17edo: Difference between revisions

← 16edo 17edo 18edo →
Prime factorization	17 (prime)
Step size	70.5882 ¢
Fifth	10\17 (705.882 ¢); (semiconvergent)
Semitones (A1:m2)	2:1 (141.2 ¢ : 70.59 ¢)
Consistency limit	3
Distinct consistency limit	3

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Latest revision as of 09:14, 21 May 2026

17 equal divisions of the octave (abbreviated 17edo or 17ed2), also called 17-tone equal temperament (17tet) or 17 equal temperament (17et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 17 equal parts of about 70.6 ¢ each. Each step represents a frequency ratio of 2^1/17, or the 17th root of 2.

English Wikipedia has an article on:

17 equal temperament

Theory

17edo is the next smallest edo to have a diatonic perfect fifth after 12edo, and is quite popular for that reason. The perfect fifth is around 4 cents sharp of just, and around 6 cents sharp of 12edo's, lending itself to a diatonic scale with more constrasting large and small steps, so it can be seen as a tuning that emphasizes the hardness of Pythagorean tuning rather than mellowing it out as in meantone. It completely misses harmonic 5, with 5/4 and 6/5 both being about halfway between its steps, but it approximates harmonics 7, 11, 13, and 23 acceptably, with a sharp tuning for all of them. It can thus be treated as a temperament of the 2.3.25.7.11.13.23 subgroup or any of its subsets, where it is quite accurate for its size.

A notable comma it tempers out is 64/63, which equates the harmonic seventh 7/4 with the pythagorean minor seventh 16/9, while its patent val does not temper out 81/80. This makes 17edo by default a superpythagorean system rather than a meantone one, being very close to 1/7-comma superpyth. Other commas it tempers out can be found in the #Commas section, each of which has its own effect on the structure of 17edo. If one wants to approximate JI with prime 5, then 17edo would not be the best option, and it would be better to use other systems like 19edo, 22edo, 27edo, or 31edo instead. That said, the 17c val (written using wart notation) does temper out 81/80 (while improving consistency as shown below in #Approximation to JI), while still tempering out 64/63, thus placing it on the meantone spectrum with the dominant extension.

As a means of extending harmony

The diatonic major triad, which is 0–6–10 steps, is quite dissonant compared to 4:5:6, as the major third is over 37 cents sharp from the traditional 5/4, and is instead closer to 9/7 or 14/11. Instead, a different construction based on the 2.3.7 subgroup follows naturally from its support of superpyth, and may be preferred. Such chords include the tetrads 6:7:8:9 and its utonal inverse, realized in 17edo as 0–4–7–10 and 0–3–6–10, respectively, in addition to the sus2-4 chord, realized as 0–3–7–10. Possible chromatic alterations include but are not limited to an approximation of 12:13:16:18, 0–2–7–10, and an approximation of 8:9:11:12, 0–3–8–10. It is important to note that the chromatic semitone in 17edo is 2 steps, rather than 1 step as in 12edo or 19edo. Similarly, the fourth-spanning triad 6:7:8 and its inverse can be used, with their wide voicing realized in 17edo as 0–14–27 and 0–13–27, respectively. Extensions of these chords include 0–12–14–27, representing 8:13:14:24, and 0–13–15–27, representing 7:12:13:21.

Since the intervals of the 2.3.7-subgroup cluster around 5edo, a pentatonic system of interval classification may be preferred over the heptatonic one, with 7/6 becoming a major interval and 8/7~9/8 becoming a minor one.

Of course, scales generated by the perfect fifth are not the only scales 17edo contains. Another type of scale is neutral third scales, which are generated by half a fifth (5\17), and take the mos patterns 4L 3s (mosh) and 7L 3s (dicoid). Other notable scales include that of bleu and glacier (generated by 2\17), and skwares (generated by 6\17). Non-mos scales also exist; a more complete list can be found in the #Scales section.

Because the 5th harmonic is not well approximated, using timbres with attenuated 5th harmonics (and its multiples) may reduce audible beating.

