User:BudjarnLambeth/Draft related tunings section

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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.

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, roughly 6 tunings should be listed, give or take a few.
• The selection of tunings should cover a range of meaningfully different tunings (eg they cover a range of different mappings and/or they approximate different harmonics well or badly).

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.

Useful links for working on this

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

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
	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
	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
	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
	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
	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
	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
	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
	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)
		2	3	5	7	11	13
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
	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
	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
	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
	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, SUBGROUP WE tuning

• 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 ¢. Its SUBGROUP WE tuning and SUBGROUP TE tuning both do this.

Approximation of harmonics in ETNAME, SUBGROUP WE tuning

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
	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 ETNAME, SUBGROUP WE tuning (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
	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
	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
	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, SUBGROUP WE tuning

• 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 ¢. Its SUBGROUP WE tuning and SUBGROUP TE tuning both do this.

Approximation of harmonics in ETNAME, SUBGROUP WE tuning

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
	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 ETNAME, SUBGROUP WE tuning (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
	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
	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
	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
	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
	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

Done

• Done (with table): 36.
• Done (table not added yet): 7, 8, 12, 14, 16, 17, 19, 22, 23, 27, 31, 32, 41, 58, 60, 72, 99.
• Done (table & some step sizes not added yet): 33, 39, 42, 45.

To-do

• High priority: 54, 64, 59.
• Medium priority pages: 25, 26, 29, 30, 34, 35, 37, 38, 9, 10, 11, 15, 18, 48, 24, 5, 6, 13, 118, 103, 111.
• Low priority pages: 104, 125, 145, 152, 159, 166, 182, 198, 212, 243, 247.

Things to note

• When rolling this 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, e.g.: "{{See also|36edo and octave stretch}}".

What to do with edonoi pages that are very close to these edos

• Edt and edf pages should be permanently kept
• Other edonoi pages should be temporarily kept until all notable information from their respective pages has been added to:
  • The "octave stretch and compression" section of the edo page.

AND/OR

• • A new "Nedo and octave stretch" page (create one of these if there is too much information to squeeze into the "octave stretch and compression" section).

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

54edo

• 139ed6 (octave is identical to 262zpi within 0.2 ¢)
• 151ed7
• 193ed12
• 263zpi (22.243c)
• 13-limit WE (22.198c) (octave is identical to 187ed11 within 0.1 ¢)
• 264zpi (22.175c) (octave is identical to 194ed12 within 0.01 ¢)
• 152ed7
• 140ed6
• 126ed5 (octave is identical to 86edt within 0.1 ¢)

64edo

• 179ed7 (octave is identical to 326zpi within 0.3 ¢)
• 165ed6
• 229ed12 (octave is identical to 221ed11 within 0.1 ¢)
• 327zpi (18.767c)
• 11-limit WE (18.755c)

pure octaves 64edo (octave is identical to 13-limit WE within 0.13 ¢

• 328zpi (18.721c)
• 180ed7
• 230ed12
• 149ed5

59edo (reduce # of edonoi or ZPI)

• 152ed6
• 294zpi (20.399c)
• 211ed12
• 295zpi (20.342c)

pure octaves 59edo octave is identical to 137ed5 within 0.05 ¢

• 13-limit WE (20.320c)
• 7-limit WE (20.301c)
• 166ed7
• 212ed12
• 296zpi (20.282c)
• 153ed6

Medium priority

25edo

• Nearby edt, ed6, ed12 and/or edf
• Nearby ed5, ed10, ed7 and/or ed11 (optional)
• 1-2 WE tunings
• Best nearby ZPI(s)

26edo

• Nearby edt, ed6, ed12 and/or edf
• Nearby ed5, ed10, ed7 and/or ed11 (optional)
• 1-2 WE tunings
• Best nearby ZPI(s)

29edo

• Nearby edt, ed6, ed12 and/or edf
• Nearby ed5, ed10, ed7 and/or ed11 (optional)
• 1-2 WE tunings
• Best nearby ZPI(s)

30edo

• Nearby edt, ed6, ed12 and/or edf
• Nearby ed5, ed10, ed7 and/or ed11 (optional)
• 1-2 WE tunings
• Best nearby ZPI(s)

34edo

• Nearby edt, ed6, ed12 and/or edf
• Nearby ed5, ed10, ed7 and/or ed11 (optional)
• 1-2 WE tunings
• Best nearby ZPI(s)

35edo

• Nearby edt, ed6, ed12 and/or edf
• Nearby ed5, ed10, ed7 and/or ed11 (optional)
• 1-2 WE tunings
• Best nearby ZPI(s)

36edo

• Nearby edt, ed6, ed12 and/or edf
• Nearby ed5, ed10, ed7 and/or ed11 (optional)
• 1-2 WE tunings
• Best nearby ZPI(s)

37edo

• Nearby edt, ed6, ed12 and/or edf
• Nearby ed5, ed10, ed7 and/or ed11 (optional)
• 1-2 WE tunings
• Best nearby ZPI(s)

