41edo: Difference between revisions

Revision as of 23:32, 30 May 2020

Theory

The 41-tET, 41-EDO, 41-ET, or 41-Tone Equal Temperament is the scale derived by dividing the octave into 41 equally-sized steps. Each step represents a frequency ratio of 29.268 cents, an interval close in size to 64/63, the septimal comma. 41-ET can be seen as a tuning of the Garibaldi temperament [1] , [2] , [3] the Magic temperament [4] and the superkleismic (41&26) temperament. It is the second smallest equal temperament (after 29edo) whose perfect fifth is closer to just intonation than that of 12-ET, and is the seventh zeta integral edo after 31; it is not, however, a zeta gap edo. This has to do with the fact that it can deal with the 11-limit fairly well, and the 13-limit perhaps close enough for government work, though its 13/10 is 14 cents sharp. Various 13-limit magic extensions are supported by 41: 13-limit magic, and less successfully necromancy and witchcraft, all merge into one in 41edo tuning. The 41f val provides a superb tuning for sorcery, giving a less-complex version of the 13-limit, and the 41ef val likewise works well for telepathy; telepathy and sorcery merging into one however not in 41edo but in 22edo.

41edo is consistent in the 15 odd limit. In fact, all of its intervals between 100 and 1100 cents in size are 15-odd-limit consonances, although 16\41 as 13/10 is debatable. (In comparison, 31edo is only consistent up to the 11-limit, and the intervals 12/31 and 19/31 have no 11-limit approximations). Treated as a no-seventeens tuning, it is consistent all the way up to 21-odd-limit.

41-ET forms the foundation of the H-System, which uses the scale degrees of 41-ET as the basic 13-limit intervals requiring fine tuning +/- 1 average JND from the 41-ET circle in 205edo. 41-ET is also used by the Kite Guitar, see below in "Instruments".

41edo is the 13th prime edo, following 37edo and coming before 43edo.

Intervals

	Cents	Approximate Ratios*	Ups and Downs Notation			Andrew's Solfege Syllables
0	0.00	1/1	perfect unison	P1	D	do
1	29.27	81/80, 64/63	up-unison	^1	^D	di
2	58.54	25/24, 28/27, 33/32	double-up unison, downminor 2nd	^^1, vm2	^^D, vEb	ro
3	87.805	21/20, 22/21, 19/18, 20/19	down-aug 1sn, minor 2nd	vA1, m2	vD#, Eb	rih
4	117.07	16/15, 15/14, 14/13	augmented 1sn, upminor 2nd	A1, ^m2	D#, ^Eb	ra
5	146.34	12/11, 13/12	mid 2nd	~2	^D#, vvE	ru
6	175.61	10/9, 11/10, 21/19	downmajor 2nd	vM2	vE	reh
7	204.88	9/8	major 2nd	M2	E	re
8	234.15	8/7, 15/13	upmajor 2nd	^M2	^E	ri
9	263.415	7/6, 22/19	downminor 3rd	vm3	vF	ma
10	292.68	32/27, 13/11, 19/16	minor 3rd	m3	F	meh
11	321.95	6/5	upminor 3rd	^m3	^F	me
12	351.22	11/9, 27/22, 16/13	mid 3rd	~3	^^F, vGb	mu
13	380.49	5/4, 26/21	downmajor 3rd	vM3	vF#, Gb	mi
14	409.76	81/64, 14/11, 24/19, 19/15	major 3rd	M3	F#, ^Gb	maa
15	439.02	9/7, 32/25	upmajor 3rd	^M3	^F#, vvG	mo
16	468.29	21/16, 13/10	down-4th	v4	vG	fe
17	497.56	4/3	perfect 4th	P4	G	fa
18	526.83	15/11, 27/20, 19/14	up-4th	^4	^G	fih
19	556.1	11/8, 18/13, 26/19	mid-4th	~4	^^G, vAb	fu
20	585.37	7/5	downaug 4th, dim 5th	vA4, d5	vG#, Ab	fi
21	614.63	10/7	aug 4th, updim 5th	A4, ^d5	G#, ^Ab	se
22	643.90	16/11, 13/9, 19/13	mid-5th	~5	vvA	su
23	673.17	22/15, 40/27, 28/19	down-5th	v5	vA	sih
24	702.44	3/2	perfect 5th	P5	A	sol
25	731.71	32/21, 20/13	up-5th	^5	^A	si
26	760.98	14/9, 25/16	downminor 6th	vm6	^^A, vBb	lo
27	790.24	128/81, 11/7, 19/12, 30/19	minor 6th	m6	vA#, Bb	leh
28	819.51	8/5, 21/13	upminor 6th	^m6	A#, ^Bb	le
29	848.78	18/11, 44/27, 13/8	mid 6th	~6	^A#, vvB	lu
30	878.05	5/3	downmajor 6th	vM6	vB	la
31	907.32	27/16, 22/13, 32/19	major 6th	M6	B	laa
32	936.59	12/7, 19/11	upmajor 6th	^M6	^B	li
33	965.85	7/4, 26/15	downminor 7th	vm7	vC	ta
34	995.12	16/9	minor 7th	m7	C	teh
35	1024.39	9/5, 20/11, 38/21	upminor 7th	^m7	^C	te
36	1053.66	11/6, 24/13	mid 7th	~7	^^C, vDb	tu
37	1082.93	15/8, 28/15, 13/7	downmajor 7th	vM7	vC#, Db	ti
38	1112.195	40/21, 21/11, 36/19, 19/10	major 7th	M7	C#, ^Db	taa
39	1141.46	48/25, 27/14, 64/33	upmajor 7th	^M7	C#^, vvD	to
40	1170.73	160/81, 63/32	dim 8ve	v8	vD	da
41	1200	2/1	perfect 8ve	P8	D	do

