimal tuning (POTE): ~2 = 1\1, ~11/10 = 166.0628
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/10 = 166.0628{{c}}
-{{Optimal ET sequence|legend=1| 65d, 159, 224, 383, 607 }}
+{{Optimal ET sequence|legend=0| 65d, 159, 224, 383, 607 }}
-Badness: 0.048943
+Badness (Smith): 0.048943
 === 13-limit ===
@@ Line 1,371: / Line 1,355: @@
 Mapping: {{mapping| 1 2 -1 -12 0 -10 | 0 -3 24 107 25 99 }}
-Optimal tuning (POTE): ~2 = 1\1, ~11/10 = 166.0628
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/10 = 166.0628{{c}}
-{{Optimal ET sequence|legend=1| 65d, 159, 224, 383, 607 }}
+{{Optimal ET sequence|legend=0| 65d, 159, 224, 383, 607 }}
-Badness: 0.024506
+Badness (Smith): 0.024506
 == Pogo ==
 {{See also| Stearnsmic clan #Pogo }}
-The pogo temperament ({{nowrap|94 &amp; 130}}) splits the period in two to address the difference between [[#Tertiaschis]] and [[#Countertertiaschis]]. The schismic tempering of the fifth is just about right for tempering out the stearnsma.
+The pogo temperament ({{nowrap| 94 & 130 }}) splits the period in two to address the difference between [[#Tertiaschis]] and [[#Countertertiaschis]]. The schismic tempering of the fifth is just about right for tempering out the stearnsma.
 [[Subgroup]]: 2.3.5.7
@@ Line 1,387: / Line 1,371: @@
 {{Mapping|legend=1| 2 1 22 2 | 0 3 -24 5 }}
+: mapping generators: ~343/243, ~9/7
-: Mapping generators: ~343/243, ~9/7
+[[Optimal tuning]] ([[POTE]]): ~343/243 = 600.000{{c}}, ~9/7 = 433.901{{c}}
-[[Optimal tuning]] ([[POTE]]): ~343/243 = 1\2, ~9/7 = 433.901
 {{Optimal ET sequence|legend=1| 36, 94, 130, 224, 354 }}
-[[Badness]]: 0.079635
+[[Badness]] (Smith): 0.079635
 === 11-limit ===
@@ Line 1,403: / Line 1,386: @@
 Mapping: {{mapping| 2 1 22 2 25 | 0 3 -24 5 -25 }}
-Optimal tuning (POTE): ~99/70 = 1\2, ~9/7 = 433.911
+Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~9/7 = 433.911{{c}}
-{{Optimal ET sequence|legend=1| 36, 94, 130, 224, 354, 578 }}
+{{Optimal ET sequence|legend=0| 36, 94, 130, 224, 354, 578 }}
-Badness: 0.031857
+Badness (Smith): 0.031857
 === 13-limit ===
@@ Line 1,416: / Line 1,399: @@
 Mapping: {{mapping| 2 1 22 2 25 -2 | 0 3 -24 5 -25 13 }}
-Optimal tuning (POTE): ~99/70 = 1\2, ~9/7 = 433.911
+Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~9/7 = 433.911{{c}}
-{{Optimal ET sequence|legend=1| 36, 94, 130, 224, 354, 578 }}
+{{Optimal ET sequence|legend=0| 36, 94, 130, 224, 354, 578 }}
-Badness: 0.017514
+Badness (Smith): 0.017514
 == Term ==
-Term tempers out the [[landscape comma]], mapping ~63/50 to the 1/3-octave period. It can be described as {{nowrap|12 &amp; 171}}, and is the unique temperament that equates a syntonic~Pythagorean comma with a stack of three [[marvel comma]]s. A [[septimal comma]] is then found as a stack of four marvel commas. In some 7-limit adaptive-tuning practice, the marvel comma corresponds to a melodic unit called a [[kleisma]], with three kleismas making a comma, so this temperament may be useful for modeling that. [[171edo]] makes for an excellent tuning.
+Term tempers out the [[landscape comma]], mapping ~63/50 to the 1/3-octave period. It can be described as {{nowrap|12 & 171}}, and is the unique temperament that equates a syntonic~Pythagorean comma with a stack of three [[marvel comma]]s. A [[septimal comma]] is then found as a stack of four marvel commas. In some 7-limit adaptive-tuning practice, the marvel comma corresponds to a melodic unit called a [[kleisma]], with three kleismas making a comma, so this temperament may be useful for modeling that. [[171edo]] makes for an excellent tuning.
 [[Subgroup]]: 2.3.5.7
@@ Line 1,430: / Line 1,413: @@
 {{Mapping|legend=1| 3 0 45 94 | 0 1 -8 -18 }}
+: mapping generators: ~63/50, ~3
-: Mapping generators: ~63/50, ~3
+[[Optimal tuning]] ([[POTE]]): ~63/50 = 400.000{{c}}, ~3/2 = 701.742{{c}}
-[[Optimal tuning]] ([[POTE]]): ~63/50 = 1＼3, ~3/2 = 701.742
 [[Minimax tuning]]:
@@ Line 1,441: / Line 1,423: @@
 {{Optimal ET sequence|legend=1| 12, 147d, 159, 171, 867, 1038, 1209, 1380, 1551, 1722 }}
-[[Badness]]: 0.019950
+[[Badness]] (Smith): 0.019950
 === Terminal ===
-The terminal temperament ({{nowrap|12 &amp; 159}}) tempers out 441/440 and 4375/4356. In this temperament, 44/35 and 63/50 are represented as one period of 1/3 octave.
+The terminal temperament ({{nowrap| 12 & 159 }}) tempers out 441/440 and 4375/4356. In this temperament, 44/35 and 63/50 are represented as one period of 1/3 octave.
