127edo, which divides the octave into 127 parts of 9.45 cents each, is another equal division interesting because of its approximations, defined by the commas it tempers out. In the 5-limit, it tempers out the würschmidt comma, 393216/390625 and hence supports würschmidt temperament. In the 7-limit, it also tempers out 225/224, and is an excellent tuning for the 7-limit extension of würschmidt which tempers this out also. In the 11-limit, it tempers out 99/98, 176/175 and 243/242, and is an excellent tuning for the 11-limit version of würschmidt, as well as minerva, the rank three temperament tempering out 99/98 and 176/175, for which it is the optimal patent val and the rank four temperament tempering out 99/98, for which it also provides the optimal patent val.
127edo is the 31st prime edo.