29edo

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29edo

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Prime factorization	29 (prime)
Step size	41.3793 ¢
Fifth	17\29 (703.448 ¢) (semiconvergent)
Semitones (A1:m2)	3:2 (124.1 ¢ : 82.76 ¢)
Consistency limit	15
Distinct consistency limit	5

29 equal divisions of the octave (abbreviated 29edo or 29ed2), also called 29-tone equal temperament (29tet) or 29 equal temperament (29et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 29 equal parts of about 41.4 ¢ each. Each step represents a frequency ratio of 2^1/29, or the 29th root of 2.

Theory

29 is the lowest edo which approximates the 3/2 just fifth more accurately than 12edo: 3/2 = 701.955… cents; 17 degrees of 29edo = 703.448… cents. Since the fifth is sharp instead of flat, 29edo is a positive temperament — a parapythagorean tuning instead of a meantone system.

[File info]	[File info]
Parapythagorean diatonic major scale and cadence in 29edo	12edo diatonic major scale and cadence, for comparison

29edo could be thought of as the "twin" of 12edo in the 5-limit, since 5-limit intervals in 12edo and 29edo are tuned with almost exactly the same absolute errors, but in opposite directions. There are other ways in which they are counterparts, like how 12 tempers out 50/49 but not 49/48; 29 does the opposite. Each also supports a particularly good tonal framework (meantone[7] and nautilus[14], respectively).

A more coincidental similarity is that just as the 12-tone scale is also a 1/2-tone scale (the whole tone being divided into 2 semitones), the 29-tone temperament may also be called 2/9-tone. This is because it has two different sizes of whole tone (4 and 5 steps wide, respectively). So the step size of 29edo may be called a 2/9-tone, just as 24edo's step size is called a quarter tone, since if 2 tones make a 5/4, (4 + 5) * 2/9 tones = 2 tones (9 steps) = 5/4 in 29edo.

Prime harmonics

3 is the only harmonic, of the intelligibly low ones anyway, that 29edo approximates very closely, and it does so quite well. Nonetheless, and rather surprisingly, 29 is the smallest equal division which consistently represents the 15-odd-limit. It is able to do this since it has an accurate 3, and the 5, 7, 11 and 13, while not very accurate, are all tuned flatly. Hence it tempers out a succession of fairly large commas: 250/243 in the 5-limit, 49/48 in the 7-limit, 55/54 in the 11-limit, and 65/64 in the 13-limit. If using these approximations is desired, 29edo actually shines, and it can be used for such things as an alternative to 19edo for negri, as well as an alternative to 22edo or 15edo for porcupine. 29edo is also an oneirotonic tuning with generator 11\29, which generates ammonite temperament.

Approximation of prime harmonics in 29edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.0	+1.5	-13.9	-17.1	-13.4	-12.9	+19.2	-7.9	-7.6	+4.9	+13.6
	Relative (%)	+0.0	+3.6	-33.6	-41.3	-32.4	-31.3	+46.4	-19.0	-18.3	+11.9	+32.8
Steps (reduced)		29 (0)	46 (17)	67 (9)	81 (23)	100 (13)	107 (20)	119 (3)	123 (7)	131 (15)	141 (25)	144 (28)

Stacking fifths

Another possible use for 29edo is as an equally tempered para-pythagorean scale. Using its fifth as a generator leads to a variant of garibaldi temperament which is not very accurate but which has relatively low 13-limit complexity. However, it gives the POL2 generator for edson temperament with essentially perfect accuracy, only 0.034 cents sharp of it.

Edson is a 2.3.7/5.11/5.13/5 subgroup temperament, and 29edo represents the 2.3.11/5.13/5 subgroup to very high accuracy, and the 2.3.7/5.11/5.13/5 to a lesser but still good accuracy, and so can be used with this subgroup, which is liberally supplied with chords such as the 1-11/7-13/7 (7:11:13) chord, the barbados triad 1-13/10-3/2 (10:13:15), the minor barbados triad 1-15/13-3/2 (26:30:39), the 1-14/11-3/2 (22:28:33) triad, the 1-13/11-3/2 (22:26:33) triad, and the petrmic triad, a 13-limit essentially tempered dyadic chord.

