User:Inthar/311edo

Consistent patent val readings

TODO: separate into more-in-tune-than-out-of-tune and more-out-of-tune-than-in-tune

Steps	Cents	Consistent patent val readings
1	3.858521	449/448
2	7.717042	224/223, 225/224
3	11.575563	150/149
4	15.434084	338/335
5	19.292605	90/89
6	23.151125	70/69, 78/77, 77/76, 76/75, 75/74, 74/73, 73/72
7	27.009646	63/62, 64/63, 65/64, 66/65, 69/68
8	30.868167	55/54, 56/55, 57/56, 58/57
9	34.726688	49/48, 50/49, 51/50, 52/51
10	38.585209	45/44, 46/45
11	42.443730	40/39, 41/40, 42/41
12	46.302251	37/36, 38/37, 39/38
13	50.160772	34/33, 35/34, 36/35
14	54.019293	32/31, 33/32
15	57.877814	30/29, 31/30
16	61.736334	28/27, 29/28
17	65.594855	27/26
18	69.453376	25/24, 26/25
19	73.311897	24/23
20	77.170418	23/22
21	81.028939	22/21
22	84.887460	21/20
23	88.745981	20/19
24	92.604502	19/18, 39/37
25	96.463023	37/35
26	100.321543	18/17, 35/33
27	104.180064	17/16
28	108.038585	33/31
29	111.897106	16/15
30	115.755627	31/29
31	119.614148	15/14
32	123.472669	29/27
33	127.331190	14/13
34	131.189711	69/64
35	135.048232	27/25, 40/37
36	138.906752	13/12
37	142.765273	25/23
38	146.623794	37/34
39	150.482315	12/11
40	154.340836	35/32
41	158.199357	23/21, 34/31
42	162.057878	45/41, 56/51
43	165.916399	11/10
44	169.774920	32/29
45	173.633441	21/19
46	177.491961	31/28
47	181.350482	10/9
48	185.209003	49/44
49	189.067524	29/26, 39/35
50	192.926045	19/17
51	196.784566	28/25
52	200.643087	55/49
53	204.501608	9/8
54	208.360129	35/31
55	212.218650	26/23
56	216.077170	17/15
57	219.935691	25/22, 42/37
58	223.794212	33/29
59	227.652733	73/64
60	231.511254	8/7
61	235.369775	55/48
62	239.228296	31/27, 39/34
63	243.086817	23/20
64	246.945338	15/13, 128/111
65	250.803859	37/32
66	254.662379	22/19
67	258.520900	29/25, 36/31
68	262.379421	64/55
69	266.237942	7/6
70	270.096463	90/77
71	273.954984	34/29, 41/35, 48/41, 75/64
72	277.813505	27/23
73	281.672026	20/17
74	285.530547	33/28, 46/39
75	289.389068	13/11
76	293.247588	32/27
77	297.106109	19/16
78	300.964630	25/21
79	304.823151	31/26, 37/31
80	308.681672	49/41, 55/46
81	312.540193	109/91
82	316.398714	6/5
83	320.257235	77/64
84	324.115756	35/29
85	327.974277	29/24
86	331.832797	23/19, 40/33
87	335.691318	17/14
88	339.549839	28/23, 73/60
89	343.408360	39/32, 50/41, 128/105
90	347.266881	11/9
91	351.125402	38/31
92	354.983923	27/22
93	358.842444	16/13
94	362.700965	37/30
95	366.559486	21/17
96	370.418006	26/21
97	374.276527	36/29, 41/33
98	378.135048	46/37, 51/41, 56/45
99	381.993569	96/77
100	385.852090	5/4
101	389.710611	124/99
102	393.569132	49/39, 64/51
103	397.427653	39/31, 44/35
104	401.286174	29/23