 Subgroup: 2.3.5.7.11
@@ Line 1,452: / Line 1,434: @@
 Mapping: {{mapping| 3 0 45 94 134 | 0 1 -8 -18 -26 }}
-Optimal tuning (POTE): ~44/35 = 1＼3, ~3/2 = 701.824
+Optimal tuning (POTE): ~44/35 = 400.000{{c}}, ~3/2 = 701.824{{c}}
 {{Optimal ET sequence|legend=0| 12, 147de, 159, 330 }}
-Badness: 0.059502
+Badness (Smith): 0.059502
 ==== 13-limit ====
@@ Line 1,465: / Line 1,447: @@
 Mapping: {{mapping| 3 0 45 94 134 168 | 0 1 -8 -18 -26 -33 }}
-Optimal tuning (POTE): ~44/35 = 1＼3, ~3/2 = 701.821
+Optimal tuning (POTE): ~44/35 = 400.000{{c}}, ~3/2 = 701.821{{c}}
 {{Optimal ET sequence|legend=0| 12f, 147def, 159, 330 }}
-Badness: 0.037082
+Badness (Smith): 0.037082
 ==== 17-limit ====
@@ Line 1,478: / Line 1,460: @@
 Mapping: {{mapping| 3 0 45 94 134 168 -2 | 0 1 -8 -18 -26 -33 3 }}
-Optimal tuning (POTE): ~34/27 = 1＼3, ~3/2 = 701.810
+Optimal tuning (POTE): ~34/27 = 400.000{{c}}, ~3/2 = 701.810{{c}}
 {{Optimal ET sequence|legend=0| 12f, 147def, 159, 171, 330 }}
-Badness: 0.027073
+Badness (Smith): 0.027073
 === Terminator ===
@@ Line 1,491: / Line 1,473: @@
 Mapping: {{mapping| 3 0 45 94 -137 | 0 1 -8 -18 31 }}
-Optimal tuning (POTE): ~63/50 = 1＼3, ~3/2 = 701.685
+Optimal tuning (POTE): ~63/50 = 400.000{{c}}, ~3/2 = 701.685{{c}}
 {{Optimal ET sequence|legend=0| 12e, 159e, 171, 183, 354, 537, 891de }}
-Badness: 0.066968
+Badness (Smith): 0.066968
 ==== 13-limit ====
@@ Line 1,504: / Line 1,486: @@
 Mapping: {{mapping| 3 0 45 94 -137 -103 | 0 1 -8 -18 31 24 }}
-Optimal tuning (POTE): ~63/50 = 1＼3, ~3/2 = 701.689
+Optimal tuning (POTE): ~63/50 = 400.000{{c}}, ~3/2 = 701.689{{c}}
 {{Optimal ET sequence|legend=0| 171, 183, 354, 891de, 1245dee, 1599ddee }}
-Badness: 0.035487
+Badness (Smith): 0.035487
 ==== 17-limit ====
@@ Line 1,517: / Line 1,499: @@
 Mapping: {{mapping| 3 0 45 94 -137 -103 -2 | 0 1 -8 -18 31 24 3 }}
-Optimal tuning (POTE): ~63/50 = 1＼3, ~3/2 = 701.688
+Optimal tuning (POTE): ~63/50 = 400.000{{c}}, ~3/2 = 701.688{{c}}
 {{Optimal ET sequence|legend=0| 171, 183, 354, 891de, 1245dee, 1599ddee }}
-Badness: 0.020434
+Badness (Smith): 0.020434
 === Semiterm ===
-The semiterm temperament ({{nowrap|12 &amp; 342}}) has a period of 1/6 octave and tempers out [[9801/9800]] (kalisma) and 151263/151250 (odiheim comma).
+The semiterm temperament ({{nowrap| 12 & 342 }}) has a period of 1/6 octave and tempers out [[9801/9800]] (kalisma) and 151263/151250 (odiheim comma).
 Subgroup: 2.3.5.7.11
@@ Line 1,531: / Line 1,513: @@
 Mapping: {{mapping| 6 0 90 188 287 | 0 1 -8 -18 -28 }}
+: mapping generators: ~55/49, ~3
-: Mapping generators: ~55/49, ~3
+Optimal tuning (POTE): ~55/49 = 200.0000{{c}}, ~3/2 = 701.7460{{c}}
-Optimal tuning (POTE): ~55/49 = 1＼6, ~3/2 = 701.7460
 {{Optimal ET sequence|legend=0| 12, 330e, 342, 1380, 1722, 2064, 2406c }}
-Badness: 0.029438
+Badness (Smith): 0.029438
 ==== 13-limit ====
@@ Line 1,547: / Line 1,528: @@
 Mapping: {{mapping| 6 0 90 188 287 355 | 0 1 -8 -18 -28 -35 }}
-Optimal tuning (POTE): ~55/49 = 1＼6, ~3/2 = 701.7256
+Optimal tuning (POTE): ~55/49 = 200.0000{{c}}, ~3/2 = 701.7256{{c}}
 {{Optimal ET sequence|legend=0| 12f, 330eff, 342f, 696f }} *
@@ Line 1,553: / Line 1,534: @@
 <nowiki>*</nowiki> optimal patent val: [[354edo|354]]
-Badness: 0.044657
+Badness (Smith): 0.044657
 === Hemiterm ===
@@ Line 1,561: / Line 1,542: @@
 Mapping: {{mapping| 3 0 45 94 8 | 0 2 -16 -36 1 }}
 : mapping generators: ~63/50, ~693/400
-Optimal tuning (POTE): ~63/50 = 1＼3, ~693/400 = 950.872 (~12/11 = 150.872)
+Optimal tuning (POTE): ~63/50 = 400.000{{c}}, ~693/400 = 950.872{{c}} (~12/11 = 150.872{{c}})
 {{Optimal ET sequence|legend=0| 24d, 159, 183, 342, 1209, 1551, 1893e, 2235ce }}
-Badness: 0.020687
+Badness (Smith): 0.020687
 ==== 13-limit ====
@@ Line 1,577: / Line 1,557: @@
 Mapping: {{mapping| 3 0 45 94 8 42 | 0 2 -16 -36 1 -13 }}
-Optimal tuning (POTE): ~63/50 = 1＼3, ~26/15 = 950.873 (~12/11 = 150.873)
+Optimal tuning (POTE): ~63/50 = 400.000{{c}}, ~26/15 = 950.873{{c}} (~12/11 = 150.873{{c}})
 {{Optimal ET sequence|legend=0| 24d, 159, 183, 342f }}
-Badness: 0.031362
+Badness (Smith): 0.031362
 ==== 17-limit ====
@@ Line 1,590: / Line 1,570: @@
 Mapping: {{mapping| 3 0 45 94 8 42 -2 | 0 2 -16 -36 1 -13 6 }}
-Optimal tuning (POTE): ~34/27 = 1＼3, ~26/15 = 950.867 (~12/11 = 150.867)
+Optimal tuning (POTE): ~34/27 = 400.000{{c}}, ~26/15 = 950.867{{c}} (~12/11 = 150.867{{c}})
 {{Optimal ET sequence|legend=0| 24d, 159, 183, 342f, 525f, 867ff }}
-Badness: 0.022316
+Badness (Smith): 0.022316
 == Altinex ==
@@ Line 1,602: / Line 1,582: @@
 {{Mapping|legend=1| 3 0 45 -32 | 0 2 -16 17 }}
 : mapping generators: ~1536/1225, ~34300/19683
-[[Optimal tuning]] ([[CTE]]): ~1536/1225 = 1＼3, ~34300/19683 = 950.9654
+[[Optimal tuning]] ([[CTE]]): ~1536/1225 = 400.000{{c}}, ~34300/19683 = 950.9654{{c}}
 {{Optimal ET sequence|legend=1| 24, …, 111c, 135, 159, 612ccdd, 771ccdd }}
-[[Badness]]: 0.422026
+[[Badness]] (Smith): 0.422026
 === 11-limit ===
@@ Line 1,618: / Line 1,597: @@
 Mapping: {{mapping| 3 0 45 -32 8 | 0 2 -16 17 1 }}
-Optimal tuning (CTE): ~44/35 = 1＼3, ~121/70 = 950.9658
+Optimal tuning (CTE): ~44/35 = 400.000{{c}}, ~121/70 = 950.9658{{c}}
-Optimal ET sequence: {{Optimal ET sequence| 24, …, 111c, 135, 159, 612ccdd, 771ccdd }}
+{{Optimal ET sequence|legend=0| 24, …, 111c, 135, 159, 612ccdd, 771ccdd }}
-Badness: 0.101224
+Badness (Smith): 0.101224
 === 13-limit ===
@@ Line 1,631: / Line 1,610: @@
 Mapping: {{mapping| 3 0 45 -32 8 42 | 0 2 -16 17 1 -13 }}
-Optimal tuning (CTE): ~44/35 = 1＼3, ~26/15 = 950.9360
+Optimal tuning (CTE): ~44/35 = 400.000{{c}}, ~26/15 = 950.9360{{c}}
