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I am aware of the more common intervals and whether or not they are dissonant, but these confuse me. Are any consonant, or are they all considered dissonant?

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All augmented and diminished intervals are — within the context of common-practice music theory — dissonant by definition.

"Consonance" and "Dissonance" are aesthetic, subjective concepts that are individually and culturally defined and which change over time. The consonance of octaves is relatively universal; but, for example, thirds were considered dissonant in early Western music until Western music decided they were consonant by the early 1400s.

By the early 15th century, in part because of the visits of the illustrious English composer John Dunstable to the courts of northern France, the third and sixth had become accepted in European music as consonant intervals (prior to this time they were considered mildly dissonant). (SOURCE: Britannica)

Similarly, both major and minor sevenths were considered dissonant in Western music ... until they weren't. Jazz and popular music, for example, treat them as consonances: that is, they don't need to be resolved.

Speaking from personal experience, I've known many people, including myself, who find major seconds quite pleasing to the ear. But at least in my case, before I found them pleasing, I found them quite ugly. Nevertheless, the common-practice music theory courses I took taught quite definitely that major seconds were dissonant.

Music theory is just that: a theory — a set of propositions intended to describe how certain music functions. To that end, it defines certain fixed concepts — consonant, dissonant, major, minor, resolution, etc. — that are (intended to be) valid only within the context of that theory. This is, in part, what gave rise the Schoenberg's idea of "the emancipation of the dissonance" (Wikipedia): that the socially/academically constructed ideas of consonance and dissonance, as well as the good/bad judgements that accompany them, need not define how music can be made.

This idea of what is dissonant or consonant, and why, is also discussed in:

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  • Part of the confusion / disagreements comes, I think, from throwing all intervals together in their octave-reduced class, but often octave spacing makes quite a difference. I consider the major second dissonant but major 9th consonant, and the perfect fourth consonant but the perfect 11th dissonant. The other thing is context. A major seventh by itself sounds rather dissonant, but a fully major seventh chord is pleasing even in close voicing. (Probably has something to with resultant fundamentals: in a major seventh chord you're rather hearing a major 14th instead of a major seventh.)
    – leftaroundabout
    Oct 18, 2021 at 21:53
  • ...and then there's instruments. What sounds consonant on string instruments is quite different from what sounds consonant on bells or even on clarinet (different kind of overtone spectrum). — Sure, cultural expectations have a lot to say as well, but very often there is a pretty good mathematical explanation for why something works in style A but not in style B.
    – leftaroundabout
    Oct 18, 2021 at 21:58

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