User:Overthink/Sandbox

Testing

Steps	Cents	Approximate Ratios	Ups and Downs Notation
0	0	1/1	D
1	3.859		^D, ^8E♭♭
2	7.717		^^D, ^9E♭♭
3	11.576		^3D, ^10E♭♭
4	15.434		^4D, ^11E♭♭
5	19.293		^5D, ^12E♭♭
6	23.151		^6D, ^13E♭♭
7	27.01		^7D, ^14E♭♭
8	30.868		^8D, v15E♭
9	34.727	49/48, 50/49, 51/50, 52/51	^9D, v14E♭
10	38.585	45/44, 46/45	^10D, v13E♭
11	42.444	40/39	^11D, v12E♭
12	46.302	39/38	^12D, v11E♭
13	50.161	34/33, 35/34, 36/35	^13D, v10E♭
14	54.019	33/32	^14D, v9E♭
15	57.878		^15D, v8E♭
16	61.736	28/27	v14D♯, v7E♭
17	65.595	27/26	v13D♯, v6E♭
18	69.453	25/24, 26/25, 51/49	v12D♯, v5E♭
19	73.312	24/23	v11D♯, v4E♭
20	77.17	23/22	v10D♯, v3E♭
21	81.029	22/21	v9D♯, vvE♭
22	84.887	21/20	v8D♯, vE♭
23	88.746	20/19	v7D♯, E♭
24	92.605	19/18	v6D♯, ^E♭
25	96.463		v5D♯, ^^E♭
26	100.322	18/17, 35/33	v4D♯, ^3E♭
27	104.18	17/16, 52/49	v3D♯, ^4E♭
28	108.039	49/46	vvD♯, ^5E♭
29	111.897	16/15	vD♯, ^6E♭
30	115.756		D♯, ^7E♭
31	119.614	15/14	^D♯, ^8E♭
32	123.473		^^D♯, ^9E♭
33	127.331	14/13	^3D♯, ^10E♭
34	131.19		^4D♯, ^11E♭
35	135.048	27/25	^5D♯, ^12E♭
36	138.907	13/12	^6D♯, ^13E♭
37	142.765	25/23, 38/35	^7D♯, ^14E♭
38	146.624	49/45	^8D♯, v15E
39	150.482	12/11	^9D♯, v14E
40	154.341	35/32	^10D♯, v13E
41	158.199	23/21	^11D♯, v12E
42	162.058		^12D♯, v11E
43	165.916	11/10	^13D♯, v10E
44	169.775	54/49	^14D♯, v9E
45	173.633	21/19	^15D♯, v8E
46	177.492	51/46	v14D𝄪, v7E
47	181.35	10/9	v13D𝄪, v6E
48	185.209	49/44	v12D𝄪, v5E
49	189.068	39/35	v11D𝄪, v4E
50	192.926	19/17	v10D𝄪, v3E
51	196.785	28/25	v9D𝄪, vvE
52	200.643		v8D𝄪, vE
53	204.502	9/8	E
54	208.36	44/39	^E, ^8F♭
55	212.219	26/23	^^E, ^9F♭
56	216.077	17/15	^3E, ^10F♭
57	219.936	25/22	^4E, ^11F♭
58	223.794		^5E, ^12F♭
59	227.653		^6E, ^13F♭
60	231.511	8/7	^7E, ^14F♭
61	235.37		^8E, v15F
62	239.228	39/34	^9E, v14F
63	243.087	23/20, 38/33	^10E, v13F
64	246.945	15/13	^11E, v12F
65	250.804	52/45	^12E, v11F
66	254.662	22/19, 51/44	^13E, v10F
67	258.521		^14E, v9F
68	262.379		^15E, v8F
69	266.238	7/6	v14E♯, v7F
70	270.096		v13E♯, v6F
71	273.955		v12E♯, v5F
72	277.814	27/23	v11E♯, v4F
73	281.672	20/17	v10E♯, v3F
74	285.531	33/28, 46/39	v9E♯, vvF
75	289.389	13/11	v8E♯, vF
76	293.248	32/27, 45/38	F
