52edt: Difference between revisions

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52edt

53edt →

Prime factorization

2² × 13

Step size

36.5761 ¢

Octave

33\52edt (1207.01 ¢)

Consistency limit

4

Distinct consistency limit

4

52 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 52edt or 52ed3), is a nonoctave tuning system that divides the interval of 3/1 into 52 equal parts of about 36.6 ¢ each. Each step represents a frequency ratio of 3^1/52, or the 52nd root of 3.

It is something of a curiosity as it really needs to be considered as a 29-limit no-twos system. While not exceptionally accurate, it gets the entire no-twos 29-limit to within 18 cents. It is distinctly flat, in the sense that 5, 7, 11, 13, 17, 19, 23 and 29 are all flat, so using something other than pure-threes tuning might be advisable. It is contorted in the 7-limit, so that it tempers out the same commas as 13edt. Other commas it tempers out includes 121/119, 209/207, 247/245, 275/273, 299/297, 325/323, 345/343, 363/361, 377/375, 437/435, 495/493, 627/625, 665/663, 667/665, 847/845, 1127/1125, 1311/1309 and 1617/1615. It is the eleventh no-twos zeta peak edt.

Harmonics

While 52edt does not improve much on 26edt's mapping of the odd primes, it still maps 11, 13, 19, and 29 slightly better than 26edt, which is notable for giving them (despite being nearly half a step off in the case of 11) a flat tendency in keeping with all the other odd primes, which allows 52edt to be the first edt that is consistent to the no-twos 29-throdd limit, which is a record unbeaten until 144edt.

Approximation of prime harmonics in 52edt
Harmonic		2	3	5	7	11	13	17	19	23
Error	Absolute (¢)	+7.0	+0.0	-6.5	-3.8	-18.2	-14.8	-3.8	-13.4	-15.0
Error	Relative (%)	+19.2	+0.0	-17.9	-10.5	-49.8	-40.5	-10.3	-36.7	-41.1
Steps (reduced)		33 (33)	52 (0)	76 (24)	92 (40)	113 (9)	121 (17)	134 (30)	139 (35)	148 (44)

Approximation of odd harmonics in 52edt
Harmonic		25	27	29	31	33	35	37	39	41	43	45
Error	Absolute (¢)	-13.1	+0.0	-14.0	+16.9	-18.2	-10.4	+3.2	-14.8	+8.3	-1.0	-6.5
Error	Relative (%)	-35.7	+0.0	-38.2	+46.1	-49.8	-28.3	+8.6	-40.5	+22.8	-2.7	-17.9
Steps (reduced)		152 (48)	156 (0)	159 (3)	163 (7)	165 (9)	168 (12)	171 (15)	173 (17)	176 (20)	178 (22)	180 (24)

Intervals

Steps	Cents	Hekts	BP nonatonic degree	Diatonic degree	Corresponding JI intervals	Comments
1	36.6	25	Qa1/3d2	Sa1	50/49~33/32~49/48
2	73.15	50	Sa1/sd2	A1/dd2	25/24~28/27~22/21~27/26~24/23~21/20~29/28
3	109.7	75	3A1/qd2	A+1/d-2	15/14~16/15~29/27~121/112
4	146.3	100	A1/m2	AA1/sm2	27/25~25/23~49/45~13/12~14/13~11/10~169/162
5	182.9	125	Sm2	sm+2	10/9
6	219.5	150	N2	m2	9/8~8/7~44/39
7	256.0	175	sM2	N2	147/128~7/6
8	292.6	200	M2/d3	M2	32/27~25/21~13/11~27/23
9	329.2	225	Qa2/3d3	SM-2/d-2	6/5	11/9-
10	365.8	250	Sa2/sd3	SM2/dd3	5/4~16/13	11/9+
11	402.3	275	3A3/qd3	SM+2	81/64~63/50~33/26~23/18
12	438.9	300	A2/P3/d4	AA2/sm3	32/25~9/7~14/11~104/81~13/10
13	475.5	325	Qa3/3d4	sm+3	21/16~98/75
14	512.1	350	Sa3/sd4	m3	4/3~27/20~162/121
15	548.6	375	3A3/qd4	N3	11/8~243/169	18/13-
16	585.2	400	A3/m4/d5	M3	7/5~25/18~112/81~88/63~32/23~29/21	18/13+
17	621.8	425	Sm4/3d5	SM-3	10/7~36/25~81/56~63/44~23/16~42/29	13/9-
18	658.4	450	N4/sd5	SM3/dd4	16/11~338/243	13/9+
19	694.95	475	sM4/qd5	SM+3/d-4	3/2~40/27~121/81
20	731.5	500	M4/m5	AA3/d4	32/21~75/49
21	768.1	525	Qa4/Sm5	d+4	25/16~14/9~11/7~81/52
22	804.7	550	Sa4/N5	P4	8/5~36/23
23	841.25	575	3A4/sM5	A-4	13/8
24	877.8	600	A4/M5/d6	A4	5/3
25	914.4	625	Qa5/3d6	A+4	27/16~42/25~22/13~46/27
26	951	650	Sa5/sd6	AA4/dd5	125/72
27	987.55	675	3A5/qd6	d-5	16/9~8/7~39/22~75/46
28	1024.1	700	A5/m6/d7	d5	9/5
29	1060.7	725	Sm6/3d7	d+5	50/27~46/25~90/49~24/13~13/7~20/11
30	1097.3	750	N6/sd7	P5	15/8
31	1133.9	775	sM6/qd7	A-5	48/25~27/14~21/11~52/27~23/12~40/21~56/29
32	1170.4	800	M6/m7	A5/dd6	49/25~64/33~96/49
33	1207.0	825	Qa6/Sm7	A+5	2/1
34	1243.6	850	Sa6/N7	AA5/sm6	33/16~100/49~49/24~729/338
35	1280.2	875	3A6/sM7	sm+6	25/12~56/27~44/21~27/13
36	1316.7	900	A6/M7/d8	m6	15/7~32/15~58/27
37	1353.3	925	Qa7/3d8	N6	54/25~50/23~98/45~13/6~169/81
38	1389.9	950	Sa7/sd8	M6	20/9~9/4-
39	1426.5	975	3A7/qd8	SM-6	9/4+~16/7
40	1463.0	1000	A7/P8/d9	SM6/dd7	147/64~7/3
41	1499.6	1025	Qa8/3d9	SM+6/sm-7	64/27~50/21~26/11~81/23
42	1536.2	1050	Sa8/sd9	AA6/sm7	12/5	22/9-
43	1572.7	1075	3A8/qd9	sm-7	5/2~32/13	22/9+
44	1609.3	1100	A8/m9	m7	81/32~63/25~33/13~23/9
45	1645.9	1125	Sm9	N7	64/45~18/7~28/11~208/81~13/5
46	1682.5	1150	N9	M7	21/8~196/75
47	1719.1	1175	sM9	SM-7	8/3~27/10
48	1755.65	1200	M9/d10	SM7/dd8	69/25~135/49	36/13-
49	1792.2	1225	Qa9/3d10	SM+7/d-8	14/5~25/9~224/81~176/63~64/23~58/21	36/13+
50	1828.8	1250	Sa9/sd10	A7/d8	20/7~72/25~81/28~63/22~23/8~84/29	26/9-
51	1865.4	1275	3A9/qd10	P-8	147/50~32/11~338/81~144/49	26/9+
52	1902.0	1300	A9/P10	P8	3/1	Tritave

