XII. Liste der besprochenen Intervalle


In den vorigen Kapiteln wurden (abgesehen von den gleichstufigen Temperaturen) folgende Intervalle besprochen:
 
Mikrointervalle
  Zahlenverhältnis         Centmaß
  R1/53 = 3/284/53 = O1/17593,1378    [R1/53] =  r/53  = 0,06820841 
  R10/53 = 310/2840/53 = O1/1759,3137    [R10/53] =  10r/53  = 0,6820841 
  R16/53 = 316/21344/53 = O1/1099,5711    [R16/53] =  16r/53  = 1,0913346 
  X = P/Ψ = (38·5)/215 = O1/614,2126    [X] =  x  = 1,9537208 
  R  = 353/284 = O1/331,9460    [R] =  r  = 3,6150459 
  Y = Φ/P = 225/(7·314) = O1/315,3899    [Y] =  y  = 3,8048148 
  Z =  Φ/Ψ = X·Y = (5·210)/(7·36) = O1/208,4129   [Z] =  z  = 5,7578022 
 
Kommata
  Q-1 = 265/ 341  = O1/60,4687    [Q-1]    = 19,8449645
  Ψ = (9/8)2:(5/4) = 34/(24·5) = 81/80 = O1/55,7976    [Ψ] =  ψ = 21,5062896
  H = 21/53  = O1/53   [H] =  h = 22,6415094
  P = 312/219  = O1/51,1509    [P] =  p = 23,4600104
  Φ = (8/7):(9/8) = 26/(7·32) = 64/63 = O1/44,0139    [Φ] =   φ = 27,2640918
  21/41  = O1/41    [21/41]    = 29,2682927
 
 kleine Sekunden
  25/24 = O1/16,9797   [25/24]    = 70,6724269
  21/20  = O1/14,2067    [21/20]    = 84,4671935
  S = 28/35 = O1/13,3001    [S] = s = 90,2249957
  135/128  = O1/13,0182    [135/128]    = 92,1787165
  21/12  = O1/12   [21/12]   = 100,0000000
  16/15  = O1/10,7401    [16/15]    = 111,7312853
  A = 37/211 = O1/10,5555    [A]   = 113,6850061
  15/14  = O1/10,0466    [15/14]    = 119,4428083
  27/25  = O1/9,0065    [27/25]    = 133,2375749
 
 große Sekunden
  S2 = 216/310  = O1/6,6500    [S2]   = 180,4499913
  10/9  = O1/6,5788    [10/9]    = 182,4037121
  T = 9/8 = 32/23  = O1/5,8849    [T] = t = 203,9100017
  256/225  = O1/5,3700    [256/225]    = 223,4625705
  8/7  = O1/5,1909    [8/7]    = 231,1740935
  21/5  = O1/5    [21/5]    = 240,0000000
 
 kleine Terzen
  7/6 = O1/4,4966   [7/6]   = 266,8709056
  75/64  = O1/4,3703   [75/64]   = 274,5824286
  32/27 = 25/33 = O1/4,0798   [25/33]   = 294,1349974
  6/5  = O1/3,8018   [6/5]   = 315,6412870
  39/214  = O1/3,7784   [39/214]    = 317,5950078
 
 große Terzen
  56/45 = O1/3,1696   [56/45]    = 378,6021909
  213/38  = O1/3,1221    [213/38]    = 384,3599931 
  5/4  = O1/3,1063    [5/4]    = 386,3137139 
  T2 = 81/64 =34/26 = O1/2,9425    [T2]    = 407,8200035 
  80/63 = O1/2,9015    [80/63]    = 413,5778057 
  9/7 = O1/2,7581   [9/7]    = 435,0840953 
 
 Quarten
  21/16  = O1/2,5490    [21/16]    = 470,7809073
  Qua = 4/3 =22/3  = O1/2,4094    [Qua]    = 498,0449991
  27/20  = O1/2,3097    [27/20]    = 519,5512887
 
 Tritoni
  25/18  = O1/2,1100   [25/18]   = 568,7174260
  7/5  = O1/2,0600   [7/5]   = 582,5121926
  1024/729 = 210/36 = O1/2,0399   [210/36]   = 588,2699948
  45/32  = O1/2,0331   [45/32]    = 590,2237156
  64/45  = O1/1,9679   [64/45]    = 609,7762844
  729/512 = 36/29 = O1/1,9616   [36/29]    = 611,7300052
  10/7  = O1/1,9434   [10/7]   = 617,4878074
  36/25  = O1/1,9009   [36/25]    = 631,2825740
 
 Quinten
  218/311  = O1/1,7686   [218/311]   = 678,4949905
  40/27  = O1/1,7635   [40/27]   = 680,4487113
  Qui = 3/2  = O1/1,7095   [Qui]   = 701,9550009
  243/160  = O1/1,6587   [243/160]   = 723,4612905
  32/21 = O1/1,6456    [32/21]   = 729,2190927
 
 kleine Sexten
  14/9 = O1/1,5688    [14/9]   = 764,9159047
  25/16  = O1/1,5531   [25/16]   = 772,6274277
  63/40 = O1/1,5259    [63/40]   = 786,4221943
  128/81 = 27/34  = O1/1,5148   [128/81]   = 792,1799965
  8/5  = O1/1,4748    [8/5]    = 813,6862861
  45/28 = O1/1,4609   [45/28]    = 821,3978091
  38/212 = O1/1,4712   [38/212]   = 825,6400069
 
 große Sexten
  400/243  = O1/1,3907   [400/243]    = 862,8524234
  215/39 = O1/1,3599   [215/39]    = 882,4049922
  5/3 = O1/1,3569   [5/3]    = 884,3587130
  27/16 = 33/24  = O1/1,3247   [33/24]    = 905,8650026
  128/75  = O1/1,2967   [128/75]    = 925,4175714
  12/7  = O1/1,2860   [12/7]    = 933,1290944
 
 Septimen
  7/4 = O1/1,2386   [7/4]   = 968,8259065
  225/128  = O1/1,2288    [225/128]   = 976,5374295
  16/9 = 24/32  = O1/1,2047   [24/32]    = 996,0899983
  9/5 = O1/1,1792   [9/5]   = 1017,5962879
  310/215 = O1/1,1770   [310/215]   = 1019,5500087
  729/400 = O1/1,1548   [729/400]   = 1039,1025775
  50/27  = O1/1,1249   [50/27]   = 1066,7624251
  28/15 = O1/1,1027   [28/15]   = 1080,5571917
  212/37  = O1/1,1047   [212/37]    = 1086,3149939
  15/8 = O1/1,1027   [15/8]   = 1088,2687147
  256/135  = O1/1,0832   [256/135]   = 1107,8212835
  243/128 = 35/27 = O1/1,0819   [35/27]    = 1109,7750043
  40/21 = O1/1,0757   [40/21]   = 1115,5328065
  48/25 = O1/1,0626   [48/25]   = 1129,3275731
 

  220/312 = O1/1,0199   [220/312]   = 1176,5399896
  160/81 = O1/1,0182   [169/81]   = 1178,4937104
  O = 2 = O1/1,0000   [O] =  o = 1200,0000000
 
Lukas Thenius, 30.3.2022