the diatonic subset of 12 tone equal temperament, then we are in the region of the historical meantone tunings, which distribute or temper out the syntonic comma. They include 1/3 comma meantone - achieves pure minor thirds 6/5; fifth is 694.786 cents; closely approximated by the diatonic scale in 19 tone equal temperament 1/4 comma meantone - achieves pure major thirds 5/4 (386.313 cents); fifth is 696.6 cents; closely approximated in 31 tone equal temperament 1/6 comma meantone - achieves a rational diatonic tritone 45/32; fifth is 698.371 cents; closely approximated in 55 tone equal temperament 1/11 comma meantone - fifth is 699.99988 cents; almost indistinguishable from 12 tone equal temperament When the fifths are exactly 3/2, or around 702 cents, the result is the Pythagorean diatonic tuning. For fifths slightly narrower than 3/2, the result is a Schismatic temperament, where the temperament is measured in terms of a fraction of a schisma - the amount by which a chain of eight fifths reduced to an octave is sharper than the just minor sixth 8/5. So for instance, a 1/8 schisma temperament will achieve a pure 8/5 in an ascending chain of eight fifths. 53 tone equal temperament achieves a good approximation to Schismatic temperament. At around 703.4-705.0 cents, with fifths mildly tempered in the wide direction, the result is major thirds with ratios near 14/11 (417.508 cents) and minor thirds around 13/11 (289.210 cents). At 705.882 cents, with fifths tempered in the wide direction by 3.929 cents, the result is the diatonic scale in 17 tone equal temperament. Beyond this point, the regular major and minor thirds approximate simple ratios of numbers with prime factors 2-3-7, such as the 9/7 or septimal major third (435.084 cents) and 7/6 or septimal minor third (266.871 cents). At the same time, the regular tones more and more closely approximate a large 8/7 tone (231.174 cents), and regular minor sevenths the "harmonic seventh" at the simple ratio of 7/4 (968.826 cents). This septimal range extends out to around 711.111 cents or 27 tone equal temperament, or a bit further. That leaves the two extremes, what we could call: the "inframeantone" range with fifths between the lower bound for the regular diatonic of 7 tone equal temperament (685.7143 cents) and the range of historical meantones beginning around 1/3-comma or 19 tone equal temperament (694.786 cents), and with the diatonic "semitones" approaching the size of