What we know, or think is likely, is that the 340 appears to have the sequential homophonic substitution component just as the 408, though some kind of randomization (in the realm of speculation) is acting upon it.
Is it really sequential homophonic substitution?
340, 2-symbol cycles: 7.37 sigma.
340, 3-symbol cycles: 8.14 sigma.
408, 2-symbol cycles: 13.80 sigma.
408, 3-symbol cycles: 27.35 sigma.
The 2 and 3-symbol cycles measurements are a derivative of smokie’s system of measuring all cycles (exluding symbols that occur only once). Notice that with the 340 there is small difference between 2 and 3-symbol cycles sigma in contrast to the 408. I cannot truly answer wether it is sequential homophonic substitution or not but at least some mechanic must be diffusing unigram repeats over short distances.
Cycle randomization hypothesis.
If you add a 26% chance (roughly) of selecting a random homophone instead of cycling/following the sequence, a good approximation is made to the randomization we see in the 340. A sigma closer to 0 indicates a better correlation.
Stats that correlate well:
Versus 340, 2-symbol cycles: -0.01 sigma.
Versus 340, 2-symbol cycles, top half (1-170): 0.54 sigma.
Versus 340, 2-symbol cycles, bottom half (171-340): -0.57 sigma.
Versus 340, 3-symbol cycles: -0.02 sigma.
Versus 340, 3-symbol cycles, top half (1-170): 0.62 sigma.
Versus 340, 3-symbol cycles, bottom half (171-340): -0.48 sigma.
Versus 340, perfect 2-symbol cycles: 0.16 sigma.
Versus 340, perfect 2-symbol cycles, top half (1-170): 0.23 sigma.
Versus 340, perfect 2-symbol cycles, bottom half (171-340): -0.53 sigma.
Versus 340, perfect 3-symbol cycles: 0.18 sigma.
Versus 340, perfect 3-symbol cycles, top half (1-170): 0.16 sigma.
Versus 340, perfect 3-symbol cycles, bottom half (171-340): -0.16 sigma.
Versus 340, midpoint shift: -0.18 sigma.
Versus 340, sequential, allow 0 repeats per symbol: -0.47 sigma.
Versus 340, rows that have no repeats, average of cipher offsets 0 to 16: 0.02 sigma.
Versus 340, unigram total per rows, average of cipher offsets 0 to 16: 0.13 sigma.
Versus 340, unigram row coverage: 0.74 sigma.
Versus 340, unigram column coverage: -0.01 sigma.
Stats that do not correlate so well:
Versus 340, symbol appearance: -2.05 sigma.
Versus 340, prime phobia: 2.12 sigma.
Versus 340, unigram distance: 2.32 sigma.
Versus 340, unique sequence length 17 repeats 26: 2.52 sigma.
Versus 340, sequential, allow 1 repeat per symbol: -2.29 sigma.
Versus 340, sequential, allow 2 repeats per symbol: -2.57 sigma.
Versus 340, sequential, allow 3 repeats per symbol: -2.44 sigma.
Versus 340, sequential, allow 4 repeats per symbol: -2.22 sigma.
Versus 340, period 2 transposed 2-symbol cycles: 2.29 sigma.
Encoding restart, top and bottom half encoded individually with random keys, hypothesis.
Individual sequential homophonic substitution for the top and bottom half of the cipher with 12% cycle randomization in each part to match the 2-symbol cycles score of the 340.
To summarize the results, I am surprised how well the 2 and 3-symbol cycle measurements line up. Also the sequential measurements with allowance for repeats line up will, an issue of the cycle randomization hypothesis. Though, a major issue for me with this hypothesis is the sigma of -4.00 for the midpoint shift measurement, which looks at how well symbols are centered around the midpoint of the cipher. Perhaps loosening up the hypothesis by allowing more of the key space to be shared could improve the midpoint shift issue a bit.
Stats that correlate well:
Versus 340, 2-symbol cycles: 0.01 sigma.
Versus 340, 2-symbol cycles, top half (1-170): 0.62 sigma.
Versus 340, 2-symbol cycles, bottom half: (171-340): -0.15 sigma.
Versus 340, 3-symbol cycles: -0.30 sigma.
Versus 340, 3-symbol cycles, top half (1-170): 0.24 sigma.
Versus 340, 3-symbol cycles, bottom half (171-340): -0.30 sigma.
Versus 340, perfect 2-symbol cycles: -0.38 sigma.
Versus 340, perfect 2-symbol cycles, top half (1-170): -0.15 sigma.
Versus 340, perfect 2-symbol cycles, bottom half (171-340): -0.72 sigma.
Versus 340, perfect 3-symbol cycles: -0.43 sigma.
Versus 340, perfect 3-symbol cycles, top half (1-170): -0.27 sigma.
Versus 340, perfect 3-symbol cycles, bottom half (171-340): -0.40 sigma.
Versus 340, sequential, allow 0 repeats per symbol: 0.22 sigma.
Versus 340, sequential, allow 1 repeat per symbol: -0.43 sigma.
Versus 340, sequential, allow 2 repeats per symbol: -0.51 sigma.
Versus 340, sequential, allow 3 repeats per symbol: -0.51 sigma.
Versus 340, sequential, allow 4 repeats per symbol: -0.40 sigma.
Versus 340, rows that have no repeats, average of cipher offsets 0 to 16: 0.51 sigma.
Versus 340, unigram total per rows, average of cipher offsets 0 to 16: -0.63 sigma.
Versus 340, unigram column coverage: 0.40 sigma.
Stats that do not correlate so well:
Versus 340, unigram row coverage: 1.58 sigma.
Versus 340, midpoint shift: -4.00 sigma. <—
Versus 340, symbol appearance: -1.56 sigma.
Versus 340, prime phobia: 1.74 sigma.
Versus 340, unigram distance: 1.82 sigma.
Versus 340, unique sequence length 17 repeats 26: 2.57 sigma.
Versus 340, period 2 transposition 2-symbol cycles: 1.61 sigma.
