Revision as of 11:03, 21 August 2025

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The guidelines

These are draft guidelines for what a standard "related tunings"-type section should look like on edo pages, using 36edo as an example.

Useful links for working on this

Temperament Calculator by Sintel (calculates WE & TE)
x31eq Temperament Finder by Graham Breed (calculates TE)

Which tunings should be listed for any given edo

The edo's pure-octaves tuning
1 to 3 nearby edonoi (eg an edt, an edf, an ed5, an ed7, an ed4/3, anything like that)
1 to 2 nearby ZPIs (or any other "infinite harmonics" optimised tuning other than ZPI)
1 to 2 subgroup TE- or WE-optimal tunings, based on the best choice(s) of subgroup for the edo
1 other equal tuning of any kind at all (optional)

Additional guidelines for selecting tunings:

In total, 3 to 8 tunings should be listed.
The selection of tunings should cover a range of meaningfully different tunings (eg with a range of different mappings).

Further instructions

Adding the comparison table at the end is optional.
The number of decimal places to use in the comparison table is up to the user's discretion, as long as it is self-consistent within the table.

Where this section should be placed on an edo page

Synopsis & infobox
(Any foundational introductory subsections)
Theory
- Harmonics
- (Any short subsections about theory unique to the edo)
- Additional properties
- Subsets and supersets
Interval table
Notation
(Any long subsections about theory unique to the edo)
Approximation to JI
Regular temperament properties
- Uniform maps
- Commas
- Rank-2 temperaments
OCTAVE STRETCH OR COMPRESSION
Scales
(Any subsections about practice unique to the edo)
Instruments
Music
See also
Notes
Further reading
External links

Note: This particular set of headings in this order is only how most edo pages look at the moment, but it might be replaced with a more intuitive standard in the future. If and when that happens, this guideline should be modified to adopt that new standard.

Example (36edo)

Octave stretch or compression

What follows is a comparison of stretched- and compressed-octave 36edo tunings.

21edf

Step size: 33.426 ¢, octave size: 1203.351 ¢

Stretching the octave of 36edo by a little over 3 ¢ results in improved primes 5, 11, and 13, but worse primes 2, 3, and 7. This approximates all harmonics up to 16 within 13.4 ¢. The tuning 21edf does this.

Approximation of harmonics in 21edf
Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+3.4	+3.4	+6.7	-11.9	+6.7	+7.2	+10.1	+6.7	-8.6	-6.4	+10.1
Error	Relative (%)	+10.0	+10.0	+20.1	-35.7	+20.1	+21.7	+30.1	+20.1	-25.6	-19.3	+30.1
Steps (reduced)		36 (15)	57 (15)	72 (9)	83 (20)	93 (9)	101 (17)	108 (3)	114 (9)	119 (14)	124 (19)	129 (3)

Approximation of harmonics in 21edf (continued)
Harmonic		13	14	15	16	17	18	19	20	21	22	23	24
Error	Absolute (¢)	+5.2	+10.6	-8.6	+13.4	+8.7	+10.1	-16.7	-5.2	+10.6	-3.1	-13.2	+13.4
Error	Relative (%)	+15.5	+31.7	-25.6	+40.1	+26.1	+30.1	-49.9	-15.6	+31.7	-9.2	-39.5	+40.1
Steps (reduced)		133 (7)	137 (11)	140 (14)	144 (18)	147 (0)	150 (3)	152 (5)	155 (8)	158 (11)	160 (13)	162 (15)	165 (18)

57edt

Step size: 33.368 ¢, octave size: 1201.235 ¢

If one intends to use both 36edo's vals for 5/1 at once, stretching the octave of 36edo by about 1 ¢ optimises 36edo for that dual-5 usage, while also making slight improvements to primes 3, 7, 11, and 13. This approximates all harmonics up to 16 within 16.6 ¢. Several almost-identical tunings do this: 57edt, 93ed6, 101ed7, 155zpi, and the 2.3.7.13-subgroup TE and WE tunings of 36et.

