List of 47-odd-limit intervals: Difference between revisions

Revision as of 22:28, 22 November 2020

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.

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...

@@ Line 37: / Line 37: @@
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+| [[45/44]]
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+| [[40/39]]
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+| [[36/35]]
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@@ Line 85: / Line 85: @@
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-| 33/32
+| [[33/32]]
 | 53.273
 | 11
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-| 32/31
+| [[32/31]]
 | 54.964
 | 31
 |-
-| 31/30
+| [[31/30]]
 | 56.767
 | 31