197edo
| ← 196edo | 197edo | 198edo → |
197edo is the equal division of the octave into 197 parts of 6.0914 cents each. It gives excellent results for tuning both marvel, the planar temperament tempering out 225/224, and catakleismic, the temperament tempering out both 225/224 and 4375/4374, which has wedgie <<6 5 22 -6 18 37||. Among patent vals, in fact, it gives the best results for both. In fact, the 11-limit patent val <197 312 457 553 682| has a comma basis [225/224, 4375/4374, 441/440, 65536/65219], so taking 225/224 and 441/440 together (prodigy temperament) also works well with 197edo, and taking 225/224, 441/440, and 4375/4374 (an alternative 11-limit catakleismic) is once again excellently tuned by 197edo.
If we use 197e, the <197 312 457 553 681| val, we can also use 197edo as an excellent tuning for the 11-limit version of marvel temperament, tempering out 385/384 as well as 225/224. If we add 4375/4374 to the comma list for 11-limit marvel, we get 11-limit catakleismic, and 197edo with the above val is also an excellent tuning for that.
197edo is the 45th prime edo.