如何计算十二平均律的多位小数逼近分数

2022-07-03 本文已影响0人蚊子表飞了看我超度你

十二平均律的多位小数逼近分数

利用多位小数的分数逼近法计算十二平均律

十二平均律的每个音是以 $\sqrt[1/12]{2}$ 为等比的频率，每个音与根音的比例分别是：
$\sqrt[1/12]{2}$ 、 $\sqrt[2/12]{2}$ 、 $\sqrt[3/12]{2}$ 、 $\sqrt[4/12]{2}$ 、 $\sqrt[5/12]{2}$ 、 $\sqrt[6/12]{2}$ 、 $\sqrt[7/12]{2}$ 、 $\sqrt[8/12]{2}$ 、 $\sqrt[9/12]{2}$ 、 $\sqrt[10/12]{2}$ 、 $\sqrt[11/12]{2}$ 、 $\sqrt[12/12]{2}$

我把每个音的计算出来的所有简化分数放在最后列表中，这里说的的所有是指可以被选择的，因为接近原值更精确分数几乎没有价值，因为动辄分子分母都是几十万的数字，所以我在程序中做了判断，分子分母其一大于1000就直接抛弃。

然后这里我与另一篇文章（写给理工科人看的乐理（三）五线谱进阶与和声理论 - 知乎 (zhihu.com)）的作者给出的分数做出了对比：

作者的：

音程	近似频率比	近似整数比	最小公倍数lcm	评估价值evaluate
小二度	1:1.06	15:16	240	0.952345
大二度	1:1.12	8:9	72	1.666842
小三度	1:1.19	5:6	30	1.228297
大三度	1:1.26	4:5	20	1.35293
纯四度	1:1.34	3:4	12	2.28244
三全音	1:1.41	7:10	70	0.920297
纯五度	1:1.50	2:3	6	2.382267
小六度	1:1.59	5:8	40	1.098599
大六度	1:1.68	3:5	15	1.232115
小七度	1:1.78	5:9	45	0.913251
大七度	1:1.89	8:15	120	0.854899
纯八度	1:2	1:2	2

根据逼近法计算的相对最优的取值（每个音的考量是综合根据误差，价值，最小公倍数得出），这里大概对比第四位小数的误差来考虑：

音程	近似频率	近似分数	最小公倍数lcm	评估价值evaluate
小二度	1.0588	18/17	306	1.9512
大二度	1.1224	55/49	2695	3.1685
小三度	1.1892	44/37	1628	3.1406
大三度	1.26	63/50	3150	2.3535
纯四度	1.3333	4/3	12	2.2824
三全音	1.4143	99/70	6930	2.2214
纯五度	1.50	3/2	6	2.3822
小六度	1.5874	227/143	32461	2.6821
大六度	1.6818	37/22	814	3.1407
小七度	1.7818	98/55	5390	2.8173
大七度	1.8877	185/98	18130	3.0594
纯八度	2	2	2

我问过原作者，他给我的答复是他的分数是根据音律本身的和谐度找到可以用来解释和谐感的分数。我这里确实反了。

以下是通过程序实现多位小数的分数逼近法计算的每个音的比例的简化分数（其中source 是音的原值，calc是当前的逼近分数的值，errors是分数与原值之间的误差，lcm是最小公倍数，evaluate是该分数的评估价值计算过程在论文中有）：

每个音的简化分数列表

$\sqrt[1/12]{2}$ 小二度——取18/17 source=1.059463094359295 calc=1.058824 erros=-0.0006396 lcm=306 evaluate=1.951231

2/1  source=1.059463094359295      calc=2            erros=0.94054  lcm=2         evaluate=-0.123892
1/1  source=1.059463094359295      calc=1            erros=-0.05946  lcm=1         evaluate=1.225775 
3/2  source=1.059463094359295      calc=1.5          erros=0.44054  lcm=6         evaluate=-0.033061
4/3  source=1.059463094359295      calc=1.333333     erros=0.2739  lcm=12        evaluate=0.022817 
5/4  source=1.059463094359295      calc=1.25         erros=0.19054  lcm=20        evaluate=0.069499 
6/5  source=1.059463094359295      calc=1.2          erros=0.14054  lcm=30        evaluate=0.113639 
7/6  source=1.059463094359295      calc=1.166667     erros=0.107204  lcm=42        evaluate=0.158164 
8/7  source=1.059463094359295      calc=1.142857     erros=0.08339  lcm=56        evaluate=0.204792 
9/8  source=1.059463094359295      calc=1.125        erros=0.06554  lcm=72        evaluate=0.254827 
10/9  source=1.059463094359295      calc=1.111111     erros=0.05165  lcm=90        evaluate=0.309808 
11/10  source=1.059463094359295      calc=1.1          erros=0.040537  lcm=110       evaluate=0.371452 
12/11  source=1.059463094359295      calc=1.090909     erros=0.03145  lcm=132       evaluate=0.442092 
13/12  source=1.059463094359295      calc=1.083333     erros=0.023870  lcm=156       evaluate=0.525585 
14/13  source=1.059463094359295      calc=1.076923     erros=0.01746  lcm=182       evaluate=0.62792  
15/14  source=1.059463094359295      calc=1.071429     erros=0.01197  lcm=210       evaluate=0.760796 
16/15  source=1.059463094359295      calc=1.066667     erros=0.0072036  lcm=240       evaluate=0.952345 
17/16  source=1.059463094359295      calc=1.0625       erros=0.00303691  lcm=272       evaluate=1.300284 
18/17  source=1.059463094359295      calc=1.058824     erros=-0.0006396  lcm=306       evaluate=1.951231 
35/33  source=1.059463094359295      calc=1.060606     erros=0.001143  lcm=1155      evaluate=1.410663 
53/50  source=1.059463094359295      calc=1.06         erros=0.00053691  lcm=2650      evaluate=1.558476 
71/67  source=1.059463094359295      calc=1.059701     erros=0.0002384  lcm=4757      evaluate=1.784027 
89/84  source=1.059463094359295      calc=1.059524     erros=0.000060715  lcm=7476      evaluate=2.279869 
107/101  source=1.059463094359295      calc=1.059406     erros=-0.00005715  lcm=10807     evaluate=2.226131 
196/185  source=1.059463094359295      calc=1.059459     erros=-0.000003635  lcm=36260     evaluate=3.159782 
285/269  source=1.059463094359295      calc=1.05948      erros=0.00001646  lcm=76665     evaluate=2.341272 
481/454  source=1.059463094359295      calc=1.059471     erros=0.000008271  lcm=218374    evaluate=2.412842 
677/639  source=1.059463094359295      calc=1.059468     erros=0.000004824  lcm=432603    evaluate=2.498548 
873/824  source=1.059463094359295      calc=1.059466     erros=0.0000029251  lcm=719352    evaluate=2.605389

$\sqrt[2/12]{2}$ 大二度——取55/49 source=1.122462048309373 calc=1.122449 erros=-0.000013069 lcm=2695 evaluate=3.168478