29 tempers out 352/351, 676/675 and 4000/3993 from the 2.3.11/5.13/5 subgroup, and in addition 196/195 and 364/363 from the 2.3.7/5.11/5.13/5 subgroup, so we have various relationships from the tempering, such as the fact that the 1-13/11-3/2 chord and the 1-14/11-3/2 chord are inverses of each other, a major-minor pairing. A larger subgroup containing both of these subgroups is the 3*29 subgroup 2.3.125.175.275.325; on this subgroup 29 tunes the same as 87, and the commas of 29 on this subgroup are the same as the 13-limit commas of 87. Still another subgroup of interest is the 2*29 subgroup 2.3.25.35.55.65.85; on this subgroup 29 tunes the same as 58 and has the same 17-limit commas.

Due to 29edo's tone-efficient mapping of 2.3.7/5.11/5.13/5, it makes sense to collapse this subgroup to 29edo. One may then expand the subgroup to the full 13-limit, adding an independent generator to reach primes 5, 7, 11, and 13 in one generator. This is mystery temperament, which has very low badness despite so many periods per octave. The 58-note MOS gives scope for harmony, with 29 15-odd-limit otonal chords and 29 utonal chords.

Interval Flavors

29edo has inframinor (arto), neogothic minor, supraminor, submajor, neogothic major, and ultramajor (tendo) thirds and sevenths. This is in contrast to systems like 31edo, where there are subminor, minor, neutral, major, and supermajor thirds and sevenths. This is due to 29edo representing 2.3.7/5.11/5.13/5 well, and ratios between two primes greater than 3 tend to land between interval categories of intervals in a 2.3.p subgroup. For example, 2.3.5 intervals are major/minor, 2.3.7 intervals are supermajor/subminor, and 2.3.11 and 2.3.13 intervals are artoneutral/tendoneutral. 31edo, on the other hand, represents 2.3.5.7.11 well, and thus has interval categories represented in 2.3.5, 2.3.7, and 2.3.11. It can also be seen from the fact that the 29&31 temperament, tritonic, maps seconds and thirds to large numbers of generators, so they differ more in tuning between the systems.

Subsets and Supersets

29edo is the 10th prime edo, following 23edo and coming before 31edo. Its supersets 58edo and 87edo correct many of the higher primes.

