Table of 198edo intervals

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This table of 198edo intervals assumes 13-limit patent val ⟨198 314 460 556 685 733].

Intervals highlighted in bold are prime harmonics or subharmonics. Note that no 7-limit interval can be represented by odd degrees, so those entries are left blank. Intervals that differ from their assigned steps by more than 50%, but no more than 100%, are shown in italic. Intervals that differ by more than 100%, or with odd limit over 729 are not shown. For clarity, an entry can contain multiple intervals if they are of comparable complexity.

# Cents Marks 5-limit 7-limit 11-limit 13-limit
0 0.00 P1 1/1
1 6.06 385/384, 441/440, 540/539 196/195, 325/324, 364/363
2 12.12 ? 126/125 121/120, 176/175 144/143
3 18.18 99/98, 100/99 91/90, 105/104
4 24.24 81/80 64/63 " 66/65, 78/77
5 30.30 55/54, 56/55 "
6 36.36 128/125 49/48, 50/49 " "
7 42.42 45/44 40/39
8 48.48 250/243 36/35 " "
9 54.54 33/32 "
10 60.60 648/625 28/27 " "
11 66.66 80/77 26/25, 27/26
12 72.72 25/24 " " "
13 78.78 22/21 "
14 84.84 m2 256/243 21/20 " "
15 90.90 539/512 96/91
16 96.96 135/128 200/189 128/121 55/52
17 103.03 35/33 52/49
18 109.09 16/15 " " "
19 115.15 77/72 "
20 121.21 ? 15/14 " "
21 127.27 264/245, 320/297 14/13
22 133.33 27/25 " " "
23 139.39 88/81 13/12
24 145.45 625/576 49/45 " "
25 151.51 12/11 "
26 157.57 800/729 35/32 " "
27 163.63 11/10 "
28 169.69 ? 54/49 " "
29 175.75 256/231 72/65
30 181.81 10/9 " " "
31 187.87 49/44 39/35
32 193.93 ? 28/25 " "
33 200.00 55/49 "
34 206.06 M2 9/8 " " "
35 212.12 112/99 "
36 218.18 256/225 245/216 " 143/126, 162/143
37 224.24 25/22 "
38 230.30 729/640 8/7 " "
39 236.36 55/48 "
40 242.42 144/125 " " "
41 248.48 231/200 15/13
42 254.54 125/108 81/70 " "
43 260.60 64/55 "
44 266.66 ? 7/6 " "
45 272.72 90/77 "
46 278.78 75/64 147/125, 288/245 " 168/143
47 284.84 33/28 "
48 290.90 m3 32/27 189/160 " 13/11
49 296.96 196/165 108/91
50 303.03 ? 25/21 " "
51 309.09 176/147 117/98, 140/117
52 315.15 6/5 " " "
53 321.21 77/64 65/54
54 327.27 ? 98/81 " "
55 333.33 40/33 63/52
56 339.39 243/200 175/144 147/121 "
57 345.45 11/9 39/32
58 351.51 768/625 49/40, 60/49 " "
59 357.57 27/22 16/13
60 363.63 100/81 216/175 121/98 "
61 369.69 99/80 26/21
62 375.75 ? 56/45 " "
63 381.81 96/77 81/65, 125/78
64 387.87 5/4 " " "
65 393.93 44/35 49/39
66 400.00 512/405 63/50 " "
67 406.06 125/99 91/72
68 412.12 M3 81/64 80/63 " 33/26
69 418.18 14/11 "
70 424.24 32/25 125/98 " "
71 430.30 77/60 50/39
72 436.36 625/486 9/7 " "
73 442.42 128/99 84/65
74 448.48 162/125 35/27 " "
75 454.54 100/77 13/10
76 460.60 125/96 64/49 " "
77 466.66 55/42, 72/55 "
78 472.72 320/243 21/16 " "
79 478.78 33/25 "
80 484.84 ? 250/189 160/121 143/108, 189/143, 224/169
81 490.90 175/132 65/49
82 496.96 P4 4/3 " " "
83 503.03 147/110 234/175
84 509.09 ? 75/56, 168/125 " "
85 515.15 66/49 35/26
86 521.21 27/20 " " "
87 527.27 110/81 65/48
88 533.33 512/375 49/36 " "
89 539.39 15/11 "
90 545.45 1000/729 48/35 " "
