User:2^67-1/Sandbox II: Difference between revisions

Latest revision as of 03:02, 4 August 2026

3-limit uniform maps between 0 and 10
Min. size	Max. size	Wart notation	Map
0.0000	0.3155	0	⟨0 0]
0.3155	0.5000	0bb	⟨0 1]
0.5000	0.9464	1b	⟨1 1]
0.9464	1.5000	1	⟨1 2]
1.5000	1.5773	2bb	⟨2 2]
1.5773	2.2083	2	⟨2 3]
2.2083	2.5000	2b	⟨2 4]
2.5000	2.8392	3b	⟨3 4]
2.8392	3.4701	3	⟨3 5]
3.4701	3.5000	3bb	⟨3 6]
3.5000	4.1010	4	⟨4 6]
4.1010	4.5000	4b	⟨4 7]
4.5000	4.7320	5b	⟨5 7]
4.7320	5.3629	5	⟨5 8]
5.3629	5.5000	5bb	⟨5 9]
5.5000	5.9938	6b	⟨6 9]
5.9938	6.5000	6	⟨6 10]
6.5000	6.6248	7bb	⟨7 10]
6.6248	7.2557	7	⟨7 11]
7.2557	7.5000	7b	⟨7 12]
7.5000	7.8866	8b	⟨8 12]
7.8866	8.5000	8	⟨8 13]
8.5000	8.5176	9bb	⟨9 13]
8.5176	9.1485	9	⟨9 14]
9.1485	9.5000	9b	⟨9 15]
9.5000	9.7794	10b	⟨10 15]
9.7794	10.4103	10	⟨10 16]

Approximation of odd harmonics in 3570edo
Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-0.106	-0.095	-0.086	+0.124	-0.057	+0.145	+0.135	-0.081	-0.034	+0.143	-0.039
Error	Relative (%)	-31.6	-28.3	-25.7	+36.8	-17.1	+43.0	+40.1	-24.2	-10.1	+42.7	-11.6
Steps (reduced)		5658 (2088)	8289 (1149)	10022 (2882)	11317 (607)	12350 (1640)	13211 (2501)	13948 (3238)	14592 (312)	15165 (885)	15681 (1401)	16149 (1869)

Approximation of odd harmonics in 4410edo
Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	+0.086	+0.081	-0.118	-0.100	-0.025	+0.017	-0.105	+0.079	-0.098	-0.033	+0.025
Error	Relative (%)	+31.5	+29.7	-43.5	-36.9	-9.3	+6.1	-38.8	+28.9	-36.0	-12.0	+9.2
Steps (reduced)		6990 (2580)	10240 (1420)	12380 (3560)	13979 (749)	15256 (2026)	16319 (3089)	17229 (3999)	18026 (386)	18733 (1093)	19370 (1730)	19949 (2309)

Approximation of prime harmonics in 7980edo
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.0000	-0.0001	+0.0021	+0.0463	-0.0397	+0.0738	+0.0070	-0.0694	-0.0037	+0.0469	-0.0732
Error	Relative (%)	+0.0	-0.1	+1.4	+30.8	-26.4	+49.1	+4.7	-46.2	-2.4	+31.2	-48.7
Steps (reduced)		7980 (0)	12648 (4668)	18529 (2569)	22403 (6443)	27606 (3666)	29530 (5590)	32618 (698)	33898 (1978)	36098 (4178)	38767 (6847)	39534 (7614)

Approximation of harmonics in 34ed30
Harmonic		2	3	4	5	6	7	8	9	10	11	12	13	14	15	16
Error	Absolute (¢)	+12.3	+3.1	+24.6	-15.4	+15.4	-78.3	+36.9	+6.1	-3.1	+5.1	+27.7	+62.3	-66.0	-12.3	+49.2
Error	Relative (%)	+7.1	+1.8	+14.2	-8.9	+8.9	-45.2	+21.3	+3.5	-1.8	+2.9	+16.0	+36.0	-38.1	-7.1	+28.4
Steps (reduced)		7 (7)	11 (11)	14 (14)	16 (16)	18 (18)	19 (19)	21 (21)	22 (22)	23 (23)	24 (24)	25 (25)	26 (26)	26 (26)	27 (27)	28 (28)

@@ Line 1: / Line 1: @@
-==Notation==
-The notation used is decatonic. 0 1 2 3 4 5 6 7 8 9 0 is the Pacific mode of the Hemipyth[10] 4L 6s MOS. # and b after a number represent alterations of raising and lowering by sqrt(256/243) respectively. ^ and v before a number represent alterations of the greenland subchroma, sqrt(50/49)~sqrt(sqrt(25/24))~sqrt(49/48) respectively.
-==Chapter 1: Fokker blocks==
-===Decatonic Fokker blocks===
-Since greenland is essentially an extension of hemipyth with extra subchromatic alterations, it follows that one should probably treat greenland in this way.
-The quintessential Fokker block, though not rank-3 in nature, is the '''hemipyth[10] block'''. This block has five modes.
 {|class = "wikitable" style="text-align: center"
 |-
@@ Line 25: / Line 14: @@
 |}
-===14-tone Fokker blocks===
+{{Uniform map|edo=2|min=0|max=10|limit=3}}
-===24-tone Fokker blocks===
-===Larger Fokker blocks===
-==Chapter 2: JI scales==
+{{Harmonics in equal|3570}}
-===Preliminary: The 7-odd-limit Tonality Diamond===
+{{Harmonics in equal|4410}}
-===The 15-odd-limit Tonality Diamond===
+{{Harmonics in equal|7980}}
-===JI detemperings of Fokker blocks===
+{{Harmonics in equal|34|30|1|intervals=integer|columns=15}}