<HTML>HT's done by machine cannot produce a beautiful tuning anymore than a temperament only using a machine can produce a beautiful ET. There will always, due to inharmonicity, be a few fifths, fourths, or incorrect thirds if you take the machine readings  exactly off a chart in HT tunings, just as there are in ET's. Following beat rate guides gets a more musical result. Starting from the machine readings, then tweaking is most helpful, but I have heard HT's proudly done which leave mistakes in beat rates, especially in the octave and a half above middle C. We all must remember that HT's are not technical tunings. They are aesthetic tunings, requiring a sensitivity to the musical balance intended by the historical harmonies. The way the tuning progresses through key changes is the essense of the tuning, not the adherance to a formula. The greatest danger in a HT are fourths in the mid-upper range which beat faster than the formula suggests, thereby throwing off the effect. A fourth which beats 1 BPS too fast is much more of a problem than a third which beats 2 BPS too fast in an isolated interval. I truly believe that one must tune and listen to HT's a great deal to appreciate them, as well as to play through real music in them. Only then will a tuner realize how to make the small deviations from cents formulas to make them truly special.                                                                   Michael Meade, RPT     </HTML>