Table of 198edo intervals
This article is a work in progress.
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. Intervals that differ from their assigned steps by more than 50% or intervals with odd limit over 729 are not shown. Note that no 7-limit interval can be represented by odd degrees, so those entries are left blank.
# | Cents | 5 limit | 7 limit | 11 limit | 13 limit |
---|---|---|---|---|---|
0 | 0.00 | 1/1 | |||
1 | 6.06 | 385/384, 441/440, 540/539 | 196/195, 325/324, 351/350, 364/363 | ||
2 | 12.12 | ? | 126/125, 245/243 | 121/120 | 144/143, 169/168 |
3 | 18.18 | 99/98, 100/99 | ? | ||
4 | 24.24 | 81/80 | 64/63 | 245/242 | 66/65, 78/77 |
5 | 30.30 | 55/54, 56/55 | ? | ||
6 | 36.36 | ? | 49/48, 50/49 | ? | ? |
7 | 42.42 | ? | 40/39 | ||
8 | 48.48 | 250/243 | 36/35 | ? | ? |
9 | 54.54 | 33/32 | 65/63 | ||
10 | 60.60 | 648/625 | 28/27 | ? | ? |
11 | 66.66 | 80/77 | 26/25, 27/26 | ||
12 | 72.72 | 25/24 | ? | 126/121 | ? |
13 | 78.78 | 22/21 | ? | ||
14 | 84.84 | ? | 21/20 | ? | ? |
15 | 90.90 | ? | 96/91 | ||
16 | 96.96 | ? | 200/189, 343/324 | 128/121 | ? |
17 | 103.03 | 35/33 | ? | ||
18 | 109.09 | 16/15 | ? | ? | ? |
19 | 115.15 | ? | ? | ||
20 | 121.21 | ? | 15/14 | ? | ? |
21 | 127.27 | ? | 14/13 | ||
22 | 133.33 | 27/25 | 175/162 | ? | ? |
23 | 139.39 | ? | 13/12 | ||
24 | 145.45 | ? | 49/45, 160/147 | ? | ? |
25 | 151.51 | 12/11 | ? | ||
26 | 157.57 | ? | 35/32 | ? | ? |
27 | 163.63 | 11/10 | ? | ||
28 | 169.69 | ? | 54/49, 441/400 | ? | ? |
29 | 175.75 | ? | ? | ||
30 | 181.81 | 10/9 | ? | ? | ? |
31 | 187.87 | ? | ? | ||
32 | 193.93 | ? | 28/25, 384/343 | 121/108 | ? |
33 | 200.00 | ? | 91/81 | ||
34 | 206.06 | 9/8 | ? | ? | 44/39 |
35 | 212.12 | ? | ? | ||
36 | 218.18 | ? | ? | ? | ? |
37 | 224.24 | ? | 91/80 | ||
38 | 230.30 | ? | 8/7 | ? | ? |
39 | 236.36 | 55/48 | ? | ||
40 | 242.42 | 144/125 | 147/128, 280/243 | ? | ? |
41 | 248.48 | ? | 15/13 | ||
42 | 254.54 | 125/108 | 81/70 | 140/121 | ? |
43 | 260.60 | 64/55 | ? | ||
44 | 266.66 | ? | 7/6 | ? | ? |
45 | 272.72 | ? | ? | ||
46 | 278.78 | ? | ? | ? | ? |
47 | 284.84 | 33/28 | ? | ||
48 | 290.90 | ? | 189/160 | ? | 13/11 |
49 | 296.96 | ? | ? | ||
50 | 303.03 | ? | 25/21, 343/288 | 144/121 | ? |
51 | 309.09 | ? | ? | ||
52 | 315.15 | 6/5 | ? | ? | ? |
53 | 321.21 | ? | ? | ||
54 | 327.27 | ? | 98/81 | ? | ? |
55 | 333.33 | ? | 63/52 | ||
56 | 339.39 | 243/200 | ? | ? | ? |
57 | 345.45 | 11/9 | 39/32 | ||
