Monarch

Archtone is a rank-3 Straddle primes temperament tempering out 64/63[+3] and 81/80[-3] in the 2.-3.+3.5.7 subgroup. The name comes from Archy and Meantone, the two temperaments combined to make Archtone. They are linearly independent, but extensions and erac tunings make use of combining the two tunings of 3. The name may also be read with the arch- prefix, implying that this is a tonality of greater scope or importance.

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110edo is approximately my standard for both Meantone septal diasem and Archy pental blackdye, with 110d 18:6:4 (50 patent 9:3:2) diasem and 110bc 16:9:4 blackdye. This exact tuning system is somewhat impractical to use, but it hints at a more general temperament (it also happens to contain a very good Intergan generator). This temperament is rank-3, generated by a Meantone fifth and an Archy fifth. In both the diasem and blackdye scales, sharp 5/4 is four Meantone fifths (optionally with the corresponding fourth split in half) and 9/7 is four Archy fifths. Similar tunings such as 86edo may replace the shared Archy 9/7 with a shared Archy 7/6 using a sharper fifth. This sacrifices 9/7 to improve sharp 7 and flat 11.