User:FloraC/Table of 540edo intervals

< User:FloraC

This table of 540edo intervals assumes the 43-limit patent val of 540edo ⟨540 856 1254 1516 1868 1998 2207 2294 2443 2623 2675 2813 2893 2930]. Prime harmonics are in bold; inconsistently mapped intervals are in italic. As is analysed in the main article, the 2.3.5.7.11.13.19-subgroup of 540edo is the same as 270edo, but primes 17 and 23 are much improved. Furthermore, 540edo can be used in the full 43-limit, but as a no-29 no-31 43-limit system, it is almost consistent to the 45-odd-limit. For this reason, intervals of 29 and 31 are given in parentheses.

#	Cents	Marks	13-limit	23-limit	31-limit	43-limit
0	0.0	P1	1/1	"	"	"
1	2.2			?	"	"
2	4.4		385/384	"	"	"
3	6.6			?	"	"
4	8.8		196/195	"	"	"
5	11.1			?	"	"
6	13.3		126/125	"	"	"
7	15.5			?	"	"
8	17.7		99/98	"	"	"
9	20.0			?	"	"
10	22.2		78/77	"	"	"
11	24.4			?	"	"
12	26.6		65/64	"	"	"
13	28.8			?	"	"
14	31.1		56/55	"	"	"
15	33.3			?	"	"
16	35.5		49/48	"	"	"
17	37.7			?	"	"
18	40.0		45/44	"	"	"
19	42.2			?	"	"
20	44.4		39/38	"	"	"
21	46.6			?	"	"
22	48.8		36/35	"	"	"
23	51.1			?	"	"
24	53.3		33/32	"	"	"
25	55.5			?	(32/31)	"
26	57.7		91/88	"	"	"
27	60.0			?	"	"
28	62.2		28/27	"	"	"
29	64.4			?	"	"
30	66.6		26/25	"	"	"
31	68.8			?	"	"
32	71.1		25/24	"	"	"
33	73.3			24/23	"	"
34	75.5		117/112	"	"	"
35	77.7			23/22	"	"
36	80.0		22/21	"	"	"
37	82.2			?	"	"
38	84.4		21/20	"	"	"
39	86.6			?	"	"
40	88.8	m2	81/77	20/19	"	"
41	91.1			?	"	"
42	93.3		96/91	19/18	"	"
43	95.5			?	"	"
44	97.7		55/52	"	"	"
45	100.0			18/17	"	"
46	102.2		35/33	"	"	"
47	104.4			17/16	"	"
48	106.6		117/110	"	"	"
49	108.8			?	"	"
50	111.1		16/15	"	"	"
51	113.3			?	"	"
52	115.5		77/72	"	31/29	"
53	117.7			?	"	"
54	120.0		15/14	"	"	"
55	122.2			?	"	"
56	124.4		130/121	"	"	"
57	126.6			?	"	"
58	128.8		14/13	"	"	"
59	131.1			?	"	"
60	133.3		27/25	"	"	"
61	135.5			?	"	"
62	137.7		13/12	"	"	"
63	140.0			?	"	"
64	142.2		88/81	38/35	"	"
65	144.4			?	"	"
66	146.6		49/45	"	"	"
67	148.8			?	"	"
68	151.1		12/11	"	"	"
69	153.3			?	"	"
70	155.5		35/32	"	"	"
71	157.7			23/21	"	"
72	160.0		169/154	"	"	"
73	162.2			?	"	"
74	164.4		11/10	"	"	"
75	166.6			?	"	"
76	168.8		54/49	"	"	"
77	171.1			?	(32/29)	"
78	173.3		243/220	21/19	"	"
79	175.5			?	"	"
80	177.7		72/65	"	"	"
81	180.0			?	"	"
82	182.2		10/9	"	"	"
83	184.4			?	"	"
84	186.6		39/35	"	"	"
85	188.8			?	"	"
86	191.1		125/112	"	"	"
87	193.3			19/17	"	"
88	195.5		28/25	"	"	"
89	197.7			?	"	"
