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Built a guitar, Myrtle/Sitka, triple X braced, so symmetrical bracing (or pretty close).
Neck has an 18mm Sapele centre lamination flanked by Idigbo (bit similar to Limba or Korina)
I've noticed that sounding the open strings in pairs, EA, DG, BE, or playing individual strings, the EA and BE strings sound quite rich in harmonics, and sort of "pulse" during the sustain/decay, quite sort of well, complex?
The middle strings DG, not so much - still sustain well, fine in volume and fundamental, but the harmonics are not so evident.
Tried different strings, D'Addario bronze, and D'Addario nickel bronze and Martin phosphor bronzes, same observations.
Any theories as to why this might be.

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The name catgut is confusing. There are two explanations for the mix up.

Catgut is an abbreviation of the word cattle gut. Gut strings are made from sheep or goat intestines, in the past even from horse, mule or donkey intestines.

Otherwise it could be from the word kitgut or kitstring. Kit meant fiddle, not kitten.

Wondering Colin, do you do spectrum analysis? If so, what frequencies are coming up.

Yes, but it's late and I don't have to hand.

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The name catgut is confusing. There are two explanations for the mix up.

Catgut is an abbreviation of the word cattle gut. Gut strings are made from sheep or goat intestines, in the past even from horse, mule or donkey intestines.

Otherwise it could be from the word kitgut or kitstring. Kit meant fiddle, not kitten.

I am wondering that too. If the top has a frequency close to the G it could be responsible for that string sounding different. If so, there are work arounds with adding side mass, or lightening up the bracing a little, to move the main top note - but others know far more than me on this topic.

Does it change if you detune by a half step, or two?

Sounds to me like you may have found a wolf.

Not so sure about the wolf, it's the same if I capo at the second or fourth fret.

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The name catgut is confusing. There are two explanations for the mix up.

Catgut is an abbreviation of the word cattle gut. Gut strings are made from sheep or goat intestines, in the past even from horse, mule or donkey intestines.

Otherwise it could be from the word kitgut or kitstring. Kit meant fiddle, not kitten.

OK, you have identified that it is those strings, not certain frequencies, that are different. Have you tried different strings? Is the saddle slot not flat on the bottom, or saddle not well seated? How is the break angle and contact of string to saddle? Check nut slots.

The 'pulse' you're hearing is most likely beating between the partials of the different strings. More beating isn't necessarily an indication of more partials; beating is more of a matter of how those partials relate to each other in pitch. You hear more beating when they're slightly off pitch from each other. There could be several things causing that to differ in string pairs.

Each of the pairs of strings you're using is tune to the interval of a fourth. If each string in a pair had the same structure of partials, and they were accurately tuned, you should hear similar beating between them, but faster in the higher pitched strings. That gives us a couple of places to look.

How are you tuning the strings? A good electronic tuner should be the most accurate way to get things right. Pluck the strings in the center to be sure you're tuning the fundamentals, and not getting as much input from upper partials.

If you're tuning them by comparing octaves then issues with the intonation of the strings could introduce differences that would give more or less beating. Tuning by 5/7 fret overtones can really cause problems, especially with the B string, so that my not be likely to be giving rise to the difference you're hearing.

Do you tend to 'sweeten' the tuning at all? That's generally a departure from 'true' 12-tone equal temperament, and will cause the intervals to be different from a 'perfect' tempered scale.

String stiffness tends to shift the upper partials sharp relative to a true harmonic series. Each string has different stiffness, and it's partials are shifted differently from the others. The B string tends to be more inharmonic than the high E, and the low E to be more so than the A, but the D and G may not be as different in that respect. So that's a possible cause.

Generally speaking the better the guitar is the more this sort of thing tends to show up, so you can take this as an indicator that you've made a pretty good one.