* Based on treating 41-edo as a 2.3.5.7.11.13.19 subgroup temperament; other approaches are possible.

Combining ups and downs notation with color notation, qualities can be loosely associated with colors:

quality	color	monzo format	examples
downminor	zo	(a, b, 0, 1)	7/6, 7/4
minor	fourthward wa	(a, b) with b < -1	32/27, 16/9
upminor	gu	(a, b, -1)	6/5, 9/5
mid	ilo	(a, b, 0, 0, 1)	11/9, 11/6
"	lu	(a, b, 0, 0, -1)	12/11, 18/11
downmajor	yo	(a, b, 1)	5/4, 5/3
major	fifthward wa	(a, b) with b > 1	9/8, 27/16
upmajor	ru	(a, b, 0, -1)	9/7, 12/7

Chord Names

All 41edo chords can be named using ups and downs. An up, down or mid immediately after the chord root affects the 3rd, 6th, 7th, and/or the 11th (every other note of a stacked-3rds chord 6-1-3-5-7-9-11-13). Alterations are always enclosed in parentheses, additions never are. Here are the zo, gu, ilo, yo and ru triads:

color of the 3rd	JI chord	notes as edosteps	notes of C chord	written name	spoken name
zo	6:7:9	0-9-24	C vEb G	Cvm	C downminor
gu	10:12:15	0-11-24	C ^Eb G	C^m	C upminor
ilo	18:22:27	0-12-24	C vvE G	C~	C mid
yo	4:5:6	0-13-24	C vE G	Cv	C downmajor or C down
ru	14:18:21	0-15-24	C ^E G	C^	C upmajor or C up

0-10-20 = D F Ab = Ddim = D dim

0-10-21 = D F ^Ab = Ddim(^5) = D dim up-five

0-10-22 = D F vvA = Dm(~5) = D minor mid-five

0-10-23 = D F vA = Dm(v5) = D minor down-five

0-10-24 = D F A = Dm = D minor

0-14-24 = D F# A = D = D or D major

0-14-25 = D F# ^A = D(^5) = D up-five

0-14-26 = D F# ^^A = D(^^5) = D double-up-five, or possibly Daug(vv5)

0-14-27 = D F# vA# = Daug(v5) = D aug down-five

0-14-28 = D F# A# = Daug = D aug

For a more complete list, see Ups and Downs Notation - Chords and Chord Progressions.

Notation

Red-Blue Notation

A red-note/blue-note system, similar to the one proposed for 36edo, is one option for notating 41edo. (This is separate from and not compatible with Kite's color notation.) We have the "white key" albitonic notes A-G (7 in total), the "black key" sharps and flats (10 in total), a "red" and "blue" version of each albitonic note (14 in total), a "red" (dark red?) version of each sharp and a "blue" (dark blue?) version of each flat (10 in total), adding up to 41. This would result in quite a colorful keyboard! Note that there are no red flats or blue sharps. Using this nomenclature the notes are:

A, red A, blue Bb, Bb, A#, red A#, blue B, B, red B, blue C, C, red C, blue Db, Db, C#, red C#, blue D, D, red D, blue Eb, Eb, D#, red D#, blue E, E, red E, blue F, F, red F, blue Gb, Gb, F#, red F#, blue G, G, red G, blue Ab, Ab, G#, red G#, blue A, A.