Intervals

See also: 29edo solfege

Degree	Cents	Approx. Ratios of the 13-limit	Chain-of-fifths notation	Ups and downs notation (EUs: v3A1 and ^d2)			SKULO interval names and notation (K or S = 1)
0	0.000	1/1	unison	P1	unison	D	P1	unison	D
1	41.379	33/32, 40/39, 45/44, 81/80, 64/63	negative diminished 2nd, double diminished 3rd	^1, vm2	up unison, downminor 2nd	^D, vEb	K1, S1, sm2	comma-wide unison, super unison, subminor 2nd	KD, SD, sEb
2	82.759	21/20, 22/21, 135/128, 256/243	minor 2nd	m2	minor 2nd	Eb	m2	minor 2nd	Eb
3	124.138	16/15, 15/14, 14/13, 13/12	augmented 1sn	^m2	upminor 2nd	^Eb	Km2	classic minor 2nd	KEb
4	165.517	12/11, 11/10, 10/9	diminished 3rd	vM2	downmajor 2nd	vE	kM2	comma-narrow/classic major 2nd	kE
5	206.897	9/8	major 2nd	M2	major 2nd	E	M2	major 2nd	E
6	248.276	8/7, 7/6, 15/13	double diminished 4th, double augmented 1sn	^M2, vm3	upmajor 2nd, downminor 3rd	^E, vF	SM2, sm3	supermajor 2nd, subminor 3rd	SE, sF
7	289.655	13/11, 32/27	minor 3rd	m3	minor 3rd	F	m3	minor 3rd	F
8	331.034	6/5, 11/9	augmented 2nd	^m3	upminor 3rd	^F	Km3	classic minor 3rd	KF
9	372.414	5/4, 16/13	diminished 4th	vM3	downmajor 3rd	vF#	kM3	classic major 3rd	kF#
10	413.793	14/11, 81/64	major 3rd	M3	major 3rd	F#	M3	major 3rd	F#
11	455.172	9/7, 13/10	double diminished 5th, double augmented 2nd	^M3, v4	upmajor 3rd down 4th	^F#, vG	SM3, s4	supermajor 3rd, sub 4th	SF#, sG
12	496.552	4/3	perfect 4th	P4	4th	G	P4	perfect 4th	G
13	537.931	11/8, 15/11	augmented 3rd	^4	up 4th	^G	K4	comma-wide 4th	KG
14	579.310	7/5, 18/13	diminished 5th	vA4, d5	downaug 4th, dim 5th	vG#, Ab	kA4, d5	comma-narrow aug 4th, dim 5th	kG#, Ab
15	620.690	10/7, 13/9	augmented 4th	A4, ^d5	aug 4th, updim 5th	G#, ^Ab	A4, Kd5	aug 4th, comma-wide dim 5th	G#, KAb
16	662.069	16/11, 22/15	diminished 6th	v5	down 5th	vA	k5	comm-narrow 5th	kA
17	703.448	3/2	perfect 5th	P5	5th	A	P5	perfect 5th	A
18	744.828	14/9, 20/13	double augmented 4th, double diminished 7th	^5, vm6	up 5th, downminor 6th	^A, vBb	S5, sm6	super 5th, subminor 6th	SA, sBb
19	786.207	11/7, 128/81	minor 6th	m6	minor 6th	Bb	m6	minor 6th	Bb
20	827.586	8/5, 13/8	augmented 5th	^m6	upminor 6th	^Bb	Km6	classic minor 6th	KBb
21	868.966	5/3, 18/11	diminished 7th	vM6	downmajor 6th	vB	kM6	classic major 6th	kB
22	910.345	22/13, 27/16	major 6th	M6	major 6th	B	M6	major 6th	B
23	951.724	7/4, 12/7, 26/15	double augmented 5th, double diminished 8ve	^M6, vm7	upmajor 6th, downminor 7th	^B, vC	SM6, sm7	supermajor 6th, subminor 7th	SB, sC
24	993.103	16/9	minor 7th	m7	minor 7th	C	m7	minor 7th	C
25	1034.483	11/6, 20/11, 9/5	augmented 6th	^m7	upminor 7th	^C	Km7	comma-wide/classic minor 7th	KC
26	1075.862	15/8, 28/15, 13/7, 24/13	diminished 8ve	vM7	downmajor 7th	vC#	kM7	classic major 7th	kC#
27	1117.241	40/21, 21/11, 256/135, 243/128	major 7th	M7	major 7th	C#	M7	major 7th	C#
28	1158.621	64/33, 39/20, 88/45, 160/81, 63/32	diminished 9th, double augmented 6th	^M7, v8	upmajor 7th, down 8ve	^C#, vD	SM7, s8	supermajor 7th, comma-narrow 8ve, sub 8ve	SC#, kD, sD
29	1200.000	2/1	octave	P8	8ve	D	P8	8ve	D

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

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

All 29edo chords can be named using ups and downs. Alterations are always enclosed in parentheses, additions never are. An up or down 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). Here are the zo, gu, 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	0-6-17	C vEb G	Cvm	C downminor
gu	10:12:15	0-8-17	C ^Eb G	C^m	C upminor
yo	4:5:6	0-9-17	C vE G	Cv	C downmajor or C down
ru	14:18:21	0-11-17	C ^E G	C^	C upmajor or C up

For a more complete list, see Ups and downs notation #Chords and Chord Progressions.

Notation

Standard notation

29edo can be notated three different ways. Using only sharps and flats, the chromatic scale from C is:

C – B♯ – D♭ – C♯ – B𝄪/E𝄫 – D – C𝄪/F𝄫 – E♭ – D♯ – F♭ – E – D𝄪/G𝄫 – F – E♯ – G♭ – F♯ – E𝄪/A𝄫 – G – F𝄪 – A♭ – G♯ – B𝄫 – A – G𝄪/C𝄫 – B♭ – A♯ – C♭ – B – A𝄪/D𝄫 – C

Here, six pairs of enharmonic equivalents exist:

• B𝄪 = E𝄫
• E𝄪 = A𝄫
• A𝄪 = D𝄫
• D𝄪 = G𝄫
• G𝄪 = C𝄫
• C𝄪 = F𝄫

Stein–Zimmermann–Gould notation

Since a sharp raises by three steps, 29edo is a good candidate for Stein–Zimmermann–Gould notation, using sharps and flats with arrows similar to 22edo:

Step offset	0	1	2	3	4	5	6	7
Sharp symbol								
Flat symbol								

Note that C♯ is enharmonic to D⁠ ⁠, and D♭ is enharmonic to C⁠ ⁠.

