We already know such scales E.g. the Wheel of 4ths or Wheel of %th and the Wheel of alternating major minor 3rds posts 32 , 79 . Also the scales in posts 184 ,185 ,186, 190.
More abstractly we may include them in the general scheme of MULTI-OCTAVE DIATONIC SCALES (IN THE SENSE THAT GIVE WHEN REDUCED TO A SINGLE OCTAVE EXACTLY THE NOTES OF THE DIATONIC SCALE) BUT ARE MADE EXCLUSIVELY NOT FROM INTERVALS OF 2NDS BUT OF INTERVALS OF 3RDS, OR COMPLEMENTARY 6THS , 4THS, AND 5THS (OR IN SEMITONES 3,4,5,7,8,9).
They are used for
1) Alternative tunings of string instruments
2) Schemes of melodies centers to improvise around theme waving patterns.
We enumerated below some more such scales.
