# List of 47-odd-limit intervals

The 47-odd-limit. Whoa.

Here is a list of the intervals within the octave belonging to the 47-odd limit -- that is, intervals between 1/1 and 2/1 which contain no odd numbers greater than 47. It is organized by interval category according to the Schulter System outlined in Regions of the Interval Spectrum.

## Pure Unison (0 cents)

ratio cents value
1/1 0

## Commas (0-30 cents)

None within the 47-odd limit.

## Dieses (30-60 cents)

ratio cents value prime limit
48/47 36.448 47
47/46 37.232 47
46/45 38.051 23
45/44 38.906 11
44/43 39.800 43
43/42 40.737 43
42/41 41.719 41
41/40 42.749 41
40/39 43.831 13
39/38 44.970 19
38/37 46/169 37
37/36 47.434 37
36/35 48.770 7
35/34 50.184 17
34/33 51.682 17
33/32 53.273 11
32/31 54.964 31
31/30 56.767 31
30/29 58.692 29

## Minor Seconds (60-125 cents)

### Small Minor Seconds (60-80 cents)

ratio cents value prime limit
29/28 60.751 29
28/27 62.961 7
27/26 65.337 13
26/25 67.900 13
25/24 70.672 5
24/23 73.681 23
47/45 75.283 47
23/22 76.956 23
45/43 78.706 43

### Middle Minor Seconds (80-100 cents)

ratio cents value prime limit
22/21 80.537 11
43/41 82.455 43
21/20 84.467 7
41/39 86.580 41
20/19 88.801 19
39/37 91.139 37
19/18 93.603 19
37/35 96.204 37
18/17 98.955 17

### Large Minor Seconds (100-125 cents)

ratio cents value prime limit
35/33 101.867 11
17/16 104.955 17
50/47 107.121 47
33/31 108.237 31
16/15 = 48/45 111.731 5
47/44 114.189 47
31/29 115.458 31
46/43 116.757 43
15/14 = 45/42 119.443 7
44/41 122.256 41
29/27 123.712 29

## Central or Zalzalian Seconds (formerly Neutral Seconds) (125-170 cents)

### Small Central Seconds (125-135 cents)

ratio cents value prime limit
43/40 125.204 43
14/13 = 42/39 128.298 13
41/38 131.549 41
27/25 133.238 5
40/37 134.970 37

### Middle Central Seconds (135-160 cents)

ratio cents value prime limit
13/12 = 39/36 138.573 13
38/35 142.373 19
25/23 144.353 23
37/34 146.389 37
12/11 = 36/33 150.637 11
47/43 153.989 47
35/32 155.140 7
23/21 157.493 23
34/31 159.920 31

### Large Central Seconds (160-170 cents)

#### Beginning of Equable Heptatonic Region (160-182 cents)

ratio cents value prime limit
45/41 161.161 41
11/10 = 33/30 165.004 11
43/39 169.035 43

#### End of Large Central Seconds Region, continuation of Equable Heptatonic Region

ratio cents value prime limit
32/29 170.423 29
21/19 173.268 19
52/47 175.021 47
31/28 176.210 31
41/37 177.718 41

## Major Seconds (180-240 cents)

### Small Major Seconds (180-200 cents)

ratio cents value prime limit
10/9 = 30/27 = 50/45 182.404 5
39/35 187.343 13
29/26 189.050 29
19/17 192.558 19
47/42 194.726 47
28/25 196.198 7
37/33 198.071 37
46/41 199.212 41

### Middle Major Seconds (200-220 cents)

ratio cents value prime limit
9/8 = 27/24 = 45/40 203.910 3
44/39 208.835 13
35/31 210.104 31
26/23 212.253 23
43/38 214.005 43
17/15 216.687 17
42/37 219.437 37

### Large Major Seconds (220-240 cents)

ratio cents value prime limit
25/22 221.309 11
33/29 223.696 29
41/36 225.152 41
8/7 = 24/21 = 40/35 231.174 7
47/41 236.444 47
39/34 237.527 17
31/27 239.171 31

## Interseptimal Region (M2-m3) (240-260 cents)

ratio cents value prime limit
54/47 240.358 47
23/20 241.961 23
38/33 244.240 19
15/13 = 45/39 247.741 13
52/45 250.304 13
37/32 251.344 37
22/19 253.805 19
29/25 256.950 29
36/31 258.874 31

## Minor Thirds (260-330 cents)

### Small Minor Thirds (260-280 cents)

ratio cents value prime limit
43/37 260.174 43
50/43 261.110 43
7/6 = 21/18 = 35/30 266.871 7
48/41 272.893 41
41/35 273.923 41
34/29 275.378 29
27/23 277.591 23
47/40 279.193 47

### Middle Minor Thirds (280-300 cents)

ratio cents value prime limit
20/17 281.358 17
33/28 284.447 11
46/39 285.792 23
13/11 = 39/33 289.210 13
45/38 292.711 19
32/27 294.135 3
19/16 297.513 19
44/37 299.974 37