105	405.144695	24/19
106	409.003215	19/15
107	412.861736	33/26
108	416.720257	14/11
109	420.578778	39/29
110	424.437299	23/18
111	428.295820	41/32, 32/25
112	432.154341	77/60
113	436.012862	9/7
114	439.871383	49/38
115	443.729904	31/24
116	447.588424	22/17
117	451.446945	83/64
118	455.305466	13/10
119	459.163987	30/23
120	463.022508	17/13, 49/32
121	466.881029	55/42, 38/29
122	470.739550	21/16
123	474.598071	25/19
124	478.456592	29/22
125	482.315113	33/25
126	486.173633	45/34, 49/37
127	490.032154	85/64
128	493.890675	278/209
129	497.749196	4/3
130	501.607717	322/241, 163/122
131	505.466238	75/56
132	509.324759	51/38
133	513.183280	35/26, 39/29
134	517.041801	31/23
135	520.900322	27/20
136	524.758842	23/17
137	528.617363	19/14
138	532.475884	34/25, 49/36, 87/64
139	536.334405	15/11
140	540.192926	41/30
141	544.051447	26/19, 37/27
142	547.909968	48/35
143	551.768489	11/8
144	555.627010	29/21, 40/29, 51/37
145	559.485531	105/76
146	563.344051	18/13
147	567.202572	25/18, 68/49
148	571.061093	89/64, 32/23
149	574.919614	39/28, 46/33
150	578.778135	88/63
151	582.636656	7/5
152	586.495177	87/62
153	590.353698	45/32, 128/91
154	594.212219	31/22, 148/105
155	598.070740	24/17, 41/29
156	601.929260	17/12, 58/41
157	605.787781	44/31, 105/74
158	609.646302	64/45, 91/64
159	613.504823	124/87
160	617.363344	10/7
161	621.221865	63/44
162	625.080386	33/23, 56/39
163	628.938907	23/16, 128/89
164	632.797428	36/25, 49/34
165	636.655949	13/9
166	640.514469	152/105
167	644.372990	29/20, 42/29, 74/51
168	648.231511	16/11, 93/64
169	652.090032	35/24
170	655.948553	19/13, 54/37
171	659.807074	60/41
172	663.665595	22/15
173	667.524116	25/17, 72/49, 128/87
174	671.382637	28/19
175	675.241158	34/23
176	679.099678	40/27
177	682.958199	46/31
178	686.816720	52/35, 58/39
179	690.675241	76/51
180	694.533762	112/75
181	698.392283	241/161, 244/163
182	702.250804	3/2
183	706.109325	209/139
184	709.967846	128/85
185	713.826367	68/45, 74/49
186	717.684887	50/33
187	721.543408	97/64
188	725.401929	38/25
189	729.260450	32/21
190	733.118971	84/55
191	736.977492	49/32, 26/17
192	740.836013	23/15
193	744.694534	20/13
194	748.553055	128/83
195	752.411576	17/11
196	756.270096	99/64
197	760.128617	48/31
198	763.987138	14/9
199	767.845659	120/77
200	771.704180	25/16
201	775.562701	36/23
202	779.421222	58/39
203	783.279743	11/7
204	787.138264	52/33
205	790.996785	30/19
206	794.855305	19/12
207	798.713826	46/29
208	802.572347	35/22, 62/39
209	806.430868	51/32, 78/49
210	810.289389	99/62
211	814.147910	8/5
212	818.006431	77/48
213	821.864952	37/23, 82/51, 45/28
214	825.723473	29/18, 66/41
215	829.581994	21/13