2/1  source=1.122462048309373      calc=2            erros=0.8775  lcm=2         evaluate=-0.093762
1/1  source=1.122462048309373      calc=1            erros=-0.1225  lcm=1         evaluate=0.911864 
3/2  source=1.122462048309373      calc=1.5          erros=0.3775  lcm=6         evaluate=0.034007 
4/3  source=1.122462048309373      calc=1.333333     erros=0.21087  lcm=12        evaluate=0.136395 
5/4  source=1.122462048309373      calc=1.25         erros=0.1275  lcm=20        evaluate=0.243975 
6/5  source=1.122462048309373      calc=1.2          erros=0.07754  lcm=30        evaluate=0.371914 
7/6  source=1.122462048309373      calc=1.166667     erros=0.044205  lcm=42        evaluate=0.542904 
8/7  source=1.122462048309373      calc=1.142857     erros=0.0203951  lcm=56        evaluate=0.81638  
9/8  source=1.122462048309373      calc=1.125        erros=0.002538  lcm=72        evaluate=1.666842 
10/9  source=1.122462048309373      calc=1.111111     erros=-0.011351  lcm=90        evaluate=0.967845 
19/17  source=1.122462048309373      calc=1.117647     erros=-0.004815  lcm=323       evaluate=1.062802 
28/25  source=1.122462048309373      calc=1.12         erros=-0.0024620  lcm=700       evaluate=1.186163 
37/33  source=1.122462048309373      calc=1.121212     erros=-0.001250  lcm=1221      evaluate=1.359732 
46/41  source=1.122462048309373      calc=1.121951     erros=-0.00051083  lcm=1886      evaluate=1.653953 
55/49  source=1.122462048309373      calc=1.122449     erros=-0.000013069  lcm=2695      evaluate=3.168478 
64/57  source=1.122462048309373      calc=1.122807     erros=0.0003450  lcm=3648      evaluate=1.681153 
119/106  source=1.122462048309373      calc=1.122642     erros=0.0001795  lcm=12614     evaluate=1.695509 
174/155  source=1.122462048309373      calc=1.122581     erros=0.0001186  lcm=26970     evaluate=1.710475 
229/204  source=1.122462048309373      calc=1.122549     erros=0.00008697  lcm=46716     evaluate=1.725898 
284/253  source=1.122462048309373      calc=1.12253      erros=0.00006760  lcm=71852     evaluate=1.741834 
339/302  source=1.122462048309373      calc=1.122517     erros=0.000054508  lcm=102378    evaluate=1.758436 
394/351  source=1.122462048309373      calc=1.122507     erros=0.000045074  lcm=138294    evaluate=1.775672 
449/400  source=1.122462048309373      calc=1.1225       erros=0.00003795  lcm=179600    evaluate=1.793635 
504/449  source=1.122462048309373      calc=1.122494     erros=0.00003238  lcm=226296    evaluate=1.812385 
559/498  source=1.122462048309373      calc=1.12249      erros=0.00002791  lcm=278382    evaluate=1.83192  
614/547  source=1.122462048309373      calc=1.122486     erros=0.000024241  lcm=335858    evaluate=1.852372 
669/596  source=1.122462048309373      calc=1.122483     erros=0.00002117  lcm=398724    evaluate=1.873943 
724/645  source=1.122462048309373      calc=1.122481     erros=0.00001857  lcm=466980    evaluate=1.896539 
779/694  source=1.122462048309373      calc=1.122478     erros=0.00001634  lcm=540626    evaluate=1.920299 
834/743  source=1.122462048309373      calc=1.122476     erros=0.00001440  lcm=619662    evaluate=1.94556  
889/792  source=1.122462048309373      calc=1.122475     erros=0.00001270  lcm=704088    evaluate=1.972383 
944/841  source=1.122462048309373      calc=1.122473     erros=0.00001120  lcm=793904    evaluate=2.000898 
999/890  source=1.122462048309373      calc=1.122472     erros=0.000009862  lcm=889110    evaluate=2.031557

$\sqrt[3/12]{2}$ 小三度——取44/37 source=1.189207115002721 calc=1.189189 erros=-0.00001793 lcm=1628 evaluate=3.140593

2/1  source=1.189207115002721      calc=2            erros=0.81079  lcm=2         evaluate=-0.059423
1/1  source=1.189207115002721      calc=1            erros=-0.18921  lcm=1         evaluate=0.723056 
3/2  source=1.189207115002721      calc=1.5          erros=0.31079  lcm=6         evaluate=0.118457 
4/3  source=1.189207115002721      calc=1.333333     erros=0.1441  lcm=12        evaluate=0.301745 
5/4  source=1.189207115002721      calc=1.25         erros=0.060793  lcm=20        evaluate=0.565631 
6/5  source=1.189207115002721      calc=1.2          erros=0.010793  lcm=30        evaluate=1.228297 
7/6  source=1.189207115002721      calc=1.166667     erros=-0.022540  lcm=42        evaluate=0.835421 
13/11  source=1.189207115002721      calc=1.181818     erros=-0.007389  lcm=143       evaluate=1.053746 
19/16  source=1.189207115002721      calc=1.1875       erros=-0.0017071  lcm=304       evaluate=1.526304 
25/21  source=1.189207115002721      calc=1.190476     erros=0.0012691  lcm=525       evaluate=1.536425 
44/37  source=1.189207115002721      calc=1.189189     erros=-0.00001793  lcm=1628      evaluate=3.140593 
69/58  source=1.189207115002721      calc=1.189655     erros=0.00044806  lcm=4002      evaluate=1.547525 
113/95  source=1.189207115002721      calc=1.189474     erros=0.0002666  lcm=10735     evaluate=1.558739 
157/132  source=1.189207115002721      calc=1.189394     erros=0.0001868  lcm=20724     evaluate=1.570386 
201/169  source=1.189207115002721      calc=1.189349     erros=0.0001420  lcm=33969     evaluate=1.58217  
245/206  source=1.189207115002721      calc=1.18932      erros=0.0001133  lcm=50470     evaluate=1.594253 
289/243  source=1.189207115002721      calc=1.1893       erros=0.00009330  lcm=70227     evaluate=1.606866 
333/280  source=1.189207115002721      calc=1.189286     erros=0.00007860  lcm=93240     evaluate=1.619776 
377/317  source=1.189207115002721      calc=1.189274     erros=0.00006733  lcm=119509    evaluate=1.633091 
421/354  source=1.189207115002721      calc=1.189266     erros=0.00005842  lcm=149034    evaluate=1.646796 
465/391  source=1.189207115002721      calc=1.189258     erros=0.00005120  lcm=181815    evaluate=1.660915 
509/428  source=1.189207115002721      calc=1.189252     erros=0.00004522  lcm=217852    evaluate=1.675589 
553/465  source=1.189207115002721      calc=1.189247     erros=0.000040197  lcm=257145    evaluate=1.690717 
597/502  source=1.189207115002721      calc=1.189243     erros=0.00003591  lcm=299694    evaluate=1.706446 
641/539  source=1.189207115002721      calc=1.189239     erros=0.00003222  lcm=345499    evaluate=1.722651 
685/576  source=1.189207115002721      calc=1.189236     erros=0.00002900  lcm=394560    evaluate=1.739545 
729/613  source=1.189207115002721      calc=1.189233     erros=0.00002616  lcm=446877    evaluate=1.757268 
773/650  source=1.189207115002721      calc=1.189231     erros=0.00002365  lcm=502450    evaluate=1.775622 
817/687  source=1.189207115002721      calc=1.189229     erros=0.00002141  lcm=561279    evaluate=1.794794 
861/724  source=1.189207115002721      calc=1.189227     erros=0.000019404  lcm=623364    evaluate=1.814738 
905/761  source=1.189207115002721      calc=1.189225     erros=0.00001759  lcm=688705    evaluate=1.835718 
949/798  source=1.189207115002721      calc=1.189223     erros=0.00001594  lcm=757302    evaluate=1.857877 
993/835  source=1.189207115002721      calc=1.189222     erros=0.00001444  lcm=829155    evaluate=1.881115

$\sqrt[4/12]{2}$ 大三度——取63/50 source=1.259921049894873 calc=1.26 erros=0.000078950 lcm=3150 evaluate=2.353493