Odd harmonics

Approximation of odd harmonics in 17edo
Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	+3.9	-33.4	+19.4	+7.9	+13.4	+6.5	-29.4	-34.4	-15.2	+23.3	+7.0
Error	Relative (%)	+5.6	-47.3	+27.5	+11.1	+19.0	+9.3	-41.7	-48.7	-21.5	+33.1	+9.9
Steps (reduced)		27 (10)	39 (5)	48 (14)	54 (3)	59 (8)	63 (12)	66 (15)	69 (1)	72 (4)	75 (7)	77 (9)

Approximation of odd harmonics in 17edo (continued)
Harmonic		25	27	29	31	33	35	37	39	41	43	45	47
Error	Absolute (¢)	+3.8	+11.8	+29.2	-15.6	+17.3	-14.0	+31.0	+10.5	-5.5	-17.4	-25.5	-30.2
Error	Relative (%)	+5.4	+16.7	+41.4	-22.1	+24.5	-19.8	+43.9	+14.8	-7.8	-24.7	-36.2	-42.8
Steps (reduced)		79 (11)	81 (13)	83 (15)	84 (16)	86 (1)	87 (2)	89 (4)	90 (5)	91 (6)	92 (7)	93 (8)	94 (9)

Subsets and supersets

17edo is the seventh prime edo, following 13edo and coming before 19edo. It does not contain any nontrivial subset edos, though it contains 17ed4 and 17ed8. 17ed8, built by taking every third step of 17edo, is a system where all odd harmonics up to the 21st are mapped exactly as in 17edo, except for the 11th. Beyond that, the 27th, 31st, 35th, and 39th harmonics are likewise mapped identically.

34edo, which doubles 17edo, provides a great correction to harmonics 5 and 17; while 68edo, which quadruples it, provides additionally the primes 7, 19, and 31.

Intervals

See also: 17edo solfege

#	Cents	Approximate ratios^{[note 1]}	Circle-of-fifths notation^{[note 2]}		Ups and downs notation (EUs: vvA1 and ^d2)			SKULO notation (U = 1)
0	0.0	1/1	Unison	D	unison	P1	D	unison	P1	D
1	70.6	24/23, 25/24, 26/25, 27/26, 28/27	Minor 2nd (Semiaugmented 1sn)	Eb (Dt)	up unison, minor 2nd	^1, m2	Eb	uber unison, minor 2nd	U1, m2	UD, Eb
2	141.2	12/11, 13/12, 14/13, 25/23	Augmented 1sn (Neutral 2nd)	D# (Ed)	augmented 1sn, mid 2nd	A1, ~2	vE	neutral 2nd	N2	UEb, uE
3	211.8	8/7, 9/8, 17/15, 25/22, 26/23	Major 2nd	E	major 2nd	M2	E	major 2nd	M2	E
4	282.4	7/6, 13/11, 20/17	Minor 3rd	F	minor 3rd	m3	F	minor 3rd	m3	F
5	352.9	11/9, 27/22, 16/13, 39/32	Diminished 4th (Neutral 3rd)	Gb (Ft)	mid 3rd	~3	^F	neutral 3rd	N3	UF, uF#
6	423.5	9/7, 14/11, 23/18, 32/25, 51/40	Major 3rd (Semidiminished 4th)	F# (Gd)	major 3rd	M3	F#	major 3rd	M3	F#
7	494.1	4/3, 21/16, 85/64	Perfect 4th	G	perfect 4th	P4	G	perfect 4th	P4	G
8	564.7	11/8, 18/13, 25/18, 32/23	Diminished 5th (Semiaugmented 4th)	Ab (Gt)	mid 4th, diminished 5th	~4, d5	^G, Ab	uber 4th/ neutral 4th	U4/N4	UG
9	635.3	13/9, 16/11, 23/16, 36/25	Augmented 4th (Semidiminished 5th)	G# (Ad)	augmented 4th, mid 5th	A4, ~5	G#, vA	unter 5th/ neutral 5th	u5/N5	uA
10	705.9	3/2, 32/21, 128/85	Perfect 5th	A	perfect 5th	P5	A	perfect 5th	P5	A
11	776.5	11/7, 14/9, 25/16, 36/23, 80/51	Minor 6th (Semiaugmented 5th)	Bb (At)	minor 6th	m6	Bb	minor 6th	m6	Bb
12	847.1	13/8, 18/11, 44/27, 64/39	Augmented 5th (Neutral 6th)	A# (Bd)	mid 6th	~6	vB	neutral 6th	N6	UBb, uB
13	917.6	12/7, 17/10, 22/13	Major 6th	B	major 6th	M6	B	major 6th	M6	B
14	988.2	7/4, 16/9, 23/13, 30/17, 44/25	Minor 7th	C	minor 7th	m7	C	minor 7th	m7	C
15	1058.8	11/6, 13/7, 24/13, 46/25	Diminished 8ve (Neutral 7th)	Db (Ct)	mid 7th	~7	^C	neutral 7th	N7	UC, uC#
16	1129.4	23/12, 25/13, 27/14, 48/25, 52/27	Major 7th (Semidiminished 8ve)	C# (Dd)	major 7th, down 8ve	M7, v8	C#	major 7th, unter octave	M7, u8	C#, uD
17	1200.0	2/1	Octave	D	octave	P8	D	octave	P8	D