90	200.0		55/49	"	"	"
91	202.2			?	"	"
92	204.4	M2	9/8	"	"	"
93	206.6			?	"	"
94	208.8		44/39	"	"	"
95	211.1			26/23	"	"
96	213.3		112/99	"	"	"
97	215.5			17/15	"	"
98	217.7		143/126	"	"	"
99	220.0			?	"	"
100	222.2		25/22	"	"	"
101	224.4			?	"	"
102	226.6		154/135	57/50	"	"
103	228.8			?	"	"
104	231.1		8/7	"	"	"
105	233.3			?	"	"
106	235.5		55/48	"	"	"
107	237.7			?	"	"
108	240.0		147/128	"	"	"
109	242.2			23/20	"	"
110	244.4		121/105	38/33	"	"
111	246.6			?	"	"
112	248.8		15/13	"	"	"
113	251.1			?	"	37/32
114	253.3		81/70	22/19	"	"
115	255.5			?	"	"
116	257.7		65/56	"	"	"
117	260.0			?	"	"
118	262.2		64/55	57/49	"	"
119	264.4			?	"	"
120	266.6		7/6	"	"	"
121	268.8			?	"	"
122	271.1		90/77	76/65	"	"
123	273.3			?	"	"
124	275.5		75/64	"	"	"
125	277.7			?	"	"
126	280.0		147/125	"	"	"
127	282.2			20/17	"	"
128	284.4		33/28	"	"	"
129	286.6			?	"	"
130	288.8		13/11	"	"	"
131	291.1			?	"	"
132	293.3	m3	32/27	"	"	"
133	295.5			?	"	"
134	297.7		108/91	19/16	"	"
135	300.0			?	"	"
136	302.2		25/21	"	"	"
137	302.2			?	"	"
138	306.6		105/88	"	"	"
139	308.8			?	"	"
140	311.1		140/117	91/76	"	"
141	313.3			?	"	"
142	315.5		6/5	"	"	"
143	317.7			?	"	"
144	320.0		65/54	"	"	"
145	322.2			?	"	"
146	324.4		135/112	76/63	"	"
147	326.6			?	"	"
148	328.8		98/81	"	"	"
149	331.1			23/19	"	"
150	333.3		40/33	"	"	"
151	335.5			17/14	"	"
152	337.7		147/121	"	"	"
153	340.0			28/23	"	"
154	342.2		39/32	"	"	"
155	344.4			?	"	"
156	346.6		11/9	"	"	"
157	348.8			?	"	"
158	351.1		49/40	"	"	"
159	353.3			?	"	"
160	355.5		27/22	"	"	"
161	357.7			?	"	"
162	360.0		16/13	"	"	"
163	362.2			?	"	"
164	364.4		100/81	"	"	"
165	366.6			21/17	"	"
166	368.8		26/21	"	"	"
167	371.1			?	"	"
168	373.3		150/121	"	"	"
169	375.5			?	"	"
170	377.7		56/45	"	"	"
171	380.0			?	"	"
172	382.2		81/65	"	"	"
173	384.4			?	"	"
174	386.6		5/4	"	"	"
175	388.8			?	"	"
176	391.1		351/280	"	"	"
177	393.3			?	"	"
178	395.5		44/35	"	"	"
179	397.7			?	"	"
180	400.0		63/50	"	"	"
181	402.2			?	"	"
182	404.4		91/72	24/19	"	"
183	406.6			?	"	"
184	408.8	M3	81/64	19/15	"	"
185	411.1			?	"	"
186	413.3		33/26	"	"	"
187	415.5			?	"	"
188	417.7		14/11	"	"	"
189	420.0			?	"	"
190	422.2		125/98	"	"	"
191	424.4			23/18	"	"
192	426.6		32/25	"	"	"
193	428.8			?	"	41/32
194	431.1		50/39	"	"	"
195	433.3			?	"	"
196	435.5		9/7	"	"	"
197	437.7			?	"	"
198	440.0		156/121	49/38	"	"
199	442.2			?	"	"
200	444.4		84/65	"	"	"
201	446.6			22/17	"	"
202	448.8		35/27	"	"	"
203	451.1			?	"	"