-Optimal ET sequence: {{Optimal ET sequence| 24, …, 111cf, 135f, 159 }}
+{{Optimal ET sequence|legend=0| 24, …, 111cf, 135f, 159 }}
-Badness: 0.054894
+Badness (Smith): 0.054894
 == Sesquiquartififths ==
@@ Line 1,643: / Line 1,622: @@
 {{Mapping|legend=1| 1 1 7 5 | 0 4 -32 -15 }}
+: napping generators: ~2, ~448/405
-: Mapping generators: ~2, ~448/405
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~448/405 = 175.434{{c}}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~448/405 = 175.434
 [[Minimax tuning]]:
@@ Line 1,654: / Line 1,632: @@
 {{Optimal ET sequence|legend=1| 41, 89, 130, 171, 814, 985, 1156, 1327, 1498, 2825bd }}
-[[Badness]]: 0.011244
+[[Badness]] (Smith): 0.011244
 === Sesquart ===
@@ Line 1,663: / Line 1,641: @@
 Mapping: {{mapping| 1 1 7 5 2 | 0 4 -32 -15 10 }}
-Optimal tuning (POTE): ~2 = 1\1, ~256/231 = 175.406
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~256/231 = 175.406{{c}}
-Optimal ET sequence: {{Optimal ET sequence| 41, 89, 130, 301e, 431e }}
+{{Optimal ET sequence|legend=0| 41, 89, 130, 301e, 431e }}
-Badness: 0.029306
+Badness (Smith): 0.029306
 ==== 13-limit ====
@@ Line 1,676: / Line 1,654: @@
 Mapping: {{mapping| 1 1 7 5 2 -2 | 0 4 -32 -15 10 39 }}
-Optimal tuning (POTE): ~2 = 1\1, ~72/65 = 175.409
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~72/65 = 175.409{{c}}
-Optimal ET sequence: {{Optimal ET sequence| 41, 89, 130, 301e, 431e }}
+{{Optimal ET sequence|legend=0| 41, 89, 130, 301e, 431e }}
-Badness: 0.022396
+Badness (Smith): 0.022396
 ===== Sesquartia =====
@@ Line 1,689: / Line 1,667: @@
 Mapping: {{mapping| 1 1 7 5 2 -2 -6 | 0 4 -32 -15 10 39 69 }}
-Optimal tuning (POTE): ~2 = 1\1, ~72/65 = 175.424
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~72/65 = 175.424{{c}}
-Optimal ET sequence: {{Optimal ET sequence| 41, 89g, 130, 171, 301e }}
+{{Optimal ET sequence|legend=0| 41, 89g, 130, 171, 301e }}
-Badness: 0.023126
+Badness (Smith): 0.023126
 ====== 19-limit ======
@@ Line 1,702: / Line 1,680: @@
 Mapping: {{mapping| 1 1 7 5 2 -2 -6 6 | 0 4 -32 -15 10 39 69 -12 }}
-Optimal tuning (POTE): ~2 = 1\1, ~21/19 = 175.419
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~21/19 = 175.419{{c}}
-Optimal ET sequence: {{Optimal ET sequence| 41, 89g, 130, 171, 301eh }}
+{{Optimal ET sequence|legend=0| 41, 89g, 130, 171, 301eh }}
-Badness: 0.020466
+Badness (Smith): 0.020466
 ====== 23-limit ======
@@ Line 1,715: / Line 1,693: @@
 Mapping: {{mapping| 1 1 7 5 2 -2 -6 6 -6 | 0 4 -32 -15 10 39 69 -12 72 }}
-Optimal tuning (POTE): ~2 = 1\1, ~21/19 = 175.412
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~21/19 = 175.412{{c}}
-Optimal ET sequence: {{Optimal ET sequence| 41i, 89gi, 130, 171, 301eh }}
+{{Optimal ET sequence|legend=0| 41i, 89gi, 130, 171, 301eh }}
-Badness: 0.019043
+Badness (Smith): 0.019043
 ===== Heartia =====
@@ Line 1,728: / Line 1,706: @@
 Mapping: {{mapping| 1 1 7 5 2 -2 0 | 0 4 -32 -15 10 39 28 }}
-Optimal tuning (POTE): ~2 = 1\1, ~72/65 = 175.386
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~72/65 = 175.386{{c}}
-Optimal ET sequence: {{Optimal ET sequence| 41, 89, 130g }}
+{{Optimal ET sequence|legend=0| 41, 89, 130g }}
-Badness: 0.028443
+Badness (Smith): 0.028443
 ====== 19-limit ======
@@ Line 1,741: / Line 1,719: @@
 Mapping: {{mapping| 1 1 7 5 2 -2 0 6 | 0 4 -32 -15 10 39 28 -12 }}
-Optimal tuning (POTE): ~2 = 1\1, ~21/19 = 175.380
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~21/19 = 175.380{{c}}
-Optimal ET sequence: {{Optimal ET sequence| 41, 89, 130g }}
+{{Optimal ET sequence|legend=0| 41, 89, 130g }}
-Badness: 0.023059
+Badness (Smith): 0.023059
 ===== Hearty =====
@@ Line 1,754: / Line 1,732: @@
 Mapping: {{mapping| 1 1 7 5 2 -2 13 | 0 4 -32 -15 10 39 -61 }}
-Optimal tuning (POTE): ~2 = 1\1, ~72/65 = 175.377
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~72/65 = 175.377{{c}}
-Optimal ET sequence: {{Optimal ET sequence| 41g, 89, 130, 609ceefgg }}
+{{Optimal ET sequence|legend=0| 41g, 89, 130, 609ceefgg }}
-Badness: 0.030680
+Badness (Smith): 0.030680
 ====== 19-limit ======
@@ Line 1,767: / Line 1,745: @@
 Mapping: {{mapping| 1 1 7 5 2 -2 13 6 | 0 4 -32 -15 10 39 -61 -12 }}
-Optimal tuning (POTE): ~2 = 1\1, ~21/19 = 175.377
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~21/19 = 175.377{{c}}
-Optimal ET sequence: {{Optimal ET sequence| 41g, 89, 130, 609ceefggh }}
+{{Optimal ET sequence|legend=0| 41g, 89, 130, 609ceefggh }}
-Badness: 0.022816
+Badness (Smith): 0.022816
 ====== 23-limit ======
@@ Line 1,780: / Line 1,758: @@
 Mapping: {{mapping| 1 1 7 5 2 -2 13 6 13 | 0 4 -32 -15 10 39 -61 -12 -58 }}
-Optimal tuning (POTE): ~2 = 1\1, ~21/19 = 175.376
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~21/19 = 175.376{{c}}
-Optimal ET sequence: {{Optimal ET sequence| 41g, 89, 130, 609ceefggh }}
+{{Optimal ET sequence|legend=0| 41g, 89, 130, 609ceefggh }}
-Badness: 0.019121
+Badness (Smith): 0.019121
 === Bisesqui ===
@@ Line 1,792: / Line 1,770: @@
 Mapping: {{mapping| 2 2 14 10 23 | 0 4 -32 -15 -55 }}
+: mapping generators: ~99/70, ~448/405
-: Mapping generators: ~99/70, ~448/405
+Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~448/405 = 175.435{{c}}
-Optimal tuning (POTE): ~99/70 = 1\2, ~448/405 = 175.435
 {{Optimal ET sequence|legend=1| 82e, 130, 212, 342, 1156, 1498, 1840d }}
-Badness: 0.016968
+Badness (Smith): 0.016968
 == Quintilipyth ==
-The quintilipyth temperament ({{nowrap|12 &amp; 253}}, formerly ''quintilischis'') slices the pythagorean fourth ([[4/3]]) into five semitones and tempers out the compass comma (9765625/9680832) in the 7-limit.
