The big one you're missing is the concept of a scale; a regular progressive sequence of tones that is the foundation of melody and chord structure within the culture's music. Even within what we consider the "Western" system of music theory, the proliferation of scale definitions and qualities allow for myriad variations to evoke different regional cultural music styles in your mind when you hear them.
Most English speakers are intuitively familiar with the sound of two basic scales, which we call the "major" and "minor" scales. Major scales sound "happy", minor scales sound "sad". But this is just the tip of the iceberg of Western music theory. Using the same relative progression of pitches, but changing which note you use as the tonal "root" of your melody, you can change the sound of your melody and invoke other human cultures for which those melodic progressions are stereotypically common. Dorian mode, for instance, is based on what would be the second note of a major scale, and gives you a juxtaposition of both major and minor scale qualities. This mode is commonly associated with old European sacred styles like plainchant and early polyphony, and in a more alien context can be used to elicit a sense of age and gravity to a race. Start one scale degree higher, on what would be the third note of a major scale, and you have Phrygian. This scale sounds vaguely Middle-Eastern, though variations of it are also common in Spanish flamenco (understandable given the Moorish influence on Spanish culture, imported from across the Gibraltar), and it's been appropriated for many styles of metal for its more dissonant-sounding early note intervals. You might use it to evoke a similar "exotic" vibe for a race or planet, or in the metal sense to create an unsettled, dissonant atmosphere of ordered chaos.
This is all really just the tip of the iceberg of human music. From this foundation of heptatonic modal music systems, you get into:
- sparser pentatonic scales (stereotypically Asian sounding, though also used in American folk styles like blues),
- non-modal variations (Harmonic Minor, Byzantine, Hungarian Minor, Phrygian Dominant etc do not follow the typical Western progression of note modifications commonly referred to as the "Circle of Fifths", and commonly include unintuitive three- and four-semitone intervals between "adjacent" notes),
- more chromatic scales that include multiple adjacent semitones (a rule called Myhill's Property discourages this in Western theory, but the most commonly taught "blues scale" is a hexatonic scale that includes the tritone in an otherwise minor pentatonic scale, producing three adjacent scale degrees a semitone apart from each other), and even into
- microtonal scales, with intervals of less than a semitone (the "minimum resolution" of Western theory) that are more accurate translations of Arabic maqam tonal systems and similar Turkish, Persian and Hindi microtonal scale systems.
Cultural styles are also commonly defined by:
- the level of tonality (the importance of a "root note" to the structure of melody and harmony; most cultural genres are very tonal, to the extent of employing sustained "drones" on or closely related to the tonal center), but atonality is notable in jazz and classical styles),
- tuning centers (the importance of the notes played being within close tolerances to defined pitch centers based on a tuning standard; Western ears expect glissandos and pitch bends only in certain places in music, while African and East Asian styles have looser rules),
- consonance (the importance of multiple different pitches intuitively "fitting together" both within a chord and through a progression of notes and chords; what's "intuitive" is very culturally-dependent) and
- rhythm structure (most cultural styles have a defined beat system, often based on a layered recurring structure of sequences of beats and notes; not all music requires one though).
All of this is also dependent on time period; Western music styles, unarguably, have progressed and regressed in many ways over the period of recorded history, and many styles and genres progress more or less in parallel. Classical music has long pushed the boundaries of what we consider "consonant" or "dissonant", and while we can very easily identify very unpleasantly-dissonant arrangements of notes, there's an in-between of pitches and chord structures that "conflict" in frequency interval and are thus "dissonant", but aren't nearly as jarring to listen to as open dissonance, and these often lend a more ethereal quality to a music style, especially at slower tempos with more sustained, slower-attack/release note qualities. The human voice excels at these styles, and can, quite ironically, create some very unearthly-sounding music.
Switch up these basic variables, and you can create "music systems" playable by human instruments that sound very alien. Bring in instruments not commonly heard by Western ears (or at least not recognizable as being from any specific human culture) and you can further increase the "this is not human music" angle as you choose. Or, you can play something instantly recognizable as big-band funk, with Huttese lyrics. Your choice.