FilterNashi

Native Chinese Mandarin speaker. Also speak some basic English and Japanese.

Amateur DTM trackmaker and willing to do musicology research.

Prefer music genres like jazz, electronic, and tradition/folk music.

Building blocks of Pergen(2/1,3/2) MoS scales

2/1

3/2

4/3

9/8

32/27

256/243

2187/2048

Pythagorean comma

Gothic comma

Mystery comma

41-comma

Mercator's comma

Garistearn comma, [149 -94⟩

[233 -147⟩

[317 -200⟩

[401 -253⟩

Qian's small comma

Qian's large comma

Satanic comma

...

ed16.67074¢

This segment is about the equal temperament of EPD16.67074cents.

This is about 71.9824EDO, so it's simply an alternative tuning of 72edo. The comma basis, mappings, etc. show up as same as 72edo.

I use this for 2.3.5.7.11.17.19 subgroup.

72edo didn't work well with 2.3.7.11.13 subgroup because it can't deal with the Harmonisma, and map it to 1 step.

see[1]

Approximation of prime harmonics in 71.9824edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.29	-1.49	-2.30	-1.34	-0.30	-6.11	-3.76	+3.73	+6.39	+5.18	+6.42
	Relative (%)	+1.8	-8.9	-13.8	-8.0	-1.8	-36.7	-22.5	+22.4	+38.3	+31.1	+38.5
Steps (reduced)		72 (0.017600000000002)	114 (42.0176)	167 (23.0352)	202 (58.0352)	249 (33.0528)	266 (50.0528)	294 (6.0704)	306 (18.0704)	326 (38.0704)	350 (62.0704)	357 (69.0704)

the intervals and the notations i used

step(s)	cents	just intervals	error (¢)	error (%)	notations(C=1/1)

ed38.80714¢

This segment is about the equal temperament of EPD38.80714cents.

This is about 30.922EDO, so it's simply an alternative tuning of 31edo. The comma basis, mappings, etc. show up as same as 31edo.

I use this for 2.3.5.7.11 subgroup.

see[2]

Approximation of prime harmonics in 30.922edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+3.0	-0.4	+7.8	+7.4	+1.1	-16.5	-15.2	-13.8	+4.8	-8.5	-7.5
	Relative (%)	+7.8	-1.0	+20.1	+19.1	+2.7	-42.5	-39.3	-35.4	+12.2	-21.8	-19.4
Steps (reduced)		31 (0.077999999999999)	49 (18.078)	72 (10.156)	87 (25.156)	107 (14.234)	114 (21.234)	126 (2.312)	131 (7.312)	140 (16.312)	150 (26.312)	153 (29.312)

the intervals and the notations i used

step(s)	cents	just intervals	error (¢)	error (%)	notations(C=1/1)

ed20.71628¢

This segment is about the equal temperament of EPD20.71628cents.

This is about 57.925EDO, so it's simply an alternative tuning of 58edo. The comma basis, mappings, etc. show up as same as 58edo.

I use this for 2.3.5.7.11.13 subgroup.

This is a hamormonismic, minor minthmic. A rastmic, and a major minthmic, which ends up it's also a grossmic.

see[3]

Approximation of odd harmonics in 57.925edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	+3.96	-10.31	+7.95	+7.92	-8.03	-7.21	-6.35	+4.84	-1.27	-8.80	-0.57
	Relative (%)	+19.1	-49.8	+38.4	+38.2	-38.8	-34.8	-30.7	+23.4	-6.1	-42.5	-2.7
Steps (reduced)		92 (34.075)	134 (18.15)	163 (47.15)	184 (10.225)	200 (26.225)	214 (40.225)	226 (52.225)	237 (5.3)	246 (14.3)	254 (22.3)	262 (30.3)

the intervals and the notations i used

step(s)	cents	just intervals	error (¢)	error (%)	notations(C=1/1)

ed63.77698¢

This segment is about the equal temperament of EPD63.77698cents.

This is about 18.8EDO, so it's simply an alternative tuning of 19edo. The comma basis, mappings, etc. show up as same as 19edo.

I use this for 2.3.5.7 subgroup.

see[4]

Approximation of odd harmonics in 18.8edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	+12.9	+22.2	+14.2	+25.9	-2.4	+27.6	-28.7	+9.9	+8.9	+27.1	-2.7
	Relative (%)	+20.3	+34.8	+22.2	+40.5	-3.7	+43.2	-45.0	+15.6	+13.9	+42.4	-4.3
Steps (reduced)		30 (11.2)	44 (6.4)	53 (15.4)	60 (3.6)	65 (8.6)	70 (13.6)	73 (16.6)	77 (1.8)	80 (4.8)	83 (7.8)	85 (9.8)

the intervals and the notations i used

step(s)	cents	just intervals	error (¢)	error (%)	notations(C=1/1)

ed44.21793¢

This segment is about the equal temperament of EPD44.21793cents.

This is about 27.1383EDO, so it's simply an alternative tuning of 27edo. The comma basis, mappings, etc. show up as same as 27edo.

I use this for 2.3.5.7 subgroup.

see[5]

Approximation of prime harmonics in 27.14edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-6.2	-0.7	-0.8	-8.5	+4.9	-19.0	+2.9	-12.8	+10.2	+6.8	-20.2
	Relative (%)	-14.0	-1.6	-1.7	-19.2	+11.1	-43.0	+6.6	-28.9	+23.1	+15.4	-45.7
Steps (reduced)		27 (27)	43 (15.86)	63 (8.72)	76 (21.72)	94 (12.58)	100 (18.58)	111 (2.44)	115 (6.44)	123 (14.44)	132 (23.44)	134 (25.44)

the intervals and the notations i used

step(s)	cents	just intervals	error (¢)	error (%)	notations(C=1/1)

56edo

I use this for 2.3.5.7.17.19 subgroup.

see[6] and the page of 56edo.

68edo

I use this for 2.3.5.7.17.19 subgroup.

see[7] and the page of 68edo.

Equal temperaments for 19-horizon

ed24.04706c~49.9021edo 50edo see[8] this one can't deal with harmonisma but i'm okay with it

ed14.93521~80.347edo 80edo see[9]

ed11.66952c~102.832edo 103edo see103h

ed9.90809c~121.113edo 121edo see[10]

Equal temperaments for 5-horizon

12edo see[11]

ed63.16848c~18.9968edo 19edo see[12]

34edo see[13]

ed22.64371c~52.9948edo 53edo see[14]