91 551.51 11/8 "
92 557.57 864/625 112/81 " 91/66
93 563.63 320/231 18/13
94 569.69 25/18 " " "
95 575.75 88/63 39/28
96 581.81 d5 ? 7/5 " "
97 587.87 108/77 "
98 593.93 45/32 343/243 484/343 55/39
99 600.00 99/70, 140/99 "
100 606.06 64/45 486/343 343/242 78/55
101 612.12 77/54 "
102 618.18 A4 ? 10/7 " "
103 624.24 63/44 56/39
104 630.30 36/25 " " "
105 636.36 231/160 13/9
106 642.42 625/432 81/56 " 132/91
107 648.48 16/11 "
108 654.54 729/500 35/24 " "
109 660.60 22/15 "
110 666.66 375/256 72/49 " "
111 672.72 81/55 96/65
112 678.78 40/27 " " "
113 684.84 49/33 52/35
114 690.90 ? 112/75, 125/84 " "
115 696.96 220/147 175/117
116 703.03 P5 3/2 " " "
117 709.09 264/175 98/65
118 715.15 ? 189/125 121/80 169/112, 216/143, 286/189
119 721.21 50/33 "
120 727.27 243/160 32/21 " "
121 733.33 55/36, 84/55 "
122 739.39 192/125 49/32 " "
123 745.45 77/50 20/13
124 751.51 125/81 54/35 " "
125 757.57 99/64 65/42
126 763.63 972/625 14/9 " "
127 769.69 120/77 39/25
128 775.75 25/16 196/125 " "
129 781.81 11/7 "
130 787.87 m6 128/81 63/40 " 52/33
131 793.93 198/125 144/91
132 800.00 405/256 100/63 " "
133 806.06 35/22 "
134 812.12 8/5 " " "
135 818.18 77/48 125/78, 130/81
136 824.24 ? 45/28 " "
137 830.30 160/99 21/13
138 836.36 81/50 175/108 196/121 "
139 842.42 44/27 13/8
140 848.48 625/384 49/30, 80/49 " "
141 854.54 18/11 64/39
142 860.60 400/243 288/175 242/147 "
143 866.66 33/20 104/63
144 872.72 ? 81/49 " "
145 878.78 128/77 108/65
146 884.84 5/3 " " "
147 890.90 147/88 117/70, 196/117
148 896.96 ? 42/25 " "
149 903.03 165/98 91/54
150 909.09 M6 27/16 320/189 " 22/13
151 915.15 56/33 "
152 921.21 128/75 245/144, 250/147 " 143/84
153 927.27 77/45 "
154 933.33 ? 12/7 " "
155 939.39 55/32 "
156 945.45 216/125 140/81 121/70 "
157 951.51 343/198, 400/231 26/15
158 957.57 125/72 " " "
159 963.63 96/55 "
160 969.69 1280/729 7/4 " "
161 975.75 44/25 "
162 981.81 225/128 432/245 " 143/81, 252/143
163 987.87 99/56 "
164 993.93 m7 16/9 " " "
165 1000.00 98/55 "
166 1006.06 ? 25/14 " "
167 1012.12 88/49 70/39
168 1018.18 9/5 " " "
169 1024.24 231/128 65/36
170 1030.30 ? 49/27 " "
171 1036.36 20/11 "
172 1042.42 729/400 64/35 " "
173 1048.48 11/6 "
174 1054.54 1152/625 90/49 " "
175 1060.60 231/125 24/13
176 1066.66 50/27 " " "
177 1072.72 245/132 13/7
178 1078.78 ? 28/15 " "
179 1084.84 144/77 "
180 1090.90 15/8 " " "
181 1096.96 66/35 49/26
182 1103.03 256/135 189/100 121/64 104/55
183 1109.09 1024/539 91/48
184 1115.15 M7 243/128 40/21 " "
185 1121.21 21/11 "
186 1127.27 48/25 " " "
187 1133.33 77/40 25/13, 52/27
188 1139.39 625/324 27/14 " "
189 1145.45 64/33 "
190 1151.51 243/125 35/18 " "
191 1157.57 88/45 39/20
192 1163.63 125/64 49/25, 96/49 " "
193 1169.69 55/28, 108/55 "
194 1175.75 160/81 63/32 " 65/33, 77/39
195 1181.81 99/50, 196/99 180/91, 208/105
196 1187.87 ? 125/63 175/88, 240/121 143/72
197 1193.93 539/270, 768/385, 880/441 195/98, 363/182, 648/325
198 1200.00 P8 2/1
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