Why are you so obsessed with thirds? If you care about short, clean fractions on a human scale, base 6 is overall better, see this table: https://youtu.be/qID2B4MK7Y0?t=992
Plus you get all the convenience of having five digits on a hand and 5 as the highest counting digit, so you can count to 55 on two hands, and all the rest of the benefits in that (totally serious) video.
Plus you get all the convenience of having five digits on a hand and 5 as the highest counting digit, so you can count to 55 on two hands, and all the rest of the benefits in that (totally serious) video.