2/1  source=1.259921049894873      calc=2            erros=0.740079  lcm=2         evaluate=-0.019793
1/1  source=1.259921049894873      calc=1            erros=-0.2599  lcm=1         evaluate=0.585194 
3/2  source=1.259921049894873      calc=1.5          erros=0.240079  lcm=6         evaluate=0.23057  
4/3  source=1.259921049894873      calc=1.333333     erros=0.07341  lcm=12        evaluate=0.594654 
5/4  source=1.259921049894873      calc=1.25         erros=-0.0099210  lcm=20        evaluate=1.35293  
9/7  source=1.259921049894873      calc=1.285714     erros=0.02579  lcm=63        evaluate=0.688878 
14/11  source=1.259921049894873      calc=1.272727     erros=0.012806  lcm=154       evaluate=0.798826 
19/15  source=1.259921049894873      calc=1.266667     erros=0.006746  lcm=285       evaluate=0.943531 
24/19  source=1.259921049894873      calc=1.263158     erros=0.003237  lcm=456       evaluate=1.160375 
29/23  source=1.259921049894873      calc=1.26087      erros=0.0009485  lcm=667       evaluate=1.6109   
34/27  source=1.259921049894873      calc=1.259259     erros=-0.0006618  lcm=918       evaluate=1.697852 
63/50  source=1.259921049894873      calc=1.26         erros=0.000078950  lcm=3150      evaluate=2.353493 
97/77  source=1.259921049894873      calc=1.25974      erros=-0.000180790  lcm=7469      evaluate=1.806194 
160/127  source=1.259921049894873      calc=1.259843     erros=-0.000078530  lcm=20320     evaluate=1.951003 
223/177  source=1.259921049894873      calc=1.259887     erros=-0.000034044  lcm=39471     evaluate=2.16982  
286/227  source=1.259921049894873      calc=1.259912     erros=-0.000009156  lcm=64922     evaluate=2.632098 
349/277  source=1.259921049894873      calc=1.259928     erros=0.000006748  lcm=96673     evaluate=2.678172 
635/504  source=1.259921049894873      calc=1.259921     erros=-4.150E-7  lcm=320040    evaluate=3.62935  
984/781  source=1.259921049894873      calc=1.259923     erros=0.000002126  lcm=768504    evaluate=2.729614

$\sqrt[5/12]{2}$ 纯四度——取4/3 source=1.334839854170034 calc=1.333333 erros=-0.0015065 lcm=12 evaluate=2.28244

2/1  source=1.334839854170034      calc=2            erros=0.6652  lcm=2         evaluate=0.026533 
1/1  source=1.334839854170034      calc=1            erros=-0.3348  lcm=1         evaluate=0.475215 
3/2  source=1.334839854170034      calc=1.5          erros=0.1652  lcm=6         evaluate=0.392914 
4/3  source=1.334839854170034      calc=1.333333     erros=-0.0015065  lcm=12        evaluate=2.28244  
7/5  source=1.334839854170034      calc=1.4          erros=0.065160  lcm=35        evaluate=0.413985 
11/8  source=1.334839854170034      calc=1.375        erros=0.0401601  lcm=88        evaluate=0.423964 
15/11  source=1.334839854170034      calc=1.363636     erros=0.02880  lcm=165       evaluate=0.431866 
19/14  source=1.334839854170034      calc=1.357143     erros=0.02230300  lcm=266       evaluate=0.439196 
23/17  source=1.334839854170034      calc=1.352941     erros=0.018101  lcm=391       evaluate=0.446209 
27/20  source=1.334839854170034      calc=1.35         erros=0.015160  lcm=540       evaluate=0.453104 
31/23  source=1.334839854170034      calc=1.347826     erros=0.01299  lcm=713       evaluate=0.459846 
35/26  source=1.334839854170034      calc=1.346154     erros=0.01131  lcm=910       evaluate=0.467017 
39/29  source=1.334839854170034      calc=1.344828     erros=0.009988  lcm=1131      evaluate=0.47379  
43/32  source=1.334839854170034      calc=1.34375      erros=0.0089101  lcm=1376      evaluate=0.480808 
47/35  source=1.334839854170034      calc=1.342857     erros=0.0080173  lcm=1645      evaluate=0.487889 
51/38  source=1.334839854170034      calc=1.342105     erros=0.007265  lcm=1938      evaluate=0.495087 
55/41  source=1.334839854170034      calc=1.341463     erros=0.006624  lcm=2255      evaluate=0.502306 
59/44  source=1.334839854170034      calc=1.340909     erros=0.0060692  lcm=2596      evaluate=0.509716 
63/47  source=1.334839854170034      calc=1.340426     erros=0.005586  lcm=2961      evaluate=0.51718  
67/50  source=1.334839854170034      calc=1.34         erros=0.0051601  lcm=3350      evaluate=0.524819 
71/53  source=1.334839854170034      calc=1.339623     erros=0.004783  lcm=3763      evaluate=0.532533 
75/56  source=1.334839854170034      calc=1.339286     erros=0.004446  lcm=4200      evaluate=0.540406 
79/59  source=1.334839854170034      calc=1.338983     erros=0.004143  lcm=4661      evaluate=0.548446 
83/62  source=1.334839854170034      calc=1.33871      erros=0.003870  lcm=5146      evaluate=0.556554 
87/65  source=1.334839854170034      calc=1.338462     erros=0.003622  lcm=5655      evaluate=0.564835 
91/68  source=1.334839854170034      calc=1.338235     erros=0.003395  lcm=6188      evaluate=0.573385 
95/71  source=1.334839854170034      calc=1.338028     erros=0.003188  lcm=6745      evaluate=0.581991 
99/74  source=1.334839854170034      calc=1.337838     erros=0.002998  lcm=7326      evaluate=0.590735 
103/77  source=1.334839854170034      calc=1.337662     erros=0.002822  lcm=7931      evaluate=0.599779 
107/80  source=1.334839854170034      calc=1.3375       erros=0.0026601  lcm=8560      evaluate=0.608865 
111/83  source=1.334839854170034      calc=1.337349     erros=0.0025095  lcm=9213      evaluate=0.618212 
115/86  source=1.334839854170034      calc=1.337209     erros=0.002369  lcm=9890      evaluate=0.627837 
119/89  source=1.334839854170034      calc=1.337079     erros=0.002239  lcm=10591     evaluate=0.637477 
123/92  source=1.334839854170034      calc=1.336957     erros=0.002117  lcm=11316     evaluate=0.647433 
127/95  source=1.334839854170034      calc=1.336842     erros=0.00200225  lcm=12065     evaluate=0.657718 
131/98  source=1.334839854170034      calc=1.336735     erros=0.001895  lcm=12838     evaluate=0.668142 
135/101  source=1.334839854170034      calc=1.336634     erros=0.001794  lcm=13635     evaluate=0.67885  
139/104  source=1.334839854170034      calc=1.336538     erros=0.001699  lcm=14456     evaluate=0.689783 
143/107  source=1.334839854170034      calc=1.336449     erros=0.0016087  lcm=15301     evaluate=0.701165 
147/110  source=1.334839854170034      calc=1.336364     erros=0.001524  lcm=16170     evaluate=0.71266  
151/113  source=1.334839854170034      calc=1.336283     erros=0.001443  lcm=17063     evaluate=0.724706 
155/116  source=1.334839854170034      calc=1.336207     erros=0.0013670  lcm=17980     evaluate=0.736837 
159/119  source=1.334839854170034      calc=1.336134     erros=0.001295  lcm=18921     evaluate=0.749258 
163/122  source=1.334839854170034      calc=1.336066     erros=0.001226  lcm=19886     evaluate=0.762236 
167/125  source=1.334839854170034      calc=1.336        erros=0.0011601  lcm=20875     evaluate=0.775691 
171/128  source=1.334839854170034      calc=1.335938     erros=0.0010976  lcm=21888     evaluate=0.789453 
175/131  source=1.334839854170034      calc=1.335878     erros=0.001038008  lcm=22925     evaluate=0.803645 
179/134  source=1.334839854170034      calc=1.335821     erros=0.00098104  lcm=23986     evaluate=0.818334 
183/137  source=1.334839854170034      calc=1.335766     erros=0.0009266  lcm=25071     evaluate=0.833522 
187/140  source=1.334839854170034      calc=1.335714     erros=0.0008744  lcm=26180     evaluate=0.849305 
191/143  source=1.334839854170034      calc=1.335664     erros=0.0008245  lcm=27313     evaluate=0.865625 
195/146  source=1.334839854170034      calc=1.335616     erros=0.0007766  lcm=28470     evaluate=0.882609 
199/149  source=1.334839854170034      calc=1.33557      erros=0.00073062  lcm=29651     evaluate=0.900289 
203/152  source=1.334839854170034      calc=1.335526     erros=0.0006865  lcm=30856     evaluate=0.91869  
207/155  source=1.334839854170034      calc=1.335484     erros=0.00064402  lcm=32085     evaluate=0.93795  
211/158  source=1.334839854170034      calc=1.335443     erros=0.00060318  lcm=33338     evaluate=0.958083 
215/161  source=1.334839854170034      calc=1.335404     erros=0.0005639  lcm=34615     evaluate=0.979166 
219/164  source=1.334839854170034      calc=1.335366     erros=0.0005260  lcm=35916     evaluate=1.00137  
223/167  source=1.334839854170034      calc=1.335329     erros=0.0004895  lcm=37241     evaluate=1.024737 
227/170  source=1.334839854170034      calc=1.335294     erros=0.0004543  lcm=38590     evaluate=1.04942  
231/173  source=1.334839854170034      calc=1.33526      erros=0.00042026  lcm=39963     evaluate=1.075653 
235/176  source=1.334839854170034      calc=1.335227     erros=0.0003874  lcm=41360     evaluate=1.10355  
239/179  source=1.334839854170034      calc=1.335196     erros=0.0003557  lcm=42781     evaluate=1.133291 
243/182  source=1.334839854170034      calc=1.335165     erros=0.0003250  lcm=44226     evaluate=1.165278 
247/185  source=1.334839854170034      calc=1.335135     erros=0.0002953  lcm=45695     evaluate=1.199802 
251/188  source=1.334839854170034      calc=1.335106     erros=0.0002665  lcm=47188     evaluate=1.237387 
255/191  source=1.334839854170034      calc=1.335079     erros=0.0002387  lcm=48705     evaluate=1.278361 
259/194  source=1.334839854170034      calc=1.335052     erros=0.0002117  lcm=50246     evaluate=1.323728 
263/197  source=1.334839854170034      calc=1.335025     erros=0.0001855  lcm=51811     evaluate=1.374445 
267/200  source=1.334839854170034      calc=1.335        erros=0.00016015  lcm=53400     evaluate=1.431702 
271/203  source=1.334839854170034      calc=1.334975     erros=0.0001355  lcm=55013     evaluate=1.497828 
275/206  source=1.334839854170034      calc=1.334951     erros=0.00011160  lcm=56650     evaluate=1.575736 
279/209  source=1.334839854170034      calc=1.334928     erros=0.00008838  lcm=58311     evaluate=1.670771 
283/212  source=1.334839854170034      calc=1.334906     erros=0.000065806  lcm=59996     evaluate=1.792673 
287/215  source=1.334839854170034      calc=1.334884     erros=0.00004387  lcm=61705     evaluate=1.962672 
291/218  source=1.334839854170034      calc=1.334862     erros=0.00002253  lcm=63438     evaluate=2.246064 
295/221  source=1.334839854170034      calc=1.334842     erros=0.000001775  lcm=65195     evaluate=3.343694 
299/224  source=1.334839854170034      calc=1.334821     erros=-0.00001843  lcm=66976     evaluate=2.321515 
594/445  source=1.334839854170034      calc=1.334831     erros=-0.000008393  lcm=264330    evaluate=2.36501  
889/666  source=1.334839854170034      calc=1.334835     erros=-0.0000050193  lcm=592074    evaluate=2.413169

