# Kestrel chords

The *kestrel tetrad* is the 13-limit essentially tempered tetrad consisting, in close position, of the steps 13/11-7/6-13/11-11/9 in a temperament tempering out the kestrel comma, 1188/1183, leading to the tempering of 1-13/11-18/13-18/11. Contained in the kestrel tetrad are the two kestrel triads, 1-7/6-18/13 and 1-13/11-18/13. Closely related tetrads require the tempering of both 1188/1183 and 540/539, with steps of 7/6-13/11-13/11-11/9, leading to the tempered version of 1-7/6-18/13-18/11, and 11/9-13/11-13/11-7/6, leading to the 1-11/9-13/9-12/7 chord. Equal temperaments tempering out both 1188/1183 and 540/539 include 41, 53, 58, 94, 103, 111, 161, 205, 214, 255. 255edo is the optimal patent val for both {1188/1183, 540/539}-tempering and 1188/1183-tempering, so nothing significant is lost in tuning accuracy by also tempering out 540/539. Kestrel tetrads are essentially tempered tetrads of the 2.7/3.11/9.13/9 just intonation subgroup.