and to note some of the distinctions, which have been too commonly confounded, between the Greek principles and our own. I will spend a few words first upon the three genera of the Greeks, since their titles belong to our modern terminology, though with meaning somewhat amplified.

genus.

The Diatonic genus admits of none but the normal Diatonic notes of the key in which a musical passage is castthose notes-namely, that accord with the signature of each key in modern music. Through inflection by sharps or flats, notes bear the same relationship to their key-note in any one key as in every other. Thus the sharps which characterize the key of A, or the flats which distinguish the key of bA, bring the notes of these keys into the same relationship with their key-note as that of the natural notes to the keynote of C. Sharps or flats, then, may exist in the Diatonic genus, but those only which belong to the signature of the key.

genus.

The Chromatic genus of the Greeks contained, in Chromatic each tetrachord, or series of four notes, two notes that we should write on the same line or in the same space, the one being raised above the other by a sharp or a natural-as C and #C, bB and B. Our modern Chromatic genus may be defined as admitting accidental sharps, flats, or naturals, which induce no modulation to another key. Let me exemplify the distinction between these two genera: a musical phrase begins in the key of C, and modulates into the key of G, and the #F that induces this modulation is marked by an accidental:

pp

SONATA, Op. 53.-Beethoven.

another phrase continues throughout in the key of C, and yet contains an accidental #F twice :

OVERTURE TO DER FREYSCHÜTZ.-Weber.

D

8

The first of these phrases is Diatonic, because the #F belongs to the key of G; the second is Chromatic, because the F does not alter the original key.

genus.

The genus I have yet to describe is called Enhar- Enharmonic monic. This, with the Greeks, comprised a smaller interval than the semitone-a note, namely, between B and C, higher in pitch than the first but not so high as the second. The word Enharmonic may perhaps be rendered inter-harmonic, and probably implied an intervening sound-having the same reference to the B between B and C that in architecture, it has to the style between the Corinthian and the Composite.

I shall have future occasion to discuss the etymology of the names of the other two genera, but may dismiss this term Enharmonic with what has now been said. There are two accounts of the origin of the Enharmonic genus. One refers it to the Eastern and Southern nations who habitually intonate smaller musical intervals than semitones-the Persians, for instance, divide their scale of an octave into eighteen sounds, whereas our modern scale is divisible into no more than twelve (the thirteenth, C, being a repetition of the first) :

1 2

3

4 5 6 7 8 9 10 11 12 13

Greek modes.

The other account ascribes the origin of this genus to a practice of sliding the voice from one to the other note in an interval of a semitone instead of attacking distinctly the two individual sounds-a practice analogous to the portamento of modern singing; and in this sense, though it is never written, the effect of the Enharmonic diesis is employed by no means rarely in the musical performances we daily witness. So far as regards musical notation, it may be said that the word enharmonic denotes the distinction between the several names that may be given to the same sound on a keyed instrument, as #C and bD; the true distinction between these two notes, which may be articulated by a voice or on an instrument such as the violin, whose notes are stopped by the fingers, presents a field for wide discussion which must be reserved till a subsequent lecture.

In the diatonic genus, the Greeks had several modes-or, as we should now call them, scalesdiffering, as do the scales of our several keys, in being higher or lower than each other, but corresponding, as do our scales, in all having the same distribution of tones and semitones. From the Greek modes, the Dorian may be cited as the standard of all, and it may thus be represented in modern notation:

The Phrygian mode began from E, and had the same distribution of tones and semitones as the Dorian, which was induced by the addition of a sharp to F and the withdrawal of the flat from B. The Lydian began from F, and had #G and C. The Mixo-Lydian began from G, and had bB and E. Each of these modes had a collateral mode at the interval of a 4th below, and this was distinguished by the addition of the prefix Hypo (under) to the name of the original ; so, the Hypo-Dorian may be counted from A with all natural notes, the Hypo-Phrygian from B, with #C and F, the Hypo-Lydian from #C, with D, F, and #G, and the Hypo-Mixo-Lydian from D with B.

and Plagal,

The original four modes were styled Authentic, and Authentic were characterized by the two predominant notes of melodies which were cast in them (equivalent to our Tonic and Dominant) being at the interval of a 5th.

The four Hypo modes were called Plagal (or sidewise, or relative), and were characterized by the two predominant notes of melodies which were cast in them being at the interval of a 4th.

These terms Authentic and Plagal have endured to our time, and still denote the same melodic affinity, defining the variable forms of any one melody for the