216	833.440514	34/21, 55/34, 89/55, 144/89
217	837.299035	60/37
218	841.157556	13/8
219	845.016077	44/27
220	848.874598	31/19
221	852.733119	18/11
222	856.591640	41/25, 64/39, 105/64
223	860.450161	23/14, 120/73
224	864.308682	28/17
225	868.167203	32/20, 38/23
226	872.025723	48/29
227	875.884244	58/35
228	879.742765	123/74, 128/77
229	883.601286	5/3
230	887.459807	182/109
231	891.318328	82/49, 92/55
232	895.176849	52/31, 62/37
233	899.035370	42/25
234	902.893891	32/19, 219/130
235	906.752412	27/16
236	910.610932	22/13
237	914.469453	39/23, 56/33
238	918.327974	17/10
239	922.186495	109/64
240	926.045016	29/17, 70/41, 41/24, 128/75
241	929.903537	65/38, 77/45
242	933.762058	12/7
243	937.620579	55/32
244	941.479100	50/29, 31/18
245	945.337621	19/11
246	949.196141	64/37
247	953.054662	26/15, 111/64
248	956.913183	40/23
249	960.771704	54/31, 68/39
250	964.630225	96/55
251	968.488746	7/4
252	972.347267	128/73
253	976.205788	58/33
254	980.064309	37/21, 44/25
255	983.922830	30/17, 113/64
256	987.781350	23/13
257	991.639871	62/35
258	995.498392	16/9
259	999.356913	98/55, 57/32
260	1003.215434	25/14
261	1007.073955	34/19
262	1010.932476	52/29, 70/39
263	1014.790997	88/49, 115/64
264	1018.649518	9/5
265	1022.508039	56/31
266	1026.366559	38/21
267	1030.225080	29/16
268	1034.083601	20/11
269	1037.942122	51/28, 82/45
270	1041.800643	31/17, 42/23
271	1045.659164	64/35, 117/64
272	1049.517685	11/6
273	1053.376206	68/37
274	1057.234727	46/25
275	1061.093248	24/13
276	1064.951768	37/20, 50/27
277	1068.810289	128/69
278	1072.668810	13/7, 119/64
279	1076.527331	54/29
280	1080.385852	28/15
281	1084.244373	58/31
282	1088.102894	15/8
283	1091.961415	62/33
284	1095.819936	32/17
285	1099.678457	17/9, 66/35
286	1103.536977	70/37, 121/64
287	1107.395498	36/19, 74/39
288	1111.254019	19/10
289	1115.112540	40/21
290	1118.971061	21/11
291	1122.829582	44/23
292	1126.688103	23/13
293	1130.546624	48/25, 25/13, 123/64
294	1134.405145	52/27
295	1138.263666	27/14, 56/29
296	1142.122186	29/15, 60/31
297	1145.980707	31/16, 64/33
298	1149.839228	33/17, 68/35, 35/18
299	1153.697749	72/37, 37/19, 76/39
300	1157.556270	39/20, 80/41, 41/21, 125/64
301	1161.414791	88/45, 45/23
302	1165.273312	96/49, 49/25, 100/51, 51/26
303	1169.131833	108/55, 55/28, 112/57, 57/29
304	1172.990354	124/63, 63/32, 128/65, 65/33
305	1176.848875	148/75
306	1180.707395	89/45
307	1184.565916	335/169
308	1188.424437	149/75
309	1192.282958	223/112, 448/225
310	1196.141479	896/449

Mapping of the 41-prime-limited add-73 77-odd-limit

Ratio (ascending)	Just value	311edo mapping		Error (cents)	MITTOOT? (Error < 1\1244 = 0.964630¢?)