If arrows are taken to have their own layer of enharmonic spellings, then in some cases notes may be best spelled with double arrows.

Kite's ups and downs notation

29edo can also be notated with Kite's ups and downs, spoken as up, downsharp, sharp, etc. Note that downsharp (v#) can be respelled as dup (^^).

Step offset	0	1	2	3	4	5	6	7
Sharp symbol
Flat symbol

Sagittal notation

This notation uses the same sagittal sequence as edos 15 and 22.

Evo flavor

Revo flavor

Approximation to JI

15-odd-limit intervals approximated in 29edo

Interval mappings

The following table shows how 15-odd-limit intervals are represented in 29edo. Prime harmonics are in bold.

As 29edo is consistent in the 15-odd-limit, the mappings by direct approximation and through the patent val are identical.

15-odd-limit intervals in 29edo

Interval and complement	Error (abs, ¢)	Error (rel, %)
1/1, 2/1	0.000	0.0
13/11, 22/13	0.445	1.1
11/10, 20/11	0.513	1.2
15/13, 26/15	0.535	1.3
13/10, 20/13	0.958	2.3
15/11, 22/15	0.980	2.4
3/2, 4/3	1.493	3.6
9/8, 16/9	2.987	7.2
7/5, 10/7	3.202	7.7
11/7, 14/11	3.715	9.0
13/7, 14/13	4.160	10.1
15/14, 28/15	4.695	11.3
15/8, 16/15	12.407	30.0
13/8, 16/13	12.941	31.3
11/8, 16/11	13.387	32.4
5/4, 8/5	13.900	33.6
13/12, 24/13	14.435	34.9
11/6, 12/11	14.880	36.0
5/3, 6/5	15.393	37.2
13/9, 18/13	15.928	38.5
11/9, 18/11	16.373	39.6
9/5, 10/9	16.886	40.8
7/4, 8/7	17.102	41.3
7/6, 12/7	18.595	44.9
9/7, 14/9	20.088	48.5

Regular temperament properties

Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Tuning error
				Absolute (¢)	Relative (%)
2.3	[46 -29⟩	[⟨29 46]]	−0.47	0.47	1.14
2.3.5	250/243, 16875/16384	[⟨29 46 67]]	+1.68	3.07	7.41
2.3.5.7	49/48, 225/224, 250/243	[⟨29 46 67 81]]	+2.78	3.28	7.91
2.3.5.7.11	49/48, 55/54, 100/99, 225/224	[⟨29 46 67 81 100]]	+3.00	2.97	7.15
2.3.5.7.11.13	49/48, 55/54, 100/99, 105/104, 225/224	[⟨29 46 67 81 100 107]]	+3.09	2.71	6.54
2.3.5.7.11.13.19	49/48, 55/54, 65/64, 77/76, 100/99, 105/104	[⟨29 46 67 81 100 107 123]]	+2.91	2.55	6.16
2.3.5.7.11.13.19.23	49/48, 55/54, 65/64, 70/69, 77/76, 100/99, 105/104	[⟨29 46 67 81 100 107 123 131]]	+2.76	2.42	5.85

• 29et (29g val) has a lower relative error than any previous equal temperament in the 23-limit. The next equal temperament doing better in this subgroup is 46.
• 29et does well in the no-17 19-limit and no-17 23-limit, being consistent to the no-17 23-odd-limit. However, 15edo is lower in relative error in both these subgroups than 29.

Commas

29et tempers out the following commas. This assumes the patent val ⟨29 46 67 81 100 107]. Cent values are rounded to 5 digits.

