Bendeler’s temperaments are found in his Organopoeia, thought to have been published around 1690, and they appear the have been heavily influenced by the 1681 proposals of his “good friend” (as he himself put it) Werckmeister. His first two temperaments use fifths tempered by 1/3 comma, making them rather poor. His third temperament is similar to Werckmeister’s well-known “No. III”, though a minor alteration in the distribution of the tempered fifths artfully produces a result which is much closer to equal temperament.
Like Werkmeister, Bendeler specified the comma as having the proportion 81:80, and therefore, at least conceptually, he meant to temper his fifths by fractions of the Sytnonic comma and not the Pythagorean. However, since Bendeler gives no monochord lengths, the only option would have been to follow his rather vague step-by-step tuning directions, and doing so, one is more likely to end-up dividing the Pythagorean comma. Therefore, I have shown them here with fifths tempered by Pythagorean comma fractions. Nonetheless, because of the imprecise nature of Bendeler’s logic, I still consider them to be Pragmatic rather than Rational circulating temperaments.