77	297.106	19/16	^F, ^8G♭♭
78	300.965	25/21	^^F, ^9G♭♭
79	304.823		^3F, ^10G♭♭
80	308.682		^4F, ^11G♭♭
81	312.54		^5F, ^12G♭♭
82	316.399	6/5	^6F, ^13G♭♭
83	320.257		^7F, ^14G♭♭
84	324.116		^8F, v15G♭
85	327.974		^9F, v14G♭
86	331.833	23/19, 40/33	^10F, v13G♭
87	335.691	17/14	^11F, v12G♭
88	339.55	28/23	^12F, v11G♭
89	343.408	39/32	^13F, v10G♭
90	347.267	11/9	^14F, v9G♭
91	351.125	49/40	^15F, v8G♭
92	354.984	27/22	v14F♯, v7G♭
93	358.842	16/13	v13F♯, v6G♭
94	362.701		v12F♯, v5G♭
95	366.559	21/17	v11F♯, v4G♭
96	370.418	26/21	v10F♯, v3G♭
97	374.277		v9F♯, vvG♭
98	378.135		v8F♯, vG♭
99	381.994		v7F♯, G♭
100	385.852	5/4	v6F♯, ^G♭
101	389.711		v5F♯, ^^G♭
102	393.569	49/39	v4F♯, ^3G♭
103	397.428	34/27, 44/35	v3F♯, ^4G♭
104	401.286		vvF♯, ^5G♭
105	405.145	24/19	vF♯, ^6G♭
106	409.003	19/15	F♯, ^7G♭
107	412.862	33/26	^F♯, ^8G♭
108	416.72	14/11	^^F♯, ^9G♭
109	420.579	51/40	^3F♯, ^10G♭
110	424.437	23/18	^4F♯, ^11G♭
111	428.296	32/25, 50/39	^5F♯, ^12G♭
112	432.154		^6F♯, ^13G♭
113	436.013	9/7	^7F♯, ^14G♭
114	439.871	49/38	^8F♯, v15G
115	443.73		^9F♯, v14G
116	447.588	22/17, 35/27	^10F♯, v13G
117	451.447		^11F♯, v12G
118	455.305	13/10	^12F♯, v11G
119	459.164	30/23	^13F♯, v10G
120	463.023	17/13	^14F♯, v9G
121	466.881		^15F♯, v8G
122	470.74	21/16	v14F𝄪, v7G
123	474.598	25/19, 46/35	v13F𝄪, v6G
124	478.457		v12F𝄪, v5G
125	482.315	33/25	v11F𝄪, v4G
126	486.174	45/34	v10F𝄪, v3G
127	490.032		v9F𝄪, vvG
128	493.891		v8F𝄪, vG
129	497.749	4/3	G
130	501.608		^G, ^8A♭♭
131	505.466		^^G, ^9A♭♭
132	509.325	51/38	^3G, ^10A♭♭
133	513.183	35/26	^4G, ^11A♭♭
134	517.042		^5G, ^12A♭♭
135	520.9	27/20	^6G, ^13A♭♭
136	524.759	23/17	^7G, ^14A♭♭
137	528.617	19/14	^8G, v15A♭
138	532.476	34/25, 49/36	^9G, v14A♭
139	536.334	15/11	^10G, v13A♭
140	540.193		^11G, v12A♭
141	544.051	26/19	^12G, v11A♭
142	547.91	48/35	^13G, v10A♭
143	551.768	11/8	^14G, v9A♭
144	555.627		^15G, v8A♭
145	559.486		v14G♯, v7A♭
146	563.344	18/13	v13G♯, v6A♭
147	567.203	25/18	v12G♯, v5A♭
148	571.061	32/23	v11G♯, v4A♭
149	574.92	39/28, 46/33	v10G♯, v3A♭
150	578.778		v9G♯, vvA♭
151	582.637	7/5	v8G♯, vA♭
152	586.495		v7G♯, A♭
153	590.354	38/27, 45/32	v6G♯, ^A♭
154	594.212		v5G♯, ^^A♭
155	598.071	24/17	v4G♯, ^3A♭