Prime limit	Ratio	Monzo	Cents	Color name	Name(s)
3	(28 digits)	[46 -29⟩	43.31	Wa-29	29-comma, mystery comma
5	78125/73728	[-13 -2 7⟩	100.29	Lasepyo	Wesley comma
5	16875/16384	[-14 3 4⟩	51.12	Laquadyo	Negri comma, double augmentation diesis
5	250/243	[1 -5 3⟩	49.17	Triyo	Porcupine comma, maximal diesis
5	(14 digits)	[16 -13 2⟩	47.21	Sasa-yoyo	Immunity comma
5	32805/32768	[-15 8 1⟩	1.95	Layo	Schisma
7	525/512	[-9 1 2 1⟩	43.41	Lazoyoyo	Avicennma, Avicenna's enharmonic diesis
7	49/48	[-4 -1 0 2⟩	35.70	Zozo	Semaphoresma, slendro diesis
7	686/675	[1 -3 -2 3⟩	27.99	Trizo-agugu	Senga
7	64827/64000	[-9 3 -3 4⟩	22.23	Laquadzo-atrigu	Squalentine comma
7	3125/3087	[0 -2 5 -3⟩	21.18	Triru-aquinyo	Gariboh comma
7	50421/50000	[-4 1 -5 5⟩	14.52	Quinzogu	Trimyna comma
7	4000/3969	[5 -4 3 -2⟩	13.47	Rurutriyo	Octagar comma
7	225/224	[-5 2 2 -1⟩	7.71	Ruyoyo	Marvel comma, septimal kleisma
7	5120/5103	[10 -6 1 -1⟩	5.76	Saruyo	Hemifamity comma
7	(16 digits)	[25 -14 0 -1⟩	3.80	Sasaru	Garischisma
11	55/54	[-1 -3 1 0 1⟩	31.77	Loyo	Telepathma
11	100/99	[2 -2 2 0 -1⟩	17.40	Luyoyo	Ptolemisma
11	121/120	[-3 -1 -1 0 2⟩	14.37	Lologu	Biyatisma
11	896/891	[7 -4 0 1 -1⟩	9.69	Saluzo	Pentacircle comma
11	441/440	[-3 2 -1 2 -1⟩	3.93	Luzozogu	Werckisma
11	4000/3993	[5 -1 3 0 -3⟩	3.03	Trithuyo	Wizardharry comma
13	65/64	[-6 0 1 0 0 1⟩	26.84	Thoyo	Wilsorma
13	91/90	[-1 -2 -1 1 0 1⟩	19.13	Thozogu	Superleap comma, biome comma
13	105/104	[-3 1 1 1 0 -1⟩	16.57	Thuzoyo	Animist comma
13	275/273	[0 -1 2 -1 1 -1⟩	12.64	Thuloruyoyo	Gassorma
13	352/351	[5 -3 0 0 1 -1⟩	4.93	Thulo	Minor minthma

Rank-2 temperaments

• List of 29et rank two temperaments by badness

Table of rank-2 temperaments by generator

Periods per 8ve	Generator*	Cents*	Associated ratio*	Temperament
1	2\29	82.8	21/20	Nautilus
1	3\29	124.1	14/13	Negri / negril / negroni
1	4\29	165.5	11/10	Porky / coendou
1	5\29	206.9	9/8	Baldy
1	6\29	248.3	15/13	Immunity / immune Hemigari
1	7\29	289.7	13/11	Gariberttet
1	8\29	331.034	23/19	Rarity
1	9\29	372.4	5/4	Sephiroth
1	10\29	413.8	9/7	Roman
1	11\29	455.2	13/10	Ammonite
1	12\29	496.6	4/3	Garibaldi / andromeda Leapday
1	13\29	537.9	15/11	Wilsec
1	14\29	579.3	7/5	Tritonic

* octave-reduced form, reduced to the first half-octave

The Tetradecatonic System

A variant of porcupine supported in 29edo is nautilus, which splits the porcupine generator in half (tempering out 49:48 in the process), thus resulting in a different mapping for 7 than standard porcupine. Nautilus also extends to the 13-limit much more easily than does standard porcupine.