$\sqrt[6/12]{2}$ 三全音——取99/70 source=1.414213562373095 calc=1.414286 erros=0.00007215 lcm=6930 evaluate=2.221397

2/1  source=1.414213562373095      calc=2            erros=0.5858  lcm=2         evaluate=0.081736 
1/1  source=1.414213562373095      calc=1            erros=-0.4142  lcm=1         evaluate=0.38279  
3/2  source=1.414213562373095      calc=1.5          erros=0.08579  lcm=6         evaluate=0.677488 
4/3  source=1.414213562373095      calc=1.333333     erros=-0.0808802  lcm=12        evaluate=0.552567 
7/5  source=1.414213562373095      calc=1.4          erros=-0.01421  lcm=35        evaluate=1.075372 
10/7  source=1.414213562373095      calc=1.428571     erros=0.01436  lcm=70        evaluate=0.920297 
17/12  source=1.414213562373095      calc=1.416667     erros=0.002453  lcm=204       evaluate=1.455487 
24/17  source=1.414213562373095      calc=1.411765     erros=-0.002449  lcm=408       evaluate=1.305681 
41/29  source=1.414213562373095      calc=1.413793     erros=-0.00042046  lcm=1189      evaluate=1.838684 
58/41  source=1.414213562373095      calc=1.414634     erros=0.00042058  lcm=2378      evaluate=1.688045 
99/70  source=1.414213562373095      calc=1.414286     erros=0.00007215  lcm=6930      evaluate=2.221397 
140/99  source=1.414213562373095      calc=1.414141     erros=-0.00007215  lcm=13860     evaluate=2.070882 
239/169  source=1.414213562373095      calc=1.414201     erros=-0.00001238  lcm=40391     evaluate=2.604137 
338/239  source=1.414213562373095      calc=1.414226     erros=0.00001238  lcm=80782     evaluate=2.453622 
577/408  source=1.414213562373095      calc=1.414216     erros=0.000002124  lcm=235416    evaluate=2.986927 
816/577  source=1.414213562373095      calc=1.414211     erros=-0.000002124  lcm=470832    evaluate=2.836413

$\sqrt[7/12]{2}$ 纯五度——取3/2 source=1.498307076876681 calc=1.5 erros=0.001693 lcm=6 evaluate=2.382267

