47-limit

The 47-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.

1 Pure Unison (0 cents)
2 Commas (0-30 cents)
3 Dieses (30-60 cents)
4 Minor Seconds (60-125 cents)
5 Central or Zalzalian Seconds (formerly Neutral Seconds) (125-170 cents)
6 Major Seconds (180-240 cents)
7 Interseptimal Region (M2-m3) (240-260 cents)
8
9 Minor Thirds (260-330 cents)
10
11 Central or Zalzalian Thirds (formerly Neutral Thirds) (330-372 cents)
12 Major Thirds (372-440 cents)
13 Interseptimal Region (M3-4) (440-468 cents)
14 Perfect Fourths (468-528 cents)
15 Superfourths (528-560 cents)
16 Tritonic Region (560-640 cents)

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 (125-170 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

End of Equable Heptatonic Region.

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...