		Steps	Cents
78/77	22.338814	6	23.151125	0.812312	TRUE
77/76	22.630833	6	23.151125	0.520293	TRUE
76/75	22.930588	6	23.151125	0.220538	TRUE
75/74	23.238390	6	23.151125	-0.087264	TRUE
74/73	23.554568	6	23.151125	-0.403443	TRUE
73/72	23.879469	6	23.151125	-0.728344	TRUE
70/69	24.910272	6	23.151125	-1.759147	FALSE
69/68	25.273939	7	27.009646	1.735708	FALSE
66/65	26.431568	7	27.009646	0.578079	TRUE
65/64	26.841376	7	27.009646	0.168271	TRUE
64/63	27.264092	7	27.009646	-0.254445	TRUE
63/62	27.700336	7	27.009646	-0.690689	TRUE
58/57	30.109177	8	30.868167	0.758990	TRUE
57/56	30.642111	8	30.868167	0.226057	TRUE
56/55	31.194250	8	30.868167	-0.326083	TRUE
55/54	31.766654	8	30.868167	-0.898486	TRUE
52/51	33.617251	9	34.726688	1.109437	FALSE
51/50	34.282983	9	34.726688	0.443705	TRUE
50/49	34.975615	9	34.726688	-0.248927	TRUE
49/48	35.696812	9	34.726688	-0.970124	FALSE
46/45	38.050632	10	38.585209	0.534577	TRUE
45/44	38.905773	10	38.585209	-0.320564	TRUE
42/41	41.718502	11	42.443730	0.725228	TRUE
41/40	42.748692	11	42.443730	-0.304962	TRUE
40/39	43.831051	11	42.443730	-1.387321	FALSE
39/38	44.969647	12	46.302251	1.332604	FALSE
77/75	45.561420	12	46.302251	0.740831	TRUE
38/37	46.168977	12	46.302251	0.133273	TRUE
75/73	46.792958	12	46.302251	-0.490707	TRUE
37/36	47.434037	12	46.302251	-1.131786	FALSE
36/35	48.770381	13	50.160772	1.390390	FALSE
35/34	50.184211	13	50.160772	-0.023439	TRUE
34/33	51.682466	13	50.160772	-1.521695	FALSE
33/32	53.272943	14	54.019293	0.746349	TRUE
65/63	54.105467	14	54.019293	-0.086175	TRUE
32/31	54.964428	14	54.019293	-0.945135	TRUE
31/30	56.766858	15	57.877814	1.110956	FALSE
30/29	58.691521	15	57.877814	-0.813707	TRUE
29/28	60.751288	16	61.736334	0.985047	FALSE
57/55	61.836361	16	61.736334	-0.100026	TRUE
28/27	62.960904	16	61.736334	-1.224569	FALSE
27/26	65.337341	17	65.594855	0.257514	TRUE
80/77	66.169865	17	65.594855	-0.575010	TRUE
26/25	67.900234	18	69.453376	1.553142	FALSE
77/74	68.799810	18	69.453376	0.653566	TRUE
51/49	69.258597	18	69.453376	0.194779	TRUE
76/73	69.723545	18	69.453376	-0.270169	TRUE
25/24	70.672427	18	69.453376	-1.219051	FALSE
73/70	72.649850	19	73.311897	0.662047	TRUE
24/23	73.680654	19	73.311897	-0.368756	TRUE
23/22	76.956405	20	77.170418	0.214013	TRUE
68/65	78.114034	20	77.170418	-0.943616	TRUE
22/21	80.537035	21	81.028939	0.491904	TRUE
65/62	81.805803	21	81.028939	-0.776864	TRUE
21/20	84.467193	22	84.887460	0.420266	TRUE
41/39	86.579743	22	84.887460	-1.692283	FALSE
20/19	88.800698	23	88.745981	-0.054717	TRUE
39/37	91.138624	24	92.604502	1.465878	FALSE
58/55	91.945538	24	92.604502	0.658964	TRUE
77/73	92.354378	24	92.604502	0.250123	TRUE
19/18	93.603014	24	92.604502	-0.998513	FALSE
37/35	96.204418	25	96.463023	0.258604	TRUE
55/52	97.103994	25	96.463023	-0.640972	TRUE
73/69	97.560123	25	96.463023	-1.097100	FALSE
18/17	98.954592	26	100.321543	1.366951	FALSE
35/33	101.866677	26	100.321543	-1.545134	FALSE
52/49	102.875849	27	104.180064	1.304215	FALSE
69/65	103.387972	27	104.180064	0.792092	TRUE
17/16	104.955410	27	104.180064	-0.775345	TRUE