2/1  source=1.498307076876681      calc=2            erros=0.50169  lcm=2         evaluate=0.14905  
1/1  source=1.498307076876681      calc=1            erros=-0.49831  lcm=1         evaluate=0.3025   
3/2  source=1.498307076876681      calc=1.5          erros=0.001693  lcm=6         evaluate=2.382267 
4/3  source=1.498307076876681      calc=1.333333     erros=-0.1650  lcm=12        evaluate=0.242925 
7/5  source=1.498307076876681      calc=1.4          erros=-0.0983071  lcm=35        evaluate=0.235381 
10/7  source=1.498307076876681      calc=1.428571     erros=-0.06974  lcm=70        evaluate=0.233969 
13/9  source=1.498307076876681      calc=1.444444     erros=-0.05386  lcm=117       evaluate=0.234641 
16/11  source=1.498307076876681      calc=1.454545     erros=-0.04376  lcm=176       evaluate=0.236166 
19/13  source=1.498307076876681      calc=1.461538     erros=-0.03677  lcm=247       evaluate=0.238158 
22/15  source=1.498307076876681      calc=1.466667     erros=-0.031640  lcm=330       evaluate=0.240507 
25/17  source=1.498307076876681      calc=1.470588     erros=-0.02772  lcm=425       evaluate=0.243012 
28/19  source=1.498307076876681      calc=1.473684     erros=-0.02462  lcm=532       evaluate=0.245756 
31/21  source=1.498307076876681      calc=1.47619      erros=-0.02212  lcm=651       evaluate=0.248424 
34/23  source=1.498307076876681      calc=1.478261     erros=-0.02004621  lcm=782       evaluate=0.251364 
37/25  source=1.498307076876681      calc=1.48         erros=-0.0183071  lcm=925       evaluate=0.25431  
40/27  source=1.498307076876681      calc=1.481481     erros=-0.01683  lcm=1080      evaluate=0.257204 
43/29  source=1.498307076876681      calc=1.482759     erros=-0.01555  lcm=1247      evaluate=0.260336 
46/31  source=1.498307076876681      calc=1.483871     erros=-0.01444  lcm=1426      evaluate=0.263373 
49/33  source=1.498307076876681      calc=1.484848     erros=-0.01346  lcm=1617      evaluate=0.2666   
52/35  source=1.498307076876681      calc=1.485714     erros=-0.01259  lcm=1820      evaluate=0.269939 
55/37  source=1.498307076876681      calc=1.486486     erros=-0.011821  lcm=2035      evaluate=0.273064 
58/39  source=1.498307076876681      calc=1.487179     erros=-0.01113  lcm=2262      evaluate=0.276259 
61/41  source=1.498307076876681      calc=1.487805     erros=-0.0105022  lcm=2501      evaluate=0.279663 
64/43  source=1.498307076876681      calc=1.488372     erros=-0.009935  lcm=2752      evaluate=0.283008 
67/45  source=1.498307076876681      calc=1.488889     erros=-0.009418  lcm=3015      evaluate=0.286398 
70/47  source=1.498307076876681      calc=1.489362     erros=-0.008945  lcm=3290      evaluate=0.289822 
73/49  source=1.498307076876681      calc=1.489796     erros=-0.008511  lcm=3577      evaluate=0.29326  
76/51  source=1.498307076876681      calc=1.490196     erros=-0.0081110  lcm=3876      evaluate=0.296734 
79/53  source=1.498307076876681      calc=1.490566     erros=-0.0077410  lcm=4187      evaluate=0.300251 
82/55  source=1.498307076876681      calc=1.490909     erros=-0.007398  lcm=4510      evaluate=0.303797 
85/57  source=1.498307076876681      calc=1.491228     erros=-0.007079007  lcm=4845      evaluate=0.307381 
88/59  source=1.498307076876681      calc=1.491525     erros=-0.006782  lcm=5192      evaluate=0.310975 
91/61  source=1.498307076876681      calc=1.491803     erros=-0.0065038  lcm=5551      evaluate=0.314647 
94/63  source=1.498307076876681      calc=1.492063     erros=-0.006244  lcm=5922      evaluate=0.318303 
97/65  source=1.498307076876681      calc=1.492308     erros=-0.005999  lcm=6305      evaluate=0.322079 
100/67  source=1.498307076876681      calc=1.492537     erros=-0.005770  lcm=6700      evaluate=0.325787 
103/69  source=1.498307076876681      calc=1.492754     erros=-0.005553  lcm=7107      evaluate=0.329629 
106/71  source=1.498307076876681      calc=1.492958     erros=-0.005349  lcm=7526      evaluate=0.333445 
109/73  source=1.498307076876681      calc=1.493151     erros=-0.005156  lcm=7957      evaluate=0.337312 
112/75  source=1.498307076876681      calc=1.493333     erros=-0.004974  lcm=8400      evaluate=0.341155 
115/77  source=1.498307076876681      calc=1.493506     erros=-0.00480058  lcm=8855      evaluate=0.345112 
118/79  source=1.498307076876681      calc=1.493671     erros=-0.004636  lcm=9322      evaluate=0.349102 
121/81  source=1.498307076876681      calc=1.493827     erros=-0.004480  lcm=9801      evaluate=0.353087 
124/83  source=1.498307076876681      calc=1.493976     erros=-0.004331  lcm=10292     evaluate=0.357162 
127/85  source=1.498307076876681      calc=1.494118     erros=-0.004189  lcm=10795     evaluate=0.361278 
130/87  source=1.498307076876681      calc=1.494253     erros=-0.00405420  lcm=11310     evaluate=0.365364 
133/89  source=1.498307076876681      calc=1.494382     erros=-0.0039251  lcm=11837     evaluate=0.369528 
136/91  source=1.498307076876681      calc=1.494505     erros=-0.0038016  lcm=12376     evaluate=0.373743 
139/93  source=1.498307076876681      calc=1.494624     erros=-0.003683  lcm=12927     evaluate=0.378049 
142/95  source=1.498307076876681      calc=1.494737     erros=-0.0035702  lcm=13490     evaluate=0.382301 
145/97  source=1.498307076876681      calc=1.494845     erros=-0.003462  lcm=14065     evaluate=0.386603 
148/99  source=1.498307076876681      calc=1.494949     erros=-0.003358  lcm=14652     evaluate=0.390971 
151/101  source=1.498307076876681      calc=1.49505      erros=-0.003258  lcm=15251     evaluate=0.3954   
154/103  source=1.498307076876681      calc=1.495146     erros=-0.003161  lcm=15862     evaluate=0.399997 
157/105  source=1.498307076876681      calc=1.495238     erros=-0.0030690  lcm=16485     evaluate=0.404459 
160/107  source=1.498307076876681      calc=1.495327     erros=-0.002980  lcm=17120     evaluate=0.409032 
163/109  source=1.498307076876681      calc=1.495413     erros=-0.002894  lcm=17767     evaluate=0.413694 
166/111  source=1.498307076876681      calc=1.495495     erros=-0.002812  lcm=18426     evaluate=0.418269 
169/113  source=1.498307076876681      calc=1.495575     erros=-0.002732  lcm=19097     evaluate=0.423037 
172/115  source=1.498307076876681      calc=1.495652     erros=-0.002655  lcm=19780     evaluate=0.427822 
175/117  source=1.498307076876681      calc=1.495726     erros=-0.0025806  lcm=20475     evaluate=0.432667 
178/119  source=1.498307076876681      calc=1.495798     erros=-0.0025088  lcm=21182     evaluate=0.43755  
181/121  source=1.498307076876681      calc=1.495868     erros=-0.002439  lcm=21901     evaluate=0.442556 
184/123  source=1.498307076876681      calc=1.495935     erros=-0.002372  lcm=22632     evaluate=0.447524 
187/125  source=1.498307076876681      calc=1.496        erros=-0.00230708  lcm=23375     evaluate=0.452562 
190/127  source=1.498307076876681      calc=1.496063     erros=-0.0022441  lcm=24130     evaluate=0.457679 
193/129  source=1.498307076876681      calc=1.496124     erros=-0.0021830  lcm=24897     evaluate=0.462873 
196/131  source=1.498307076876681      calc=1.496183     erros=-0.002124  lcm=25676     evaluate=0.468082 
199/133  source=1.498307076876681      calc=1.496241     erros=-0.0020665  lcm=26467     evaluate=0.473412 
202/135  source=1.498307076876681      calc=1.496296     erros=-0.002010781  lcm=27270     evaluate=0.478793 
205/137  source=1.498307076876681      calc=1.49635      erros=-0.001957  lcm=28085     evaluate=0.484172 
208/139  source=1.498307076876681      calc=1.496403     erros=-0.0019042  lcm=28912     evaluate=0.489748 
211/141  source=1.498307076876681      calc=1.496454     erros=-0.001853  lcm=29751     evaluate=0.495374 
214/143  source=1.498307076876681      calc=1.496503     erros=-0.0018036  lcm=30602     evaluate=0.500985 
217/145  source=1.498307076876681      calc=1.496552     erros=-0.001755  lcm=31465     evaluate=0.506809 
220/147  source=1.498307076876681      calc=1.496599     erros=-0.0017084  lcm=32340     evaluate=0.51254  
223/149  source=1.498307076876681      calc=1.496644     erros=-0.001663  lcm=33227     evaluate=0.518362 