It is a weird coincidence how 52edt intones any 52edo intervals within plus or minus 6.5 cents when it is supposed to have nothing to do with this other tuning:

52edt	52edo	Discrepancy
365.761	369.231	−3.47
512.065	507.692	+4.373
877.825	876.923	+0.902
1243.586	1246.154	−2.168
1389.89	1384.615	+5.275
1755.651	1753.846	+1.805
2121.411	2123.077	−1.666
2633.476	2630.769	+2.647

…and so on

@@ Line 1: / Line 1: @@
-<h2>IMPORTED REVISION FROM WIKISPACES</h2>
+{{Infobox ET}}
-This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
+{{ED intro}}
-: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-10-20 11:50:16 UTC</tt>.<br>
-: The original revision id was <tt>596254978</tt>.<br>
-: The revision comment was: <tt></tt><br>
-The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
-<h4>Original Wikitext content:</h4>
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">The 52 equal division of 3, the tritave, divides it into 52 equal parts of 36.576 cents each, corresponding to 32.808 edo. It is something of a curiosity as it really needs to be considered as a 29-limit no-twos system. While not super-accurate, it gets the entire no-twos 29-limit to within 18 cents. It is distinctly flat, in the sense that 5, 7, 11, 13, 17, 19, 23 and 29 are all flat, so using something other than pure-threes tuning might be advisable. It is contorted in the 11-limit, so that it tempers out the same commas as [[26edt]] in the 11-limit and [[13edt]] in the 7-limit. Other commas it tempers out includes 121/119, 209/207, 247/245, 275/273, 299/297, 325/323, 345/343, 363/361, 377/375, 437/435, 495/493, 627/625, 665/663, 667/665, 847/845, 1127/1125, 1311/1309 and 1617/1615. It is the eleventh [[The Riemann Zeta Function and Tuning#Removing%20primes|no-twos zeta peak edt]].
-==Intervals==
+It is something of a curiosity as it really needs to be considered as a 29-limit no-twos system. While not exceptionally accurate, it gets the entire no-twos 29-limit to within 18 cents. It is distinctly flat, in the sense that 5, 7, 11, 13, 17, 19, 23 and 29 are all flat, so using something other than pure-threes tuning might be advisable. It is contorted in the 7-limit, so that it tempers out the same commas as [[13edt]]. Other commas it tempers out includes 121/119, 209/207, 247/245, 275/273, 299/297, 325/323, 345/343, 363/361, 377/375, 437/435, 495/493, 627/625, 665/663, 667/665, 847/845, 1127/1125, 1311/1309 and 1617/1615. It is the eleventh [[the Riemann zeta function and tuning#Removing primes|no-twos zeta peak edt]].
-||~ Steps ||~ Cents ||~ BP nonatonic degree ||~ Diatonic degree ||~ Corresponding JI intervals ||~ Comments ||~ Generator for... ||
-|| 1 || 36.6 || Qa1/3d2 || Sa1 || 50/49~33/32~49/48 ||   ||   ||
-|| 2 || 73.15 || Sa1/sd2 || A1/dd2 || 25/24~28/27~22/21~27/26~24/23~21/20~29/28 ||   ||   ||
-|| 3 || 109.7 || 3A1/qd2 || A+1/d-2 || 15/14~16/15~29/27~121/112 ||   ||   ||
-|| 4 || 146.3 || A1/m2 || AA1/sm2 || 27/25~25/23~49/45~13/12~14/13~11/10~169/162 ||   ||   ||
-|| 5 || 182.9 || Sm2 || sm+2 || 10/9 ||   ||   ||
-|| 6 || 219.5 || N2 || m2 || 9/8~8/7~44/39 ||   ||   ||
-|| 7 || 256.0 || sM2 || N2 || 147/128~7/6 ||   ||   ||
-|| 8 || 292.6 || M2/d3 || M2 || 32/27~25/21~13/11~27/23 ||   ||   ||
-|| 9 || 329.2 || Qa2/3d3 || SM-2/d-2 || 6/5 || 11/9- ||   ||
-|| 10 || 365.8 || Sa2/sd3 || SM2/dd3 || 5/4~16/13 || 11/9+ ||   ||
-|| 11 || 402.3 || 3A3/qd3 || SM+2 || 81/64~63/50~33/26~23/18 ||   ||   ||
-|| 12 || 438.9 || A2/P3/d4 || AA2/sm3 || 32/25~9/7~14/11~104/81~13/10 ||   ||   ||
-|| 13 || 475.5 || Qa3/3d4 || sm+3 || 21/16~98/75 ||   ||   ||
-|| 14 || 512.1 || Sa3/sd4 || m3 || 4/3~27/20~162/121 ||   ||   ||
-|| 15 || 548.6 || 3A3/qd4 || N3 || 11/8~243/169 || 18/13- ||   ||
-|| 16 || 585.2 || A3/m4/d5 || M3 || 7/5~25/18~112/81~88/63~32/23~29/21 || 18/13+ ||   ||
-|| 17 || 621.8 || Sm4/3d5 || SM-3 || 10/7~36/25~81/56~63/44~23/16~42/29 || 13/9- ||   ||
-|| 18 || 658.4 || N4/sd5 || SM3/dd4 || 16/11~338/243 || 13/9+ ||   ||
-|| 19 || 694.95 || sM4/qd5 || SM+3/d-4 || 3/2~40/27~121/81 ||   ||   ||
-|| 20 || 731.5 || M4/m5 || AA3/d4 || 32/21~75/49 ||   ||   ||
-|| 21 || 768.1 || Qa4/Sm5 || d+4 || 25/16~14/9~11/7~81/52 ||   ||   ||
-|| 22 || 804.7 || Sa4/N5 || P4 || 8/5~36/23 ||   ||   ||
-|| 23 || 841.25 || 3A4/sM5 || A-4 || 13/8 ||   ||   ||
-|| 24 || 877.8 || A4/M5/d6 || A4 || 5/3 ||   ||   ||
-|| 25 || 914.4 || Qa5/3d6 || A+4 || 27/16~42/25~22/13~46/27 ||   ||   ||
-|| 26 || 951.0 || Sa5/sd6 || AA4/dd5 || 125/72 ||   ||   ||
-|| 27 || 987.55 || 3A5/qd6 || d-5 || 16/9~8/7~39/22~75/46 ||   ||   ||
-|| 28 || 1024.1 || A5/m6/d7 || d5 || 9/5 ||   ||   ||
-|| 29 || 1060.7 || Sm6/3d7 || d+5 || 50/27~46/25~90/49~24/13~13/7~20/11 ||   ||   ||
-|| 30 || 1097.3 || N6/sd7 || P5 || 15/8 ||   ||   ||
-|| 31 || 1133.9 || sM6/qd7 || A-5 || 48/25~27/14~21/11~52/27~23/12~40/21~56/29 ||   ||   ||
-|| 32 || 1170.4 || M6/m7 || A5/dd6 || 49/25~64/33~96/49 ||   ||   ||
-|| 33 || 1207.0 || Qa6/Sm7 || A+5 || 2/1 ||   ||   ||
-|| 34 || 1243.6 || Sa6/N7 || AA5/sm6 || 33/16~100/49~49/24~729/338 ||   ||   ||
-|| 35 || 1280.2 || 3A6/sM7 || sm+6 || 25/12~56/27~44/21~27/13 ||   ||   ||
-|| 36 || 1316.7 || A6/M7/d8 || m6 || 15/7~32/15~58/27 ||   ||   ||
