User:Overthink/Sandbox

User:Overthink/Sandbox (size comparison)

Approximation of prime harmonics in 10257edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31	37	41	43	47	53	59	61
Error	Absolute (¢)	+0.0000	+0.0046	-0.0019	-0.0046	-0.0456	-0.0480	-0.0124	+0.0009	-0.0205	-0.0364	-0.0224	-0.0425	-0.0481	-0.0231	-0.0489	-0.0328	-0.0316	+0.0500
	Relative (%)	+0.0	+4.0	-1.6	-3.9	-39.0	-41.0	-10.6	+0.7	-17.5	-31.1	-19.2	-36.3	-41.1	-19.8	-41.8	-28.0	-27.0	+42.7
Steps (reduced)		10257 (0)	16257 (6000)	23816 (3302)	28795 (8281)	35483 (4712)	37955 (7184)	41925 (897)	43571 (2543)	46398 (5370)	49828 (8800)	50815 (9787)	53433 (2148)	54952 (3667)	55657 (4372)	56973 (5688)	58751 (7466)	60338 (9053)	60832 (9547)

Approximation of odd harmonics in 10195edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23	25	27	29	31	33	35
Error	Absolute (¢)	+0.0362	-0.0067	+0.0020	-0.0454	+0.0111	+0.0020	+0.0295	+0.0372	+0.0446	+0.0381	+0.0336	-0.0134	-0.0092	-0.0137	-0.0037	+0.0473	-0.0048
	Relative (%)	+30.7	-5.7	+1.7	-38.5	+9.5	+1.7	+25.0	+31.6	+37.9	+32.4	+28.6	-11.4	-7.8	-11.6	-3.1	+40.2	-4.0
Steps (reduced)		16159 (5964)	23672 (3282)	28621 (8231)	32317 (1732)	35269 (4684)	37726 (7141)	39831 (9246)	41672 (892)	43308 (2528)	44780 (4000)	46118 (5338)	47344 (6564)	48476 (7696)	49527 (8747)	50508 (9728)	51428 (453)	52293 (1318)

Compressed 49edo:

Approximation of harmonics in 138ed7

Harmonic		2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-3.8	+2.2	-7.6	-3.4	-1.7	+0.0	-11.5	+4.3	-7.2	-1.3	-5.5	+2.4	-3.8	-1.2	+9.1	+1.8	+0.5	+4.5	-11.0	+2.2	-5.1	-8.9
	Relative (%)	-15.7	+8.9	-31.3	-13.8	-6.8	+0.0	-47.0	+17.7	-29.5	-5.4	-22.5	+9.9	-15.7	-4.9	+37.4	+7.4	+2.1	+18.6	-45.1	+8.9	-21.0	-36.3
Steps (reduced)		49 (49)	78 (78)	98 (98)	114 (114)	127 (127)	138 (0)	147 (9)	156 (18)	163 (25)	170 (32)	176 (38)	182 (44)	187 (49)	192 (54)	197 (59)	201 (63)	205 (67)	209 (71)	212 (74)	216 (78)	219 (81)	222 (84)

Approximation of harmonics in 127ed6

Harmonic		2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-3.2	+3.2	-6.4	-1.9	+0.0	+1.8	-9.5	+6.4	-5.1	+0.9	-3.2	+4.8	-1.4	+1.3	+11.7	+4.4	+3.2	+7.3	-8.2	+5.0	-2.3	-6.0
	Relative (%)	-13.0	+13.0	-26.1	-7.7	+0.0	+7.4	-39.1	+26.1	-20.7	+3.7	-13.0	+19.6	-5.7	+5.3	+47.9	+18.2	+13.0	+29.8	-33.8	+20.4	-9.3	-24.4
Steps (reduced)		49 (49)	78 (78)	98 (98)	114 (114)	127 (0)	138 (11)	147 (20)	156 (29)	163 (36)	170 (43)	176 (49)	182 (55)	187 (60)	192 (65)	197 (70)	201 (74)	205 (78)	209 (82)	212 (85)	216 (89)	219 (92)	222 (95)

Approximation of harmonics in 114ed5

Harmonic		2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.4	+4.5	-4.7	+0.0	+2.1	+4.1	-7.1	+8.9	-2.4	+3.7	-0.3	+7.8	+1.7	+4.5	-9.5	+7.8	+6.6	+10.7	-4.7	+8.6	+1.3	-2.3
	Relative (%)	-9.7	+18.3	-19.4	+0.0	+8.6	+16.7	-29.1	+36.6	-9.7	+15.2	-1.1	+31.9	+7.0	+18.3	-38.9	+31.7	+26.9	+43.9	-19.4	+35.0	+5.5	-9.4
Steps (reduced)		49 (49)	78 (78)	98 (98)	114 (0)	127 (13)	138 (24)	147 (33)	156 (42)	163 (49)	170 (56)	176 (62)	182 (68)	187 (73)	192 (78)	196 (82)	201 (87)	205 (91)	209 (95)	212 (98)	216 (102)	219 (105)	222 (108)