226/151  source=1.498307076876681      calc=1.496689     erros=-0.001618  lcm=34126     evaluate=0.524479 
229/153  source=1.498307076876681      calc=1.496732     erros=-0.0015751  lcm=35037     evaluate=0.530428 
232/155  source=1.498307076876681      calc=1.496774     erros=-0.001533  lcm=35960     evaluate=0.536548 
235/157  source=1.498307076876681      calc=1.496815     erros=-0.001492  lcm=36895     evaluate=0.542747 
238/159  source=1.498307076876681      calc=1.496855     erros=-0.001452  lcm=37842     evaluate=0.549046 
241/161  source=1.498307076876681      calc=1.496894     erros=-0.001413  lcm=38801     evaluate=0.555436 
244/163  source=1.498307076876681      calc=1.496933     erros=-0.001375  lcm=39772     evaluate=0.561909 
247/165  source=1.498307076876681      calc=1.49697      erros=-0.001337  lcm=40755     evaluate=0.568778 
250/167  source=1.498307076876681      calc=1.497006     erros=-0.00130109  lcm=41750     evaluate=0.575364 
253/169  source=1.498307076876681      calc=1.497041     erros=-0.001266  lcm=42757     evaluate=0.582063 
256/171  source=1.498307076876681      calc=1.497076     erros=-0.0012311  lcm=43776     evaluate=0.589089 
259/173  source=1.498307076876681      calc=1.49711      erros=-0.001197  lcm=44807     evaluate=0.596233 
262/175  source=1.498307076876681      calc=1.497143     erros=-0.001164  lcm=45850     evaluate=0.603377 
265/177  source=1.498307076876681      calc=1.497175     erros=-0.001132  lcm=46905     evaluate=0.610544 
268/179  source=1.498307076876681      calc=1.497207     erros=-0.00110037  lcm=47972     evaluate=0.617967 
271/181  source=1.498307076876681      calc=1.497238     erros=-0.00106951  lcm=49051     evaluate=0.625491 
274/183  source=1.498307076876681      calc=1.497268     erros=-0.0010393  lcm=50142     evaluate=0.633158 
277/185  source=1.498307076876681      calc=1.497297     erros=-0.00100978  lcm=51245     evaluate=0.640947 
280/187  source=1.498307076876681      calc=1.497326     erros=-0.00098087  lcm=52360     evaluate=0.648889 
283/189  source=1.498307076876681      calc=1.497354     erros=-0.0009526  lcm=53487     evaluate=0.656965 
286/191  source=1.498307076876681      calc=1.497382     erros=-0.0009249  lcm=54626     evaluate=0.665206 
289/193  source=1.498307076876681      calc=1.497409     erros=-0.0008978  lcm=55777     evaluate=0.673593 
292/195  source=1.498307076876681      calc=1.497436     erros=-0.0008712  lcm=56940     evaluate=0.682173 
295/197  source=1.498307076876681      calc=1.497462     erros=-0.0008451  lcm=58115     evaluate=0.690948 
298/199  source=1.498307076876681      calc=1.497487     erros=-0.0008196  lcm=59302     evaluate=0.699863 
301/201  source=1.498307076876681      calc=1.497512     erros=-0.0007946  lcm=60501     evaluate=0.70897  
304/203  source=1.498307076876681      calc=1.497537     erros=-0.00077013  lcm=61712     evaluate=0.718251 
307/205  source=1.498307076876681      calc=1.497561     erros=-0.00074610  lcm=62935     evaluate=0.727757 
310/207  source=1.498307076876681      calc=1.497585     erros=-0.0007225  lcm=64170     evaluate=0.737496 
313/209  source=1.498307076876681      calc=1.497608     erros=-0.0006994  lcm=65417     evaluate=0.747429 
316/211  source=1.498307076876681      calc=1.49763      erros=-0.0006767  lcm=66676     evaluate=0.757619 
319/213  source=1.498307076876681      calc=1.497653     erros=-0.0006545  lcm=67947     evaluate=0.768005 
322/215  source=1.498307076876681      calc=1.497674     erros=-0.0006327  lcm=69230     evaluate=0.778655 
325/217  source=1.498307076876681      calc=1.497696     erros=-0.0006112  lcm=70525     evaluate=0.789645 
328/219  source=1.498307076876681      calc=1.497717     erros=-0.00059018  lcm=71832     evaluate=0.800857 
331/221  source=1.498307076876681      calc=1.497738     erros=-0.0005695  lcm=73151     evaluate=0.812396 
334/223  source=1.498307076876681      calc=1.497758     erros=-0.0005492  lcm=74482     evaluate=0.824244 
337/225  source=1.498307076876681      calc=1.497778     erros=-0.0005293  lcm=75825     evaluate=0.836392 
340/227  source=1.498307076876681      calc=1.497797     erros=-0.0005097200  lcm=77180     evaluate=0.848916 
343/229  source=1.498307076876681      calc=1.497817     erros=-0.00049048  lcm=78547     evaluate=0.861814 
346/231  source=1.498307076876681      calc=1.497835     erros=-0.0004716  lcm=79926     evaluate=0.875082 
349/233  source=1.498307076876681      calc=1.497854     erros=-0.0004530  lcm=81317     evaluate=0.888811 
352/235  source=1.498307076876681      calc=1.497872     erros=-0.0004347  lcm=82720     evaluate=0.903005 
355/237  source=1.498307076876681      calc=1.49789      erros=-0.0004168  lcm=84135     evaluate=0.917584 
358/239  source=1.498307076876681      calc=1.497908     erros=-0.0003991  lcm=85562     evaluate=0.932778 
361/241  source=1.498307076876681      calc=1.497925     erros=-0.0003818  lcm=87001     evaluate=0.948402 
364/243  source=1.498307076876681      calc=1.497942     erros=-0.0003647  lcm=88452     evaluate=0.96471  
367/245  source=1.498307076876681      calc=1.497959     erros=-0.0003479  lcm=89915     evaluate=0.981629 
370/247  source=1.498307076876681      calc=1.497976     erros=-0.0003314  lcm=91390     evaluate=0.999198 
373/249  source=1.498307076876681      calc=1.497992     erros=-0.00031511  lcm=92877     evaluate=1.017584 
376/251  source=1.498307076876681      calc=1.498008     erros=-0.00029911  lcm=94376     evaluate=1.036738 
379/253  source=1.498307076876681      calc=1.498024     erros=-0.0002834  lcm=95887     evaluate=1.05672  
382/255  source=1.498307076876681      calc=1.498039     erros=-0.0002679  lcm=97410     evaluate=1.077726 
385/257  source=1.498307076876681      calc=1.498054     erros=-0.00025260  lcm=98945     evaluate=1.09987  
388/259  source=1.498307076876681      calc=1.498069     erros=-0.0002376  lcm=100492    evaluate=1.123088 
391/261  source=1.498307076876681      calc=1.498084     erros=-0.0002228  lcm=102051    evaluate=1.147676 
394/263  source=1.498307076876681      calc=1.498099     erros=-0.00020822  lcm=103622    evaluate=1.173752 
397/265  source=1.498307076876681      calc=1.498113     erros=-0.0001939  lcm=105205    evaluate=1.201404 
400/267  source=1.498307076876681      calc=1.498127     erros=-0.0001797  lcm=106800    evaluate=1.231166 
403/269  source=1.498307076876681      calc=1.498141     erros=-0.0001658  lcm=108407    evaluate=1.262887 
406/271  source=1.498307076876681      calc=1.498155     erros=-0.00015210  lcm=110026    evaluate=1.297123 
409/273  source=1.498307076876681      calc=1.498168     erros=-0.0001386  lcm=111657    evaluate=1.334294 
412/275  source=1.498307076876681      calc=1.498182     erros=-0.0001253  lcm=113300    evaluate=1.374934 
415/277  source=1.498307076876681      calc=1.498195     erros=-0.0001121  lcm=114955    evaluate=1.42013  
418/279  source=1.498307076876681      calc=1.498208     erros=-0.00009919  lcm=116622    evaluate=1.470142 
421/281  source=1.498307076876681      calc=1.498221     erros=-0.00008644  lcm=118301    evaluate=1.526791 
424/283  source=1.498307076876681      calc=1.498233     erros=-0.00007386  lcm=119992    evaluate=1.592015 
427/285  source=1.498307076876681      calc=1.498246     erros=-0.00006146  lcm=121695    evaluate=1.668771 
430/287  source=1.498307076876681      calc=1.498258     erros=-0.00004924  lcm=123410    evaluate=1.762007 
433/289  source=1.498307076876681      calc=1.49827      erros=-0.000037181  lcm=125137    evaluate=1.880986 
436/291  source=1.498307076876681      calc=1.498282     erros=-0.00002529  lcm=126876    evaluate=2.045361 
439/293  source=1.498307076876681      calc=1.498294     erros=-0.00001356  lcm=128627    evaluate=2.313074 
442/295  source=1.498307076876681      calc=1.498305     erros=-0.000001992  lcm=130390    evaluate=3.143089 
445/297  source=1.498307076876681      calc=1.498316     erros=0.000009421  lcm=132165    evaluate=2.465345 
887/592  source=1.498307076876681      calc=1.498311     erros=0.000003734  lcm=525104    evaluate=2.567703

