One reason that Indian music sounds so different to the Westerner is that the major/minor tonal system is not used. Harmony, and specifically tonal harmony, has been the basic organizing principle in Western music - classical, folk, and popular - for centuries. In this system, a piece of music is in a certain key, which means it uses the notes of a particular major or minor scale. The harmonies developed using those notes are an integral, basic part of the development and form of the music. Most of the complexity of Western music lies in its harmonies and counterpoint.
The music of India does not emphasize harmony and does not feature counterpoint. In fact, most Indian classical music features a single voice or instrument on the melody, accompanied by drone and percussion. There is no counterpoint and no chord progression at all. Instead, the interest and complexity of this music lies in its melodies and its rhythms. (Just as Indian music can seem confusing and static to someone accustomed to listening for harmonic progressions, Western melodies - based on only two types of scales - and Western rhythms - based on only a few popular meters - may sound overly similar and repetitive to someone accustomed to Indian music.)
Western music divides an octave into the twelve notes of the chromatic scale. But most pieces of music mainly use only seven of these notes, the seven notes of the major or minor key that the piece is in. Indian music also has an octave divided into twelve notes. These twelve notes are called swaras; they are not tuned like the notes of the chromatic scale (please see below). Also similarly to Western music, only seven notes are available for any given piece of music.
But there are important differences, too. Western scales come in only two different "flavors": major and minor. The two are quite different from each other, but any major key sounds pretty much like any other major key, and any minor key sounds basically like every other minor key. This is because the relationships between the various notes of the scale are the same in every major key, and a different set of relationships governs the notes of every minor key. (Please see Major Keys and Scales and Beginning Harmonic Analysis for more on this.)
The seven-note thats of Indian music, on the other hand, come in many different "flavors". The interval pattern varies from one that to the next, and so the relationships between the notes are also different. There are ten popular thats in Hindustani music, and Carnatic music includes over seventy mela.
Although the first note of an Indian scale is often given as C, Indian
thats and ragas are not fixed in
pitch; any raga may actually begin on any pitch. The important information about each
that and
raga "scale" is the pattern of
intervals, the (relative) relationship between the notes, not absolute
frequencies.
Making for even more variety, a piece of Indian classical music may not even use all seven of the notes in the that. The music will be in a particular raga, which may use five, six, or all seven of the notes in the that. And a that can generate more than just three ragas (one pentatonic, one hexatonic, and one full raga). For example, Bilawal raga includes all 7 notes of Bilawal that (which corresponds to the Western C major scale). Meanwhile, Deshkar and Durga are both five-note ragas that are also based on Bilawal that. Deshkar omits the two notes (Ma and Ni) corresponding to F and B; and Durga omits the two notes (Ga and Ni) corresponding to E and B.
Further confusing the issue for the novice, the two traditions often use the same name for completely different ragas, and there can be disagreement even within a tradition as to the name or proper execution of a particular raga. Ragas may be invented, combined, borrowed from other traditions, or dropped from the repertoire, so the tradition itself, including the "theory", is in many ways more fluid and more varied than the Western tradition.
It is also important to understand that a raga is not just a collection of the notes that are allowed to be played in a piece of music. There are also rules governing how the notes may be used; for example, the notes used in an ascending scale (aroha) may be different from the notes in a descending scale (avaroha). Some notes will be considered main pitches, the "tonic" or "most consonant" in that raga, while other notes are heard mostly as ornaments or dissonances that need to be resolved to a main note. Particular ornaments or particular note sequences may also be considered typical of a raga. The raga may even affect the tuning of the piece.
If this seems overly complicated, remember that the melodic and harmonic "rules" for major keys are quite different from those of minor keys. (Consider the melodic and harmonic minor scales, as well as the tendency to use different harmonic progressions.) This actually is quite analogous; the big difference is that Indian music has so many more scale types. Since the nuance and complexity of Indian music are focused in the melody rather than the harmony, it is this large number of scales that allows for a great and varied tradition.
Those who are particularly interested in modes and scales may notice that there is a rough correlation between some Hindustani thats and the Western church modes. For example, the pattern of intervals in Asavari is similar to that of the Aeolian mode (or natural minor scale), and that of Bilawal is similar to the Ionian mode (or major scale). Some thats do not correlate at all with the Western modes (for example, take a close look at Purvi and Todi, above), but others that do include Bhairavi (similar to Phrygian mode), Kafi (Dorian),
Kalyan (Lydian), and Khamaj (Mixolydian). Even for these, however, it is important to remember the differences between the traditions. For example, not only is Asavari used in a very different way from either Aeolian mode or the natural minor scale, the scale notes are actually only roughly the same, since the Indian modes use a different system of tuning.