### Large Minor Thirds (300-330 cents)

ratio cents value prime limit
25/21 301.847 7
56/47 303.319 47
31/26 304.508 31
37/31 306.308 37
43/36 307.608 43
6/5 = 18/15 = 30/25 = 42/35 = 54/45 315.641 5
47/39 323.024 47
41/34 324.107 41
35/29 325.562 29
29/24 327.622 29
52/43 329.010 43

## Central or Zalzalian Thirds (formerly Neutral Thirds) (330-372 cents)

### Small Central Thirds (330-342 cents)

ratio cents value prime limit
23/19 330.761 23
40/33 333.041 11
17/14 336.130 17
45/37 338.880 37
28/23 340.552 23

### Middle Central Thirds (342-360 cents)

ratio cents value prime limit
39/32 342.483 13
50/41 343.565 41
11/9 = 33/27 347.408 11
38/31 352.477 31
27/22 354.547 11
43/35 356.378 43
16/13 = 48/39 359.472 13

### Large Central Thirds (360-372 cents)

ratio cents value prime limit
37/30 363.075 37
58/47 364.071 47
21/17 365.825 17
47/38 367.994 47
26/21 369.747 13

## Major Thirds (372-440 cents)

### Small Major Thirds (372-400 cents)

ratio cents value prime limit
31/25 372.408 31
36/29 374.333 29
41/33 375.789 41
46/37 376.930 37
56/45 378.602 7
5/4 = 15/12 = 25/20 = 35/28 = 45/36 386.314 5
54/43 394.347 43
44/35 396.178 11
39/31 397.447 31
34/27 399.090 17

### Middle Major Thirds (400-423 cents)

ratio cents value prime limit
29/23 401.303 29
24/19 404.442 19
43/34 406.562 43
19/15 409.244 19
52/41 411.465 41
33/26 412.745 13
47/37 414.163 47
14/11 = 42/33 417.508 11
37/29 421.767 37
60/47 422.762 47

### Large Major Thirds (423-440 cents)

ratio cents value prime limit
23/18 424.364 23
32/25 427.373 5
41/32 429.062 41
50/39 430.145 13
9/7 = 27/21 = 45/35 435.084 7
58/45 439.353 29

## Interseptimal Region (M3-4) (440-468 cents)

ratio cents value prime limit
40/31 441.278 31
31/24 443.081 31
22/17 446.363 17
35/27 449.275 7
48/37 450.611 37
13/10 = 39/30 454.214 13
56/43 457.308 43
43/33 458.245 43
30/23 459.994 23
47/36 461.597 47
17/13 464.428 17
38/29 467.936 29

## Perfect Fourths (468-528 cents)

### Small Perfect Fourths (468-491 cents)

ratio cents value prime limit
21/16 470.781 7
46/35 473.135 23
25/19 475.114 19
54/41 476.803 41
29/22 478.259 29
62/47 479.529 47
33/25 480.646 11
37/28 482.518 37
41/31 484.027 41
45/34 485.268 17

### Middle Perfect Fourths (491-505 cents)

ratio cents value prime limit
4/3 = 12/9 = 20/15 = 36/27 = 36/27 = 44/33 = 52/39 = 60/45 498.045 3

### Large Perfect Fourths (505-528 cents)

ratio cents value prime limit
47/35 510.367 47
43/32 511.518 43
39/29 512.905 29
35/26 514.612 13
31/23 516.761 31
58/43 518.059 43
27/20 519.551 5
50/37 521.283 37
23/17 523.319 23
42/31 525.745 31

## Superfourths (528-560 cents)

ratio cents value prime limit
19/14 528.687 19
34/25 532.328 17
64/47 534.493 47
15/11 = 45/33 536.951 11
56/41 539.764 41
41/30 540.794 41
26/19 543.015 19
37/27 545.479 37
48/35 546.815 7
11/8 = 33/24 551.318 11
62/45 554.812 31
40/29 556.737 29
29/21 558.796 29
47/34 560.551 47

## Tritonic Region (560-640 cents)

### Small Tritones (560-577 cents)

ratio cents value prime limit
18/13 = 54/39 563.382 13
43/31 566.382 43
25/18 568.717 5
32/23 571.726 23
39/28 573.657 13
46/33 575.001 23
60/43 576.751 43

### Middle Tritones (577-623 cents)

ratio cents value prime limit
7/5 = 21/15 = 35/25 582.512 7
66/47 587.766 47
52/37 589.184 37
45/32 590.224 5
38/27 591.648 19
31/22 593.718 31
24/17 597.000 17
41/29 599.485 41
58/41 600.515 41
17/12 603.000 17
44/31 606.282 31
27/19 608.352 19
64/45 609.776 5
37/26 610.816 37
47/33 612.234 47
10/7 = 30/21 = 50/35 617.488 7

### Large Tritones (623-640 cents)

ratio cents value prime limit
43/30 623.249 43
33/23 624.999 23
56/39 626.343 13
23/16 628.274 23
36/25 631.283 5
62/43 633.518 43
13/9 = 39/27 636.618 13
68/47 639.449 47

...to be continued...