Table XV.— Comparative Table of Equal Temper iments. (See 



System- 

 atic No. 



Name. 



Log!). 



Error of Vth. 



Error of Hli-d. 





Error of 3rd. 



Melodic Errors. 



Harnio 



nicEmrs. 



CompaiTison. 



Order. 





Order. 





Ord 



er. 



EiTor. 



Order. 





Order. 





Sum of 

 Orders. 



Order 

 of sums. 



2, 13^ 19 



85 

 30 



Mesotonic 



Cycle of 81 



Least Errors and Beats 



Woolhoiise's Equal Harmony . . 



•1747426 



•1746703 

 •1746439 

 •1746388 



32 

 31 



34 

 35 



- ^001.3616 



- •0013488 

 -•0014197 

 -•0014205 

 -•0014474 

 -•0014525 



2 

 1 

 6 

 7 

 9 

 10 



- -0000514 

 



-■0002838 

 -■0002870 

 - -0003946 



- -0004150 



1' 

 1) 



1 





- •001.3102 

 -•0013488 

 -•0011359 



- •0011335 



- •0010528 

 -•0010375 



2 

 4 



8 

 9 



-0001527 

 •0001528 

 •0001541 

 •0001542 

 -00015.59 

 •0001562 



11 

 12 

 6 

 6 



2 



•0001513 

 •0001665 

 •0001363 

 •0001361 

 •0001389 

 •0001338 



63 

 164 

 64 

 66 

 68 



21 

 2( 



5 



17 

 15 

 34 

 10 

 47 



Least Beats of V and III 



Equal and opp. Beats of 3 and 4 



•1747723 

 '1746359 

 •1747872 

 •1746200 

 ■1747900 



30 

 37 

 29 



28 



-•0013190 

 -•0014554 

 - -0013039 

 -■0014713 

 -•0013013 



3 

 11 



4 

 13 



5 



+ -0001190 



- -0004266 

 +■0001794 



- -0004902 

 + -0001898 



19 

 11 

 20 

 10 

 21 



-■0014380 

 - ^0010288 

 -■00148.33 

 - -0009811 

 - -0014911 



11 



5 

 12 

 7 



■0001535 

 •0001564 

 •0001541 

 •0001578 

 •0001543 



15 



16 

 4 

 17 



•0001709 

 •0001337 

 •0001718 

 •0001342 

 •0001812 



70 

 71 

 74 

 77 



6 



9 

 10 



43 



9 

 16 

 5 



Dr. Smith's Equal Harmony . . 



Least Beats of 3, HI, V 



Equal Beats of 6 and V 



•1745974 



•1745927 

 •1744404 

 •1748582 



27 

 40 

 41 

 26 



- •00149.39 

 -•0012694 

 -•0014986 

 -•0015309 

 -•0012331 



14 



18 



- -0005806 

 - -0003174 

 - -0005994 

 -■0007286 

 + -0004626 



22 



7 

 24 



- -0009133 



- -001-5868 



- -0008992 

 -■0008023 



- ■0016957 



14 

 10 

 15 

 18 

 13 



•0001601 

 •0001563 

 •0001606 

 ■0001648 

 ■0001597 



7 



18 

 8 

 9 



19 



•0001367 

 •0002029 

 •0001375 

 •0001451 

 •0002325 



83 

 86 

 86 

 93 

 94 



11 

 12 

 13 

 14 

 15 



^21° 



37 

 24, 27 

 4 



Equal Errors of ni and 3 



Botnieu's Theoretic 



Equal and opp. Beats of 6 and 4 



Druhisch's least Errors 



Equal and opp. Beats of III & V 



•1745199 

 •1745163 

 •1748924 

 •1749200 

 •1749352 

 •1749188 



42 

 44 

 25 

 23 

 22 

 24 



- ^0015414 

 -•0015750 

 -•0011989 

 - ^0011713 

 -•0011561 

 -•0011725 



19 



22 

 15 

 17 

 19 

 16 



— -0007707 

 -■0009050 

 + -0005994 

 + ■0007108 

 + ■0007706 

 + ■0007050 



6 

 5 

 25 



20 



- ■0006700 

 -■0017983 

 -■0018811 

 -■0019267 

 -■0018775 



16 

 17 

 20 

 21 



26 



'0001664 

 •0001719 

 •0001639 

 •0001679 

 •0001705 

 •0001983 



10 

 14 

 20 

 22 

 28 

 21 



•0001485 

 •0001628 

 •0002625 

 •0002950 

 •0003127 

 •0002936 



96 

 101 

 102 

 110 

 1114 

 1114 



16 



18 

 19 

 201 

 20 ( 



6 

 38 



12, 18 

 46 

 49 





■1749674 

 •1745200 

 •17429.30 

 •1750123 

 •1750175 

 •1742807 



21 

 43 

 45 

 20 

 19 

 46 



- -0011239 

 -■0015713 

 -•0017983 

 -■0010790 

 -•00107.38 

 -•0018106 



21 

 20 



23 



+ •0008994 

 -•0008902 

 -■0017982 

 +■0010790 

 +■0011008 

 -•0018474 



80 

 23 



31 

 32 

 2 





28 

 24 

 25 

 29 



•0001764 

 •0001706 

 •0002329 

 •0001863 

 •0001875 

 •0002375 



24 

 18 

 25 

 29 

 80 

 26 



•0003533 

 •0001589 

 •0003587 

 •0004168 

 •0004247 

 •0003858 



119 

 121 

 125 

 127 

 1130 

 1130 



21 

 22 

 23 

 24 

 251 

 25 f 



Equal Beats of IH and 4 



Cycle of 22 



Perfect 3rds and Vltlis 



EiTors of III and V eq. and op 

 Smimir's Cycle of 43 



- ■0016811 

 