The mos Nautilus[14] contains both "even" tetrads (approximating 4:5:6:7 or its inverse) as well as "odd" tetrads (approximating the "Bohlen-Pierce-like" chord 9:11:13:15, or its inverse). Both types are recognizable and consonant, if somewhat heavily tempered. Moreover, one of the four types of tetrads may be built on each scale degree of Nautilus[14], thus there are as many chords as there are notes, so Nautilus[14] has a "circulating" quality to it with as much freedom of modulation as possible. To be exact, there are 4 "major-even", 4 "minor-even", 3 "major-odd", and 3 "minor-odd" chords.

Nautilus[14] scale (Lsssssssssssss) in 29edo

14-note mosses are worth looking at because taking every other note of them gives a heptatonic, and in many cases diatonic-like, scale. Nautilus[14] is no exception; although the resulting porcupine "diatonic" scale sounds somewhat different from diatonic scales generated from fifths, it can still provide some degree of familiarity. Furthermore, every diatonic chord progression will have at least one loose analogue in Nautilus[14], although the chord types might change (for instance, it is possible to have a I–IV–V chord progression where the I is major-odd, and the IV and V are both major-even; the V in this case being on a narrow or "odd" fifth rather than a perfect or "even" fifth).

The fact that the generator size is also a step size means that nautilus makes a good candidate for a generalized keyboard; the fingering of Nautilus[14] becomes very simple as a result, perhaps even simpler than with traditional keyboards, despite there being more notes.

If one can tolerate the tuning error (which is roughly equal to that of 12edo, albeit in the opposite direction for the 5- and 7-limits), this tetradecatonic scale is worth exploring. 29edo is often neglected since it falls so close to the much more popular and well-studied 31edo, but 29 does have its own advantages, and this is one of them.

Nicetone

29edo is not a meantone system, but it could nonetheless be used as a basis for common-practice music if one considers the superfourth as a consonant, alternative type of fourth, and the 11:13:16 as an alternative type of consonant "doubly minor" triad. We can then use a diatonic scale such as 5435453 (which resembles Didymus' 5-limit JI diatonic scale, but with the syntonic comma being exaggerated in size). This scale has a very similar harmonic structure to a meantone diatonic scale, except that one of its minor triads is doubly-minor.

Such a scale could be called "Nicetone" as a play on meantone. Since it preserves most of the same 5-limit relationships, nicetone is only slightly xenharmonic (in contrast to superpyth, which is quite blatantly so). The fact that 29edo's superfourth is within a cent of 15:11, and its 13:11 is within half a cent of a just 13:11, are both happy accidents. One just has to make sure that one is using a timbre that allows these higher-limit harmonic relationships to sound apparent and consonant enough to substitute for their simpler counterparts. The nicetone scale is also the cradle of the superdiatonic scales 522352253 and 3243324323 in between the leapfrog diatonic and chromatic scales.

Nicetone scale 5435453 and cadence in 29edo

Octave stretch or compression

29edo's primes 5, 7, 11 and 13 are all tuned flat and the 3 has relatively little error, so 29edo can benefit from octave stretching. Some stretched-octave 29edo tunings include 116zpi or 96ed10.

Scales

MOS scales

Main article: List of MOS scales in 29edo

Important MOSes include:

• Leapfrog diatonic 5L 2s 5552552 (17\29, 1\1)
• Leapfrog chromatic 5L 7s 3232323223232322 (17\29, 1\1)
• Porcupine 1L 6s 4444445 (4\29, 1\1)
• Porcupine 7L 1s 44444441 (4\29, 1\1)
• Negri 1L 8s 333333335 (3\29, 1\1)
• Negri 9L 1s 3333333332 (3\29, 1\1)
• Semaphore 4L 1s 56666 (6\29, 1\1)
• Semaphore 5L 4s 551515151 (6\29, 1\1)
• Semaphore 5L 9s 41411411411411 (6\29, 1\1)
• Nautilus 1L 13s 22222222222223 (2\29, 1\1)
• Nautilus 14L 1s 222222222222221 (2\29, 1\1)