156	601.929	17/12	v3G♯, ^4A♭
157	605.788		vvG♯, ^5A♭
158	609.646	27/19	vG♯, ^6A♭
159	613.505		G♯, ^7A♭
160	617.363	10/7	^G♯, ^8A♭
161	621.222		^^G♯, ^9A♭
162	625.08	33/23	^3G♯, ^10A♭
163	628.939	23/16	^4G♯, ^11A♭
164	632.797	36/25, 49/34	^5G♯, ^12A♭
165	636.656	13/9	^6G♯, ^13A♭
166	640.514		^7G♯, ^14A♭
167	644.373		^8G♯, v15A
168	648.232	16/11	^9G♯, v14A
169	652.09	35/24, 51/35	^10G♯, v13A
170	655.949	19/13	^11G♯, v12A
171	659.807		^12G♯, v11A
172	663.666	22/15	^13G♯, v10A
173	667.524	25/17	^14G♯, v9A
174	671.383	28/19	^15G♯, v8A
175	675.241	34/23	v14G𝄪, v7A
176	679.1	40/27	v13G𝄪, v6A
177	682.958	49/33	v12G𝄪, v5A
178	686.817	52/35	v11G𝄪, v4A
179	690.675		v10G𝄪, v3A
180	694.534		v9G𝄪, vvA
181	698.392		v8G𝄪, vA
182	702.251	3/2	A
183	706.109		^A, ^8B♭♭
184	709.968		^^A, ^9B♭♭
185	713.826		^3A, ^10B♭♭
186	717.685	50/33	^4A, ^11B♭♭
187	721.543		^5A, ^12B♭♭
188	725.402	35/23, 38/25	^6A, ^13B♭♭
189	729.26	32/21	^7A, ^14B♭♭
190	733.119		^8A, v15B♭
191	736.977	26/17, 49/32	^9A, v14B♭
192	740.836	23/15	^10A, v13B♭
193	744.695	20/13	^11A, v12B♭
194	748.553		^12A, v11B♭
195	752.412	17/11, 54/35	^13A, v10B♭
196	756.27		^14A, v9B♭
197	760.129		^15A, v8B♭
198	763.987	14/9	v14A♯, v7B♭
199	767.846		v13A♯, v6B♭
200	771.704	25/16, 39/25	v12A♯, v5B♭
201	775.563	36/23	v11A♯, v4B♭
202	779.421		v10A♯, v3B♭
203	783.28	11/7	v9A♯, vvB♭
204	787.138	52/33	v8A♯, vB♭
205	790.997	30/19	v7A♯, B♭
206	794.855	19/12	v6A♯, ^B♭
207	798.714		v5A♯, ^^B♭
208	802.572	27/17, 35/22	v4A♯, ^3B♭
209	806.431	51/32	v3A♯, ^4B♭
210	810.289		vvA♯, ^5B♭
211	814.148	8/5	vA♯, ^6B♭
212	818.006		A♯, ^7B♭
213	821.865	45/28	^A♯, ^8B♭
214	825.723		^^A♯, ^9B♭
215	829.582	21/13	^3A♯, ^10B♭
216	833.441	34/21	^4A♯, ^11B♭
217	837.299		^5A♯, ^12B♭
218	841.158	13/8	^6A♯, ^13B♭
219	845.016	44/27	^7A♯, ^14B♭
220	848.875	49/30	^8A♯, v15B
221	852.733	18/11	^9A♯, v14B
222	856.592		^10A♯, v13B
223	860.45	23/14	^11A♯, v12B
224	864.309	28/17	^12A♯, v11B
225	868.167	33/20, 38/23	^13A♯, v10B
226	872.026		^14A♯, v9B
227	875.884		^15A♯, v8B
228	879.743		v14A𝄪, v7B
229	883.601	5/3	v13A𝄪, v6B
230	887.46		v12A𝄪, v5B
231	891.318		v11A𝄪, v4B
232	895.177		v10A𝄪, v3B
233	899.035	42/25	v9A𝄪, vvB