58 | 351.51 | ? | 49/40, 60/49 | ? | ? |
59 | 357.57 | 27/22 | 16/13 | ||
60 | 363.63 | 100/81 | ? | ? | ? |
61 | 369.69 | ? | 26/21 | ||
62 | 375.75 | ? | 56/45 | ? | ? |
63 | 381.81 | ? | ? | ||
64 | 387.87 | 5/4 | ? | ? | ? |
65 | 393.93 | ? | ? | ||
66 | 400.00 | ? | 63/50, 432/343 | 121/96 | ? |
67 | 406.06 | ? | ? | ||
68 | 412.12 | ? | 80/63 | ? | 33/26 |
69 | 418.18 | 14/11 | ? | ||
70 | 424.24 | ? | ? | ? | ? |
71 | 430.30 | ? | ? | ||
72 | 436.36 | 625/486 | 9/7 | ? | ? |
73 | 442.42 | 128/99 | ? | ||
74 | 448.48 | 162/125 | 35/27 | ? | ? |
75 | 454.54 | ? | 13/10 | ||
76 | 460.60 | ? | 64/49, 98/75 | ? | ? |
77 | 466.66 | ? | ? | ||
78 | 472.72 | ? | 21/16 | ? | ? |
79 | 478.78 | ? | ? | ||
80 | 484.84 | ? | ? | ? | ? |
81 | 490.90 | ? | ? | ||
82 | 496.96 | 4/3 | ? | ? | ? |
83 | 503.03 | ? | ? | ||
84 | 509.09 | ? | 343/256 | ? | ? |
85 | 515.15 | ? | ? | ||
86 | 521.21 | 27/20 | ? | ? | ? |
87 | 527.27 | ? | ? | ||
88 | 533.33 | ? | 49/36, 200/147 | ? | ? |
89 | 539.39 | 15/11 | ? | ||
90 | 545.45 | 1000/729 | 48/35 | ? | ? |
91 | 551.51 | 11/8 | ? | ||
92 | 557.57 | ? | 441/320 | ? | ? |
93 | 563.63 | ? | 18/13 | ||
94 | 569.69 | 25/18 | ? | ? | ? |
95 | 575.75 | ? | ? | ||
96 | 581.81 | ? | 7/5 | ? | ? |
97 | 587.87 | ? | ? | ||
98 | 593.93 | ? | 343/243, 800/567 | ? | ? |
99 | 600.00 | 99/70, 140/99 | ? | ||
100 | 606.06 | ? | 486/343, 567/400 | ? | ? |
101 | 612.12 | ? | ? | ||
102 | 618.18 | ? | 10/7 | ? | ? |
103 | 624.24 | ? | ? | ||
104 | 630.30 | 36/25 | ? | ? | ? |
105 | 636.36 | ? | 13/9 | ||
106 | 642.42 | ? | 640/441 | ? | ? |
107 | 648.48 | 16/11 | ? | ||
108 | 654.54 | 729/500 | 35/24 | ? | ? |
109 | 660.60 | 22/15 | ? | ||
110 | 666.66 | ? | 72/49, 147/100 | ? | ? |
111 | 672.72 | ? | ? | ||
112 | 678.78 | 40/27 | ? | ? | ? |
113 | 684.84 | ? | ? | ||
114 | 690.90 | ? | 512/343 | ? | ? |
115 | 696.96 | ? | ? | ||
116 | 703.03 | 3/2 | ? | ? | ? |
117 | 709.09 | ? | ? | ||
118 | 715.15 | ? | ? | ? | ? |
119 | 721.21 | ? | ? | ||
120 | 727.27 | 32/21 | ? | ? | |
121 | 733.33 | ? | ? | ||
122 | 739.39 | ? | 49/32, 75/49 | ? | ? |
123 | 745.45 | ? | 20/13 | ||
124 | 751.51 | 125/81 | 54/35 | ? | ? |
125 | 757.57 | 99/64 | ? | ||
126 | 763.63 | 972/625 | 14/9 | ? | ? |
127 | 769.69 | ? | ? | ||
128 | 775.75 | ? | ? | ? | ? |
129 | 781.81 | 11/7 | ? | ||
130 | 787.87 | ? | 63/40 | ? | 52/33 |
131 | 793.93 | ? | ? | ||