↑ Based on treating 17edo as a 2.3.25.7.11.13.85.23 subgroup temperament; other approaches are also possible.
↑ Half-sharps and half-flats (denoted "t" and "d", respectively) can be used to alter the note by a single step, since sharps and flats each span two edosteps. Using half-sharps and half-flats may be preferable for compatibility with the ups-and-downs notation in 34edo, in which an up or down respectively constitute a quarter-sharp or quarter-flat.

Interval quality and chord names in color notation

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

Quality	Color	Monzo format	Examples
minor	zo	(a, b, 0, 1)	7/6, 7/4
minor	fourthward wa	(a, b), b < -1	32/27, 16/9
mid	ilo	(a, b, 0, 0, 1)	11/9, 11/6
mid	lu	(a, b, 0, 0, -1)	12/11, 18/11
major	fifthward wa	(a, b), b > 1	9/8, 27/16
major	ru	(a, b, 0, -1)	9/7, 12/7

All 17edo chords can be named using ups and downs. Here are the zo, ilo and ru triads:

Color of the 3rd	JI chord	Notes as edosteps	Notes of C chord	Written name	Spoken name
zo	6:7:9	0-4-10	C Eb G	Cm	C minor
ilo	18:22:27	0-5-10	C vE G	C~	C mid
ru	14:18:21	0-6-10	C E G	C	C major or C

Alterations are always enclosed in parentheses, additions never are. 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).

0-4-9 = C Eb vG = Cm(v5) = C minor down-five

0-5-9 = C vE vG = C~(v5) = C mid down-five

0-6-11 = C E ^G = C(^5) = C up-five

0-4-10-14 = C Eb G Bb = Cm7 = C minor seven

0-5-10-14 = C vE G Bb = C~,7 = C mid add seven

0-6-10-15 = C E G vB = C,~7 = C add mid-seven

0-5-10-15 = C vE G vB = C~7 = C mid-seven

For a more complete list, see Ups and downs notation #Chords and chord progressions.

Notation

Ups and downs notation

Spoken as up, sharp, upsharp, etc. Note that up can be respelled as downsharp. The gamut runs D, ^D/Eb, D#/vE, E, F etc.

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

Quarter tone notation

Since a sharp raises by 2 steps, 17edo can be notated using quarter-tone accidentals.

Step offset	−4	−3	−2	−1	0	+1	+2	+3	+4
Symbol

Sagittal notation

This notation uses the same sagittal sequence as edos 24, 31, and 38, and is a subset of the notation for 34edo.

Evo and Revo flavors

Alternative Evo flavor

Evo-SZ flavor

Because it contains no Sagittal symbols, this Evo-SZ Sagittal notation is identical to the Stein-Zimmerman notation.

Sagittal songbook diagram

From the appendix to The Sagittal Songbook by Jacob A. Barton, a diagram of how to notate 17edo in the Revo flavor of Sagittal:

3L 4s (mosh) notation

The notation of Neutral[7]. The generator is the perfect 3rd. Notes are denoted as sLsLsLs = DEFGABCD, and raising and lowering by a chroma (L − s), 1 edostep in this instance, is denoted by ♯ and ♭.

#	Cents	Note	Name	Associated ratios
0	0.0	D	Perfect 1sn	1/1
1	70.6	D#	Augmented 1sn	33/32
2	141.2	Eb	Minor 2nd	12/11
3	211.8	E	Major 2nd	9/8
4	282.4	Fb	Diminished 3rd	32/27
5	352.9	F	Perfect 3rd	11/9, 27/22
6	423.5	F#	Augmented 3rd	81/64
7	494.1	G	Minor 4th	4/3
8	564.7	G#	Major 4th	11/8
9	635.3	Ab	Minor 5th	16/11
10	705.9	A	Major 5th	3/2
11	776.5	Bb	Diminished 6th	128/81
12	847.1	B	Perfect 6th	18/11, 44/27
13	917.6	B#	Augmented 6th	27/16
14	988.2	Cb	Minor 7th	16/9
15	1058.8	C	Major 7th	11/6
16	1129.4	Db	Diminished 8ve	64/33
17	1200.0	D	Perfect 8ve	2/1

Approximation to JI

15-odd-limit interval mappings

The following tables show how 15-odd-limit intervals are represented in 17edo. Prime harmonics are in bold; inconsistent intervals are in italics.

