Now for hq things get (if you can believe it) even more complicated and non-retail. Most crafters have at least a cursory understanding of HQ tiers:

0-10 skill = T0 = 1-2% hq

11-30 skill = T1 = ~10% hq

31-50 skill = T2 = ~25% hq

51+ skill = T3 = ~50% hq

The same basic tiers are in place however subcrafts do not factor in, and they are not based on your level difference (as in retail) they are instead based on "difficulty" (which as you may remember from last paragraph is level difference affected by a bunch of other garbage). Not only is the day/moon/direction affecting difficulty and HQ tier, it's also affecting HQ rates directly. This means that HQ rates can vary wildly depending on when you synth and where you're facing.

Let's take the level 75 wind synth of elemental staves as an example. On retail for the best HQ rate you would want 100 skill + 3 (adv. support) + 2 (gear) + 1 (furniture) = 106 skill = 31 levels above cap = T2 = ~25% hq rate. Synth on new moon darks facing east if you want a small boost to hqs, and that's pretty much the end of it.

On Nasomi server the furniture doesn't work yet, so the maximum attainable skill is 100 + 3 (adv support) + 2 (gear) = 105. Okay on its own that's a difficulty of -30 = T1 = 10%, but the story doesn't end there. Synthing on darksday or iceday will raise difficulty by 1 and boost HQ rate by 33%. Synthing on new moon will raise difficulty by a further 1 and boost by a further 33%. So new moon iceday will be difficulty 28 (still T1) with two 33% boosts to hq rate totaling a roughly 16% chance at hq.

Well that difficulty of -30 is awfully close to the difficulty -31 we'd need to get T2 status... Let's examine some of the ways we could lower difficulty. We could synth on neutral moon lightsday. That would be -31 difficulty = T2 = 30% HQ rate; however lightsday incurs a 33% penalty to overall hq rate landing you at ~20% for final hq rate.

That's nicer than new moon ice by a little bit but let's examine other options. Perhaps if we used moon to get us the difficulty we need. Neutral day + exactly 100% moon would lower difficulty by 1 = -31 = T2 = 30%... but full moon incurs the same -33% penalty to HQs that lightsday does still landing us at 20% hq rate.