$\sqrt[8/12]{2}$ 小六度——取227/143 source=1.587401051968199 calc=1.587413 erros=0.00001154 lcm=32461 evaluate=2.682113

2/1  source=1.587401051968199      calc=2            erros=0.4126  lcm=2         evaluate=0.233956 
1/1  source=1.587401051968199      calc=1            erros=-0.58740  lcm=1         evaluate=0.231066 
3/2  source=1.587401051968199      calc=1.5          erros=-0.0874011  lcm=6         evaluate=0.669407 
5/3  source=1.587401051968199      calc=1.666667     erros=0.07927  lcm=15        evaluate=0.512846 
8/5  source=1.587401051968199      calc=1.6          erros=0.01260  lcm=40        evaluate=1.098599 
11/7  source=1.587401051968199      calc=1.571429     erros=-0.01597  lcm=77        evaluate=0.85345  
19/12  source=1.587401051968199      calc=1.583333     erros=-0.0040677  lcm=228       evaluate=1.211684 
27/17  source=1.587401051968199      calc=1.588235     erros=0.0008342  lcm=459       evaluate=1.747823 
46/29  source=1.587401051968199      calc=1.586207     erros=-0.001194  lcm=1334      evaluate=1.360418 
73/46  source=1.587401051968199      calc=1.586957     erros=-0.0004445  lcm=3358      evaluate=1.589088 
100/63  source=1.587401051968199      calc=1.587302     erros=-0.00009946  lcm=6300      evaluate=2.102681 
127/80  source=1.587401051968199      calc=1.5875       erros=0.00009895  lcm=10160     evaluate=2.001137 
227/143  source=1.587401051968199      calc=1.587413     erros=0.00001154  lcm=32461     evaluate=2.682113 
327/206  source=1.587401051968199      calc=1.587379     erros=-0.00002241  lcm=67362     evaluate=2.235351 
554/349  source=1.587401051968199      calc=1.587393     erros=-0.0000085018  lcm=193346    evaluate=2.427322 
781/492  source=1.587401051968199      calc=1.587398     erros=-0.000002678  lcm=384252    evaluate=2.779881

$\sqrt[9/12]{2}$ 大六度——取37/22 source=1.681792830507429 calc=1.681818 erros=0.00002535 lcm=814 evaluate=3.14071

2/1  source=1.681792830507429      calc=2            erros=0.31821  lcm=2         evaluate=0.346771 
1/1  source=1.681792830507429      calc=1            erros=-0.6818  lcm=1         evaluate=0.166343 
3/2  source=1.681792830507429      calc=1.5          erros=-0.1818  lcm=6         evaluate=0.35133  
5/3  source=1.681792830507429      calc=1.666667     erros=-0.01513  lcm=15        evaluate=1.232115 
7/4  source=1.681792830507429      calc=1.75         erros=0.068207  lcm=28        evaluate=0.442592 
12/7  source=1.681792830507429      calc=1.714286     erros=0.03249  lcm=84        evaluate=0.526111 
17/10  source=1.681792830507429      calc=1.7          erros=0.018207  lcm=170       evaluate=0.624537 
22/13  source=1.681792830507429      calc=1.692308     erros=0.010515  lcm=286       evaluate=0.750008 
27/16  source=1.681792830507429      calc=1.6875       erros=0.0057072  lcm=432       evaluate=0.925835 
32/19  source=1.681792830507429      calc=1.684211     erros=0.002418  lcm=608       evaluate=1.224592 
37/22  source=1.681792830507429      calc=1.681818     erros=0.00002535  lcm=814       evaluate=3.14071  
42/25  source=1.681792830507429      calc=1.68         erros=-0.001793  lcm=1050      evaluate=1.235825 
79/47  source=1.681792830507429      calc=1.680851     erros=-0.0009418  lcm=3713      evaluate=1.241179 
116/69  source=1.681792830507429      calc=1.681159     erros=-0.0006334  lcm=8004      evaluate=1.246668 
153/91  source=1.681792830507429      calc=1.681319     erros=-0.0004741  lcm=13923     evaluate=1.252264 
190/113  source=1.681792830507429      calc=1.681416     erros=-0.00037690  lcm=21470     evaluate=1.257858 
227/135  source=1.681792830507429      calc=1.681481     erros=-0.0003113  lcm=30645     evaluate=1.263641 
264/157  source=1.681792830507429      calc=1.681529     erros=-0.0002642  lcm=41448     evaluate=1.269315 
301/179  source=1.681792830507429      calc=1.681564     erros=-0.0002286  lcm=53879     evaluate=1.275214 
338/201  source=1.681792830507429      calc=1.681592     erros=-0.00020079071  lcm=67938     evaluate=1.2812   
375/223  source=1.681792830507429      calc=1.681614     erros=-0.0001785  lcm=83625     evaluate=1.287194 
412/245  source=1.681792830507429      calc=1.681633     erros=-0.00016018  lcm=100940    evaluate=1.29336  
449/267  source=1.681792830507429      calc=1.681648     erros=-0.0001449  lcm=119883    evaluate=1.299553 
486/289  source=1.681792830507429      calc=1.681661     erros=-0.0001319  lcm=140454    evaluate=1.305988 
523/311  source=1.681792830507429      calc=1.681672     erros=-0.000120805  lcm=162653    evaluate=1.312284 
560/333  source=1.681792830507429      calc=1.681682     erros=-0.0001111  lcm=186480    evaluate=1.31897  
597/355  source=1.681792830507429      calc=1.68169      erros=-0.00010269  lcm=211935    evaluate=1.325371 
634/377  source=1.681792830507429      calc=1.681698     erros=-0.00009522  lcm=239018    evaluate=1.332057 
671/399  source=1.681792830507429      calc=1.681704     erros=-0.00008857  lcm=267729    evaluate=1.338866 
708/421  source=1.681792830507429      calc=1.68171      erros=-0.00008262  lcm=298068    evaluate=1.345757 
745/443  source=1.681792830507429      calc=1.681716     erros=-0.00007725  lcm=330035    evaluate=1.352822 
782/465  source=1.681792830507429      calc=1.68172      erros=-0.0000724004  lcm=363630    evaluate=1.359929 
819/487  source=1.681792830507429      calc=1.681725     erros=-0.00006798  lcm=398853    evaluate=1.367212 
856/509  source=1.681792830507429      calc=1.681729     erros=-0.000063950  lcm=435704    evaluate=1.374564 
893/531  source=1.681792830507429      calc=1.681733     erros=-0.0000602505  lcm=474183    evaluate=1.382066 
930/553  source=1.681792830507429      calc=1.681736     erros=-0.00005684  lcm=514290    evaluate=1.389742 
967/575  source=1.681792830507429      calc=1.681739     erros=-0.00005370007  lcm=556025    evaluate=1.397478