15-odd-limit intervals in 17edo (direct approximation, even if inconsistent)
Interval and complement	Error (abs, ¢)	Error (rel, %)
1/1, 2/1	0.000	0.0
13/9, 18/13	1.324	1.9
13/12, 24/13	2.604	3.7
3/2, 4/3	3.927	5.6
11/9, 18/11	5.533	7.8
11/7, 14/11	6.021	8.5
13/8, 16/13	6.531	9.3
13/11, 22/13	6.857	9.7
9/8, 16/9	7.855	11.1
11/6, 12/11	9.461	13.4
9/7, 14/9	11.555	16.4
13/7, 14/13	12.878	18.2
11/8, 16/11	13.388	19.0
7/6, 12/7	15.482	21.9
7/5, 10/7	17.806	25.2
7/4, 8/7	19.409	27.5
15/14, 28/15	21.734	30.8
11/10, 20/11	23.828	33.8
15/11, 22/15	27.755	39.3
9/5, 10/9	29.361	41.6
15/8, 16/15	29.445	41.7
13/10, 20/13	30.685	43.5
5/3, 6/5	33.288	47.2
5/4, 8/5	33.373	47.3
15/13, 26/15	34.612	49.0

15-odd-limit intervals in 17edo (patent val mapping)
Interval and complement	Error (abs, ¢)	Error (rel, %)
1/1, 2/1	0.000	0.0
13/9, 18/13	1.324	1.9
13/12, 24/13	2.604	3.7
3/2, 4/3	3.927	5.6
11/9, 18/11	5.533	7.8
11/7, 14/11	6.021	8.5
13/8, 16/13	6.531	9.3
13/11, 22/13	6.857	9.7
9/8, 16/9	7.855	11.1
11/6, 12/11	9.461	13.4
9/7, 14/9	11.555	16.4
13/7, 14/13	12.878	18.2
11/8, 16/11	13.388	19.0
7/6, 12/7	15.482	21.9
7/4, 8/7	19.409	27.5
15/8, 16/15	29.445	41.7
5/4, 8/5	33.373	47.3
15/13, 26/15	35.976	51.0
5/3, 6/5	37.300	52.8
13/10, 20/13	39.904	56.5
9/5, 10/9	41.227	58.4
15/11, 22/15	42.833	60.7
11/10, 20/11	46.760	66.2
15/14, 28/15	48.855	69.2
7/5, 10/7	52.782	74.8

15-odd-limit intervals by 17c val mapping
Interval and complement	Error (abs, ¢)	Error (rel, %)
1/1, 2/1	0.000	0.0
13/9, 18/13	1.324	1.9
13/12, 24/13	2.604	3.7
3/2, 4/3	3.927	5.6
11/9, 18/11	5.533	7.8
11/7, 14/11	6.021	8.5
13/8, 16/13	6.531	9.3
13/11, 22/13	6.857	9.7
9/8, 16/9	7.855	11.1
11/6, 12/11	9.461	13.4
9/7, 14/9	11.555	16.4
13/7, 14/13	12.878	18.2
11/8, 16/11	13.388	19.0
7/6, 12/7	15.482	21.9
7/5, 10/7	17.806	25.2
7/4, 8/7	19.409	27.5
15/14, 28/15	21.734	30.8
11/10, 20/11	23.828	33.8
15/11, 22/15	27.755	39.3
9/5, 10/9	29.361	41.6
13/10, 20/13	30.685	43.5
5/3, 6/5	33.288	47.2
15/13, 26/15	34.612	49.0
5/4, 8/5	37.216	52.7
15/8, 16/15	41.143	58.3

Selected 13-limit intervals

Tuning by ear

17edo is very close to a circle of seventeen 25/24 chromatic semitones: (25/24)¹⁷ is only 1.43131 cents sharp of an octave. This means that if you can tune seventeen 25/24's accurately (by say, tuning 5/4 up, 3/2 down and 5/4 up, taking care to minimize the error at each step), you have a shot at approximating 17edo within melodic just noticeable difference.