Interval classes could also be named by analogy. The natural, colorless, or gray interval classes are the Pythagorean ones (which show up in the standard diatonic scale), while "red" and "blue" versions are one step higher or lower. Gray thirds, sixths, and sevenths are usually more dissonant than their colorful counterparts, but the reverse is true of fourths and fifths.

The step size of 41edo is small enough that the smallest interval (the "red/blue unison", seventh-tone, comma, diesis or whatever you want to call it) is actually fairly consonant with most timbres; it resembles a "noticeably out of tune unison" rather than a minor second, and has its own distinct character and appeal.

If "red" is replaced by "up", "blue" by "down", and "neutral" by "mid", and if "gray" is omitted, this notation becomes essentially the same as ups and downs notation. The only difference is the use of minor tritone and major tritone.

Selected just intervals by error

	prime 2	prime 3	prime 5	prime 7	prime 11	prime 13	prime 17	prime 19
error	0.0¢	+0.48¢	-5.8¢	-3.0¢	+4.8¢	+8.3¢	+12.1¢	-4.8¢
fifthspan	0	+1	-8	-14	-18	+20	+7	-3

The following table shows how some prominent just intervals are represented in 41edo (ordered by absolute error).

Interval, complement	Error (abs., in cents)
4/3, 3/2	0.484
9/8, 16/9	0.968
15/14, 28/15	2.370
7/5, 10/7	2.854
8/7, 7/4	2.972
7/6, 12/7	3.456
13/11, 22/13	3.473
11/9, 18/11	3.812
9/7, 14/9	3.940
12/11, 11/6	4.296
11/8, 16/11	4.780
16/15, 15/8	5.342
5/4, 8/5	5.826
6/5, 5/3	6.310
10/9, 9/5	6.794
18/13, 13/9	7.285
14/11, 11/7	7.752
13/12, 24/13	7.769
16/13, 13/8	8.253
15/11, 22/15	10.122
11/10, 20/11	10.606
14/13, 13/7	11.225
15/13, 26/15	13.595
13/10, 20/13	14.079

Relationship to 12-edo

Whereas 12-edo has a circle of twelve 5ths, 41-edo has a spiral of twelve 5ths (since 24\41 is on the 7\12 kite in the scale tree). This spiral of 5th shows 41-edo in a 12-edo-friendly format. Excellent for introducing 41-edo to musicians unfamiliar with microtonal music. There are 12 "-ish" categories, where "-ish" means ±1 edostep. The 6 mid intervals are uncategorized, since they are all so far from 12edo. The two innermost and two outermost intervals on the spiral are duplicates.

The same spiral, but with notes not intervals:

Commas

41 EDO tempers out the following commas using its patent val, < 41 65 95 115 142 152 168 174 185 199 203 |.

Prime Limit	Ratio	Cents	Monzo	color name		Name
3		19.84	\| 65 -41 >	Wa-41	41-edo	'41-tone' comma
5		57.27	\| -5 -10 9 >	Tritriyo	y⁹	shibboleth
"		31.57	\| -25 7 6 >	Lala-tribiyo	LLy³	Ampersand's comma
"	3125/3072	29.61	\| -10 -1 5 >	Laquinyo	Ly⁵	small diesis, magic comma
"	20000/19683	27.66	\| 5 -9 4 >	Saquadyo	sy⁴	minimal diesis, tetracot comma
"		25.71	\| 20 -17 3 >	Sasa-triyo	ssy³	roda
"	32805/32768	1.95	\| -15 8 1 >	Layo	Ly	schisma
7	15625/15309	35.37	\| 0 -7 6 -1 >	Rutribiyo	ry⁶	great BP diesis
"		22.41	\| -10 7 8 -7 >	Lasepru-aquadbiyo	Lr⁷y⁸	blackjackisma
"	875/864	21.90	\| -5 -3 3 1 >	Zotriyo	zy³	keema
"	3125/3087	21.18	\| 0 -2 5 -3 >	Triru-aquinyo	r³y⁵	major BP diesis, gariboh
"		19.95	\| 10 -11 2 1 >	Sazoyoyo	szyy	tolerma
"	33075/32768	16.14	\| -15 3 2 2 >	Labizoyo	Lzzyy	mirwomo comma
"	245/243	14.19	\| 0 -5 1 2 >	Zozoyo	zzy	minor BP diesis, sensamagic
"	4000/3969	13.47	\| 5 -4 3 -2 >	Rurutriyo	rry³	septimal semicomma, octagar
"		9.15	\| -15 0 -2 7 >	Lasepzo-agugu	Lz⁷gg	quince
"	1029/1024	8.43	\| -10 1 0 3 >	Latrizo	Lz³	gamelan residue, gamelisma
"	225/224	7.71	\| -5 2 2 -1 >	Ruyoyo	ryy	septimal kleisma, marvel comma
"	16875/16807	6.99	\| 0 3 4 -5 >	Quinru-aquadyo	r⁵y⁴	small BP diesis, mirkwai
"	10976/10935	6.48	\| 5 -7 -1 3 >	Satrizo-agu	sz³g	hemimage
"	5120/5103	5.76	\| 10 -6 1 -1 >	Saruyo	sry	Beta 5, Garibaldi comma, hemifamity
"		3.80	\| 25 -14 0 -1 >	Sasaru	ssr	Beta 2, septimal schisma, garischisma
"	2401/2400	0.72	\| -5 -1 -2 4 >	Bizozogu	z⁴gg	Breedsma
11		29.72	\| 15 0 1 0 -5 >	Saquinlu-ayo	s1u⁵y	thuja comma
"	245/242	21.33	\| -1 0 1 2 -2 >	Luluzozoyo	1uuzzy	cassacot
"	100/99	17.40	\| 2 -2 2 0 -1 >	Luyoyo	1uyy	Ptolemy's comma, ptolemisma
"	1344/1331	16.83	\| 6 1 0 1 -3 >	Trilu-azo	1u³z	hemimin
"	896/891	9.69	\| 7 -4 0 1 -1 >	Saluzo	s1uz	undecimal semicomma, pentacircle (minthma * gentle)
"	65536/65219	8.39	\| 16 0 0 -2 -3 >	Satrilu-aruru	s1u³rr	orgonisma
"	243/242	7.14	\| -1 5 0 0 -2 >	Lulu	1uu	neutral third comma, rastma
"	385/384	4.50	\| -7 -1 1 1 1 >	Lozoyo	1ozg	undecimal kleisma, keenanisma
"	441/440	3.93	\| -3 2 -1 2 -1 >	Luzozogu	1uzzg	Werckmeister's undecimal septenarian schisma, werckisma
"	1375/1372	3.78	\| -2 0 3 -3 1 >	Lotriruyo	1or³y	moctdel
"	540/539	3.21	\| 2 3 1 -2 -1 >	Lururuyo	1urry	Swets' comma, swetisma
"	3025/3024	0.57	\| -4 -3 2 -1 2 >	Loloruyoyo	1ooryy	Lehmerisma
"		0.15	\| -1 2 -4 5 -2 >	Luluquinzo-aquadgu	1uuz⁵g⁴	odiheim
13	105/104	16.57	\| -3 1 1 1 0 -1 >	Thuzoyo	3uzy	small tridecimal comma, animist
"	28672/28431	14.61	\| 12 -7 0 1 0 -1 >	Sathuzo	s3uz	secorian
"	275/273	12.64	\| 0 -1 2 -1 1 -1 >	Thuloruyoyo	3u1oryy	gassorma
"	144/143	12.06	\| 4 2 0 0 -1 -1 >	Thulu	3u1u	grossma
"	196/195	8.86	\| 2 -1 -1 2 0 -1 >	Thuzozogu	3uzzg	mynucuma
"	640/637	8.13	\| 7 0 1 -2 0 -1 >	Thururuyo	3urry	huntma
"	1188/1183	7.30	\| 2 3 0 -1 1 -2 >	Thuthuloru	3uu1or	kestrel comma
"	325/324	5.34	\| -2 -4 2 0 0 1 >	Thoyoyo	3oyy	marveltwin
"	352/351	4.93	\| 5 -3 0 0 1 -1 >	Thulo	3u1o	minthma
"	364/363	4.76	\| 2 -1 0 1 -2 1 >	Tholuluzo	3o1uuz	gentle comma
"	847/845	4.09	\| 0 0 -1 1 2 -2 >	Thuthulolozogu	3uu1oozg	cuthbert
"	729/728	2.38	\| -3 6 0 -1 0 -1 >	Lathuru	L3ur	squbema
"	4096/4095	0.42	\| 12 -2 -1 -1 0 -1 >	Sathurugu	s3urg	tridecimal schisma, Sagittal schismina
"	10648/10647	0.16	\| 3 -2 0 -1 3 -2 >	Thuthutrilo-aru	3uu1o³r	harmonisma
17	2187/2176	8.73	\| -7 7 0 0 0 0 -1 >	Lasu	L17u	septendecimal comma
"	256/255	6.78	\| 8 -1 -1 0 0 0 -1 >	Sugu	17ug	septendecimal kleisma
"	715/714	2.42	\| -1 -1 1 -1 1 1 -1 >	Sutholoruyo	17u3o1ory	septendecimal bridge comma
19	210/209	8.26	\| 1 1 1 1 -1 0 0 -1 >	Nuluzoyo	19u1uzy	spleen comma
"	361/360	4.80	\| -3 -2 -1 0 0 0 0 2 >	Nonogu	19oog2	go comma
"	513/512	3.38	\| -9 3 0 0 0 0 0 1 >	Lano	L19o	undevicesimal comma, Boethius' comma
"	1216/1215	1.42	\| 6 -5 -1 0 0 0 0 1 >	Sanogu	s19og	Eratosthenes' comma
23	736/729	16.54	\| 5 -6 0 0 0 0 0 0 1 >	Sa-twenty-tho	s23o	vicesimotertial comma
29	145/144	11.98	\| -4 -2 1 0 0 0 0 0 0 1 >	Twenty-noyo	29oy	29th-partial chroma