-|| 37 || 1353.3 || Qa7/3d8 || N6 || 54/25~50/23~98/45~13/6~169/81 ||   ||   ||
-|| 38 || 1389.9 || Sa7/sd8 || M6 || 20/9 ||   ||   ||
-|| 39 || 1426.5 || 3A7/qd8 || SM-6 || 9/4~16/7 ||   ||   ||
-|| 40 || 1463.0 || A7/P8/d9 || SM6/dd7 || 147/64~7/3 ||   ||   ||
-|| 41 || 1499.6 || Qa8/3d9 || SM+6/sm-7 || 64/27~50/21~26/11~81/23 ||   ||   ||
-|| 42 || 1536.2 || Sa8/sd9 || AA6/sm7 || 12/5 || 22/9- ||   ||
-|| 43 || 1572.7 || 3A8/qd9 || sm-7 || 5/2~32/13 || 22/9+ ||   ||
-|| 44 || 1609.3 || A8/m9 || m7 || 81/32~63/25~33/13~23/9 ||   ||   ||
-|| 45 || 1645.9 || Sm9 || N7 || 64/45~18/7~28/11~208/81~13/5 ||   ||   ||
-|| 46 || 1682.5 || N9 || M7 || 21/8~196/75 ||   ||   ||
-|| 47 || 1719.1 || sM9 || SM-7 || 8/3~27/10 ||   ||   ||
-|| 48 || 1755.65 || M9/d10 || SM7/dd8 || 69/25~135/49 || 36/13- ||   ||
-|| 49 || 1792.2 || Qa9/3d10 || SM+7/d-8 || 14/5~25/9~224/81~176/63~64/23~58/21 || 36/13+ ||   ||
-|| 50 || 1828.8 || Sa9/sd10 || A7/d8 || 20/7~72/25~81/28~63/22~23/8~84/29 || 26/9- ||   ||
-|| 51 || 1865.4 || 3A9/qd10 || P-8 || 147/50~32/11~338/81~144/49 || 26/9+ ||   ||
-|| 52 || 1902.0 || A9/P10 || P8 || 3/1 || Tritave ||   ||
-It is a weird coincidence how 52edt intones any [[52edo]] intervals within plus or minus 6.5 cents when it is supposed to have nothing to do with this other tuning:
+== Harmonics ==
+While 52edt does not improve much on [[26edt]]'s mapping of the odd primes, it still maps 11, 13, 19, and 29 ''slightly'' better than 26edt, which is notable for giving them (despite being nearly half a step off in the case of 11) a flat tendency in keeping with all the other odd primes, which allows 52edt to be the first edt that is [[consistent]] to the no-twos 29-[[throdd limit]], which is a record unbeaten until [[144edt]].
+{{Harmonics in equal|52|3|1|intervals=prime|columns=9}}
+{{Harmonics in equal|52|3|1|start=12|collapsed=1|intervals=odd}}
-||~ 52edt ||~ 52edo ||~ Discrepancy ||
+== Intervals ==
-|| 365.761 || 369.231 || -3.47 ||
+{| class="wikitable"
-|| 512.065 || 507.692 || +4.373 ||
+|-
-|| 877.825 || 876.923 || +0.902 ||
+! Steps
-|| 1243.586 || 1246.154 || -2.168 ||
+! Cents
-|| 1389.89 || 1384.615 || +5.275 ||
+! Hekts
-|| 1755.651 || 1753.846 || +1.805 ||
+! BP nonatonic degree
-|| 2121.411 || 2123.077 || -1.666 ||
+! Diatonic degree
-|| 2633.476 || 2630.769 || +2.647 ||
+! Corresponding JI intervals
-…and so on</pre></div>
+! Comments
-<h4>Original HTML content:</h4>
+! Generator for...
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;52edt&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 52 equal division of 3, the tritave, divides it into 52 equal parts of 36.576 cents each, corresponding to 32.808 edo. It is something of a curiosity as it really needs to be considered as a 29-limit no-twos system. While not super-accurate, it gets the entire no-twos 29-limit to within 18 cents. It is distinctly flat, in the sense that 5, 7, 11, 13, 17, 19, 23 and 29 are all flat, so using something other than pure-threes tuning might be advisable. It is contorted in the 11-limit, so that it tempers out the same commas as &lt;a class="wiki_link" href="/26edt"&gt;26edt&lt;/a&gt; in the 11-limit and &lt;a class="wiki_link" href="/13edt"&gt;13edt&lt;/a&gt; in the 7-limit. Other commas it tempers out includes 121/119, 209/207, 247/245, 275/273, 299/297, 325/323, 345/343, 363/361, 377/375, 437/435, 495/493, 627/625, 665/663, 667/665, 847/845, 1127/1125, 1311/1309 and 1617/1615. It is the eleventh &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Removing%20primes"&gt;no-twos zeta peak edt&lt;/a&gt;.&lt;br /&gt;
+|-
-&lt;br /&gt;
+| 1
-&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Intervals&lt;/h2&gt;
+| 36.6
+| 25
+| Qa1/3d2
+| Sa1
+| 50/49~33/32~49/48
+|
+|
+|-
+| 2
+| 73.15
+| 50
+| Sa1/sd2
+| A1/dd2
+| 25/24~28/27~22/21~27/26~24/23~21/20~29/28
+|
+|
+|-
+| 3
+| 109.7
+| 75
+| 3A1/qd2
+| A+1/d-2
+| 15/14~16/15~29/27~121/112
+|
+|
+|-
+| 4
+| 146.3
+| 100
+| A1/m2
+| AA1/sm2
+| 27/25~25/23~49/45~13/12~14/13~11/10~169/162
+|
+|
+|-
+| 5
+| 182.9
+| 125
+| Sm2
+| sm+2
+| 10/9
+|
+|
+|-
+| 6
+| 219.5
+| 150
+| N2
+| m2
+| 9/8~8/7~44/39
+|
+|
+|-
+| 7
+| 256.0
+| 175
+| sM2
+| N2
+| 147/128~7/6
+|
+|
+|-
+| 8
+| 292.6
+| 200
+| M2/d3
+| M2
+| 32/27~25/21~13/11~27/23
+|
+|
+|-
+| 9
+| 329.2
+| 225
+| Qa2/3d3
+| SM-2/d-2
+| 6/5
+| 11/9-
+|
+|-
+| 10
+| 365.8
+| 250
+| Sa2/sd3
+| SM2/dd3
+| 5/4~16/13
+| 11/9+
+|
+|-
+| 11
+| 402.3
+| 275
+| 3A3/qd3
+| SM+2
+| 81/64~63/50~33/26~23/18
+|
+|
+|-
+| 12
+| 438.9
+| 300
+| A2/P3/d4
+| AA2/sm3
+| 32/25~9/7~14/11~104/81~13/10
+|
+|
+|-
+| 13
+| 475.5
+| 325
+| Qa3/3d4
+| sm+3
+| 21/16~98/75
+|
+|
+|-
+| 14
+| 512.1
+| 350
+| Sa3/sd4
+| m3
+| 4/3~27/20~162/121
+|
+|
+|-
+| 15
+| 548.6
+| 375
+| 3A3/qd4
+| N3
+| 11/8~243/169
+| 18/13-
+|
+|-
+| 16
+| 585.2
+| 400
+| A3/m4/d5
+| M3
+| 7/5~25/18~112/81~88/63~32/23~29/21
+| 18/13+
+|
+|-
+| 17
+| 621.8
+| 425
+| Sm4/3d5
+| SM-3
+| 10/7~36/25~81/56~63/44~23/16~42/29
+| 13/9-
+|
+|-
+| 18
+| 658.4
+| 450
+| N4/sd5
+| SM3/dd4
+| 16/11~338/243
+| 13/9+
+|
+|-
+| 19
+| 694.95
+| 475
+| sM4/qd5
+| SM+3/d-4
+| 3/2~40/27~121/81
+|
+|
+|-
+| 20
+| 731.5
+| 500