- ^0020580 

 -■0021736 

 +•0000368 



41 



22 

 42 



Cycle of 67 



Cycle of 67 



liomieu's Anacratic 



Musicians' Cycle of 55 



•1751830 



■17.52270 

 •1751938 

 ■1751456 



18 

 47 

 16 

 17 

 48 



-•0019683 

 -■0018117 

 - -0008643 

 -•0008975 

 -•00194.57 



25 

 28 



31 



+ •0015218 

 -•0018518 

 +•0021378 

 + •0026050 

 -•0023878 



8 



3 

 3 



3 



3 

 5 

 4 



-•0026901 

 + •0000401 

 -■0028021 

 -■0027025 

 +■0004421 



27 

 80 



31 

 34 



•0002177 

 •0002378 

 •0002568 

 •0002482 

 •0002961 



31 

 27 

 34 



•0006077 

 •0008873 

 •0008306 

 •0007656 

 •0006140 



134 

 136 

 147 

 148 

 149 



26 

 27 

 28 

 29 

 80 



64 



51 

 67 

 50, 53 



Marsh's 



X}rohisch's V and HI combinec 



Nov Wolf 



•1752790 

 •1754169 

 •175.5418 

 ■175.5562 

 •1756008 



15 

 14 

 13 

 12 

 11 



- •0008123 

 -•0006744 



- •0005495 



- •0005351 



- •0004905 



83 

 34 

 35 

 37 



+•00214.58 

 + •0026974 

 +•0031970 

 +•0032646 

 +•0034333 



87 

 38 

 39 

 40 

 41 



-■0029581 

 -•0038718 

 -•0037465 

 -•0037897 

 -•0039235 





35 

 37 



•0002794 

 •0008511 

 •0004297 

 •0004397 

 ■0004714 



35 

 37 



40 



•0009600 

 •0013524 

 ■0017784 

 •0018256 

 •0019940 



160 

 157 

 160 

 163 

 168 



81 



33 

 34 

 35 



55 

 45 

 66 



86!52 

 40 



Least III and V AVolves 



Cycle of 45 



Drohiscli's Cycle of 118 . . 



Least Wolf Seats 



Cycle of 65 



■1757201 

 ■1738940 



•1 760259 

 •17.50275 

 •1759867 



10 

 49 

 9 



8 



-•0003712 



- •0021973 

 -•0003356 



- •0000654 

 - -0001638 



- -0001046 



38 

 36 

 39 

 43 

 41 

 42 



+ •0039102 

 - •0033942 

 + •0040526 

 +•0051334 

 +•0047898 

 + •0049766 



42 

 16 

 43 

 48 

 44 

 45 



- ^0042814 

 + ■0011969 



- -0043882 

 - -0051988 



- -0049036 

 - -0050812 



40 



41 

 51 

 43 

 44 



■0005648 

 ■0004461 

 ■0005939 

 •0009584 

 •0007564 

 •0008164 



42 

 36 

 43 

 28 

 45 

 46 



■0024829 

 •0012835 

 •0026391 

 •0039900 

 •0034669 

 •0037795 



1175 

 176 

 176 

 181 

 184 



8 

 3 

 3 



3 

 4( 



3 



!i 



3 



68 

 32 

 59 

 44 

 48 

 1 



26 



No III M'olf 



Drobisc/i's \io\m 



No 3i-d Wolf 



X. Merca/ur and Drobiscli . . . 



Pyth.\goee.\n 



Error of V and 3 eq. and opp. . 



•1760300 

 •1760322 

 •1700368 

 •1760800 



•1760913 

 •1733938 



5 

 4 

 3 



50 



51 



- •0000613 



- •0000591 



- -0000545 

 -•0000113 



- •0024213 

 



- -0026975 



44 



40 

 47 

 40 

 48 

 48 



+•0051498 

 + •0051586 

 + •0051770 

 + •0053498 

 -•0042902 

 +•0053950 

 -•00539.50 



46 



50 

 26 

 51 

 84 



--00.52111 

 _. 00.521 77 

 - -0052315 

 -■00-53611 

 - -0018689 

 - -0053950 



45 

 46 

 47 

 49 



50 

 48 



•0008628 

 •0008651 

 •0008708 

 •0009185 

 •0006244 

 •0009314 

 •0009028 



47 

 48 

 49 

 50 

 41 

 61 

 44 



•0040169 

 •0040292 

 •0040549 

 •0043004 

 •0019977 

 •00436.59 

 •0082188 



187 

 1192 

 192 

 198 

 199 

 201 

 225 



41 

 421 

 42} 

 48 

 44 

 45 

 46 