234	902.894	32/19	v8A𝄪, vB
235	906.752	27/16	B
236	910.611	22/13	^B, ^8C♭
237	914.469	39/23	^^B, ^9C♭
238	918.328	17/10	^3B, ^10C♭
239	922.186	46/27	^4B, ^11C♭
240	926.045		^5B, ^12C♭
241	929.904		^6B, ^13C♭
242	933.762	12/7	^7B, ^14C♭
243	937.621		^8B, v15C
244	941.479		^9B, v14C
245	945.338	19/11	^10B, v13C
246	949.196	45/26	^11B, v12C
247	953.055	26/15	^12B, v11C
248	956.913	33/19, 40/23	^13B, v10C
249	960.772		^14B, v9C
250	964.63		^15B, v8C
251	968.489	7/4	v14B♯, v7C
252	972.347		v13B♯, v6C
253	976.206		v12B♯, v5C
254	980.064	44/25	v11B♯, v4C
255	983.923	30/17	v10B♯, v3C
256	987.781	23/13	v9B♯, vvC
257	991.64	39/22	v8B♯, vC
258	995.498	16/9	C
259	999.357		^C, ^8D♭♭
260	1003.215	25/14	^^C, ^9D♭♭
261	1007.074	34/19	^3C, ^10D♭♭
262	1010.932		^4C, ^11D♭♭
263	1014.791		^5C, ^12D♭♭
264	1018.65	9/5	^6C, ^13D♭♭
265	1022.508		^7C, ^14D♭♭
266	1026.367	38/21	^8C, v15D♭
267	1030.225	49/27	^9C, v14D♭
268	1034.084	20/11	^10C, v13D♭
269	1037.942	51/28	^11C, v12D♭
270	1041.801	42/23	^12C, v11D♭
271	1045.659		^13C, v10D♭
272	1049.518	11/6	^14C, v9D♭
273	1053.376		^15C, v8D♭
274	1057.235	35/19, 46/25	v14C♯, v7D♭
275	1061.093	24/13	v13C♯, v6D♭
276	1064.952	50/27	v12C♯, v5D♭
277	1068.81		v11C♯, v4D♭
278	1072.669	13/7	v10C♯, v3D♭
279	1076.527		v9C♯, vvD♭
280	1080.386	28/15	v8C♯, vD♭
281	1084.244		v7C♯, D♭
282	1088.103	15/8	v6C♯, ^D♭
283	1091.961		v5C♯, ^^D♭
284	1095.82	32/17, 49/26	v4C♯, ^3D♭
285	1099.678	17/9	v3C♯, ^4D♭
286	1103.537		vvC♯, ^5D♭
287	1107.395	36/19	vC♯, ^6D♭
288	1111.254	19/10	C♯, ^7D♭
289	1115.113	40/21	^C♯, ^8D♭
290	1118.971	21/11	^^C♯, ^9D♭
291	1122.83	44/23	^3C♯, ^10D♭
292	1126.688	23/12	^4C♯, ^11D♭
293	1130.547	25/13, 48/25	^5C♯, ^12D♭
294	1134.405	52/27	^6C♯, ^13D♭
295	1138.264	27/14	^7C♯, ^14D♭
296	1142.122		^8C♯, v15D
297	1145.981		^9C♯, v14D
298	1149.839	33/17, 35/18	^10C♯, v13D
299	1153.698		^11C♯, v12D
300	1157.556	39/20	^12C♯, v11D
301	1161.415	45/23	^13C♯, v10D
302	1165.273	49/25, 51/26	^14C♯, v9D
303	1169.132		^15C♯, v8D
304	1172.99		v14C𝄪, v7D
305	1176.849		v13C𝄪, v6D
306	1180.707		v12C𝄪, v5D
307	1184.566		v11C𝄪, v4D
308	1188.424		v10C𝄪, v3D
309	1192.283		v9C𝄪, vvD
310	1196.141		v8C𝄪, vD
311	1200	2/1	D

