As the title says, what's the difference between "modal music" and "tonal music"? Is there also any other classification besides "modal music" and "tonal music"?
"Modal" and "tonal" both describe works that:
The difference between modal and tonal are in the harmonic languages surrounding the tonal center. Tonality implies the system of common-practice harmony well-established by the eighteenth century that uses major and minor keys. The tonal center of a tonal work is the first note of the major or minor scale in use as the pitch collection. The harmonic implications of tonality are more than just the use of major and minor scales, as functional harmony is also a feature of tonal music. The progression from the dominant sonority (a major triad with or without a minor seventh from the triad root based on the fifth note of the major or minor scale in use, or a similar-sounding substitute such as a fully-diminished seventh chord based on the leading tone) to the tonic triad to end a work is just one characteristic of functional harmony. This characteristic is so important that, if the dominant sonority is instead a minor chord (thereby lacking the leading tone), the work no longer sounds tonal. This means that even in a minor key, the seventh note of the scale is very often raised so that it becomes the leading tone.
Modal music uses diatonic scales that are not necessarily major or minor and does not use functional harmony as we understand it within tonality. The term modal is most often associated with the eight church modes. The tonal center of these modes is called its "final." All the church modes use a pattern of half and whole steps that could be played on the white keys of a piano. You may notice that there are only four different patterns among the church modes; the difference between e.g. "dorian" and "hypodorian" is whether the final occurs at or near the bottom of the melodic range or whether the final occurs in the middle of the melodic range. The term "modal" has expanded in more modern music to encompass any non-tonal music that uses a diatonic pitch collection and has a tonal center.
There are many types of music other than modal and tonal. Some examples include:
I did not even touch on music that does not use pitches at all; for example, an unpitched percussion work would clearly not be modal or tonal.
There are entire books on functional harmony, modes, etc., but I hope this has been a reasonable summary to answer your question.
Modern modal music has 7 modes built from the major scale.. You can have a composition in all but the last one since the 1st 3rd and 5th notes of this mode will result in a diminished triad which is unstable.Modes are also built on the melodic and harmonic minor scales. Fewer compositions are seen using the major modes and all modes in jazz are used to improvise.
Natural modes are of the harmonic and melodic relationships to the tonal center or chord center of the progression and these are built from different steps of the diatonic scale. The scale of the mode is the notes in stepwise succession. Other modes that are altered or come from a diatonic variant such as harmonic or melodic minor (Dorian #4 or Lydian #5) or harmonic major (Mixolydian b2) can be used to provide a tonal center or chord center in a progression also.
A progression with the same chord set as the major scale that being in C using 7th chords
Cmaj7 Dm7 Em7 Fmaj7 Gdom7 Am7 Bhd7
based around the Em chord but in the key of C would be Phrygian. Say a progression of
Em7 Am7 Bhd7 Em7
to have the i-iv-v-i represented in the Phrygian iii-vi- vii-iii.
Now Phrygian is part of two diatonic sets. The prodominate major (such as Ionian-Aeolian) Mixolydian-Phrygian and the Prodominate minor Phrygian-Ionian. Secondary dominants and secondary half diminished can be used for your progressions to reinforce the definitive major (Ionian) or the definitive minor (Phrygian).
The book to get is "Modal Diatonicism" available on Amazon.com and at Barnes and Noble. It has in depth theory and method for modal writing and explains the diatonic sets and their secondaries with the resulting diatonic variants for each. It has 100+ notational examples and is extremely useful as a text for understanding modes and as a reference for compositional methods.