9. A discord is a combination in which both its logical origin in a musical scheme and its acoustic roughness show that it cannot form a point of repose.
10. The perfect concords and perfect intervals are those comprised within the first four members of the harmonic series, namely, the octave, as between numbers 1 and 2 of the series (see Ex. 1 above); the 5th, as between Nos. 2 and 3; and the 4th, as between Nos. 3 and 4.
11. All notes exactly one or more octaves apart are regarded as harmonically identical.
12. The root of a chord is that note from which the whole or the most important parts of the chord appear (if distributed in the right octaves) as members of the harmonic series.
13. A chord is inverted when its lowest note is not its root.
14. The major triad is a concord containing three different notes which (octaves being disregarded) are identical with the first, third and fifth members of the harmonic series (the second and fourth members being negligible as octaves).
15. The minor triad is a concord containing the same intervals as the major triad in a different order; in consequence it is artificial, as one of its notes is not derivable from the harmonic series.
16. Unessential discords are those that are treated purely as the phenomena of transition, delay or ornament, in an otherwise concordant harmony.
17. Essential discords are those which are so treated that the mind tends to regard them as definite chords possessing roots.
18. A key is an harmonic system in which there is never any doubt as to which note or triad shall be the final note of music in that system, nor of the relations between that note or chord and the other notes or chords. (In this sense the church modes are either not keys or else they are subtle mixtures of keys.)