41-equal approximates just intonation very closely. Prime 3 is extremely accurate, and primes 5 and 7 are both flat, which means their errors partially cancel out in ratios such as 7/5. Unfortunately prime 11 is sharp, so the errors add up, and 11/10 is nearly 11¢ sharp.

prime	2/1	3/2	5/4	7/4	11/8	13/8	17/16	19/16
error	0.0¢	+0.48¢	-5.8¢	-3.0¢	+4.8¢	+8.3¢	+12.1¢	-4.8¢

The 41 notes can be named with ups and downs. A sharp equals four ups (two frets), thus an up is a quarter-sharp. A minor 2nd equals three ups. Both 81/80 and 64/63 are equal to one up.

41-equal notes from C to D

C	^C	^^C = vvC#	vC#	C#	^C#
		vDb	Db	^Db	^^Db = vvD	vD	D

41-equal intervals from perfect unison to major 2nd

P1	^1	^^1 = vvA1	vA1	A1	^A1
		vm2	m2	^m2	~2	vM2	M2

All 41 intervals:

• P1 ^1
• vm2 m2 ^m2 ~2 vM2 M2 ^M2
• vm3 m3 ^m3 ~3 vM3 M3 ^M3
• v4 P4 ^4
• ~4/vd5 vA4/d5 A4/^d5 ^A4/~5
• v5 P5 ^5
• vm6 m6 ^m6 ~6 vM6 M6 ^M6
• vm7 m7 ^m7 ~7 vM7 M7 ^M7
• v8 P8

Solfege (-u = up, -o = down, -a = plain, -i = mid, Fr- = flat Re, etc.)

• Da Du
• Fro Fra Fru Ri Ro Ra Ru
• No Na Nu Mi Mo Ma Mu
• Fo Fa Fu
• Fi/Sho Po/Sha Pa/Shu Pu/Si
• So Sa Su
• Flo Fla Flu Li Lo La Lu
• Tho Tha Thu Ti To Ta Tu
• Do Da

The most dissonant intervals are the off-perfect ones ^1, v4, ^4, v5, ^5 and v8.

step	cents	interval
0	0¢	perfect unison	P1	D
1	29	up-unison	^1	^D
2	59	double-up 1sn, downminor 2nd	^^1, vm2	^^D, vEb
3	88	down-aug 1sn, minor 2nd	vA1, m2	vD#, Eb
4	117	augmented 1sn, upminor 2nd	A1, ^m2	D#, ^Eb
5	146	mid 2nd	~2	^D#, vvE
6	176	downmajor 2nd	vM2	vE
7	205	major 2nd	M2	E
8	234	upmajor 2nd	^M2	^E
9	263	downminor 3rd	vm3	vF
10	293	minor 3rd	m3	F
11	322	upminor 3rd	^m3	^F
12	351	mid 3rd	~3	^^F, vGb
13	380	downmajor 3rd	vM3	vF#, Gb
14	410	major 3rd	M3	F#, ^Gb
15	439	upmajor 3rd	^M3	^F#, vvG
16	468	down-4th	v4	vG
17	498	perfect 4th	P4	G
18	527	up-4th	^4	^G
19	556	mid-4th	~4	^^G, vAb
20	585	downaug 4th, dim 5th	vA4, d5	vG#, Ab
21	615	aug 4th, updim 5th	A4, ^d5	G#, ^Ab
22	644	mid-5th	~5	vvA
23	673	down-5th	v5	vA
24	702	perfect 5th	P5	A
25	732	up-5th	^5	^A
26	761	downminor 6th	vm6	^^A, vBb
27	790	minor 6th	m6	vA#, Bb
28	820	upminor 6th	^m6	A#, ^Bb
29	849	mid 6th	~6	^A#, vvB
30	878	downmajor 6th	vM6	vB
31	907	major 6th	M6	B
32	937	upmajor 6th	^M6	^B
33	966	downminor 7th	vm7	vC
34	995	minor 7th	m7	C
35	1024	upminor 7th	^m7	^C
36	1054	mid 7th	~7	^^C, vDb
37	1083	downmajor 7th	vM7	vC#, Db
38	1112	major 7th	M7	C#, ^Db
39	1141	upmajor 7th	^M7	C#^, vvD
40	1171	dim 8ve	v8	vD
41	1200	perfect 8ve	P8	D

This chart shows 41-equal in terms of 12-equal. "-ish" means ±1 step of 41. The 12 categories circled in red correspond to the notes of 12-equal. The two innermost and two outermost intervals are duplicates.