Scratchwork

The following tables show how 15-odd-limit intervals are represented in 5edo. Prime harmonics are in bold; inconsistent intervals are in italics.

15-odd-limit intervals in 5edo (direct approximation, even if inconsistent)

Interval and complement	Error (abs, ¢)	Error (rel, %)
1/1, 2/1	0.000	0.0
15/13, 26/15	7.741	3.2
7/4, 8/7	8.826	3.7
3/2, 4/3	18.045	7.5
13/10, 20/13	25.786	10.7
7/6, 12/7	26.871	11.2
9/8, 16/9	36.090	15.0
9/7, 14/9	44.916	18.7
13/11, 22/13	49.210	20.5
15/11, 22/15	56.951	23.7
9/5, 10/9	57.596	24.0
11/7, 14/11	62.492	26.0
11/8, 16/11	71.318	29.7
11/10, 20/11	74.996	31.2
5/3, 6/5	75.641	31.5
13/9, 18/13	83.382	34.7
11/6, 12/11	89.363	37.2
5/4, 8/5	93.686	39.0
13/12, 24/13	101.427	42.3
7/5, 10/7	102.512	42.7
11/9, 18/11	107.408	44.8
13/7, 14/13	111.702	46.5
15/8, 16/15	111.731	46.6
15/14, 28/15	119.443	49.8
13/8, 16/13	119.472	49.8

15-odd-limit intervals in 5edo (patent val mapping)

Interval and complement	Error (abs, ¢)	Error (rel, %)
1/1, 2/1	0.000	0.0
15/13, 26/15	7.741	3.2
7/4, 8/7	8.826	3.7
3/2, 4/3	18.045	7.5
13/10, 20/13	25.786	10.7
7/6, 12/7	26.871	11.2
9/8, 16/9	36.090	15.0
9/7, 14/9	44.916	18.7
9/5, 10/9	57.596	24.0
11/7, 14/11	62.492	26.0
11/8, 16/11	71.318	29.7
5/3, 6/5	75.641	31.5
13/9, 18/13	83.382	34.7
11/6, 12/11	89.363	37.2
5/4, 8/5	93.686	39.0
13/12, 24/13	101.427	42.3
7/5, 10/7	102.512	42.7
11/9, 18/11	107.408	44.8
15/8, 16/15	111.731	46.6
13/8, 16/13	119.472	49.8
15/14, 28/15	120.557	50.2
13/7, 14/13	128.298	53.5
11/10, 20/11	165.004	68.8
15/11, 22/15	183.049	76.3
13/11, 22/13	190.790	79.5

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15 June 2026

• diffhist N 1-3-5-9-11-13-15 enaeikosany 07:38 +1,134 Yourmusic Productions talk contribs (Create Page.)
• Upload log 07:21 Yourmusic Productions talk contribs uploaded File:1-3-5-9-11-13-15 Enaeikosany (rotated).png (Made with [https://nickvuci.github.io/ScaleCircle ''ScaleCircle''] by Nick Vuci.)
• Upload log 07:21 Yourmusic Productions talk contribs uploaded File:1-3-5-9-11-13-15 Enaeikosany.png (Made with [https://nickvuci.github.io/ScaleCircle ''ScaleCircle''] by Nick Vuci.)