38edo

Approximation of harmonics in 38edo

Harmonic		2	3	4	5	6	7	8	9	10	11	12	13
Error	Absolute (¢)	+0.0	-7.2	+0.0	-7.4	-7.2	+10.1	+0.0	-14.4	-7.4	-14.5	-7.2	+12.1
	Relative (%)	+0.0	-22.9	+0.0	-23.3	-22.9	+32.1	+0.0	-45.7	-23.3	-45.8	-22.9	+38.3
Steps (reduced)		38 (0)	60 (22)	76 (0)	88 (12)	98 (22)	107 (31)	114 (0)	120 (6)	126 (12)	131 (17)	136 (22)	141 (27)

• Nearby edt, ed6, ed12 and/or edf
• Nearby ed5, ed10, ed7 and/or ed11 (optional)
• 1-2 WE tunings
• Best nearby ZPI(s)

9edo

• Nearby edt, ed6, ed12 and/or edf
• Nearby ed5, ed10, ed7 and/or ed11 (optional)
• 1-2 WE tunings
• Best nearby ZPI(s)

10edo

• Nearby edt, ed6, ed12 and/or edf
• Nearby ed5, ed10, ed7 and/or ed11 (optional)
• 1-2 WE tunings
• Best nearby ZPI(s)

11edo

• Nearby edt, ed6, ed12 and/or edf
• Nearby ed5, ed10, ed7 and/or ed11 (optional)
• 1-2 WE tunings
• Best nearby ZPI(s)

15edo

• Nearby edt, ed6, ed12 and/or edf
• Nearby ed5, ed10, ed7 and/or ed11 (optional)
• 1-2 WE tunings
• Best nearby ZPI(s)

18edo

• Nearby edt, ed6, ed12 and/or edf
• Nearby ed5, ed10, ed7 and/or ed11 (optional)
• 1-2 WE tunings
• Best nearby ZPI(s)

48edo

• Nearby edt, ed6, ed12 and/or edf
• Nearby ed5, ed10, ed7 and/or ed11 (optional)
• 1-2 WE tunings
• Best nearby ZPI(s)

24edo

• Nearby edt, ed6, ed12 and/or edf
• Nearby ed5, ed10, ed7 and/or ed11 (optional)
• 1-2 WE tunings
• Best nearby ZPI(s)

5edo

• Nearby edt, ed6, ed12 and/or edf
• Nearby ed5, ed10, ed7 and/or ed11 (optional)
• 1-2 WE tunings
• Best nearby ZPI(s)

6edo

• Nearby edt, ed6, ed12 and/or edf
• Nearby ed5, ed10, ed7 and/or ed11 (optional)
• 1-2 WE tunings
• Best nearby ZPI(s)

13edo

• Main: "13edo and optimal octave stretching"
• 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)

118edo (choose ZPIS)

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

103edo (narrow down edonoi, choose ZPIS)

• 163edt
• 239ed5
• 266ed6
• 289ed7
• 356ed11
• 369ed12
• 381ed13
• 421ed17
• 466ed23
• 13-limit WE (11.658c)
• Best nearby ZPI(s)

111edo (choose ZPIS)

• Nearby edt, ed6, ed12 and/or edf
• Nearby ed5, ed10, ed7 and/or ed11 (optional)
• 1-2 WE tunings
• Best nearby ZPI(s)

Low priority

104edo

• Nearby edt, ed6, ed12 and/or edf
• Nearby ed5, ed10, ed7 and/or ed11 (optional)
• 1-2 WE tunings
• Best nearby ZPI(s)

125edo

• Nearby edt, ed6, ed12 and/or edf
• Nearby ed5, ed10, ed7 and/or ed11 (optional)
• 1-2 WE tunings
• Best nearby ZPI(s)

145edo

• Nearby edt, ed6, ed12 and/or edf
• Nearby ed5, ed10, ed7 and/or ed11 (optional)
• 1-2 WE tunings
• Best nearby ZPI(s)

152edo

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

159edo

• Nearby edt, ed6, ed12 and/or edf
• Nearby ed5, ed10, ed7 and/or ed11 (optional)
• 1-2 WE tunings
• Best nearby ZPI(s)

166edo

• Nearby edt, ed6, ed12 and/or edf
• Nearby ed5, ed10, ed7 and/or ed11 (optional)
• 1-2 WE tunings
• Best nearby ZPI(s)

182edo

• Nearby edt, ed6, ed12 and/or edf
• Nearby ed5, ed10, ed7 and/or ed11 (optional)
• 1-2 WE tunings
• Best nearby ZPI(s)

198edo

• Nearby edt, ed6, ed12 and/or edf
• Nearby ed5, ed10, ed7 and/or ed11 (optional)
• 1-2 WE tunings
• Best nearby ZPI(s)

212edo

• Nearby edt, ed6, ed12 and/or edf
• Nearby ed5, ed10, ed7 and/or ed11 (optional)
• 1-2 WE tunings
• Best nearby ZPI(s)

243edo

• Nearby edt, ed6, ed12 and/or edf
• Nearby ed5, ed10, ed7 and/or ed11 (optional)
• 1-2 WE tunings
• Best nearby ZPI(s)

247edo

• Nearby edt, ed6, ed12 and/or edf
• Nearby ed5, ed10, ed7 and/or ed11 (optional)
• 1-2 WE tunings
• Best nearby ZPI(s)