Well temperaments

• George Secor's 29-tone high tolerance temperament

Approximations of 12edo scales

• Akebono I: 5 2 10 5 7
• Blues Aeolian Hexatonic: 7 5 3 2 2 10
• Blues Aeolian Pentatonic I: 7 5 5 2 10
• Blues Aeolian Pentatonic II: 7 10 2 5 5
• Blues Dorian Hexatonic: 7 5 5 5 2 6
• Blues Dorian Pentatonic: 7 10 5 2 5
• Blues Dorian Septatonic: 7 5 3 2 5 2 5
• Blues Pentachordal: 5 2 5 3 2 12
• Dominant Pentatonic: 5 5 7 7 5
• Dorian: 5 2 5 5 5 2 5
• Double Harmonic: 2 8 2 5 2 8 2
• Hirajoshi: 5 2 10 2 10
• Locrian (modified): 2 5 5 3 4 5 5
• Lydian: 5 5 5 2 5 5 2
• Major: 5 5 2 5 5 5 2
• Minor: 5 2 5 5 2 5 5
• Minor Harmonic: 5 2 5 5 2 8 2
• Minor Hexatonic: 5 2 5 5 7 5
• Minor Melodic: 5 2 5 5 5 5 2
• Minor Pentatonic: 7 5 5 7 5
• Mixolydian: 5 5 2 5 5 2 5
• Mixolydian Pentatonic: 10 2 5 7 5
• Phrygian: 2 5 5 5 2 5 5
• Phrygian Dominant: 2 8 2 5 2 5 5
• Phrygian Dominant Hexatonic: 2 8 2 5 7 5
• Phrygian Dominant Pentatonic: 10 2 5 2 10
• Phrygian Pentatonic: 2 5 10 2 10
• Picardy Pentatonic: 5 5 5 2 10

Other notable scales

• Bridgetown9
• Bridgetown14
• Escala Tonal de 17 tonos - Charles Loli
• 5-limit / Pinetone major pentatonic: 5 4 8 4 8
• 5-limit / Pinetone minor pentatonic: 8 4 5 8 4
• Palace (subset of Porky[22]): 4 3 5 5 4 3 5
• Marvel augmented hexatonic (subset of Negri[9]): 6 3 8 3 6 3
• Marvel double harmonic hexatonic (subset of Negri[9]): 3 6 3 8 6 3, 3 6 8 3 6 3
• Marvel double harmonic major (subset of Negri[9]): 3 6 3 5 3 6 3
• Nicetone, Zarlino/Ptolemy, "JI" major: 5 4 3 5 4 5 3
• Nicetone, inverse of Zarlino/Ptolemy, "JI" minor: 5 3 4 5 3 5 4
• 5-limit melodic minor: 5 3 4 5 4 5 3
• 5-limit harmonic minor: 5 3 4 5 3 6 3
• 5-limit harmonic major (inverse of 5-limit harmonic major): 5 4 3 5 3 6 3
• tetrachordal 5-limit major: 5 4 3 5 5 4 3
• tetrachordal 5-limit minor (inverse of tetrachordal 5-limit major): 5 3 4 5 5 3 4
• chromatic tetrachord octave species: 2 8 2 5 2 8 2, 8 2 2 5 8 2 2, 2 2 8 5 2 2 8
• Blackdye / syntonic dipentatonic: 1 4 3 4 1 4 3 4 1 4
• Blackville / Marvel dipentatonic: 2 3 4 3 2 3 4 3 2 3]

Instruments

Guitar 29EDO from Peru - Charles Loli and Antonio Huamani

Bass 29EDO from Peru - Charles Loli and Antonio Huamani

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• Lumatone mapping for 29edo

Music

Modern renderings

Johann Sebastian Bach

• Contrapunctus 4 from The Art of Fugue, BWV 1080 (1742–1749) – rendered by Claudi Meneghin (2024)
• Contrapunctus 11 from The Art of Fugue, BWV 1080 (1742–1749) – rendered by Claudi Meneghin (2024)
• BACH - RICERCAR a 6 from the Musical Offering, tuned into 29-EDO, BWV 1079 (1742-1749) - rendered by Claudi Meneghin (2025)
• Bach, Art of Fugue: Contrapunctus 11, tuned into 29-edo (harpischord) (1740-1746) - rendered by Claudi Meneghin (2025)
• BACH, NEVERENDING CANON, but it has the SHEPARD EFFECT and is tuned into 29edo (1742-1749) - rendered by Claudi Meneghin (2025)