33/31	108.237371	28	108.038585	-0.198786	TRUE
82/77	108.918557	28	108.038585	-0.879971	TRUE
49/46	109.377466	28	108.038585	-1.338880	FALSE
16/15	111.731285	29	111.897106	0.165821	TRUE
78/73	114.693192	30	115.755627	1.062435	FALSE
31/29	115.458378	30	115.755627	0.297249	TRUE
77/72	116.233847	30	115.755627	-0.478220	TRUE
15/14	119.442808	31	119.614148	0.171340	TRUE
74/69	121.114691	31	119.614148	-1.500543	FALSE
44/41	122.255537	32	123.472669	1.217132	FALSE
73/68	122.834061	32	123.472669	0.638608	TRUE
29/27	123.712192	32	123.472669	-0.239523	TRUE
14/13	128.298245	33	127.331190	-0.967055	FALSE
69/64	130.229348	34	131.189711	0.960362	TRUE
55/51	130.721246	34	131.189711	0.468465	TRUE
41/38	131.549389	34	131.189711	-0.359679	TRUE
68/63	132.219501	34	131.189711	-1.029791	FALSE
27/25	133.237575	35	135.048232	1.810657	FALSE
40/37	134.969675	35	135.048232	0.078556	TRUE
13/12	138.572661	36	138.906752	0.334092	TRUE
38/35	142.373396	37	142.765273	0.391878	TRUE
63/58	143.158714	37	142.765273	-0.393441	TRUE
25/23	144.353080	37	142.765273	-1.587807	FALSE
62/57	145.567555	38	146.623794	1.056239	FALSE
37/34	146.388629	38	146.623794	0.235165	TRUE
49/45	147.428097	38	146.623794	-0.804303	TRUE
12/11	150.637059	39	150.482315	-0.154743	TRUE
82/75	154.479977	40	154.340836	-0.139141	TRUE
35/32	155.139620	40	154.340836	-0.798784	TRUE
23/21	157.493440	41	158.199357	0.705917	TRUE
80/73	158.524243	41	158.199357	-0.324886	TRUE
57/52	158.940355	41	158.199357	-0.740998	TRUE
34/31	159.919837	41	158.199357	-1.720480	FALSE
45/41	161.161310	42	162.057878	0.896568	TRUE
56/51	161.915496	42	162.057878	0.142382	TRUE
11/10	165.004228	43	165.916399	0.912170	TRUE
76/69	167.283668	43	165.916399	-1.367269	FALSE
54/49	168.213190	44	169.774920	1.561730	FALSE
75/68	169.627019	44	169.774920	0.147901	TRUE
32/29	170.422806	44	169.774920	-0.647886	TRUE
21/19	173.267891	45	173.633441	0.365549	TRUE
73/66	174.516527	45	173.633441	-0.883087	TRUE
31/28	176.209666	46	177.491961	1.282295	FALSE
72/65	177.068626	46	177.491961	0.423335	TRUE
41/37	177.718367	46	177.491961	-0.226405	TRUE
51/46	178.636063	46	177.491961	-1.144102	FALSE
10/9	182.403712	47	181.350482	-1.053230	FALSE
69/62	185.193776	48	185.209003	0.015228	TRUE
49/44	186.333871	48	185.209003	-1.124867	FALSE
39/35	187.343042	49	189.067524	1.724482	FALSE
29/26	189.049532	49	189.067524	0.017992	TRUE
77/69	189.914501	49	189.067524	-0.846977	TRUE
19/17	192.557607	50	192.926045	0.368438	TRUE
28/25	196.198479	51	196.784566	0.586087	TRUE
65/58	197.264181	51	196.784566	-0.479616	TRUE
37/33	198.071096	51	196.784566	-1.286530	FALSE
46/41	199.211942	52	200.643087	1.431145	FALSE
55/49	199.979843	52	200.643087	0.663244	TRUE
64/57	200.531983	52	200.643087	0.111104	TRUE
73/65	200.948095	52	200.643087	-0.305008	TRUE
82/73	201.272935	52	200.643087	-0.629848	TRUE
9/8	203.910002	53	204.501608	0.591606	TRUE
62/55	207.403916	54	208.360129	0.956212	TRUE
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152/77	1177.369167	305	1176.848875	-0.520293	TRUE
77/39	1177.661186	305	1176.848875	-0.812312	TRUE