Approximation of harmonics in 57edt
Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+1.2	+0.0	+2.5	+16.6	+1.2	+1.3	+3.7	+0.0	-15.6	-13.7	+2.5
Error	Relative (%)	+3.7	+0.0	+7.4	+49.7	+3.7	+3.9	+11.1	+0.0	-46.6	-41.2	+7.4
Steps (reduced)		36 (36)	57 (0)	72 (15)	84 (27)	93 (36)	101 (44)	108 (51)	114 (0)	119 (5)	124 (10)	129 (15)

Approximation of harmonics in 57edt (continued)
Harmonic		13	14	15	16	17	18	19	20	21	22	23	24
Error	Absolute (¢)	-2.6	+2.5	+16.6	+4.9	+0.1	+1.2	+7.7	-14.3	+1.3	-12.5	+10.6	+3.7
Error	Relative (%)	-7.9	+7.6	+49.7	+14.8	+0.3	+3.7	+23.2	-42.9	+3.9	-37.5	+31.9	+11.1
Steps (reduced)		133 (19)	137 (23)	141 (27)	144 (30)	147 (33)	150 (36)	153 (39)	155 (41)	158 (44)	160 (46)	163 (49)	165 (51)

36edo

Step size: 33.333 ¢, octave size: 1200.000 ¢

Pure-octaves 36edo approximates all harmonics up to 16 within 15.3 ¢.

Approximation of harmonics in 36edo
Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+0.0	-2.0	+0.0	+13.7	-2.0	-2.2	+0.0	-3.9	+13.7	+15.3	-2.0
Error	Relative (%)	+0.0	-5.9	+0.0	+41.1	-5.9	-6.5	+0.0	-11.7	+41.1	+46.0	-5.9
Steps (reduced)		36 (0)	57 (21)	72 (0)	84 (12)	93 (21)	101 (29)	108 (0)	114 (6)	120 (12)	125 (17)	129 (21)

Approximation of harmonics in 36edo (continued)
Harmonic		13	14	15	16	17	18	19	20	21	22	23	24
Error	Absolute (¢)	-7.2	-2.2	+11.7	+0.0	-5.0	-3.9	+2.5	+13.7	-4.1	+15.3	+5.1	-2.0
Error	Relative (%)	-21.6	-6.5	+35.2	+0.0	-14.9	-11.7	+7.5	+41.1	-12.3	+46.0	+15.2	-5.9
Steps (reduced)		133 (25)	137 (29)	141 (33)	144 (0)	147 (3)	150 (6)	153 (9)	156 (12)	158 (14)	161 (17)	163 (19)	165 (21)

36et, 13-limit TE tuning

Step size: 33.304 ¢, octave size: 1198.929 ¢

Compressing the octave of 36edo by about 2 ¢ results in much improved primes 5 and 11, but much worse primes 7 and 13. This approximates all harmonics up to 16 within 11.6 ¢. The 11- and 13-limit TE tunings of 36et both do this, as do their respective WE tunings.

Approximation of harmonics in 13-limit TE tuning of 36et
Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-1.1	-3.7	-2.1	+11.2	-4.7	-5.2	-3.2	-7.3	+10.1	+11.6	-5.8
Error	Relative (%)	-3.2	-11.0	-6.4	+33.6	-14.2	-15.5	-9.6	-21.9	+30.4	+34.9	-17.4
Step		36	57	72	84	93	101	108	114	120	125	129

Approximation of harmonics in 13-limit TE tuning of 36et (continued)
Harmonic		13	14	15	16	17	18	19	20	21	22	23	24
Error	Absolute (¢)	-11.1	-6.2	+7.5	-4.3	-9.3	-8.4	-2.1	+9.0	-8.8	+10.6	+0.2	-6.9
Error	Relative (%)	-33.5	-18.7	+22.6	-12.9	-28.0	-25.1	-6.2	+27.2	-26.5	+31.7	+0.6	-20.6
Step		133	137	141	144	147	150	153	156	158	161	163	165