+| M4/m5
+| AA3/d4
+| 32/21~75/49
+|
+|
+|-
+| 21
+| 768.1
+| 525
+| Qa4/Sm5
+| d+4
+| 25/16~14/9~11/7~81/52
+|
+|
+|-
+| 22
+| 804.7
+| 550
+| Sa4/N5
+| P4
+| 8/5~36/23
+|
+|
+|-
+| 23
+| 841.25
+| 575
+| 3A4/sM5
+| A-4
+| 13/8
+|
+|
+|-
+| 24
+| 877.8
+| 600
+| A4/M5/d6
+| A4
+| 5/3
+|
+|
+|-
+| 25
+| 914.4
+| 625
+| Qa5/3d6
+| A+4
+| 27/16~42/25~22/13~46/27
+|
+|
+|-
+| 26
+| 951
+| 650
+| Sa5/sd6
+| AA4/dd5
+| 125/72
+|
+|
+|-
+| 27
+| 987.55
+| 675
+| 3A5/qd6
+| d-5
+| 16/9~8/7~39/22~75/46
+|
+|
+|-
+| 28
+| 1024.1
+| 700
+| A5/m6/d7
+| d5
+| 9/5
+|
+|
+|-
+| 29
+| 1060.7
+| 725
+| Sm6/3d7
+| d+5
+| 50/27~46/25~90/49~24/13~13/7~20/11
+|
+|
+|-
+| 30
+| 1097.3
+| 750
+| N6/sd7
+| P5
+| 15/8
+|
+|
+|-
+| 31
+| 1133.9
+| 775
+| sM6/qd7
+| A-5
+| 48/25~27/14~21/11~52/27~23/12~40/21~56/29
+|
+|
+|-
+| 32
+| 1170.4
+| 800
+| M6/m7
+| A5/dd6
+| 49/25~64/33~96/49
+|
+|
+|-
+| 33
+| 1207.0
+| 825
+| Qa6/Sm7
+| A+5
+| 2/1
+|
+|
+|-
+| 34
+| 1243.6
+| 850
+| Sa6/N7
+| AA5/sm6
+| 33/16~100/49~49/24~729/338
+|
+|
+|-
+| 35
+| 1280.2
+| 875
+| 3A6/sM7
+| sm+6
+| 25/12~56/27~44/21~27/13
+|
+|
+|-
+| 36
+| 1316.7
+| 900
+| A6/M7/d8
+| m6
+| 15/7~32/15~58/27
+|
+|
+|-
+| 37
+| 1353.3
+| 925
+| Qa7/3d8
+| N6
+| 54/25~50/23~98/45~13/6~169/81
+|
+|
+|-
+| 38
+| 1389.9
+| 950
+| Sa7/sd8
+| M6
+| 20/9~9/4-
+|
+|
+|-
+| 39
+| 1426.5
+| 975
+| 3A7/qd8
+| SM-6
+| 9/4+~16/7
+|
+|
+|-
+| 40
+| 1463.0
+| 1000
+| A7/P8/d9
+| SM6/dd7
+| 147/64~7/3
+|
+|
+|-
+| 41
+| 1499.6
+| 1025
+| Qa8/3d9
+| SM+6/sm-7
+| 64/27~50/21~26/11~81/23
+|
+|
+|-
+| 42
+| 1536.2
+| 1050
+| Sa8/sd9
+| AA6/sm7
+| 12/5
+| 22/9-
+|
+|-
+| 43
+| 1572.7
+| 1075
+| 3A8/qd9
+| sm-7
+| 5/2~32/13
+| 22/9+
+|
+|-
+| 44
+| 1609.3
+| 1100
+| A8/m9
+| m7
+| 81/32~63/25~33/13~23/9
+|
+|
+|-
+| 45
+| 1645.9
+| 1125
+| Sm9
+| N7
+| 64/45~18/7~28/11~208/81~13/5
+|
+|
+|-
+| 46
+| 1682.5
+| 1150
+| N9
+| M7
+| 21/8~196/75
+|
+|
+|-
+| 47
+| 1719.1
+| 1175
+| sM9
+| SM-7
+| 8/3~27/10
+|
+|
+|-
+| 48
+| 1755.65
+| 1200
+| M9/d10
+| SM7/dd8
+| 69/25~135/49
+| 36/13-
+|
+|-
+| 49
+| 1792.2
+| 1225
+| Qa9/3d10
+| SM+7/d-8
+| 14/5~25/9~224/81~176/63~64/23~58/21
+| 36/13+
+|
+|-
+| 50
+| 1828.8
+| 1250
+| Sa9/sd10
+| A7/d8
+| 20/7~72/25~81/28~63/22~23/8~84/29
+| 26/9-
+|
+|-
+| 51
+| 1865.4
+| 1275
+| 3A9/qd10
+| P-8
+| 147/50~32/11~338/81~144/49
+| 26/9+
+|
+|-
+| 52
+| 1902.0
+| 1300
+| A9/P10
+| P8
+| 3/1
+| Tritave
+|
+|}
-&lt;table class="wiki_table"&gt;
+It is a weird coincidence how 52edt intones any [[52edo|52edo]] intervals within plus or minus 6.5 cents when it is supposed to have nothing to do with this other tuning:
-    &lt;tr&gt;
-        &lt;th&gt;Steps&lt;br /&gt;
-&lt;/th&gt;
-        &lt;th&gt;Cents&lt;br /&gt;
-&lt;/th&gt;
-        &lt;th&gt;BP nonatonic degree&lt;br /&gt;
-&lt;/th&gt;
-        &lt;th&gt;Diatonic degree&lt;br /&gt;
-&lt;/th&gt;
-        &lt;th&gt;Corresponding JI intervals&lt;br /&gt;
-&lt;/th&gt;
-        &lt;th&gt;Comments&lt;br /&gt;
-&lt;/th&gt;
-        &lt;th&gt;Generator for...&lt;br /&gt;
-&lt;/th&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;1&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;36.6&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;Qa1/3d2&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;Sa1&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;50/49~33/32~49/48&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;2&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;73.15&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;Sa1/sd2&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;A1/dd2&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;25/24~28/27~22/21~27/26~24/23~21/20~29/28&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;3&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;109.7&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;3A1/qd2&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;A+1/d-2&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;15/14~16/15~29/27~121/112&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;4&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;146.3&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;A1/m2&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;AA1/sm2&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;27/25~25/23~49/45~13/12~14/13~11/10~169/162&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;5&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;182.9&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;Sm2&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;sm+2&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;10/9&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;6&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;219.5&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;N2&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;m2&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;9/8~8/7~44/39&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;7&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;256.0&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;sM2&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;N2&