Temperaments

List of edo-distinct 41et rank two temperaments

Table of Temperaments by generator

Degree	Cents	Temperament(s)	Pergen	Some MOS Scales Available
1	29.27	Sepla-sezo = [-100 33 0 17>	(P8, P4/17)
2	58.54	Hemimiracle	(P8, P5/12)
3	87.805	88cET (approx), octacot	(P8, P5/8)
4	117.07	Miracle	(P8, P5/6)
5	146.34	Bohlen-Pierce/bohpier	(P8, P12/13)
6	175.61	Tetracot/bunya/monkey	(P8, P5/4)	13-tone MOS: 1 5 1 5 1 5 1 5 5 1 5 1 5
7	204.88	Baldy	(P8, c³P4/20)	11-tone MOS: 6 1 6 6 1 6 1 6 1 6 1
8	234.15	Rodan/guiron	(P8, P5/3)	11-tone MOS: 7 1 7 1 7 1 7 1 1 7 1
9	263.415	Septimin	(P8, ccP4/11)	9-tone MOS: 5 4 5 5 4 5 4 5 4
10	292.68	Quasitemp	(P8, c³P4/14)
11	321.95	Superkleismic	(P8, ccP4/9)	11-tone MOS: 5 3 5 3 3 5 3 3 5 3 3
12	351.22	Hemififths/karadeniz	(P8, P5/2)	10-tone MOS: 5 2 5 5 2 5 5 5 2 5
13	380.49	Magic/witchcraft	(P8, P12/5)	10-tone MOS: 2 9 2 2 9 2 2 9 2 2
14	409.76	Hocus	(P8, c³P4/10)
15	439.02	Sasa-tritribizo = [5 -35 0 18>	(P8, c⁶P5/18)	11-tone MOS: 4 3 4 4 4 3 4 4 3 4 4
16	468.29	Barbad	(P8, c⁷P4/19)
17	497.56	Schismatic (helmholtz, garibaldi, cassandra)	(P8, P5)
18	526.83	Trismegistus	(P8, c⁶P5/15)	9-tone MOS: 5 5 3 5 5 5 5 3 5
19	556.1	Sasa-quadquadlu = [57 -1 0 0 -16>	(P8, c⁷P4/16)
20	585.37	Pluto	(P8, c³P4/7)

Scales and modes

A list of 41edo modes (MOS and others).

Harmonic Scale

41edo is the first edo to do some justice to Mode 8 of the harmonic series, which Dante Rosati calls the "Diatonic Harmonic Series Scale," consisting of overtones 8 through 16 (sometimes made to repeat at the octave).