+The quintilipyth temperament ({{nowrap| 12 & 253 }}, formerly ''quintilischis'') slices the pythagorean fourth ([[4/3]]) into five semitones and tempers out the compass comma (9765625/9680832) in the 7-limit.
 [[Subgroup]]: 2.3.5.7
@@ Line 1,810: / Line 1,787: @@
 {{Mapping|legend=1| 1 2 -1 -4 | 0 -5 40 82 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~625/588 = 99.625
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~625/588 = 99.625{{c}}
 {{Optimal ET sequence|legend=1| 12, 253, 265 }}
-[[Badness]]: 0.253966
+[[Badness]] (Smith): 0.253966
 === 11-limit ===
@@ Line 1,823: / Line 1,800: @@
 Mapping: {{mapping| 1 2 -1 -4 -7 | 0 -5 40 82 126 }}
-Optimal tuning (POTE): ~2 = 1\1, ~35/33 = 99.616
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~35/33 = 99.616{{c}}
 {{Optimal ET sequence|legend=0| 12, 253, 265, 518c, 783cc }}
-Badness: 0.113044
+Badness (Smith): 0.113044
 === 13-limit ===
@@ Line 1,836: / Line 1,813: @@
 Mapping: {{mapping| 1 2 -1 -4 -7 -9 | 0 -5 40 82 126 153 }}
-Optimal tuning (POTE): ~2 = 1\1, ~35/33 = 99.612
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~35/33 = 99.612{{c}}
 {{Optimal ET sequence|legend=0| 12f, 253, 518c, 771cc }}
-Badness: 0.069127
+Badness (Smith): 0.069127
 === 17-limit ===
@@ Line 1,849: / Line 1,826: @@
 Mapping: {{mapping| 1 2 -1 -4 -7 -9 5 | 0 -5 40 82 126 153 -11 }}
-Optimal tuning (POTE): ~2 = 1\1, ~18/17 = 99.612
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~18/17 = 99.612{{c}}
 {{Optimal ET sequence|legend=0| 12f, 253, 518c, 771cc }}
-Badness: 0.045992
+Badness (Smith): 0.045992
 === 19-limit ===
@@ Line 1,862: / Line 1,839: @@
 Mapping: {{mapping| 1 2 -1 -4 -7 -9 5 4 | 0 -5 40 82 126 153 -11 3 }}
-Optimal tuning (POTE): ~2 = 1\1, ~18/17 = 99.615
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~18/17 = 99.615{{c}}
 {{Optimal ET sequence|legend=0| 12f, 253, 265, 518ch }}
-Badness: 0.038155
+Badness (Smith): 0.038155
 == Quintaschis ==
-The quintaschis temperament ({{nowrap|12 &amp; 289}}) slices the fourth (4/3) into five semitones and tempers out 49009212/48828125 in the 7-limit.
+The quintaschis temperament ({{nowrap| 12 & 289 }}) slices the fourth (4/3) into five semitones and tempers out 49009212/48828125 in the 7-limit.
 [[Subgroup]]: 2.3.5.7
@@ Line 1,877: / Line 1,854: @@
 {{Mapping|legend=1| 1 2 -1 -5 | 0 -5 40 94 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~200/189 = 99.664
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~200/189 = 99.664{{c}}
 {{Optimal ET sequence|legend=1| 12, …, 289, 301, 590, 891, 1192 }}
-[[Badness]]: 0.132890
+[[Badness]] (Smith): 0.132890
 === 11-limit ===
@@ Line 1,890: / Line 1,867: @@
 Mapping: {{mapping| 1 2 -1 -5 -8 | 0 -5 40 94 138 }}
-Optimal tuning (POTE): ~2 = 1\1, ~35/33 = 99.653
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~35/33 = 99.653{{c}}
-{{Optimal ET sequence|legend=1| 12, …, 277d, 289 }}
+{{Optimal ET sequence|legend=0| 12, …, 277d, 289 }}
-Badness: 0.111477
+Badness (Smith): 0.111477
 ==== 13-limit ====
@@ Line 1,903: / Line 1,880: @@
 Mapping: {{mapping| 1 2 -1 -5 -8 -11 | 0 -5 40 94 138 177 }}
-Optimal tuning (POTE): ~2 = 1\1, ~35/33 = 99.658
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~35/33 = 99.658{{c}}
-{{Optimal ET sequence|legend=1| 12f, …, 277dff, 289 }}
+{{Optimal ET sequence|legend=0| 12f, …, 277dff, 289 }}
-Badness: 0.074218
+Badness (Smith): 0.074218
 ==== 17-limit ====
@@ Line 1,916: / Line 1,893: @@
 Mapping: {{mapping| 1 2 -1 -5 -8 -11 5 | 0 -5 40 94 138 177 -11 }}
-Optimal tuning (POTE): ~2 = 1\1, ~18/17 = 99.656
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~18/17 = 99.656{{c}}
-{{Optimal ET sequence|legend=1| 12f, 277dff, 289 }}
+{{Optimal ET sequence|legend=0| 12f, 277dff, 289 }}
-Badness: 0.050571
+Badness (Smith): 0.050571
 ==== 19-limit ====
@@ Line 1,929: / Line 1,906: @@
 Mapping: {{mapping| 1 2 -1 -5 -8 -11 5 4 | 0 -5 40 94 138 177 -11 3 }}
-Optimal tuning (POTE): ~2 = 1\1, ~18/17 = 99.659
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~18/17 = 99.659{{c}}
-{{Optimal ET sequence|legend=1| 12f, 289 }}
+{{Optimal ET sequence|legend=0| 12f, 289 }}
-Badness: 0.042120
+Badness (Smith): 0.042120
 === Quintahelenic ===
@@ Line 1,942: / Line 1,919: @@
 Mapping: {{mapping| 1 2 -1 -5 -9 | 0 -5 40 94 150 }}
-Optimal tuning (POTE): ~2 = 1\1, ~200/189 = 99.671
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~200/189 = 99.671{{c}}
-{{Optimal ET sequence|legend=1| 12, …, 289e, 301, 915 }}