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;147/128~7/6&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;8&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;292.6&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;M2/d3&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;M2&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;32/27~25/21~13/11~27/23&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;9&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;329.2&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;Qa2/3d3&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;SM-2/d-2&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;6/5&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;11/9-&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;10&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;365.8&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;Sa2/sd3&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;SM2/dd3&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;5/4~16/13&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;11/9+&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;11&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;402.3&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;3A3/qd3&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;SM+2&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;81/64~63/50~33/26~23/18&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;12&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;438.9&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;A2/P3/d4&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;AA2/sm3&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;32/25~9/7~14/11~104/81~13/10&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;13&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;475.5&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;Qa3/3d4&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;sm+3&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;21/16~98/75&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;14&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;512.1&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;Sa3/sd4&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;m3&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;4/3~27/20~162/121&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;15&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;548.6&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;3A3/qd4&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;N3&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;11/8~243/169&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;18/13-&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;16&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;585.2&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;A3/m4/d5&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;M3&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;7/5~25/18~112/81~88/63~32/23~29/21&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;18/13+&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;17&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;621.8&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;Sm4/3d5&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;SM-3&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;10/7~36/25~81/56~63/44~23/16~42/29&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;13/9-&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;18&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;658.4&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;N4/sd5&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;SM3/dd4&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;16/11~338/243&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;13/9+&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;19&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;694.95&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;sM4/qd5&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;SM+3/d-4&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;3/2~40/27~121/81&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;20&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;731.5&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;M4/m5&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;AA3/d4&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;32/21~75/49&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;21&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;768.1&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;Qa4/Sm5&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;d+4&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;25/16~14/9~11/7~81/52&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;22&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;804.7&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;Sa4/N5&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;P4&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;8/5~36/23&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
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-        &lt;td&gt;23&lt;br /&gt;
