2.3.5.7.11.13.19.29 subgroup
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The 2.3.5.7.11.13.19.29 subgroup (a.k.a. yazalathanatwena in color notation, hereon referred to as the subgroup) consists of just intonation intervals such that the highest prime factor in all ratios is 29, but without 17 or 23. It is thus a subset of the 29-limit, or alternatively, it can be seen as the 13-limit with extra primes 19 and 29, or the 2.3.5.7.11.13.19 subgroup with 29 added in.
This subgroup is a rank-8 system, and can be modeled in a 6-dimensional lattice, with the primes 3, 5, 7, 11, 13, 19 and 29represented by each dimension. The prime 2 does not appear in typical lattices because octave equivalence is presumed. If octave equivalence is not presumed, a seventh dimension is needed.
This subgroup is significant because 29 mirrors 27 in the 24::32 harmonic series segment, and 27 is already present in the 3-limit; thus any fifth-bounded chord involving 27 over the root has a harmonic (i.e. frequency-scale) inverse involving 29 in this subgroup. 29/16 is close to 9/5, a kind of superminor seventh, which provides a special "utonal" flavor to otonal chords without clashing too much with the fundamental. Meanwhile, primes 17 and 23 may be considered to clash with the fundamental, being close to a semitone and a tritone when octave reduced, so people may wish to exclude them. Therefore the subgroup can be considered to complete the harmonic series up to the lower half of the fifth octave without the more difficult ones near the edges. The same reasons also give rise to the 2.3.5.7.11.13.19 subgroup as a retraction.
Regular temperaments
Rank-1 temperaments (edos)
Edos which represents the subgroup better (monotonic in the subgroup and decreasing TE error): 41, 53*, 58h, 72, 77, 80, 87* (94), 99ef, 103h* (113, 118f, 118), 121, 130, 140, 152fj, 159, 183, 190, 198, 217, 224, 243e, 270, 422, 472, 494h, 552... and so on. Edos in parenthesis are inconsistent in the subgroup.
* Monotonicity considered for {1, 3, 5, 7, 9, 11, 13, 15, 19, 21, 27, 29} (omission of 25 is intentional)