$\sqrt[10/12]{2}$ 小七度——取98/55 source=1.781797436280679 calc=1.781818 erros=0.000020746 lcm=5390 evaluate=2.817271

2/1  source=1.781797436280679      calc=2            erros=0.21820  lcm=2         evaluate=0.51063  
1/1  source=1.781797436280679      calc=1            erros=-0.7818  lcm=1         evaluate=0.106904 
3/2  source=1.781797436280679      calc=1.5          erros=-0.2818  lcm=6         evaluate=0.160983 
5/3  source=1.781797436280679      calc=1.666667     erros=-0.1151  lcm=15        evaluate=0.350879 
7/4  source=1.781797436280679      calc=1.75         erros=-0.03180  lcm=28        evaluate=0.773994 
9/5  source=1.781797436280679      calc=1.8          erros=0.018203  lcm=45        evaluate=0.913251 
16/9  source=1.781797436280679      calc=1.777778     erros=-0.0040197  lcm=144       evaluate=1.316625 
25/14  source=1.781797436280679      calc=1.785714     erros=0.003917  lcm=350       evaluate=1.135012 
41/23  source=1.781797436280679      calc=1.782609     erros=0.0008113  lcm=943       evaluate=1.603563 
57/32  source=1.781797436280679      calc=1.78125      erros=-0.0005474  lcm=1824      evaluate=1.631183 
98/55  source=1.781797436280679      calc=1.781818     erros=0.000020746  lcm=5390      evaluate=2.817271 
155/87  source=1.781797436280679      calc=1.781609     erros=-0.0001882  lcm=13485     evaluate=1.660455 
253/142  source=1.781797436280679      calc=1.78169      erros=-0.00010730  lcm=35926     evaluate=1.691696 
351/197  source=1.781797436280679      calc=1.781726     erros=-0.00007155  lcm=69147     evaluate=1.725504 
449/252  source=1.781797436280679      calc=1.781746     erros=-0.000051405  lcm=113148    evaluate=1.762171 
547/307  source=1.781797436280679      calc=1.781759     erros=-0.00003848  lcm=167929    evaluate=1.802202 
645/362  source=1.781797436280679      calc=1.781768     erros=-0.000029480  lcm=233490    evaluate=1.846338 
743/417  source=1.781797436280679      calc=1.781775     erros=-0.00002286  lcm=309831    evaluate=1.895361 
841/472  source=1.781797436280679      calc=1.78178      erros=-0.00001778  lcm=396952    evaluate=1.950699 
939/527  source=1.781797436280679      calc=1.781784     erros=-0.00001376  lcm=494853    evaluate=2.014143

$\sqrt[11/12]{2}$ 大七度——185/98 source=1.887748625363387 calc=1.887755 erros=0.000006477 lcm=18130 evaluate=3.059427

2/1  source=1.887748625363387      calc=2            erros=0.1123  lcm=2         evaluate=0.799105 
1/1  source=1.887748625363387      calc=1            erros=-0.8877  lcm=1         evaluate=0.051734 
3/2  source=1.887748625363387      calc=1.5          erros=-0.3877  lcm=6         evaluate=0.022429 
5/3  source=1.887748625363387      calc=1.666667     erros=-0.22108  lcm=15        evaluate=0.067405 
7/4  source=1.887748625363387      calc=1.75         erros=-0.1377  lcm=28        evaluate=0.137487 
9/5  source=1.887748625363387      calc=1.8          erros=-0.08775  lcm=45        evaluate=0.230147 
11/6  source=1.887748625363387      calc=1.833333     erros=-0.05442  lcm=66        evaluate=0.354469 
13/7  source=1.887748625363387      calc=1.857143     erros=-0.0306058  lcm=91        evaluate=0.534676 
15/8  source=1.887748625363387      calc=1.875        erros=-0.01275  lcm=120       evaluate=0.854899 
17/9  source=1.887748625363387      calc=1.888889     erros=0.0011403  lcm=153       evaluate=1.850635 
32/17  source=1.887748625363387      calc=1.882353     erros=-0.005396  lcm=544       evaluate=0.900129 
49/26  source=1.887748625363387      calc=1.884615     erros=-0.003133  lcm=1274      evaluate=0.951455 
66/35  source=1.887748625363387      calc=1.885714     erros=-0.0020343  lcm=2310      evaluate=1.009779 
83/44  source=1.887748625363387      calc=1.886364     erros=-0.001385  lcm=3652      evaluate=1.077285 
100/53  source=1.887748625363387      calc=1.886792     erros=-0.0009562  lcm=5300      evaluate=1.157313 
117/62  source=1.887748625363387      calc=1.887097     erros=-0.0006519  lcm=7254      evaluate=1.25553  
134/71  source=1.887748625363387      calc=1.887324     erros=-0.0004247  lcm=9514      evaluate=1.382736 
151/80  source=1.887748625363387      calc=1.8875       erros=-0.0002486  lcm=12080     evaluate=1.563465 
168/89  source=1.887748625363387      calc=1.88764      erros=-0.00010818  lcm=14952     evaluate=1.878503 
185/98  source=1.887748625363387      calc=1.887755     erros=0.000006477  lcm=18130     evaluate=3.059427 
353/187  source=1.887748625363387      calc=1.887701     erros=-0.00004809060  lcm=66011     evaluate=1.908132 
538/285  source=1.887748625363387      calc=1.887719     erros=-0.00002933  lcm=153330    evaluate=1.939874 
723/383  source=1.887748625363387      calc=1.887728     erros=-0.000020166  lcm=276909    evaluate=1.974212 
908/481  source=1.887748625363387      calc=1.887734     erros=-0.00001474  lcm=436748    evaluate=2.011387

$\sqrt[12/12]{2}$ 纯八度

参考：

多位小数的分数逼近法-维普期刊中文期刊服务平台