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-        &lt;td&gt;&lt;br /&gt;
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-        &lt;td&gt;&lt;br /&gt;
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-        &lt;td&gt;&lt;br /&gt;
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-        &lt;td&gt;&lt;br /&gt;
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-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
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-    &lt;tr&gt;
-        &lt;td&gt;26&lt;br /&gt;
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-        &lt;td&gt;Sa5/sd6&lt;br /&gt;
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-        &lt;td&gt;AA4/dd5&lt;br /&gt;
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-        &lt;td&gt;125/72&lt;br /&gt;
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-        &lt;td&gt;&lt;br /&gt;
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-        &lt;td&gt;&lt;br /&gt;
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-    &lt;tr&gt;
-        &lt;td&gt;27&lt;br /&gt;
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-        &lt;td&gt;987.55&lt;br /&gt;
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-        &lt;td&gt;3A5/qd6&lt;br /&gt;
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-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;28&lt;br /&gt;
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-        &lt;td&gt;A5/m6/d7&lt;br /&gt;
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-        &lt;td&gt;d5&lt;br /&gt;
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-        &lt;td&gt;9/5&lt;br /&gt;
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-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;29&lt;br /&gt;
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-        &lt;td&gt;1060.7&lt;br /&gt;
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-        &lt;td&gt;Sm6/3d7&lt;br /&gt;
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-        &lt;td&gt;d+5&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;50/27~46/25~90/49~24/13~13/7~20/11&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;30&lt;br /&gt;
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-        &lt;td&gt;1097.3&lt;br /&gt;
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-        &lt;td&gt;N6/sd7&lt;br /&gt;
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-        &lt;td&gt;P5&lt;br /&gt;
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-        &lt;td&gt;15/8&lt;br /&gt;
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-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;31&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1133.9&lt;br /&gt;
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-        &lt;td&gt;sM6/qd7&lt;br /&gt;
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-        &lt;td&gt;A-5&lt;br /&gt;
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-        &lt;td&gt;48/25~27/14~21/11~52/27~23/12~40/21~56/29&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;32&lt;br /&gt;
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-        &lt;td&gt;1170.4&lt;br /&gt;
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-        &lt;td&gt;M6/m7&lt;br /&gt;
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-        &lt;td&gt;A5/dd6&lt;br /&gt;
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-        &lt;td&gt;49/25~64/33~96/49&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;33&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1207.0&lt;br /&gt;
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-        &lt;td&gt;Qa6/Sm7&lt;br /&gt;
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-        &lt;td&gt;A+5&lt;br /&gt;
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-        &lt;td&gt;2/1&lt;br /&gt;
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-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
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-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;34&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1243.6&lt;br /&gt;
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-        &lt;td&gt;Sa6/N7&lt;br /&gt;
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-        &lt;td&gt;AA5/sm6&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;33/16~100/49~49/24~729/338&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;35&lt;br /&gt;
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-        &lt;td&gt;1280.2&lt;br /&gt;
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-        &lt;td&gt;3A6/sM7&lt;br /&gt;
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-        &lt;td&gt;sm+6&lt;br /&gt;
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-        &lt;td&gt;25/12~56/27~44/21~27/13&lt;br /&gt;
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-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;36&lt;br /&gt;
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-        &lt;td&gt;1316.7&lt;br /&gt;
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-        &lt;td&gt;A6/M7/d8&lt;br /&gt;