+{{Optimal ET sequence|legend=0| 12, …, 289e, 301, 915 }}
-Badness: 0.082225
+Badness (Smith): 0.082225
 ==== 13-limit ====
@@ Line 1,955: / Line 1,932: @@
 Mapping: {{mapping| 1 2 -1 -5 -9 -11 | 0 -5 40 94 150 177 }}
-Optimal tuning (POTE): ~2 = 1\1, ~200/189 = 99.661
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~200/189 = 99.661{{c}}
-{{Optimal ET sequence|legend=1| 12f, …, 289e, 301 }}
+{{Optimal ET sequence|legend=0| 12f, …, 289e, 301 }}
-Badness: 0.055570
+Badness (Smith): 0.055570
 ===== 17-limit =====
@@ Line 1,968: / Line 1,945: @@
 Mapping: {{mapping| 1 2 -1 -5 -9 -11 5 | 0 -5 40 94 150 177 -11 }}
-Optimal tuning (POTE): ~2 = 1\1, ~18/17 = 99.665
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~18/17 = 99.665{{c}}
 {{Optimal ET sequence|legend=1| 12f, 289e, 301 }}
-Badness: 0.040412
+Badness (Smith): 0.040412
 ===== 19-limit =====
@@ Line 1,981: / Line 1,958: @@
 Mapping: {{mapping| 1 2 -1 -5 -9 -11 5 4 | 0 -5 40 94 150 177 -11 3 }}
-Optimal tuning (POTE): ~2 = 1\1, ~18/17 = 99.668
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~18/17 = 99.668{{c}}
-{{Optimal ET sequence|legend=1| 12f, 301 }}
+{{Optimal ET sequence|legend=0| 12f, 301 }}
-Badness: 0.036840
+Badness (Smith): 0.036840
 ==== Quintahelenoid ====
@@ Line 1,994: / Line 1,971: @@
 Mapping: {{mapping| 1 2 -1 -5 -9 14 | 0 -5 40 94 150 -124 }}
-Optimal tuning (POTE): ~2 = 1\1, ~200/189 = 99.672
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~200/189 = 99.672{{c}}
-{{Optimal ET sequence|legend=1| 12, 301, 614, 915 }}
+{{Optimal ET sequence|legend=0| 12, 301, 614, 915 }}
-Badness: 0.066108
+Badness (Smith): 0.066108
 ===== 17-limit =====
@@ Line 2,007: / Line 1,984: @@
 Mapping: {{mapping| 1 2 -1 -5 -9 14 5 | 0 -5 40 94 150 -124 -11 }}
-Optimal tuning (POTE): ~2 = 1\1, ~18/17 = 99.671
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~18/17 = 99.671{{c}}
-{{Optimal ET sequence|legend=1| 12, 301 }}
+{{Optimal ET sequence|legend=0| 12, 301 }}
-Badness: 0.047908
+Badness (Smith): 0.047908
 ===== 19-limit =====
@@ Line 2,020: / Line 1,997: @@
 Mapping: {{mapping| 1 2 -1 -5 -9 14 5 4 | 0 -5 40 94 150 -124 -11 3 }}
-Optimal tuning (POTE): ~2 = 1\1, ~18/17 = 99.672
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~18/17 = 99.672{{c}}
-{{Optimal ET sequence|legend=1| 12, 301 }}
+{{Optimal ET sequence|legend=0| 12, 301 }}
-Badness: 0.039542
+Badness (Smith): 0.039542
 == Sextilifourths ==
-The sextilifourths ({{nowrap|130 &amp; 159}}, also known as ''sextilischis'', formerly ''sextilififths'') temperament slices the fourth (4/3) into six small semitones, which serves as both 21/20 and 22/21.
+The sextilifourths ({{nowrap| 130 & 159 }}, also known as ''sextilischis'', formerly ''sextilififths'') temperament slices the fourth (4/3) into six small semitones, which serves as both 21/20 and 22/21.
 [[Subgroup]]: 2.3.5.7
@@ Line 2,034: / Line 2,011: @@
 {{Mapping|legend=1| 1 2 -1 -1 | 0 -6 48 55 }}
+: mapping generators: ~2, ~21/2
-: Mapping generators: ~2, ~21/2
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~21/20 = 83.053{{c}}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~21/20 = 83.053
 {{Optimal ET sequence|legend=1| 29, 72cd, 101, 130, 289, 419 }}
-[[Badness]]: 0.108794
+[[Badness]] (Smith): 0.108794
 === 11-limit ===
@@ Line 2,050: / Line 2,026: @@
 Mapping: {{mapping| 1 2 -1 -1 0 | 0 -6 48 55 50 }}
-Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 83.049
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~21/20 = 83.049{{c}}
-{{Optimal ET sequence|legend=1| 29, 72cde, 101e, 130, 289 }}
+{{Optimal ET sequence|legend=0| 29, 72cde, 101e, 130, 289 }}
-Badness: 0.045457
+Badness (Smith): 0.045457
 === 13-limit ===
@@ Line 2,063: / Line 2,039: @@
 Mapping: {{mapping| 1 2 -1 -1 0 1 | 0 -6 48 55 50 39 }}
-Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 83.049
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~21/20 = 83.049{{c}}
-{{Optimal ET sequence|legend=1| 29, 72cdef, 101e, 130, 289 }}
+{{Optimal ET sequence|legend=0| 29, 72cdef, 101e, 130, 289 }}
-Badness: 0.025276
+Badness (Smith): 0.025276
 == Septiquarschis ==
-The septiquarschis temperament ({{nowrap|89 &amp; 94}}) splits septimal minor seventh ([[7/4]]) into four generators and tempers out 829440/823543 (mynaslender comma) and 67108864/66706983 (septiness comma).
+The septiquarschis temperament ({{nowrap| 89 & 94 }}) splits septimal minor seventh ([[7/4]]) into four generators and tempers out 829440/823543 (mynaslender comma) and 67108864/66706983 (septiness comma).