204	453.3		13/10	"	"	"
205	455.5			?	"	"
206	457.7		125/96	99/76	"	"
207	460.0			30/23	"	"
208	462.2		64/49	"	"	"
209	464.4			17/13	"	"
210	466.6		55/42	"	"	"
211	468.8			?	"	"
212	471.1		21/16	"	"	"
213	473.3			?	"	"
214	475.5		154/117	25/19	"	"
215	477.7			?	"	"
216	480.0		33/25	"	"	"
217	482.2			?	"	"
218	484.4		143/108	"	"	"
219	486.6			?	"	"
220	488.8		65/49	"	"	"
221	491.1			?	"	"
222	493.3		117/88	"	"	"
223	495.5			?	"	"
224	497.7	P4	4/3	"	"	"
225	500.0			?	"	"
226	502.2		147/110	"	"	"
227	504.4			?	"	"
228	506.6		75/56	"	"	"
229	508.8			?	"	"
230	511.1		121/90	"	"	43/32
231	513.3			?	"	"
232	515.5		35/26	"	"	"
233	517.7			?	"	"
234	520.0		27/20	"	"	"
235	522.2			?	"	"
236	524.4		65/48	23/17	"	"
237	526.6			?	"	"
238	528.8		110/81	19/14	"	"
239	531.1			?	"	"
240	533.3		49/36	"	"	"
241	535.5			?	"	"
242	537.7		15/11	"	"	"
243	540.0			?	"	"
244	542.2		160/117	26/19	"	"
245	544.4			?	"	"
246	546.6		48/35	"	"	"
247	547.7			?	"	"
248	551.1		11/8	"	"	"
249	553.3			?	"	"
250	555.5		91/66	"	"	"
251	557.7			?	"	"
252	560.0		112/81	105/76	"	"
253	562.2			?	"	"
254	564.4		18/13	"	"	"
255	566.6			?	"	"
256	568.8		25/18	"	"	"
257	571.1			32/23	"	"
258	573.3		39/28	"	"	"
259	575.5			?	"	"
260	577.7		88/63	"	"	"
261	580.0			?	"	"
262	582.2		7/5	"	"	"
263	584.4			?	"	"
264	586.6	d5	108/77	80/57	"	"
265	588.8			?	"	"
266	591.1		45/32	38/27	"	"
267	593.3			?	"	"
268	595.5		55/39	"	"	"
269	597.7			24/17	"	"
270	600.0		99/70	"	"	"
271	602.2			17/12	"	"
272	604.4		78/55	"	"	"
273	606.6			?	"	"
274	608.8		64/45	27/19	"	"
275	611.1			?	"	"
276	613.3	A4	77/54	57/40	"	"
277	615.5			?	"	"
278	617.7		10/7	"	"	"
279	620.0			?	"	"
280	622.2		63/44	"	"	"
281	624.4			?	"	"
282	626.6		56/39	"	"	"
283	628.8			23/16	"	"
284	631.1		36/25	"	"	"
285	633.3			?	"	"
286	635.5		13/9	"	"	"
287	637.7			?	"	"
288	640.0		81/56	"	"	"
289	642.2			?	"	"
290	644.4		132/91	"	"	"
291	646.6			?	"	"
292	648.8		16/11	"	"	"
293	651.1			?	"	"
294	653.3		35/24	"	"	"
295	655.5			?	"	"
296	657.7		117/80	19/13	"	"
297	660.0			?	"	"
298	662.2		22/15	"	"	"
299	664.4			?	"	"
300	666.6		72/49	"	"	"
301	668.8			?	"	"
302	671.1		81/55	28/19	"	"
303	673.3			?	"	"
304	675.5		65/44	34/23	"	"
305	677.7			?	"	"
306	680.0		40/27	"	"	"
307	682.2			?	"	"
308	684.4		49/33	"	"	"
309	686.6			?	"	"
310	688.8		125/84	"	"	64/43
311	691.1			?	"	"
312	693.3		112/75	"	"	"
313	695.5			?	"	"
314	697.7		175/117	"	"	"
315	700.0			?	"	"
316	702.2	P5	3/2	"	"	"
