I'll throw in a couple cents here....I would say that the fullest tone is produced by the least amount of restrictions in the breathing apparatus. While there are times we might want to actually create a thin, piercing, shrill, whatever, tone, most of us are going for deeper, fuller, "bigger" tone. Breathing actually involves the coordinated participation of several groups of muscles, and the adult who is not interfering or constricting with at least some of them is very, very rare.
The diaphragm could be considered the starter, since it is at the geographic bottom of the air column, but freedom of the intercostals, which move the ribs, is also beneficial, and finally the upper area of the chest expands also (check out movement in your collar bone ). Diaphragmic breathing gets a lot of emphasis since so many (especially) westerners have shut down this part of their breathing. Also, if you depend on all your breath expansion in your collarbone, its gonna give you a lot less than if you get it from your diaphragm. Movement in the diaphragm probably affects overall air volume more than the other muscle groups, but freedom in them greatly benefits flexibility and tone.As the entire breathing mechanism becomes more free, tone will improve.
Tone is also greatly affected by the openness of the throat and mouth, (it is possible to breathe with freedom while constricting in the throat, mouth, lips etc.). I think even sinuses and head cavities affect tone. The greater freedom we learn to allow through all the structures that create and surround the column of air, the bigger tone we will have, and the greater fluency to vary it.
So how do you improve tone? Don't restrict. Don't interfere with any of the structures that create and surround the column of air, while still constricting where necessary. This may sound flippant but I don't mean it that way. It is not relaxation- would you describe Michael Jordan as relaxed when he's playing basketball? How about Tiger Woods hitting a golf ball, or Fred Astair dancing? Certainly there is something that calls to mind relaxing there, since these guys are not using any excess tension, or constricting one bit more than they need to achieve their activity. Our job is no less athletic or coordinated, just a little harder to see, like most things related to the harp. We need to apply muscular contraction to a certain degree to create embouchure, get a good seal with the harp, create a single hole, hold the harp, start an in-breath, etc. etc. Our problems come from overdoing what is necessary, and largely because we have a lifetime of experience overdoing in all our activities.
So one way of turning that around and opening up a larger chamber for bigger tone is to apply awareness to ourselves in the process of doing our beloved activity. Certainly the exercises as described by Mr. Hunter, if done consciously , will provide an arena in which to become aware of how we restrict our breathing and interfere with the production of a note. And so would Mr. Michalek's suggestion to become aware of the resonant chambers that we use in our mouth/throat to produce a note. The more we could expand our field of attention to become aware of all the mechanisms we are bringing in to play this little tin sandwich, then we can allow them to operate with less restriction, interference and tightness, and more freedom, and expansion.