Comparison of stretched and compressed tunings
Tuning	Octave size (cents)	Prime error (cents)						Mapping of primes 2–13 (steps)
Tuning	Octave size (cents)	2	3	5	7	11	13	Mapping of primes 2–13 (steps)
21edf	1203.351	+3.3	+3.3	−12.0	+7.2	−6.5	+5.1	36, 57, 83, 101, 124, 133
57edt	1201.235	+1.2	0.0	+16.6	+1.3	−13.7	−2.6	36, 57, 84, 101, 124, 133
155zpi	1200.587	+0.6	−1.0	+15.1	−0.5	−16.0	−5.0	36, 57, 83, 101, 124, 133
36edo	1200.000	0.0	−2.0	+13.7	−2.2	+15.3	−7.2	36, 57, 84, 101, 125, 133
13-limit TE	1198.929	−1.1	−3.7	+11.2	−5.2	+11.6	−11.1	36, 57, 84, 101, 125, 133
11-limit TE	1198.330	−1.7	−4.6	+9.8	−6.8	+9.5	−13.4	36, 57, 84, 101, 125, 133

Blank template

Octave stretch or compression

What follows is a comparison of stretched- and compressed-octave EDONAME tunings.

ZPINAME

Step size: NNN ¢, octave size: NNN ¢

_ing the octave of EDONAME by around NNN ¢ results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN ¢. The tuning ZPINAME does this.

Approximation of harmonics in ZPINAME
Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+0.0	-2.0	+0.0	+13.7	-2.0	+31.2	+0.0	-3.9	+13.7	+48.7	-2.0
Error	Relative (%)	+0.0	-2.0	+0.0	+13.7	-2.0	+31.2	+0.0	-3.9	+13.7	+48.7	-2.0
Step		12	19	24	28	31	34	36	38	40	42	43

Approximation of harmonics in ZPINAME (continued)
Harmonic		13	14	15	16	17	18	19	20	21	22	23	24
Error	Absolute (¢)	-40.5	+31.2	+11.7	+0.0	-5.0	-3.9	+2.5	+13.7	+29.2	+48.7	-28.3	-2.0
Error	Relative (%)	-40.5	+31.2	+11.7	+0.0	-5.0	-3.9	+2.5	+13.7	+29.2	+48.7	-28.3	-2.0
Step		44	46	47	48	49	50	51	52	53	54	54	55

EDONOI

Step size: NNN ¢, octave size: NNN ¢

_ing the octave of EDONAME by around NNN ¢ results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN ¢. The tuning EDONOI does this.

Approximation of harmonics in EDONOI
Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+0.0	-2.0	+0.0	+13.7	-2.0	+31.2	+0.0	-3.9	+13.7	+48.7	-2.0
Error	Relative (%)	+0.0	-2.0	+0.0	+13.7	-2.0	+31.2	+0.0	-3.9	+13.7	+48.7	-2.0
Steps (reduced)		12 (0)	19 (7)	24 (0)	28 (4)	31 (7)	34 (10)	36 (0)	38 (2)	40 (4)	42 (6)	43 (7)

Approximation of harmonics in EDONOI (continued)
Harmonic		13	14	15	16	17	18	19	20	21	22	23	24
Error	Absolute (¢)	-40.5	+31.2	+11.7	+0.0	-5.0	-3.9	+2.5	+13.7	+29.2	+48.7	-28.3	-2.0
Error	Relative (%)	-40.5	+31.2	+11.7	+0.0	-5.0	-3.9	+2.5	+13.7	+29.2	+48.7	-28.3	-2.0
Steps (reduced)		44 (8)	46 (10)	47 (11)	48 (0)	49 (1)	50 (2)	51 (3)	52 (4)	53 (5)	54 (6)	54 (6)	55 (7)

ETNAME, TETUNING

Step size: NNN ¢, octave size: NNN ¢

_ing the octave of EDONAME by around NNN ¢ results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN ¢. The tuning TETUNING does this.