14 June 2026

• diffhist 152edo 16:54 +47 Overthink talk contribs (→Rank-2 temperaments: trinity)
• Deletion log 12:47 FloraC talk contribs deleted page 249edo (XW:NG)
• diffhist m 346edo 12:47 +4 FloraC talk contribs
• diffhist 346edo 12:46 +259 FloraC talk contribs (I think we can keep this one. Expand)
• Deletion log 12:26 FloraC talk contribs deleted page 355edo (XW:NG)
• Deletion log 12:25 FloraC talk contribs deleted page 259edo (Essentially contentless page)
• Deletion log 12:24 FloraC talk contribs deleted page 329edo (XW:NG)
• Deletion log 12:23 FloraC talk contribs deleted page 356edo (Contentless page)
• Deletion log 12:23 FloraC talk contribs deleted page 366edo (Contentless page)
• Deletion log 12:22 FloraC talk contribs deleted page 387edo (Contentless page)
• Deletion log 12:22 FloraC talk contribs deleted page 702edo (Contentless page)
• diffhist 2.3.5.7.13 subgroup 11:52 +79 FloraC talk contribs (→Regular temperaments: correct factual error (cotoneum does keep the chain of fifths))
• diffhist 2.3.5.7.11.13.19 subgroup 11:47 −1,033 FloraC talk contribs (Lots of these are copied from 2.3.5.7.13, which doesn't make much sense here. Rework)
• diffhist 2.3.5.7.13 subgroup 11:37 −72 FloraC talk contribs (→Regular temperaments: neutrality (7-limit doesn't need to be singled out here))
• diffhist m 2.3.5.7.13 subgroup 11:36 +12 FloraC talk contribs (Improve wording & linking)
• diffhist Garischismic family 10:45 +610 FloraC talk contribs (Extend androschismic to 2.3.5.7.11.13.19)
• diffhist Music of Georgia 10:40 +186 Naren talk contribs (Add link to GVM field recordings)
• diffhist m 2.3.5.7.11.13.19 subgroup 07:11 −49 FloraC talk contribs (Cleanup & recategorize)
• Deletion log 07:05 FloraC talk contribs deleted page Talk:2.11.13.17.19 subgroup (Deleted together with the associated page with reason: Relocated to user namespace)
• Deletion log 07:05 FloraC talk contribs deleted page 2.11.13.17.19 subgroup (Relocated to user namespace)
• Move log 07:04 FloraC talk contribs moved page User talk:2.11.13.17.19 subgroup to User talk:Cmloegcmluin/2.11.13.17.19 subgroup without leaving a redirect
• Move log 07:04 FloraC talk contribs moved page User:2.11.13.17.19 subgroup to User:Cmloegcmluin/2.11.13.17.19 subgroup without leaving a redirect
• diffhist N 1-3-5-7-11-13-15 pentatriandekany 06:53 +1,544 Yourmusic Productions talk contribs (Create Page.)
• Upload log 06:32 Yourmusic Productions talk contribs uploaded File:1-3-5-7-11-13-15 Pentatriandekany.png (Made with [https://nickvuci.github.io/ScaleCircle ''ScaleCircle''] by Nick Vuci.)
• diffhist 119edo 01:57 +68 Overthink talk contribs (→Theory: 119be)
• diffhist 9-odd-limit 01:47 +82 Overthink talk contribs (add image)
• Upload log 01:46 Overthink talk contribs uploaded File:9-odd-limit.png (All 9-odd-limit intervals within an octave with labels, on a cent ruler.)
• diffhist 3-odd-limit 01:27 +185 Overthink talk contribs (perfect consonances)
• diffhist Gallery of combination product sets 01:24 +254 BudjarnLambeth talk contribs (Add new pages)
• diffhist 7-odd-limit 01:22 +82 Overthink talk contribs (add image)
• diffhist File:5-odd-limit.png 01:21 +86 Overthink talk contribs (add summary)
• Upload log 01:20 Overthink talk contribs uploaded File:7-odd-limit.png (All 7-odd-limit intervals within an octave with labels, on a cent ruler.)
• diffhist 5-odd-limit 01:08 +82 Overthink talk contribs (add image)
• Upload log 01:05 Overthink talk contribs uploaded File:5-odd-limit.png
• diffhist m List of microtonal software plugins 00:41 +257 Inisil talk contribs (→Instrument plugins with microtonal support) Tag: Visual edit
• diffhist 719edo 00:38 +36 Overthink talk contribs (mark)
• diffhist 709edo 00:38 +27 Overthink talk contribs (mark this)
• diffhist 346edo 00:15 +1 Overthink talk contribs (nominate for deletion (doesn't appear in the optimal ET sequence for harry or jove; it is an ok tuning, but not quite notable))
• diffhist 336edo 00:11 −43 Overthink talk contribs (delete intervals (laggy))
• diffhist 239edo 00:06 +16 Overthink talk contribs (→Intervals: move to separate page to reduce lag)
• diffhist N Table of 239edo intervals 00:05 +25 Overthink talk contribs (move to separate page to reduce lag)
• diffhist m 245edo 00:04 +2 Overthink talk contribs (oops)
• diffhist 245edo 00:04 +19 Overthink talk contribs (nominate for deletion)

13 June 2026

• diffhist List of microtonal software plugins 20:21 +34 Contribution talk contribs (→Instrument plugins with microtonal support)
• diffhist List of microtonal software plugins 20:20 +218 Contribution talk contribs Tag: Visual edit
• diffhist Zoomoozophone 19:22 +53 Naren talk contribs (Replace dead link with archive link) Tag: Visual edit: Switched
• diffhist The Library 18:51 +199 Naren talk contribs (Add Experimental Musical Instruments to Periodicals)