Regular temperament properties

Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Tuning error
Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Absolute (¢)	Relative (%)
2.3	[27 -17⟩	[⟨17 27]]	−1.24	1.24	1.76
2.3.7	64/63, 17496/16807	[⟨17 27 48]]	−3.13	2.85	4.05
2.3.7.11	64/63, 99/98, 243/242	[⟨17 27 48 59]]	−3.31	2.49	3.54
2.3.7.11.13	64/63, 78/77, 99/98, 144/143	[⟨17 27 48 59 63]]	−3.00	2.31	3.28

17et is lower in relative error than any previous equal temperaments in the no-5 11- and 13-limit. The next equal temperaments doing better in these subgroups are 41 and 207, respectively.

Uniform maps

13-limit uniform maps between 16.8 and 17.2
Min. size	Max. size	Wart notation	Map
16.7196	16.8899	17def	⟨17 27 39 47 58 62]
16.8899	16.9103	17de	⟨17 27 39 47 58 63]
16.9103	16.9198	17d	⟨17 27 39 47 59 63]
16.9198	17.0117	17	⟨17 27 39 48 59 63]
17.0117	17.1601	17c	⟨17 27 40 48 59 63]
17.1601	17.1994	17cff	⟨17 27 40 48 59 64]
17.1994	17.2760	17ceeff	⟨17 27 40 48 60 64]

Commas

17et tempers out the following commas. (Note: This assumes patent val ⟨17 27 39 48 59 63 69 72 77], cent values rounded to 1/100 of a cent.)

Prime limit	Ratio^{[note 1]}	Monzo	Cents	Color name	Name
3	(18 digits)	[27 -17⟩	66.76	Sasawa	Gothic comma
5	25/24	[-3 -1 2⟩	70.76	Yoyo	Dicot comma
5	32805/32768	[-15 8 1⟩	1.95	Layo	Schisma
7	64/63	[6 -2 0 -1⟩	27.26	Ru	Septimal comma
7	525/512	[-9 1 2 1⟩	43.41	Lazoyoyo	Avicennma
7	245/243	[0 -5 1 2⟩	14.19	Zozoyo	Sensamagic comma
7	1728/1715	[6 3 -1 -3⟩	13.07	Triru-agu	Orwellisma
7	17496/16807	[3 7 0 -5⟩	69.56	Quinru	Bleu comma
7	19683/19208	[-3 9 0 -4⟩	42.29	Laquadru	Skwares comma
7	(12 digits)	[-6 -8 2 5⟩	1.12	Quinzo-ayoyo	Wizma
11	45/44	[-2 2 1 0 -1⟩	38.91	Luyo	Cake comma
11	99/98	[-1 2 0 -2 1⟩	17.58	Loruru	Mothwellsma
11	896/891	[7 -4 0 1 -1⟩	9.69	Saluzo	Pentacircle comma
11	243/242	[-1 5 0 0 -2⟩	7.14	Lulu	Rastma, neutral thirds comma
11	385/384	[-7 -1 1 1 1⟩	4.50	Lozoyo	Keenanisma
13	40/39	[3 -1 1 0 0 -1⟩	43.83	Thuyo	Unintendo comma
13	65/64	[-6 0 1 0 0 1⟩	26.84	Thoyo	Wilsorma
13	78/77	[1 1 0 -1 -1 1⟩	22.34	Tholuru	Negustma
13	144/143	[4 2 0 0 -1 -1⟩	12.06	Thulu	Grossma
13	169/168	[-3 -1 0 -1 0 2⟩	10.27	Thothoru	Buzurgisma, dhanvantarisma
13	352/351	[5 -3 0 0 1 -1⟩	4.93	Thulo	Major minthma
13	364/363	[2 -1 0 1 -2 1⟩	4.76	Tholuluzo	Minor minthma
13	512/507	[9 -1 0 0 0 -2⟩	16.99	Thuthu	Tridecimal neutral thirds comma
13	1352/1331	[3 0 0 0 -3 2⟩	27.10	Bithotrilu	Lovecraft comma
13	2197/2187	[0 -7 0 0 0 3⟩	7.90	Satritho	Threedie
23	162/161	[1 4 0 -1 0 0 0 0 -1⟩	10.72	Twethuru	Minor kirnbergerisma
23	208/207	[4 -2 0 0 0 1 0 0 -1⟩	8.34	Twethutho	Vicetone comma
23	253/252	[-2 -2 0 -1 1 0 0 0 1⟩	6.86	Twetholoru	Middle neutravicema
23	529/528	[-4 -1 0 0 -1 0 0 0 2⟩	3.28	Bitwetho-alu	Preziosisma
23	736/729	[5 -6 0 0 0 0 0 0 1⟩	16.54	Satwetho	23-limit Tenney/Cage comma (HEJI)

↑ Ratios longer than 10 digits are presented by placeholders with informative hints.