317	704.4			?	"	"
318	706.6		176/117	"	"	"
319	708.8			?	"	"
320	711.1		98/65	95/63	"	"
321	713.3			?	"	"
322	715.5		121/80	"	"	"
323	717.7			?	"	"
324	720.0		50/33	"	"	"
325	721.1			?	"	"
326	724.4		117/77	38/25	"	"
327	726.6			?	"	"
328	728.8		32/21	"	"	"
329	731.1			?	"	"
330	733.3		55/36	"	"	"
331	735.5			26/17	"	"
332	737.7		49/32	"	"	"
333	740.0			23/15	"	"
334	742.2		135/88	"	"	"
335	744.4			?	"	"
336	746.6		20/13	"	"	"
337	748.8			?	"	"
338	751.1		54/35	"	"	"
339	753.3			17/11	"	"
340	755.5		65/42	"	"	"
341	757.7			?	"	"
342	760.0		121/78	76/49	"	"
343	762.2			?	"	"
344	764.4		14/9	"	"	"
345	766.6			?	"	"
346	768.8		39/25	"	"	"
347	771.1			?	"	64/41
348	773.3		25/16	"	"	"
349	775.5			36/23	"	"
350	777.7		196/125	"	"	"
351	780.0			?	"	"
352	782.2		11/7	"	"	"
353	784.4			?	"	"
354	786.6		52/33	"	"	"
355	788.8			?	"	"
356	791.1	m6	128/81	30/19	"	"
357	793.3			?	"	"
358	795.5		144/91	19/12	"	"
359	797.7			?	"	"
360	800.0		100/63	"	"	"
361	802.2			?	"	"
362	804.4		35/22	"	"	"
363	806.6			?	"	"
364	808.8		351/220	"	"	"
365	811.1			?	"	"
366	813.3		8/5	"	"	"
367	815.5			?	"	"
368	817.7		77/48	"	"	"
369	820.0			?	"	"
370	822.2		45/28	"	"	"
371	824.4			?	"	"
372	826.6		121/75	"	"	"
373	828.8			?	"	"
374	831.1		21/13	"	"	"
375	833.3			34/21	"	"
376	835.5		81/50	"	"	"
377	837.7			?	"	"
378	840.0		13/8	"	"	"
379	842.2			?	"	"
380	844.4		44/27	"	"	"
381	846.6			?	"	"
382	848.8		49/30	"	"	"
383	851.1			?	"	"
384	853.3		18/11	"	"	"
385	855.5			?	"	"
386	857.7		64/39	"	"	"
387	860.0			23/14	"	"
388	862.2		242/147	"	"	"
389	864.4			28/17	"	"
390	866.6		33/20	"	"	"
391	868.8			38/23	"	"
392	871.1		81/49	"	"	"
393	873.3			?	"	"
394	875.5		224/135	63/38	"	"
395	877.7			?	"	"
396	880.0		108/65	"	"	"
397	882.2			?	"	"
398	884.4		5/3	"	"	"
399	886.6			?	"	"
400	888.8		117/70	"	"	"
401	891.1			?	"	"
402	893.3		176/105	"	"	"
403	895.5			?	"	"
404	897.7		42/25	"	"	"
405	900.0			?	"	"
406	902.2		91/54	32/19	"	"
407	904.4			?	"	"
408	906.6	M6	27/16	"	"	"
409	908.8			?	"	"
410	911.1		22/13	"	"	"
411	913.3			?	"	"
412	915.5		56/33	"	"	"
413	917.7			17/10	"	"
414	920.0		143/84	"	"	"
415	922.2			?	"	"
416	924.4		75/44	"	"	"
417	926.6			?	"	"
418	928.8		77/45	"	"	"
419	931.1			?	"	"
420	933.3		12/7	"	"	"
421	935.5			?	"	"
422	937.7		55/32	"	"	"
423	940.0			?	"	"
424	942.2		112/65	"	"	"
425	944.4			?	"	"
426	946.6		121/70	19/11	"	"
427	948.8			?	"	64/37
428	951.1		26/15	"	"	"
429	953.3			?	"	"
430	955.5		125/72	33/19	"	"
