User:BudjarnLambeth/Bird’s eye view of rank-2 temperaments

This is a page to easily navigate to temperaments that fit your interests.

Low complexity temperaments are likely to be of most interest to artists new to music tuning theory. That is because they tend to approximate all of the important intervals within less than 30 notes (occasionally even less than 12!), so they are the most practical to map onto a physical instrument.

Medium and higher complexity temperaments provide a bigger range of new intervals, and they approximate those intervals more accurately, but they may be unwieldy, requiring dozens or even hundreds of notes to approximate all the important intervals.

Feel free to add temperaments to the appropriate category if they are not already here. (If you're not sure which category to put them in, put them in honorable mentions).

1. Low complexity temperaments

Temperaments which approximate most of their consonant intervals with less than 30 notes, and where those intervals are mostly less than 20 cents out of tune.

(For comparison, in 12edo, most intervals are about 10 cents out of tune, with better fifths but less good thirds.)

1.1 5-limit

Meantone, augmented, mavila, porcupine, blackwood, diminished, srutal

1.2 7-limit

Blacksmith, septimal diminished, dominant, august, pajara, semaphore, septimal meantone, injera, septimal negri, augene

1.3 No-2s subgroups of 7-limit

1.4 Other subgroups of 7-limit

1.5 11-limit

1.6 No-2s subgroups of 11-limit

1.7 Other subgroups of 11-limit

1.8 13-limit

1.9 No-2s of 13-limit

1.10 No-2s subgroups of 13-limit

1.11 Other subgroups of 13-limit

1.12 Higher limits

1.13 No-2s higher limit subgroups

1.13 Other higher limit subgroups

2. Medium complexity temperaments

Temperaments which approximate most of their consonant intervals with less than 60 notes, and where those intervals are mostly less than 5 cents out of tune.

2.1 5-limit

Magic, ripple, hanson, negri, tetracot, superpyth, helmholtz, sensi, passion, wuerschmidt, compton, amity, orson

2.2 7-limit

keemun, catler, hedgehog, septimal superpyth, septimal sensi, lemba, septimal porcupine, flattone, septimal magic, doublewide, nautilus, beatles, liese, cynder, orwell, garibaldi, myna, miracle

2.3 No-2s subgroups of 7-limit

2.4 Other subgroups of 7-limit

2.5 11-limit

2.6 No-2s subgroups of 11-limit

2.7 Other subgroups of 11-limit

2.8 13-limit

2.9 No-2s of 13-limit

2.10 No-2s subgroups of 13-limit

2.11 Other subgroups of 13-limit

2.12 Higher limits

2.13 No-2s higher limit subgroups

2.14 Other higher limit subgroups

3. High complexity temperaments

Temperaments where most of their consonant intervals are less than 1 cent out of tune.

3.1 5-limit

Vishnu, luna

3.2 7-limit

Ennealimmal

3.3 No-2s subgroups of 7-limit

3.4 Other subgroups of 7-limit

3.5 11-limit

3.6 No-2s subgroups of 11-limit

3.7 Other subgroups of 11-limit

3.8 13-limit

3.9 No-2s of 13-limit

3.10 No-2s subgroups of 13-limit

3.11 Other subgroups of 13-limit

3.12 Higher limits

3.13 No-2s higher limit subgroups

3.14 Other higher limit subgroups

4. Honorable mentions

Temperaments which are interesting in some way, but might not meet the criteria for the other lists.

4.1 5-limit

4.2 7-limit

4.3 No-2s subgroups of 7-limit

4.4 Other subgroups of 7-limit

4.5 11-limit

4.6 No-2s subgroups of 11-limit

4.7 Other subgroups of 11-limit

4.8 13-limit

4.9 No-2s of 13-limit

4.10 No-2s subgroups of 13-limit

4.11 Other subgroups of 13-limit

4.12 Higher limits

4.13 No-2s higher limit subgroups

4.14 Other higher limit subgroups

5. Exoemperaments

Temperaments where most intervals are at least 20 cents out of tune.

5.1 5-limit

Father, bug

5.2 7-limit

5.3 No-2s subgroups of 7-limit

5.4 Other subgroups of 7-limit

5.5 11-limit

5.6 No-2s subgroups of 11-limit

5.7 Other subgroups of 11-limit

5.8 13-limit

5.9 No-2s of 13-limit

5.10 No-2s subgroups of 13-limit

5.11 Other subgroups of 13-limit

5.12 Higher limits

5.13 No-2s higher limit subgroups

5.14 Other higher limit subgroups