 [[Subgroup]]: 2.3.5.7
@@ Line 2,078: / Line 2,054: @@
 {{Mapping|legend=1| 1 3 -9 2 | 0 -7 -56 4 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~147/128 = 242.614
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~147/128 = 242.614{{c}}
 {{Optimal ET sequence|legend=1| 89, 94, 183, 460d, 643d, 1103dd }}
-[[Badness]]: 0.187047
+[[Badness]] (Smith): 0.187047
 === 11-limit ===
@@ Line 2,091: / Line 2,067: @@
 Mapping: {{mapping| 1 3 -9 2 -2 | 0 -7 -56 4 27 }}
-Optimal tuning (POTE): ~2 = 1\1, ~147/128 = 242.616
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~147/128 = 242.616{{c}}
-{{Optimal ET sequence|legend=1| 89, 94, 183, 460d, 643d, 826dd }}
+{{Optimal ET sequence|legend=0| 89, 94, 183, 460d, 643d, 826dd }}
-Badness: 0.052002
+Badness (Smith): 0.052002
 === 13-limit ===
@@ Line 2,104: / Line 2,080: @@
 Mapping: {{mapping| 1 3 -9 2 -2 13 | 0 -7 -56 4 27 -46 }}
-Optimal tuning (POTE): ~2 = 1\1, ~147/128 = 242.610
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~147/128 = 242.610{{c}}
-{{Optimal ET sequence|legend=1| 89, 94, 183, 277, 460d }}
+{{Optimal ET sequence|legend=0| 89, 94, 183, 277, 460d }}
-Badness: 0.035315
+Badness (Smith): 0.035315
 == Tsaharuk ==
@@ Line 2,118: / Line 2,094: @@
 {{Mapping|legend=1| 1 1 7 0 | 0 5 -40 24 }}
+: mapping generators: ~2, ~243/224
-: Mapping generators: ~2, ~243/224
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~243/224 = 140.350{{c}}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~243/224 = 140.350
 {{Optimal ET sequence|legend=1| 17, 60c, 77, 94, 171 }}
-[[Badness]]: 0.030697
+[[Badness]] (Smith): 0.030697
 === 11-limit ===
@@ Line 2,134: / Line 2,109: @@
 Mapping: {{mapping| 1 1 7 0 1 | 0 5 -40 24 21 }}
-Optimal tuning (POTE): ~2 = 1\1, ~88/81 = 140.365
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~88/81 = 140.365{{c}}
-{{Optimal ET sequence|legend=1| 17, 60ce, 77, 94, 171e, 265e, 436ee }}
+{{Optimal ET sequence|legend=0| 17, 60ce, 77, 94, 171e, 265e, 436ee }}
-Badness: 0.063499
+Badness (Smith): 0.063499
 === 13-limit ===
@@ Line 2,147: / Line 2,122: @@
 Mapping: {{mapping| 1 1 7 0 1 3 | 0 5 -40 24 21 6 }}
-Optimal tuning (POTE): ~2 = 1\1, ~13/12 = 140.363
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~13/12 = 140.363{{c}}
-{{Optimal ET sequence|legend=1| 17, 60ce, 77, 94, 171e, 436ee }}
+{{Optimal ET sequence|legend=0| 17, 60ce, 77, 94, 171e, 436ee }}
-Badness: 0.037886
+Badness (Smith): 0.037886
 == Quanharuk ==
@@ Line 2,159: / Line 2,134: @@
 {{Mapping|legend=1| 1 0 15 12 | 0 5 -40 -29 }}
+: mapping generators: ~2, ~56/45
-: Mapping generators: ~2, ~56/45
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~56/45 = 380.355{{c}}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~56/45 = 380.355
 {{Optimal ET sequence|legend=1| 41, 142, 183, 224, 1303d, 1527cd, 1751cd, 1975cd }}
-[[Badness]]: 0.071950
+[[Badness]] (Smith): 0.071950
 === 11-limit ===
@@ Line 2,175: / Line 2,149: @@
 Mapping: {{mapping| 1 0 15 12 -7 | 0 5 -40 -29 33 }}
-Optimal tuning (POTE): ~2 = 1\1, ~56/45 = 380.352
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~56/45 = 380.352{{c}}
-{{Optimal ET sequence|legend=1| 41, 142, 183, 224, 631d, 855d, 1079d }}
+{{Optimal ET sequence|legend=0| 41, 142, 183, 224, 631d, 855d, 1079d }}
-Badness: 0.031549
+Badness (Smith): 0.031549
 === 13-limit ===
@@ Line 2,188: / Line 2,162: @@
 Mapping: {{mapping| 1 0 15 12 -7 -15 | 0 5 -40 -29 33 59 }}
-Optimal tuning (POTE): ~2 = 1\1, ~56/45 = 380.351
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~56/45 = 380.351{{c}}
-{{Optimal ET sequence|legend=1| 41, 142, 183, 224, 631d, 855d }}
+{{Optimal ET sequence|legend=0| 41, 142, 183, 224, 631d, 855d }}
-Badness: 0.021392
+Badness (Smith): 0.021392
 == Quadrant ==
-The ''quadrant'' temperament ({{nowrap|12 &amp; 224}}) has a period of quarter octave and tempers out the [[dimcomp comma]], 390625/388962. In this temperament, 25/21 is mapped into quarter octave.
+The ''quadrant'' temperament ({{nowrap| 12 & 224 }}) has a period of quarter octave and tempers out the [[dimcomp comma]], 390625/388962. In this temperament, 25/21 is mapped into quarter octave.
 [[Subgroup]]: 2.3.5.7
@@ Line 2,202: / Line 2,176: @@
 {{Mapping|legend=1| 4 0 60 119 | 0 1 -8 -17 }}
+: mapping generators: ~25/21, ~3
-: Mapping generators: ~25/21, ~3
+[[Optimal tuning]] ([[POTE]]): ~25/21 = 300.0000{{c}}, ~3/2 = 701.8234{{c}}
-[[Optimal tuning]] ([[POTE]]): ~25/21 = 1\4, ~3/2 = 701.8234
 {{Optimal ET sequence|legend=1| 212, 224, 436, 660, 1096c }}
-[[Badness]]: 0.110242
+[[Badness]] (Smith): 0.110242
 === 11-limit ===
@@ Line 2,218: / Line 2,191: @@
 Mapping: {{mapping| 4 0 60 119 185 | 0 1 -8 -17 -27 }}
-Optimal tuning (POTE): ~25/21 = 1\4, ~3/2 = 701.8176
+Optimal tuning (POTE): ~25/21 = 300.0000{{c}}, ~3/2 = 701.8176{{c}}
-{{Optimal ET sequence|legend=1| 212, 224, 436, 660 }}
+{{Optimal ET sequence|legend=0| 212, 224, 436, 660 }}
-Badness: 0.045738
+Badness (Smith): 0.045738
 === 13-limit ===
@@ Line 2,231: / Line 2,204: @@
 Mapping: {{mapping| 4 0 60 119 185 224 | 0 1 -8 -17 -27 -33 }}
-Optimal tuning (POTE): ~25/21 = 1\4, ~3/2 = 701.8158
+Optimal tuning (POTE): ~25/21 = 300.0000{{c}}, ~3/2 = 701.8158{{c}}
-{{Optimal ET sequence|legend=1| 212, 224, 436, 660 }}
+{{Optimal ET sequence|legend=0| 212, 224, 436, 660 }}
-Badness: 0.027243
+Badness (Smith): 0.027243
 == Septant ==
-The ''septant'' temperament ({{nowrap|224 &amp; 301}}) has a period of 1/7 octave and tempers out the [[akjaysma]], {{monzo| 47 -7 -7 -7 }}.
+The septant temperament ({{nowrap| 224 & 301 }}) has a period of 1/7 octave and tempers out the [[akjaysma]], {{monzo| 47 -7 -7 -7 }}.