Approximation of harmonics in TETUNING
Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+0.0	-2.0	+0.0	+13.7	-2.0	+31.2	+0.0	-3.9	+13.7	+48.7	-2.0
Error	Relative (%)	+0.0	-2.0	+0.0	+13.7	-2.0	+31.2	+0.0	-3.9	+13.7	+48.7	-2.0
Step		12	19	24	28	31	34	36	38	40	42	43

Approximation of harmonics in TETUNING (continued)
Harmonic		13	14	15	16	17	18	19	20	21	22	23	24
Error	Absolute (¢)	-40.5	+31.2	+11.7	+0.0	-5.0	-3.9	+2.5	+13.7	+29.2	+48.7	-28.3	-2.0
Error	Relative (%)	-40.5	+31.2	+11.7	+0.0	-5.0	-3.9	+2.5	+13.7	+29.2	+48.7	-28.3	-2.0
Step		44	46	47	48	49	50	51	52	53	54	54	55

EDONAME

Step size: NNN ¢, octave size: NNN ¢

Pure-octaves EDONAME approximates all harmonics up to 16 within NNN ¢.

Approximation of harmonics in EDONAME
Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+0.0	-2.0	+0.0	+13.7	-2.0	+31.2	+0.0	-3.9	+13.7	+48.7	-2.0
Error	Relative (%)	+0.0	-2.0	+0.0	+13.7	-2.0	+31.2	+0.0	-3.9	+13.7	+48.7	-2.0
Steps (reduced)		12 (0)	19 (7)	24 (0)	28 (4)	31 (7)	34 (10)	36 (0)	38 (2)	40 (4)	42 (6)	43 (7)

Approximation of harmonics in EDONAME (continued)
Harmonic		13	14	15	16	17	18	19	20	21	22	23	24
Error	Absolute (¢)	-40.5	+31.2	+11.7	+0.0	-5.0	-3.9	+2.5	+13.7	+29.2	+48.7	-28.3	-2.0
Error	Relative (%)	-40.5	+31.2	+11.7	+0.0	-5.0	-3.9	+2.5	+13.7	+29.2	+48.7	-28.3	-2.0
Steps (reduced)		44 (8)	46 (10)	47 (11)	48 (0)	49 (1)	50 (2)	51 (3)	52 (4)	53 (5)	54 (6)	54 (6)	55 (7)

ETNAME, TETUNING

Step size: NNN ¢, octave size: NNN ¢

_ing the octave of EDONAME by around NNN ¢ results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN ¢. The tuning TETUNING does this.

Approximation of harmonics in TETUNING
Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+0.0	-2.0	+0.0	+13.7	-2.0	+31.2	+0.0	-3.9	+13.7	+48.7	-2.0
Error	Relative (%)	+0.0	-2.0	+0.0	+13.7	-2.0	+31.2	+0.0	-3.9	+13.7	+48.7	-2.0
Step		12	19	24	28	31	34	36	38	40	42	43

Approximation of harmonics in TETUNING (continued)
Harmonic		13	14	15	16	17	18	19	20	21	22	23	24
Error	Absolute (¢)	-40.5	+31.2	+11.7	+0.0	-5.0	-3.9	+2.5	+13.7	+29.2	+48.7	-28.3	-2.0
Error	Relative (%)	-40.5	+31.2	+11.7	+0.0	-5.0	-3.9	+2.5	+13.7	+29.2	+48.7	-28.3	-2.0
Step		44	46	47	48	49	50	51	52	53	54	54	55

EDONOI

Step size: NNN ¢, octave size: NNN ¢

_ing the octave of EDONAME by around NNN ¢ results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN ¢. The tuning EDONOI does this.

Approximation of harmonics in EDONOI
Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+0.0	-2.0	+0.0	+13.7	-2.0	+31.2	+0.0	-3.9	+13.7	+48.7	-2.0
Error	Relative (%)	+0.0	-2.0	+0.0	+13.7	-2.0	+31.2	+0.0	-3.9	+13.7	+48.7	-2.0
Steps (reduced)		12 (0)	19 (7)	24 (0)	28 (4)	31 (7)	34 (10)	36 (0)	38 (2)	40 (4)	42 (6)	43 (7)

Approximation of harmonics in EDONOI (continued)
Harmonic		13	14	15	16	17	18	19	20	21	22	23	24
Error	Absolute (¢)	-40.5	+31.2	+11.7	+0.0	-5.0	-3.9	+2.5	+13.7	+29.2	+48.7	-28.3	-2.0
Error	Relative (%)	-40.5	+31.2	+11.7	+0.0	-5.0	-3.9	+2.5	+13.7	+29.2	+48.7	-28.3	-2.0
Steps (reduced)		44 (8)	46 (10)	47 (11)	48 (0)	49 (1)	50 (2)	51 (3)	52 (4)	53 (5)	54 (6)	54 (6)	55 (7)

ZPINAME

Step size: NNN ¢, octave size: NNN ¢

_ing the octave of EDONAME by around NNN ¢ results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN ¢. The tuning ZPINAME does this.