Nicolaus Bruhns

• Prelude in E Minor "The Great" – rendered by Claudi Meneghin (2023)
• Prelude in E Minor "The Little" – rendered by Claudi Meneghin (2024)

Kate Bush

• Army Dreamers [short clip] (1980) - microtonal cover in 29edo by Bryan Deister (2025)

C418

• Cat (2011) - microtonal cover in 29edo by Bryan Deister (2026)

Dorian Concept

• Hide (2023/2024) – microtonal cover in 29edo by Bryan Deister (2025)

Alan Fennah as "Alternative Radio" (see Buster)

• Concertina Ballerina (1983) – microtonal cover in 29edo by Bryan Deister (2026)

Toby Fox

• A Cyber's World via Deltarune Chapter 2 (2021) – microtonal cover in 29edo by Bryan Deister (2023)
• Dialtone via Deltarune Chapter 2 (2021) – microtonal cover in 29edo by Bryan Deister (2024)

Bart Howard

• Fly Me to the Moon (29-TET) microtonal cover] (1954) – microtonal cover in 29edo by (Stephen Weigel on Lumatone/soft synthesizer and Clarissa on trumpet) (2026)
  • (original performance video)
  • (transcription)

Kikiyama (via Yume 2kki)

• Lotus Waters (2004) - microtonal cover in 29edo by Bryan Deister (2025)

King Crimson

• Discipline - microtonal cover in 29edo by Bryan Deister (2025)

James Roach

• Pipeorgankind (2012) – microtonal cover in 29edo by Bryan Deister (2024) (the title of the microtonal cover video also includes "Homestuck", but this appears to be an error)

21st century

Charles Loli A. (site^{[dead link]})

• Mp3 29EDO - Escala tonal de 17 notas ^{[dead link]}

CellularAutomaton

• Minnow (2024)

Bryan Deister

• Glass Animals - Life Itself (2023)
• microtonal improvisation in 29edo (2023)
• 29edo groove (2025)
• an idea in 29edo (2026)

duckapus

• Gen 28: Musicbox (2024)

E8 Heterotic

• Glaukos Circuit (2019) – chiptune

Pedro Laranjeira Finisterra

• Submerged (2024)

Francium

• "Chill Bells" from Melancholie (2023) Spotify | Bandcamp | YouTube
• from XenRhythms (2024)
  • "All 29" – Spotify | Bandcamp | YouTube
  • "Do Not Immerse Yourself In Fire Or Water" – Spotify | Bandcamp | YouTube – in Immunity[14], 29edo tuning
• Plane Sonatina No. 1 (2025)
• Strank Running (2025)

groundfault

• "The Lake Reflects a Black Sky" from A New Dusk (2024) – Bandcamp | YouTube (0:00–2:38) – in part, the rest being in 31edo and 20edo

Igliashon Jones

• Paint in the Water 29
• Nautilus Reverie
• Howling of the Holy

Budjarn Lambeth

• 29edo Porky15 Improvisation (2024)

Claudi Meneghin

• Porcupine Canon 3-in-1 on the Lament Bass (29EDO) (2026)

NullPointerException Music

• "Chamber", from Edolian (2020)

Mats Öljare

• The Crowning Song ^{[dead link]}
• Nine Days Later ^{[dead link]}
• Stranded at Sea ^{[dead link]}

Ray Perlner

• 29 EDO Fugue in Negri 9 Lssssssss "Austro-Hungarian Minor"
• Fugue for 29EDO Piano in Porcupine 7 ssLssss "Zebrian"

Chris Vaisvil

• Route 14 in Bridgetown

Randy Wells (Australopithecine XEN)

• Toy Shoppe (2024)
• The Sea of Swirly Twirly Gumdrops (2024)

Xotla

• "Nodal Plane" from Micro Biological (2019) – Spotify | Bandcamp | YouTube – in part, the other part being in 22edo
• "Microclusters" from Microtonal Allsorts (2023) – Spotify | Bandcamp | YouTube

See also

• Unque's approach
• Extraclassical tonality
• 67ed5 – octave-stretched 29edo, improves harmonics 5.7.11.13.17 but damages 2.3