Overtones in "Mode 8":	8	9	10	11	12	13	14	15	16
...as JI Ratio from 1/1:	1/1	9/8	5/4	11/8	3/2	13/8	7/4	15/8	2/1
...in cents:	0	203.9	386.3	551.3	702.0	840.5	968.8	1088.3	1200.0
Nearest degree of 41edo:	0	7	13	19	24	29	33	37	41
...in cents:	0	204.9	380.5	556.1	702.4	848.8	965.9	1082.9	1200.0

While each overtone of Mode 8 is approximated within a reasonable degree of accuracy, the steps between the intervals are not uniquely represented. (41edo is, after all, a temperament.)

7\41 (7 degrees of 41edo) (204.9 cents) stands in for just ratio 9/8 (203.9 cents) -- a close match.

6\41 (175.6 cents) stands in for both 10/9 (182.4 cents) and 11/10 (165.0 cents).

5\41 (146.3 cents) stands in for both 12/11 (150.6 cents) and 13/12 (138.6 cents).

4\41 (117.1 cents) stands in for 14/13 (128.3 cents), 15/14 (119.4 cents), and 16/15 (111.7 cents).

The scale in 41, as adjacent steps, thus goes: 7 6 6 5 5 4 4 4.

Nonoctave Temperaments

Taking every third degree of 41edo produces a scale extremely close to 88cET or 88-cent equal temperament (or the 8th root of 3:2). Likewise, taking every fifth degree produces a scale very close to the equal-tempered Bohlen-Pierce Scale (or the 13th root of 3). See chart:

deg of 41edo	deg of 88cET	cents	cents	cents	deg of BP	deg of 41edo
3 degrees of 41edo (near 88cET)			overlap	5 degrees of 41edo (near BP)
0	0		0		0	0
3	1	87.8
				146.3	1	5
6	2	175.6
9	3	263.4
				292.7	2	10
12	4	351.2
15	5		439.0		3	15
18	6	526.8
				585.4	4	20
21	7	614.6
24	8	702.4
				731.7	5	25
27	9	790.2
30	10		878.0		6	30
33	11	965.9
				1024.4	7	35
36	12	1053.7
39	13	1141.5
				1170.7	8	40
[ second octave ]
1	14	29.2
4	15		117.1		9	4
7	16	204.9
				263.4	10	9
10	17	292.7
13	18	380.5
				409.8	11	14
16	19	468.3
19	20		556.1		12	19
22	21	643.9
				702.4	13	24
25	22	731.7
28	23	819.5
				848.8	14	29
31	24	907.3
34	25		995.1		15	34
37	26	1082.9
				1141.5	16	39
40	27	1170.7
[ third octave ]
2	28	58.5
				87.8	17	3
5	29	146.3
8	30		234.1		18	8
11	31	322.0
				380.5	19	13
14	32	409.8
17	33	497.6
				526.8	20	18
20	34	585.3
23	35		673.2		21	23
26	36	761.0
				819.5	22	28
29	37	848.8
32	38	936.6
				965.9	23	33
35	39	1024.4
38	40		1112.2		24	38

Instruments

41-EDO Electric guitar, by Gregory Sanchez.

41-EDO Classical guitar, by Ron Sword.

The Kite Guitar (see also Kite Tuning) is a guitar fretting using every other step of 41-edo, i.e. 41-ED4 or "20½-edo". However, the interval between two adjacent open strings is always an odd number of 41-edosteps. Thus each string only covers half of 41-edo, but the full edo can be found on every pair of adjacent strings.The Kite Tuning makes 41-edo about as playable as 19-edo or 22-edo, although there are certain trade-offs. If the interval between strings is 13\41, 25 of the 41 intervals are in easy reach: vm2, ^m2, vM2, M2, ^M2, vm3, ^m3, vM3, ^M3, P4, ~4, d5, A4, ~5, P5, vm6, ^m6, vM6, ^M6, vm7, m7, ^m7, vM7, ^M7, P8.

A possible system to tune keyboards in 41EDO is discussed in http://launch.groups.yahoo.com/group/tuning/message/74155.

Music

EveningHorizon play by Cameron Bobro

Links

Wikipedia article on 41edo
Magic22 as srutis describes a possible use of 41edo for indian music.
see also Magic family
Sword, Ron. "Tetracontamonophonic Scales for Guitar"
Taylor, Cam. Intervals, Scales and Chords in 41EDO, a work in progress using just intonation concepts and simplified Sagittal notation.

^ "Schismic Temperaments" at x31eq.com the website of Graham Breed
^ "Lattices with Decimal Notation" at x31eq.com
^ Schismatic temperament
^ Magic temperament

41edo: Difference between revisions

Revision as of 23:32, 30 May 2020

Contents

Theory