Approximation of harmonics in ZPINAME
Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+0.0	-2.0	+0.0	+13.7	-2.0	+31.2	+0.0	-3.9	+13.7	+48.7	-2.0
Error	Relative (%)	+0.0	-2.0	+0.0	+13.7	-2.0	+31.2	+0.0	-3.9	+13.7	+48.7	-2.0
Step		12	19	24	28	31	34	36	38	40	42	43

Approximation of harmonics in ZPINAME (continued)
Harmonic		13	14	15	16	17	18	19	20	21	22	23	24
Error	Absolute (¢)	-40.5	+31.2	+11.7	+0.0	-5.0	-3.9	+2.5	+13.7	+29.2	+48.7	-28.3	-2.0
Error	Relative (%)	-40.5	+31.2	+11.7	+0.0	-5.0	-3.9	+2.5	+13.7	+29.2	+48.7	-28.3	-2.0
Step		44	46	47	48	49	50	51	52	53	54	54	55

Plan for roll-out

Edo pages which currently have an "octave stretch", "related tunings", "zeta properties", etc. section:

Done: 36 edo.
High priority pages: 7, 12, 17, 19, 22, 27, 31, 41, 58 & 72 edos.
Medium-high priority pages: 8, 13, 14, 16, 23, 60, 99, 103, 118, & 152 edos.
Low-medium priority pages: 32, 33, 39, 42, 45, 54, 59 & 64 edos.
Low priority pages: 111, 125, 145, 159, 166, 182, 198, 212, 243 & 247 edos.

This standard will need to be rolled out to those above pages.

It can optionally be rolled out to other edo pages later.

Things to note

When rolling it out try not to delete existing body text but instead rework it where possible.
This section will not replace any "n-edo and octave stretch" pages. Still, add this section to the relevant edo page, but also link to the "n-edo and octave stretch" page at the top of this section, using the see also Template, eg: "{{See also|36edo and octave stretch}}".

Possible tunings to be used on each page

You can remove some of these or add more that aren't listed here; this section is pretty much just brainstorming.

(Used https://x31eq.com/temper-pyscript/net.html, used WE instead of TE cause it kept defaulting to WE and I kept not remembering to switch it)

High-priority

7edo

11edt
18ed6
2.3.5.11.13 WE ( 172.390c)
2.3.11.13 WE (171.993c)
15zpi (172.495c)

12edo (too many edonoi)

40ed10
7edf
19edt
31ed6
5-limit WE (99.868c)
7-limit WE (99.664c)
2.3.5.17.19 WE (99.930c)
34zpi (99.807c)

17edo

27edt
44ed6
2.3.7.11 WE (70.392c)
2.3.7.11.13 WE ( 70.410c)
56zpi (70.403c)

19edo

49ed6
30ed3
11edf
2.3.5.11 WE (63.192c)
13-limit WE ( 63.291c)
65zpi (63.331c)

22edo

123ed48 (try to find a simpler but similar tuning)
11-limit WE (54.494c)
13-limit WE ( 54.546c)
80zpi ( 54.483c)

27edo

43edt
70ed6
90ed10
97ed12
7-limit WE (44.306c)
13-limit WE (44.375c)
105zpi (44.674c)
106zpi (44.302c)

31edo

80ed6
111ed12
229ed169 (try to find a simpler but similar tuning)
11-limit WE (38.748c)
13-limit WE (38.725c)
127zpi (38.737c)

41edo

65edt
106ed6
147ed12
11-limit WE (29.277c)
13-limit WE (29.267c)
184zpi (29.277c)

58edo

92edt
150ed6
7-limit WE (20.667c)
13-limit WE (20.663c)
288zpi (20.736c)
289zpi (20.666c)