--Overthink (talk) 04:41, 29 September 2025 (UTC)

How

far

can

this

= ? =

oh this is the limit

← 3731edo

3732edo

3733edo →

Prime factorization	22 × 3 × 311
Step size	0.321543 ¢
Fifth	2183\3732 (701.929 ¢)
Semitones (A1:m2)	353:281 (113.5 ¢ : 90.35 ¢)
Consistency limit	9
Distinct consistency limit	9

Approximation of odd harmonics in 3732edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-0.026	-0.140	-0.016	-0.051	+0.129	-0.013	+0.156	-0.132	-0.085	-0.041	+0.021
	Relative (%)	-8.0	-43.6	-4.9	-16.0	+40.1	-4.1	+48.4	-41.1	-26.5	-12.9	+6.7
Steps (reduced)		5915 (2183)	8665 (1201)	10477 (3013)	11830 (634)	12911 (1715)	13810 (2614)	14581 (3385)	15254 (326)	15853 (925)	16392 (1464)	16882 (1954)

Approximation of prime harmonics in 9999edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31	37	41	43	47
Error	Absolute (¢)	+0.0000	-0.0048	+0.0049	+0.0310	+0.0172	+0.0364	+0.0551	-0.0033	-0.0115	+0.0058	-0.0011	-0.0389	-0.0195	-0.0266	-0.0401
	Relative (%)	+0.0	-4.0	+4.1	+25.8	+14.3	+30.3	+45.9	-2.7	-9.6	+4.8	-0.9	-32.4	-16.2	-22.1	-33.4
Steps (reduced)		9999 (0)	15848 (5849)	23217 (3219)	28071 (8073)	34591 (4594)	37001 (7004)	40871 (875)	42475 (2479)	45231 (5235)	48575 (8579)	49537 (9541)	52089 (2094)	53570 (3575)	54257 (4262)	55540 (5545)

Approximation of prime harmonics in 10158edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.0000	-0.0058	-0.0172	-0.0131	+0.0111	-0.0079	-0.0529	-0.0529	-0.0404	-0.0438	+0.0324
	Relative (%)	+0.0	-4.9	-14.6	-11.1	+9.4	-6.7	-44.8	-44.8	-34.2	-37.1	+27.4
Steps (reduced)		10158 (0)	16100 (5942)	23586 (3270)	28517 (8201)	35141 (4667)	37589 (7115)	41520 (888)	43150 (2518)	45950 (5318)	49347 (8715)	50325 (9693)

Approximation of prime harmonics in 7464edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31	37	41	43	47
Error	Absolute (¢)	+0.0000	-0.0257	+0.0207	-0.0156	-0.0318	-0.0132	+0.0285	+0.0754	+0.0215	+0.0048	-0.0195	-0.0579	+0.0373	+0.0579	-0.0725
	Relative (%)	+0.0	-16.0	+12.9	-9.7	-19.8	-8.2	+17.7	+46.9	+13.4	+3.0	-12.1	-36.0	+23.2	+36.0	-45.1
Steps (reduced)		7464 (0)	11830 (4366)	17331 (2403)	20954 (6026)	25821 (3429)	27620 (5228)	30509 (653)	31707 (1851)	33764 (3908)	36260 (6404)	36978 (7122)	38883 (1563)	39989 (2669)	40502 (3182)	41459 (4139)

← 4047edo

4048edo

4049edo →

Prime factorization	24 × 11 × 23
Step size	0.296443 ¢
Fifth	2368\4048 (701.976 ¢) (→ 148\253)
Semitones (A1:m2)	384:304 (113.8 ¢ : 90.12 ¢)
Consistency limit	11
Distinct consistency limit	11

Approximation of prime harmonics in 4048edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	+0.021	-0.049	-0.051	+0.065	-0.113	-0.015	+0.115	-0.112	-0.032	+0.123
	Relative (%)	+0.0	+7.2	-16.5	-17.3	+22.1	-38.0	-5.0	+38.9	-37.9	-10.7	+41.3
Steps (reduced)		4048 (0)	6416 (2368)	9399 (1303)	11364 (3268)	14004 (1860)	14979 (2835)	16546 (354)	17196 (1004)	18311 (2119)	19665 (3473)	20055 (3863)