I find the application to music frustrating. Before it meant having the requisite ministers. Music at Mass was normative as a part of the solemn Mass, which was itself the normative liturgy. Everything else references it. In a similar way, the office is solemn when it has incense and assistants in cope, but this became a thing for Sundays and more important feasts only, but it could be done in theory daily, but this is only done at Lauds and Vespers. The other hours are never solemn, and Vespers is more solemn than Lauds, I more than II.

Yes, you have the solemn tones, but the solemn tones ad lib. can be used daily, the solemn preface and Pater Noster tones are used for all but the lowest rank of feasts (same with the “tonus festivus” of the Deus in Adjutorium of the office) and for many votive Masses. Only functions for the dead categorically exclude a solemn tone.

Now? It has no connection to what it used to mean, and _solemnity_ means the highest rank of feast, but they want to call _feast_ something intermediate when it should just be the default name. It creates a lot of needless confusion.

(Show lexicon entry in Lewis & Short ...)

https://www.perseus.tufts.edu/hopper/morph?l=sollemnis&la=la#lexicon

sollemnis (less correctly sōlemnis, sollennis, sōlennis , sollempnis ), e, adj. sollus, i. e. totus-annus, prop. that takes place every year; in relig. lang. of solemnities,

I.yearly, annual; hence, in gen.,
I. Lit., stated, established, appointed: “sollemne, quod omnibus annis praestari debet,” ...
II. Transf., according as the idea of the religious or that of the established, stated nature of the thing qualified predominates.
...

[EDIT]url corrected

I can’t say that the definition of solemn has ever presented a problem to me. In the old mass it just denotes a specific form of celebration, or more broadly a higher degree of importance calling for more effort and splendour in the celebration. With the more free-form optionitis of the new mass emerged a concept of progressive solemnity, which boils down to more singing = more solemnity, plus the same general idea of effort and splendour. That said I don’t see how “containing all the parts” is a good definition.

At the Cathedral of Our Lady of Walsingham a 'solemn high mass' is - everything (except the homily) is sung, incense is offered, a deacon, a sub-deacon (who is an ordained acolyte) and the thurifer wearing a tunicle.All should be wearig a tunicle. and quite a number of servers, the choir and enthusiastic people. A solemn high mass is offered every Sunday and Solemnity throughout the year. On very special occasions a solemn Te Deum is sung following the mass.

Whoops. Mea culpa.

I am guessing that the definition referred to in the original post was in reference to the German/Austrian traditions of Mass compositions in the eighteenth century. A Missa solemnis in that context has all the movements, and is also often distinguished by being a longer setting. This is in contrast to a Missa brevis, which in some times and places meant just a Kyrie/Gloria pair or a Missa ferialis, which had no Gloria or Credo. There were other traditions like the Landsmesse, which shortens the text of the Gloria for rural parish use.