72edo

144edt
186ed6
11-limit WE ( 16.677c)
13-limit WE (16.680c)
380zpi (16.678c)

Medium-high priority

8edo

1ed148.5c
No-7s 17-limit WE (147.895c)
No-7s 19-limit WE (148.148c)
18zpi (153.463c)
19zpi (147.467c)

13edo

2.5.11.13 WE (92.483c)
2.5.7.13 WE (92.804c)
2.3 WE (91.405c) (good for opposite 7 mapping)
38zpi (92.531c)

14edo

22edt
36ed6
11-limit WE (85.842c)
13-limit WE (85.759c)
42zpi (86.329c)

16edo

25edt
41ed6
57ed12
2.5.7.13 WE (75.105c)
13-limit WE (75.315c)
15zpi (75.262c)

23edo (too many edonoi, too many ZPIs)

Main: "23edo and octave stretching"
36edt
59ed6
60ed6
68ed8
11ed7/5
1ed33/32
2.3.5.13 WE (52.447c)
2.7.11 WE (51.962c)
13-limit WE (52.237c)
83zpi (53.105c)
84zpi (52.615c)
85zpi (52.114c)
86zpi ( 51.653c)
87zpi (51.201c)

60edo (too many edonoi, too many zpis)

95edt
139ed5
155ed6
208ed11
255ed19
27ed23 (great for catnip temperament)
13-limit WE (20.013c)
299zpi (20.128c)
300zpi (20.093c)
301zpi (20.027c)
302zpi (19.962c)
303zpi (19.913c)
304zpi (19.869c)

99edo

157edt
256ed6
7-limit WE (12.117c)
13-limit WE (12.123c)
567zpi (12.138c)
568zpi (12.115c)

103edo (too many edonoi)

163edt
239ed5
289ed7
356ed11
381ed13
421ed17
466ed23
13-limit WE (11.658c)
Best nearby ZPI(s)

118edo

187edt
69edf
13-limit WE (10.171c)
Best nearby ZPI(s)

152edo

241edt
13-limit WE ( 7.894c)
Best nearby ZPI(s)

Low-medium priority

32edo (too many edonoi, too many zpis)

90ed7
51edt
75ed5
1ed46/45
11-limit WE (37.453c)
13-limit WE (37.481c)
131zpi (37.862c)
132zpi (37.662c)
133zpi (37.418c)
134zpi (37.176c)

33edo (too many edonoi)

76ed5
92ed7
52edt
1ed47/46
114ed11
122ed13
93ed7
23edPhi
77ed5
123ed13
115ed11
11-limit WE (36.349c)
13-limit WE (36.357c)
137zpi (36.628c)
138zpi (36.394c)
139zpi (36.179c)

39edo

62edt
101ed6
39ed255/128 (replace with something similar but simpler)
2.3.5.11 WE (30.703c)
2.3.7.11.13 WE (30.787c)
13-limit WE (30.757c)
171zpi (30.973c)
172zpi (30.836c)
173zpi (30.672c)

42edo (^replace w something similar but simpler)

42ed257/128^
42ed255/128^
APS720jot^
APS715jot^
7-limit WE (28.484c)
13-limit WE (28.534c)
189zpi (28.689c)
190zpi (28.572c)
191zpi (28.444c)

45edo

126ed7
APS3.21farab (replace with something similar but simpler)
7-limit WE (26.745c)
13-limit WE (26.695c)
207zpi (26.762)
208zpi (26.646)
209zpi (26.550)

54edo

86edt
126ed5
152ed7
APS4/5méride (replace with something similar but simpler)
2.3.7.11.13 WE (22.180c)
13-limit WE (22.198c)
262zpi (22.313c)
263zpi (22.243c)
264zpi (22.175c)

59edo (too many ZPIs)

93edt
166ed7
203ed11
7-limit WE (20.301c)
11-limit WE (20.310c)
13-limit WE (20.320c)
293zpi (20.454c)
294zpi (20.399c)
295zpi (20.342c)
296zpi (20.282c)
297zpi (20.229c)

64edo (too many ZPIs)