132 | 800.00 | ? | 100/63, 343/216 | 192/121 | ? |
133 | 806.06 | ? | ? | ||
134 | 812.12 | 8/5 | ? | ? | ? |
135 | 818.18 | ? | ? | ||
136 | 824.24 | ? | 45/28 | ? | ? |
137 | 830.30 | ? | 21/13 | ||
138 | 836.36 | 81/50 | ? | ? | ? |
139 | 842.42 | 44/27 | 13/8 | ||
140 | 848.48 | ? | 49/30, 80/49 | ? | ? |
141 | 854.54 | 18/11 | 64/39 | ||
142 | 860.60 | 400/243 | ? | ? | ? |
143 | 866.66 | ? | 104/63 | ||
144 | 872.72 | ? | 81/49 | ? | ? |
145 | 878.78 | ? | ? | ||
146 | 884.84 | 5/3 | ? | ? | ? |
147 | 890.90 | ? | ? | ||
148 | 896.96 | ? | 42/25, 576/343 | 121/72 | ? |
149 | 903.03 | ? | ? | ||
150 | 909.09 | ? | 320/189 | ? | 22/13 |
151 | 915.15 | 56/33 | ? | ||
152 | 921.21 | ? | ? | ? | ? |
153 | 927.27 | ? | ? | ||
154 | 933.33 | ? | 12/7 | ? | ? |
155 | 939.39 | 55/32 | ? | ||
156 | 945.45 | 216/125 | 140/81 | 121/70 | ? |
157 | 951.51 | ? | 26/15 | ||
158 | 957.57 | 125/72 | 243/140, 256/147 | ? | ? |
159 | 963.63 | 96/55 | ? | ||
160 | 969.69 | ? | 7/4 | ? | ? |
161 | 975.75 | ? | 160/91 | ||
162 | 981.81 | ? | ? | ? | ? |
163 | 987.87 | ? | ? | ||
164 | 993.93 | 16/9 | ? | ? | 39/22 |
165 | 1000.00 | ? | 162/91 | ||
166 | 1006.06 | ? | 25/14, 343/192 | 216/121 | ? |
167 | 1012.12 | ? | ? | ||
168 | 1018.18 | 9/5 | ? | ? | ? |
169 | 1024.24 | ? | ? | ||
170 | 1030.30 | ? | 49/27, 800/441 | ? | ? |
171 | 1036.36 | 20/11 | ? | ||
172 | 1042.42 | ? | 64/35 | ? | ? |
173 | 1048.48 | 11/6 | ? | ||
174 | 1054.54 | ? | 90/49, 147/80 | ? | ? |
175 | 1060.60 | ? | 24/13 | ||
176 | 1066.66 | 50/27 | 384/175 | ? | ? |
177 | 1072.72 | ? | 13/7 | ||
178 | 1078.78 | ? | 28/15 | ? | ? |
179 | 1084.84 | ? | ? | ||
180 | 1090.90 | 15/8 | ? | ? | ? |
181 | 1096.96 | 66/35 | ? | ||
182 | 1103.03 | ? | 189/100, 648/343 | 121/64 | ? |
183 | 1109.09 | ? | 91/48 | ||
184 | 1115.15 | ? | 40/21 | ? | ? |
185 | 1121.21 | 21/11 | ? | ||
186 | 1127.27 | 48/25 | ? | 121/63 | ? |
187 | 1133.33 | 77/40 | 25/13, 52/27 | ||
188 | 1139.39 | 625/324 | 27/14 | ? | ? |
189 | 1145.45 | 64/33 | 126/65 | ||
190 | 1151.51 | 243/125 | 35/18 | ? | ? |
191 | 1157.57 | ? | 39/20 | ||
192 | 1163.63 | ? | 96/49, 49/25 | ? | ? |
193 | 1169.69 | 108/55, 55/27 | ? | ||
194 | 1175.75 | 160/81 | 63/32 | 484/245 | 65/33, 77/39 |
195 | 1181.81 | 196/99, 99/50 | ? | ||
196 | 1187.87 | ? | 125/63, 486/245 | 240/121 | 143/72, 336/169 |
197 | 1193.93 | 768/385, 880/441, 539/270 | 195/98, 648/325, 700/351, 363/182 | ||
198 | 1200.00 | 2/1 |