431	957.7			40/23	"	"
432	960.0		195/112	"	"	"
433	962.2			?	"	"
434	964.4		96/55	"	"	"
435	966.6			?	"	"
436	968.8		7/4	"	"	"
437	971.1			?	"	"
438	973.3		135/77	100/57	"	"
439	975.5			?	"	"
440	977.7		44/25	"	"	"
441	980.0			?	"	"
442	982.2		143/81	"	"	"
443	984.8			30/17	"	"
444	986.6		99/56	"	"	"
445	988.8			23/13	"	"
446	991.1		39/22	"	"	"
447	993.3			?	"	"
448	995.5	m7	16/9	"	"	"
449	997.7			?	"	"
450	1000.0		98/55	57/32	"	"
451	1002.2			?	"	"
452	1004.4		25/14	"	"	"
453	1006.6			34/19	"	"
454	1008.8		224/125	"	"	"
455	1011.1			?	"	"
456	1013.3		70/39	"	"	"
457	1015.5			?	"	"
458	1017.7		9/5	"	"	"
459	1020.0			?	"	"
460	1022.2		65/36	"	"	"
461	1024.4			?	"	"
462	1026.6		405/224	38/21	"	"
463	1028.8			?	(29/16)	"
464	1031.1		49/27	"	"	"
465	1033.3			?	"	"
466	1035.5		20/11	"	"	"
467	1037.7			?	"	"
468	1040.0		175/96	"	"	"
469	1042.2			42/23	"	"
470	1044.4		64/35	"	"	"
471	1046.6			?	"	"
472	1048.8		11/6	"	"	"
473	1051.1			?	"	"
474	1053.3		90/49	"	"	"
475	1055.5			?	"	"
476	1057.7		81/44	35/19	"	"
477	1060.0			?	"	"
478	1062.2		24/13	"	"	"
479	1064.4			?	"	"
480	1066.6		50/27	"	"	"
481	1068.8			?	"	"
482	1071.1		13/7	"	"	"
483	1073.3			?	"	"
484	1075.5		121/65	"	"	"
485	1077.7			?	"	"
486	1080.0		28/15	"	"	"
487	1082.2			?	"	"
488	1084.4		144/77	"	"	"
489	1086.6			?	"	"
490	1088.8		15/8	"	"	"
491	1091.1			?	"	"
492	1093.3		220/117	"	"	"
493	1095.5			32/17	"	"
494	1097.7		49/26	"	"	"
495	1100.0			17/9	"	"
496	1102.2		104/55	"	"	"
497	1104.4			?	"	"
498	1106.6		91/48	36/19	"	"
499	1108.8			?	"	"
500	1111.1	M7	154/81	19/10	"	"
501	1113.3			?	"	"
502	1115.5		40/21	"	"	"
503	1117.7			?	"	"
504	1120.0		21/11	"	"	"
505	1122.2			44/23	"	"
506	1124.4		224/117	"	"	"
507	1126.6			23/12	"	"
508	1128.8		48/25	"	"	"
509	1131.1			?	"	"
510	1133.3		25/13	"	"	"
511	1135.5			?	"	"
512	1137.7		27/14	"	"	"
513	1140.0			?	"	"
514	1142.2		176/91	"	"	"
515	1144.4			?	(31/16)	"
516	1146.6		64/33	"	"	"
517	1148.8			?	"	"
518	1151.1		35/18	"	"	"
519	1153.3			?	"	"
520	1155.5		39/20	"	"	"
521	1157.7			?	"	"
522	1160.0		88/45	"	"	"
523	1162.2			?	"	"
524	1164.4		49/25	"	"	"
525	1166.6			?	"	"
526	1168.8		55/28	"	"	"
527	1171.1			?	"	"
528	1173.3		63/32	"	"	"
529	1175.5			?	"	"
530	1177.7		77/39	75/38	"	"
531	1180.0			?	"	"
532	1182.2		99/50	"	"	"
533	1184.4			?	"	"
534	1186.6		125/63	"	"	"
535	1188.8			?	"	"
536	1191.1		175/88	"	"	"
537	1193.3			?	"	"
538	1195.5		648/325	"	"	"
539	1197.7			?	"	"
540	1200.0	P8	2/1	"	"	"