149ed5
180ed7
222ed11
64ed257/128 (replace with something similar but simpler)
11-limit WE (18.755c)
13-limit WE (18.752c)
325zpi (18.868c)
326zpi (18.816c)
327zpi (18.767c)
328zpi (18.721c)
329zpi (18.672c)
330zpi (18.630c)

Low priority

(add brainstorm list here)

User:BudjarnLambeth/Draft related tunings section: Difference between revisions

Revision as of 11:03, 21 August 2025

Contents

The guidelines

Example (36edo)

Octave stretch or compression

Blank template

Octave stretch or compression

Plan for roll-out

Possible tunings to be used on each page

Navigation menu

@@ Line 192: / Line 192: @@
 * 2.3.5.11.13 WE (	172.390c)
 * 2.3.11.13 WE (171.993c)
-* Best nearby ZPI(s)
+* 15zpi (172.495c)
 edo (too many edonoi)
@@ Line 202: / Line 202: @@
 * 7-limit WE (99.664c)
 * 2.3.5.17.19 WE (99.930c)
-* Best nearby ZPI(s)
+* 34zpi (99.807c)
 edo
@@ Line 209: / Line 209: @@
 * 2.3.7.11 WE (70.392c)
 * 2.3.7.11.13 WE (	70.410c)
-* Best nearby ZPI(s)
+* 56zpi (70.403c)
 edo
@@ Line 217: / Line 217: @@
 * 2.3.5.11 WE (63.192c)
 * 13-limit WE (	63.291c)
-* Best nearby ZPI(s)
+* 65zpi (63.331c)
 edo
@@ Line 223: / Line 223: @@
 * 11-limit WE (54.494c)
 * 13-limit WE (	54.546c)
-* Best nearby ZPI(s)
+* 80zpi (	54.483c)
 edo
@@ Line 232: / Line 232: @@
 * 7-limit WE (44.306c)
 * 13-limit WE (44.375c)
-* Best nearby ZPI(s)
+* 105zpi (44.674c)
+* 106zpi (44.302c)
 edo
@@ Line 240: / Line 241: @@
 * 11-limit WE (38.748c)
 * 13-limit WE (38.725c)
-* Best nearby ZPI(s)
+* 127zpi (38.737c)
 edo
@@ Line 248: / Line 249: @@
 * 11-limit WE (29.277c)
 * 13-limit WE (29.267c)
-* Best nearby ZPI(s)
+* 184zpi (29.277c)
 edo
@@ Line 255: / Line 256: @@
 * 7-limit WE (20.667c)
 * 13-limit WE (20.663c)
-* Best nearby ZPI(s)
+* 288zpi (20.736c)
+* 289zpi (20.666c)
 edo
@@ Line 262: / Line 264: @@
 * 11-limit WE (	16.677c)
 * 13-limit WE (16.680c)
-* Best nearby ZPI(s)
+* 380zpi (16.678c)
 ; Medium-high priority
@@ Line 270: / Line 272: @@
 * No-7s 17-limit WE (147.895c)
 * No-7s 19-limit WE (148.148c)
-* Best nearby ZPI(s)
+* 18zpi (153.463c)
+* 19zpi (147.467c)
 edo
@@ Line 276: / Line 279: @@
 * 2.5.7.13 WE (92.804c)
 * 2.3 WE (91.405c) (good for opposite 7 mapping)
-* Best nearby ZPI(s)
+* 38zpi (92.531c)
 edo
@@ Line 283: / Line 286: @@
 * 11-limit WE (85.842c)
 * 13-limit WE (85.759c)
-* Best nearby ZPI(s)
+* 42zpi (86.329c)
 edo
@@ Line 291: / Line 294: @@
 * 2.5.7.13 WE (75.105c)
 * 13-limit WE (75.315c)
-* Best nearby ZPI(s)
+* 15zpi (75.262c)
-edo (too many edonoi)
+edo (too many edonoi, too many ZPIs)
 * Main: "23edo and octave stretching"
 * 36edt
@@ Line 304: / Line 307: @@
 * 2.7.11 WE (51.962c)
 * 13-limit WE (52.237c)