 [[Subgroup]]: 2.3.5.7
@@ Line 2,245: / Line 2,218: @@
 {{Mapping|legend=1| 7 0 105 -56 | 0 1 -8 7 }}
+: mapping generators: ~8575/7776, ~3
-: Mapping generators: ~8575/7776, ~3
+[[Optimal tuning]] ([[POTE]]): ~8575/7776 = 171.429{{c}}, ~3/2 = 701.702{{c}}
-[[Optimal tuning]] ([[POTE]]): ~8575/7776 = 1\7, ~3/2 = 701.702
 {{Optimal ET sequence|legend=1| 77, 147, 224, 301, 525, 826, 1351 }}
-[[Badness]]: 0.111142
+[[Badness]] (Smith): 0.111142
 === 11-limit ===
@@ Line 2,261: / Line 2,233: @@
 Mapping: {{mapping| 7 0 105 -56 -120 | 0 1 -8 7 13 }}
-Optimal tuning (POTE): ~495/448 = 1\7, ~3/2 = 701.719
+Optimal tuning (POTE): ~495/448 = 171.429{{c}}, ~3/2 = 701.719{{c}}
-{{Optimal ET sequence|legend=1| 77, 147, 224, 301, 525 }}
+{{Optimal ET sequence|legend=0| 77, 147, 224, 301, 525 }}
-Badness: 0.044122
+Badness (Smith): 0.044122
 === 13-limit ===
@@ Line 2,274: / Line 2,246: @@
 Mapping: {{mapping| 7 0 105 -56 -120 37 | 0 1 -8 7 13 -1 }}
-Optimal tuning (POTE): ~495/448 = 1\7, ~3/2 = 701.724
+Optimal tuning (POTE): ~495/448 = 171.429{{c}}, ~3/2 = 701.724{{c}}
-{{Optimal ET sequence|legend=1| 77, 147, 224, 525 }}
+{{Optimal ET sequence|legend=0| 77, 147, 224, 525 }}
-Badness: 0.024706
+Badness (Smith): 0.024706
 == Octant ==
-The octant temperament ({{nowrap|224 &amp; 472}}) has a period of 1/8 octave. In this temperament, 12/11, 35/27, and 99/70 are mapped into 1\8, 3\8, and 4\8 respectively.
+The octant temperament ({{nowrap| 224 & 472 }}) has a period of 1/8 octave. In this temperament, 12/11, 35/27, and 99/70 are mapped into 1\8, 3\8, and 4\8 respectively.
 [[Subgroup]]: 2.3.5.7
@@ Line 2,288: / Line 2,260: @@
 {{Mapping|legend=1| 8 0 120 -117 | 0 1 -8 11 }}
+: mapping generators: ~42875/39366, ~3
-: Mapping generators: ~42875/39366, ~3
+[[Optimal tuning]] ([[POTE]]): ~42875/39366 = 150.000{{c}}, ~3/2 = 701.713{{c}}
-[[Optimal tuning]] ([[POTE]]): ~42875/39366 = 1\8, ~3/2 = 701.713
 {{Optimal ET sequence|legend=1| 24, 224, 472, 696, 1168 }}
-[[Badness]]: 0.157186
+[[Badness]] (Smith): 0.157186
 === 11-limit ===
@@ Line 2,304: / Line 2,275: @@
 Mapping: {{mapping| 8 0 120 -117 15 | 0 1 -8 11 1 }}
-Optimal tuning (POTE): ~12/11 = 1\8, ~3/2 = 701.713
+Optimal tuning (POTE): ~12/11 = 150.000{{c}}, ~3/2 = 701.713{{c}}
-{{Optimal ET sequence|legend=1| 24, 224, 472, 696, 1168 }}
+{{Optimal ET sequence|legend=0| 24, 224, 472, 696, 1168 }}
-Badness: 0.044778
+Badness (Smith): 0.044778
 === 13-limit ===
@@ Line 2,317: / Line 2,288: @@
 Mapping: {{mapping| 8 0 120 -117 15 93 | 0 1 -8 11 1 -5 }}
-Optimal tuning (POTE): ~12/11 = 1\8, ~3/2 = 701.725
+Optimal tuning (POTE): ~12/11 = 150.000{{c}}, ~3/2 = 701.725{{c}}
-{{Optimal ET sequence|legend=1| 24, 224, 472, 696 }}
+{{Optimal ET sequence|legend=0| 24, 224, 472, 696 }}
-Badness: 0.030425
+Badness (Smith): 0.030425
 == Nonant ==
-The ''nonant'' temperament ({{nowrap|36 &amp; 135}}) has a period of 1/9 octave and tempers out the [[septimal ennealimma]], {{monzo| -11 -9 0 9 }}.
+The ''nonant'' temperament ({{nowrap| 36 & 135 }}) has a period of 1/9 octave and tempers out the [[septimal ennealimma]], {{monzo| -11 -9 0 9 }}.
 [[Subgroup]]: 2.3.5.7
@@ Line 2,331: / Line 2,302: @@
 {{Mapping|legend=1| 9 0 135 11 | 0 1 -8 1 }}
+: mapping generators: ~2592/2401, ~3
-: Mapping generators: ~2592/2401, ~3
+[[Optimal tuning]] ([[CTE]]): ~2592/2401 = 133.3333{{c}}, ~3/2 = 701.7232{{c}}
-[[Optimal tuning]] ([[CTE]]): ~2592/2401 = 1\9, ~3/2 = 701.7232
 {{Optimal ET sequence|legend=1| 36, 99c, 135, 171 }}
-[[Badness]]: 0.069896
+[[Badness]] (Smith): 0.069896
 === 11-limit ===
@@ Line 2,347: / Line 2,317: @@
 Mapping: {{mapping| 9 0 135 11 131 | 0 1 -8 1 -7 }}
-Optimal tuning (CTE): ~242/225 = 1\9, ~3/2 = 701.8398
+Optimal tuning (CTE): ~242/225 = 133.3333{{c}}, ~3/2 = 701.8398{{c}}
-Optimal ET sequence: {{Optimal ET sequence| 36, 99c, 135, 171, 477ce, 648cee }}
+{{Optimal ET sequence|legend=0| 36, 99c, 135, 171, 477ce, 648cee }}
-Badness: 0.126910
+Badness (Smith): 0.126910
 === 13-limit ===
@@ Line 2,360: / Line 2,330: @@
 Mapping: {{mapping| 9 0 135 11 131 -38 | 0 1 -8 1 -7 5 }}
-Optimal tuning (CTE): ~242/225 = 1\9, ~3/2 = 701.7998
+Optimal tuning (CTE): ~242/225 = 133.3333{{c}}, ~3/2 = 701.7998{{c}}
-Optimal ET sequence: {{Optimal ET sequence| 36, 99cf, 135, 171 }}
+{{Optimal ET sequence|legend=0| 36, 99cf, 135, 171 }}
-Badness: 0.076195
+Badness (Smith): 0.076195
 == Tridecafifths ==
@@ Line 2,374: / Line 2,344: @@
 {{Mapping|legend=1| 1 1 7 6 | 0 13 -104 -71 }}
+: mapping generators: ~2, ~1323/1280
-: Mapping generators: ~2, ~1323/1280
+[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~1323/1280 = 53.9741{{c}}
-[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~1323/1280 = 53.9741
 {{Optimal ET sequence|legend=1| 89, 200, 289 }}
-[[Badness]]: 0.432580
+[[Badness]] (Smith): 0.432580
 === 11-limit ===
@@ Line 2,390: / Line 2,359: @@
 Mapping: {{mapping| 1 1 7 6 4 | 0 13 -104 -71 -12 }}
-Optimal tuning (CTE): ~2 = 1\1, ~33/32 = 53.9744
+Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~33/32 = 53.9744{{c}}
-Optimal ET sequence: {{Optimal ET sequence| 89, 200, 289 }}
+{{Optimal ET sequence|legend=0| 89, 200, 289 }}
