A musical scale is a sequence of musical intervals in a certain range, such as an octave; a mode is a cyclic permutation of a scale; a key is a mode at a certain pitch‐level; a raga is a melodic pattern of a key. There are 66 heptatonic scales, 462 heptatonic modes, and 5544 heptatonic keys. For each key there are thousands of possible ragas, or a total of many millions of ragas.
Most writers, confusing scales and modes, have listed comparatively few of the possible scales. The older writers were further limited by harmonic considerations. Slonimsky's scales and melodic patterns (1947) are mostly ragas, in which, as with Schillinger (1946), symmetry is paramount; Slonimsky's pentatonic and heptatonic scales are actually modes.
The inverse of a scale contains the same intervals in reverse order. The complement of a scale contains all the notes of an octave not in the scale itself. A scale may be measured by the total mean‐square deviation of all its intervals.
The notation of a heptatonic scale as a harp scale (with seven letter names) agrees with the deviation index. However, the function of notes in the scale may often be expressed by fewer than seven letter names or by two different names for the same note. For the composer, the intensive study of individual scales will be more rewarding than the listing of thousands of keys or millions of ragas.