-* Best nearby ZPI(s)
+* 83zpi (53.105c)
+* 84zpi (52.615c)
+* 85zpi (52.114c)
+* 86zpi (	51.653c)
+* 87zpi (51.201c)
-edo (too many edonoi)
+edo (too many edonoi, too many zpis)
 * 95edt
 * 139ed5
@@ Line 314: / Line 321: @@
 * 27ed23 (great for catnip temperament)
 * 13-limit WE (20.013c)
-* Best nearby ZPI(s)
+* 299zpi (20.128c)
+* 300zpi (20.093c)
+* 301zpi (20.027c)
+* 302zpi (19.962c)
+* 303zpi (19.913c)
+* 304zpi (19.869c)
 edo
@@ Line 321: / Line 333: @@
 * 7-limit WE (12.117c)
 * 13-limit WE (12.123c)
-* Best nearby ZPI(s)
+* 567zpi (12.138c)
+* 568zpi (12.115c)
 edo (too many edonoi)
@@ Line 347: / Line 360: @@
 ; Low-medium priority
-edo
+edo (too many edonoi, too many zpis)
 * 90ed7
 * 51edt
@@ Line 354: / Line 367: @@
 * 11-limit WE (37.453c)
 * 13-limit WE (37.481c)
-* Best nearby ZPI(s)
+* 131zpi (37.862c)
+* 132zpi (37.662c)
+* 133zpi (37.418c)
+* 134zpi (37.176c)
 edo (too many edonoi)
@@ Line 370: / Line 386: @@
 * 11-limit WE (36.349c)
 * 13-limit WE (36.357c)
-* Best nearby ZPI(s)
+* 137zpi (36.628c)
+* 138zpi (36.394c)
+* 139zpi (36.179c)
 edo
@@ Line 379: / Line 397: @@
 * 2.3.7.11.13 WE (30.787c)
 * 13-limit WE (30.757c)
-* Best nearby ZPI(s)
+* 171zpi (30.973c)
+* 172zpi (30.836c)
+* 173zpi (30.672c)
 edo (^replace w something similar but simpler)
@@ Line 388: / Line 408: @@
 * 7-limit WE (28.484c)
 * 13-limit WE (28.534c)
-* Best nearby ZPI(s)
+* 189zpi (28.689c)
+* 190zpi (28.572c)
+* 191zpi (28.444c)
 edo
@@ Line 395: / Line 417: @@
 * 7-limit WE (26.745c)
 * 13-limit WE (26.695c)
-* Best nearby ZPI(s)
+* 207zpi (26.762)
+* 208zpi (26.646)
+* 209zpi (26.550)
 edo
@@ Line 404: / Line 428: @@
 * 2.3.7.11.13 WE (22.180c)
 * 13-limit WE (22.198c)
-* Best nearby ZPI(s)
+* 262zpi (22.313c)
+* 263zpi (22.243c)
+* 264zpi (22.175c)
-edo
+edo (too many ZPIs)
 * 93edt
 * 166ed7
@@ Line 413: / Line 439: @@
 * 11-limit WE (20.310c)
 * 13-limit WE (20.320c)
-* Best nearby ZPI(s)
+* 293zpi (20.454c)
+* 294zpi (20.399c)
+* 295zpi (20.342c)
+* 296zpi (20.282c)
+* 297zpi (20.229c)
-edo
+edo (too many ZPIs)
 * 149ed5
 * 180ed7
@@ Line 422: / Line 452: @@
 * 11-limit WE (18.755c)
 * 13-limit WE (18.752c)
-* Best nearby ZPI(s)
+* 325zpi (18.868c)
+* 326zpi (18.816c)
+* 327zpi (18.767c)
+* 328zpi (18.721c)
+* 329zpi (18.672c)
+* 330zpi (18.630c)
 ; Low priority
 (add brainstorm list here)

User:BudjarnLambeth/Draft related tunings section: Difference between revisions

Revision as of 11:03, 21 August 2025

The guidelines

Example (36edo)

Octave stretch or compression

Blank template

Octave stretch or compression

Plan for roll-out

Possible tunings to be used on each page

Navigation menu

Search