-Badness: 0.127820
+Badness (Smith): 0.127820
 == Subgroup extensions ==
@@ Line 2,407: / Line 2,376: @@
 {{Mapping|legend=3| 1 0 15 0 0 0 -7 | 0 1 -8 0 0 0 7 }}
+: mapping generators: ~2, ~3
-: [[gencom]]: [2 3; 256/255 1458/1445]
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~3/2 = 701.491{{c}}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 701.491
 {{Optimal ET sequence|legend=1| 12, 41, 53, 65 }}
@@ Line 2,416: / Line 2,384: @@
 [[Tp tuning #T2 tuning|RMS error]]: 0.4842 cents
-==== 2.3.5.17.19 ====
+==== 2.3.5.17.19 subgroup ====
-[[Subgroup]]: 2.3.5.17.19
+Subgroup: 2.3.5.17.19
-[[Comma list]]: 171/170, 256/255, 324/323
-{{Mapping|legend=2| 1 0 15 -7 9 | 0 1 -8 7 -3 }}
+Comma list: 171/170, 256/255, 324/323
-{{Mapping|legend=3| 1 0 15 0 0 0 -7 9 | 0 1 -8 0 0 0 7 -3 }}
+Subgroup-val mapping: {{mapping| 1 0 15 -7 9 | 0 1 -8 7 -3 }}
-: [[gencom]]: [2 3; 171/170 256/255 324/323]
+Gencom mapping: {{mapping| 1 0 15 0 0 0 -7 9 | 0 1 -8 0 0 0 7 -3 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 701.470
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.470{{c}}
-{{Optimal ET sequence|legend=1| 12, 41, 53, 65 }}
+{{Optimal ET sequence|legend=0| 12, 41, 53, 65 }}
-[[Tp tuning #T2 tuning|RMS error]]: 0.5374 cents
+RMS error: 0.5374 cents
 === Nestoria (2.3.5.19) ===
@@ Line 2,444: / Line 2,410: @@
 {{Mapping|legend=2| 1 0 15 9 | 0 1 -8 -3 }}
+{{Mapping|legend=3| 1 0 15 0 0 0 0 9 | 0 1 -8 0 0 0 0 -3 }}
 : mapping generators: ~2, ~3
-{{Mapping|legend=3| 1 0 15 0 0 0 0 9 | 0 1 -8 0 0 0 0 -3 }}
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~3/2 = 701.746{{c}}
-: [[gencom]]: [2 3; 361/360 513/512]
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 701.746
 {{Optimal ET sequence|legend=1| 12, 29, 41, 53, 118, 171 }}
@@ Line 2,464: / Line 2,427: @@
 {{Mapping|legend=2| 1 0 15 14 | 0 2 -16 -13 }}
-: Mapping generators: ~2, ~26/15
 {{Mapping|legend=3| 1 0 15 0 0 14 | 0 2 -16 0 0 -13 }}
+: mapping generators: ~2, ~26/15
-: [[gencom]]: [2 26/15; 676/675 32805/32768]
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~26/15 = 950.855{{c}}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~26/15 = 950.855
 {{Optimal ET sequence|legend=1| 24, 53, 130, 183, 236 }}
@@ Line 2,478: / Line 2,438: @@
 ==== Dakota (2.3.5.13.19) ====
-[[Subgroup]]: 2.3.5.13.19
+Subgroup: 2.3.5.13.19
-[[Comma list]]: 361/360, 513/512, 676/675
+Comma list: 361/360, 513/512, 676/675
-[[Sval]] [[mapping]]: [{{val| 1 0 15 14 9 }}, {{val| 0 2 -16 -13 -6 }}]
+Subgroup-val mapping: {{mapping| 1 0 15 14 9 | 0 2 -16 -13 -6 }}
-[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~26/15 = 950.8199
+Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~26/15 = 950.8199{{c}}
-{{Optimal ET sequence|legend=1| 24, 29, 53, 130, 183, 236h, 289h }}
+{{Optimal ET sequence|legend=0| 24, 29, 53, 130, 183, 236h, 289h }}
-[[Badness]]: 0.00575
+Badness (Smith): 0.00575
-===== 2.3.5.13.19.37 =====
+===== 2.3.5.13.19.37 subgroup =====
-[[Subgroup]]: 2.3.5.13.19.37
+Subgroup: 2.3.5.13.19.37
-[[Comma list]]: 361/360, 481/480, 513/512, 676/675
+Comma list: 361/360, 481/480, 513/512, 676/675
-[[Sval]] [[mapping]]: [{{val| 1 0 15 14 9 6 }}, {{val| 0 2 -16 -13 -6 -1 }}]
+Subgroup-val mapping: {{mapping| 1 0 15 14 9 6 | 0 2 -16 -13 -6 -1 }}
-[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~26/15 = 950.8187
+Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~26/15 = 950.8187{{c}}
-{{Optimal ET sequence|legend=1| 24, 29, 53, 183, 236h, 289hl, 631fhhll }}
+{{Optimal ET sequence|legend=0| 24, 29, 53, 183, 236h, 289hl, 631fhhll }}
-[[Badness]]: 0.00357
+Badness (Smith): 0.00357
 === Quintilischis (2.3.5.17) ===
@@ Line 2,511: / Line 2,471: @@
 {{Mapping|legend=2| 1 2 -1 5 | 0 -5 40 -11 }}
-: Mapping generators: ~2, ~18/17
 {{Mapping|legend=3| 1 2 -1 0 0 0 5 | 0 -5 40 0 0 0 -11 }}
+: mapping generators: ~2, ~18/17
-: [[gencom]]: [2 18/17; 32805/32768 1419857/1417176]
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~18/17 = 99.649{{c}}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~18/17 = 99.649
 {{Optimal ET sequence|legend=1| 12, 253, 265, 277, 289 }}
@@ Line 2,524: / Line 2,481: @@
 [[Tp tuning #T2 tuning|RMS error]]: 0.0719 cents
-==== 2.3.5.17.19 ====
+==== 2.3.5.17.19 subgroup ====
-[[Subgroup]]: 2.3.5.17.19
+Subgroup: 2.3.5.17.19
-[[Comma list]]: 4624/4617, 6144/6137, 6885/6859
+Comma list: 4624/4617, 6144/6137, 6885/6859
-{{Mapping|legend=2| 1 2 -1 5 4 | 0 -5 40 -11 3 }}
+Subgroup-val mapping: {{mapping| 1 2 -1 5 4 | 0 -5 40 -11 3 }}
-{{Mapping|legend=3| 1 2 -1 0 0 0 5 4 | 0 -5 40 0 0 0 -11 3 }}
+Gencom mapping: {{mapping| 1 2 -1 0 0 0 5 4 | 0 -5 40 0 0 0 -11 3 }}
-: [[gencom]]: [2 18/17; 4624/4617 6144/6137 6885/6859]
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~18/17 = 99.652{{c}}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~18/17 = 99.652
+{{Optimal ET sequence|legend=0| 12, 253, 265, 277, 289 }}
-{{Optimal ET sequence|legend=1| 12, 253, 265, 277, 289 }}
-[[Tp tuning #T2 tuning|RMS error]]: 0.1636 cents
+RMS error: 0.1636 cents
 [[Category:Temperament families]]

Schismatic family: Difference between revisions