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-        &lt;td&gt;m6&lt;br /&gt;
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-        &lt;td&gt;15/7~32/15~58/27&lt;br /&gt;
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-        &lt;td&gt;&lt;br /&gt;
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-        &lt;td&gt;&lt;br /&gt;
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-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;37&lt;br /&gt;
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-        &lt;td&gt;1353.3&lt;br /&gt;
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-        &lt;td&gt;Qa7/3d8&lt;br /&gt;
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-        &lt;td&gt;N6&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;54/25~50/23~98/45~13/6~169/81&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;38&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1389.9&lt;br /&gt;
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-        &lt;td&gt;Sa7/sd8&lt;br /&gt;
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-        &lt;td&gt;M6&lt;br /&gt;
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-        &lt;td&gt;20/9&lt;br /&gt;
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-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;39&lt;br /&gt;
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-        &lt;td&gt;1426.5&lt;br /&gt;
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-        &lt;td&gt;3A7/qd8&lt;br /&gt;
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-        &lt;td&gt;SM-6&lt;br /&gt;
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-        &lt;td&gt;9/4~16/7&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;40&lt;br /&gt;
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-        &lt;td&gt;1463.0&lt;br /&gt;
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-        &lt;td&gt;A7/P8/d9&lt;br /&gt;
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-        &lt;td&gt;SM6/dd7&lt;br /&gt;
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-        &lt;td&gt;147/64~7/3&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
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-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;41&lt;br /&gt;
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-        &lt;td&gt;1499.6&lt;br /&gt;
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-        &lt;td&gt;Qa8/3d9&lt;br /&gt;
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-        &lt;td&gt;SM+6/sm-7&lt;br /&gt;
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-        &lt;td&gt;64/27~50/21~26/11~81/23&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;42&lt;br /&gt;
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-        &lt;td&gt;1536.2&lt;br /&gt;
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-        &lt;td&gt;Sa8/sd9&lt;br /&gt;
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-        &lt;td&gt;AA6/sm7&lt;br /&gt;
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-        &lt;td&gt;12/5&lt;br /&gt;
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-        &lt;td&gt;22/9-&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;43&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1572.7&lt;br /&gt;
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-        &lt;td&gt;3A8/qd9&lt;br /&gt;
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-        &lt;td&gt;sm-7&lt;br /&gt;
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-        &lt;td&gt;5/2~32/13&lt;br /&gt;
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-        &lt;td&gt;22/9+&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;44&lt;br /&gt;
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-        &lt;td&gt;1609.3&lt;br /&gt;
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-        &lt;td&gt;A8/m9&lt;br /&gt;
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-        &lt;td&gt;m7&lt;br /&gt;
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-        &lt;td&gt;81/32~63/25~33/13~23/9&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
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-    &lt;tr&gt;
-        &lt;td&gt;45&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1645.9&lt;br /&gt;
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-        &lt;td&gt;Sm9&lt;br /&gt;
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-        &lt;td&gt;N7&lt;br /&gt;
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-        &lt;td&gt;64/45~18/7~28/11~208/81~13/5&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;46&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1682.5&lt;br /&gt;
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-        &lt;td&gt;N9&lt;br /&gt;
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-        &lt;td&gt;M7&lt;br /&gt;
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-        &lt;td&gt;21/8~196/75&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;47&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1719.1&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;sM9&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;SM-7&lt;br /&gt;