Note that due to the inaccurate prime 5, the rather large commas 25/24, 525/512, 45/44, and 40/39 are all tempered out by 17edo's patent val.

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods per 8ve	Generator	Cents	Associated ratio	Temperament
1	2\17	141.18	13/12	Bleu / progression (17c) / glacier
1	3\17	211.76	8/7~9/8	Machine
1	3\17	211.76	26/23	Shoal (trivial tuning)
1	4\17	282.35	13/11	Huxley / lovecraft / subklei (17c)
1	5\17	352.94	11/9	Suhajira / neutrominant (17c) / beatles (17c) / dichotic (17) Hemif / mohamaq (17c) / salsa (17)
1	6\17	423.53	9/7	Skwares / squares (17c) / sentinel (17) / sidi (17)
1	7\17	494.12	4/3	Archy / supra / quasisuper (17c) / dominant (17c) / superpyth (17) / schism (17) Fiventeen
1	8\17	564.71	7/5	Lee / liese (17c) / pycnic (17) Progress (17c)

Octave stretch or compression

17edo's approximations of harmonics 3, 7, 11, and 13 are all tempered sharp, so 17edo adapts well to slightly compressing the octave, if that is acceptable. 44ed6, 27edt and 56zpi are good demonstrations of this, where the octaves are flattened by about 1.5, 2.5 cents and 3 cents respectively.

Scales

Antipental blues: 4 3 1 2 4 3
Blues Peruvian: 4 3 1 1 1 4 3
Hydra: 3 3 1 1 2 3 2 1 1
Husayni Ascending: 2 2 3 3 2 2 3
Otonal 17: 3 2 3 2 2 2 3
Scorp: 3 2 3 1 3 2 3
Screamapillar: 3 3 2 2 3 3 1
sLmLs: 2 5 3 5 2

MOS scales

Main article: MOS scales of 17edo

diatonic (leapfrog/archy) 5L 2s 3 3 3 1 3 3 1 (10\17, 1\1)
neutrominant 3L 4s 3 2 3 2 3 2 2 (5\17, 1\1) (dedicated article: 17edo neutral scale)
neutrominant 7L 3s 2 2 2 1 2 2 1 2 2 1 (5\17, 1\1)
squares 3L 5s 1 1 4 1 4 1 4 (6\17, 1\1)
squares 3L 8s 1 3 1 1 3 1 1 3 (6\17, 1\1)
lovecraft 4L 5s 3 1 3 1 3 1 3 1 1 (4\17, 1\1)

Well temperaments

Instruments

Fretted String Instruments

17 note per octave conversion from a "standard" Stratocaster copy - conversion by Brad Smith

17edo soprano Harmony ukulele with a 3D printed fretboard - conversion by Tristan Bay

Keyboards

Lumatone mappings for 17edo are available.

The Striso Board can be tuned in many ways, but as it has 17 notes per octave and is organised in a circle of fifths based layout, it works particularly well with 17edo, letting you play far wider stretches of notes than a standard keyboard.

It is possible to rebuild some standard MIDI keyboards to have 17 note per octave by combining parts from multiple keyboards, as with the finished product shown in the following videos by Stephen Weigel and Chris Vaisvil:

Take This Stone (17-TET microtonal cover) (2025)
DIY microtonal piano - 17 notes per octave (2026)

Music

Main article: 17edo/Music

See also: Category:17edo tracks

YouTube playlist of 17edo pieces
YouTube videos tagged with 17edo

Compositions from the Seventeen Tone Piano Project

Introductory Materials

SeventeenTheory, an introduction to 17edo theory, through the eyes of the SeventeenTonePianoProject.
The 17-tone Puzzle by George Secor, another introduction into 17edo theory.
17edo tetrachords
Proyect 17-Perú ^[forbidden]

[1] Based on treating 17edo as a 2.3.25.7.11.13.85.23 subgroup temperament; other approaches are also possible.

[2] Half-sharps and half-flats (denoted "t" and "d", respectively) can be used to alter the note by a single step, since sharps and flats each span two edosteps. Using half-sharps and half-flats may be preferable for compatibility with the ups-and-downs notation in 34edo, in which an up or down respectively constitute a quarter-sharp or quarter-flat.

[3] Ratios longer than 10 digits are presented by placeholders with informative hints.

[note 1]

[note 2]

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17edo: Difference between revisions

Latest revision as of 09:14, 21 May 2026

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