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-        &lt;td&gt;8/3~27/10&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;48&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1755.65&lt;br /&gt;
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-        &lt;td&gt;M9/d10&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;SM7/dd8&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;69/25~135/49&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;36/13-&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;49&lt;br /&gt;
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-&lt;/td&gt;
-        &lt;td&gt;Qa9/3d10&lt;br /&gt;
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-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
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-    &lt;tr&gt;
-        &lt;td&gt;50&lt;br /&gt;
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-        &lt;td&gt;1828.8&lt;br /&gt;
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-        &lt;td&gt;Sa9/sd10&lt;br /&gt;
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-        &lt;td&gt;A7/d8&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;20/7~72/25~81/28~63/22~23/8~84/29&lt;br /&gt;
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-        &lt;td&gt;26/9-&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
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-    &lt;tr&gt;
-        &lt;td&gt;51&lt;br /&gt;
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-        &lt;td&gt;1865.4&lt;br /&gt;
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-        &lt;td&gt;3A9/qd10&lt;br /&gt;
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-        &lt;td&gt;147/50~32/11~338/81~144/49&lt;br /&gt;
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-        &lt;td&gt;26/9+&lt;br /&gt;
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-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
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-    &lt;tr&gt;
-        &lt;td&gt;52&lt;br /&gt;
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-        &lt;td&gt;1902.0&lt;br /&gt;
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-        &lt;td&gt;A9/P10&lt;br /&gt;
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-        &lt;td&gt;P8&lt;br /&gt;
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-        &lt;td&gt;3/1&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;Tritave&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-&lt;/table&gt;
-&lt;br /&gt;
+{| class="wikitable"
-It is a weird coincidence how 52edt intones any &lt;a class="wiki_link" href="/52edo"&gt;52edo&lt;/a&gt; intervals within plus or minus 6.5 cents when it is supposed to have nothing to do with this other tuning:&lt;br /&gt;
+|-
-&lt;br /&gt;
+! 52edt
+! 52edo
+! Discrepancy
-&lt;table class="wiki_table"&gt;
+|-
-    &lt;tr&gt;
+| 365.761
-        &lt;th&gt;52edt&lt;br /&gt;
+| 369.231
-&lt;/th&gt;
+| −3.47
-        &lt;th&gt;52edo&lt;br /&gt;
+|-
-&lt;/th&gt;
+| 512.065
-        &lt;th&gt;Discrepancy&lt;br /&gt;
+| 507.692
-&lt;/th&gt;
+| +4.373
-    &lt;/tr&gt;
+|-
-    &lt;tr&gt;
+| 877.825
-        &lt;td&gt;365.761&lt;br /&gt;
+| 876.923
-&lt;/td&gt;
+| +0.902
-        &lt;td&gt;369.231&lt;br /&gt;
+|-
-&lt;/td&gt;
+| 1243.586
-        &lt;td&gt;-3.47&lt;br /&gt;
+| 1246.154
-&lt;/td&gt;
+| −2.168
-    &lt;/tr&gt;
+|-
-    &lt;tr&gt;
+| 1389.89
-        &lt;td&gt;512.065&lt;br /&gt;
+| 1384.615
-&lt;/td&gt;
+| +5.275
-        &lt;td&gt;507.692&lt;br /&gt;
+|-
-&lt;/td&gt;
+| 1755.651
-        &lt;td&gt;+4.373&lt;br /&gt;
+| 1753.846
-&lt;/td&gt;
+| +1.805
-    &lt;/tr&gt;
+|-
-    &lt;tr&gt;
+| 2121.411
-        &lt;td&gt;877.825&lt;br /&gt;
+| 2123.077
-&lt;/td&gt;
+| −1.666
-        &lt;td&gt;876.923&lt;br /&gt;
+|-
-&lt;/td&gt;
+| 2633.476
-        &lt;td&gt;+0.902&lt;br /&gt;
+| 2630.769
-&lt;/td&gt;
+| +2.647
-    &lt;/tr&gt;
+|}
-    &lt;tr&gt;
+…and so on
-        &lt;td&gt;1243.586&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1246.154&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;-2.168&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;1389.89&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1384.615&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;+5.275&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;1755.651&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1753.846&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;+1.805&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;2121.411&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;2123.077&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;-1.666&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;2633.476&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;2630.769&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;+2.647&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-&lt;/table&gt;
-…and so on&lt;/body&gt;&lt;/html&gt;</pre></div>

52edt: Difference between revisions

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