PURE POLYPHONY The first matter of principle that emerged from the chaos was that if the parallel movement of perfect concords was right, every thing else was wrong. A few compositions show an evenly-balanced conflict of opposing principles. Our wonderful English rota "Sumer is icumen in" sounds to us like a tuneful six-part double canon spoilt (or rendered quaint) by numerous consecutive 5ths. Its contemporaries were more likely to have regarded it as a beautiful scheme of perfect concords spoilt or illuminated by dangerous licences. There was no room for prolonged doubt as to where the path of progress and freedom lay. And if the basis of harmony was to be independent melody, then one of the main cares of the composer was to prevent his independent melodies from lapsing into duplications. Fifths and octaves will still form (as they do at the present day) cardinal points in every chord that is dwelt upon ; but no two voices can double each other for two consecutive octaves or 5ths without dissolving their integrity in a false resonance.
As to discords the criterion ceased to be acoustical. After centuries of trial and error, musicians accepted 3rds and 6ths as concords; and all discords became equal to one another in mild ness when they occurred as unaccented passing-notes proceeding by diatonic conjunct notes between one concord and the next. Polyphony made musical accents far stronger than those of speech; and so the behaviour of accented discords was more restricted. The accented discord must be "prepared" by first appearing as a concord. It then becomes a discord by being held or "suspended" while the other voices move against it ; after which it must "resolve" by a step downwards. Upward resolutions are harsh and cf complex import, intelligible only in a later system, and so are discords that skip.
Ex. 3 shows passing-notes (marked*) moving up and down between concords: Four three-note chords attained the rank of concords. (Two of them were only inversions of the other two.) First, of course, there was the major triad, the upper three notes (4, 5, 6) of the sestina (Ex. I). All doublings and differences of octave are neg ligible in the distribution of a chord so long as they do not bring its middle or upper notes into the bass. All the following examples are concords identical with the sestina and with each other, though the positions that leave two parts low at a distance from the upper parts, or that double the 3rd, are acoustically as rough as many a discord. Positions (d) and (e) could be justified only in cir cumstances of great polyphonic or instrumental interest.
The essential intervals are those of position (a) and comprise a perfect 5th (G—D), a major 3rd from the bass (G—B) and a minor 3rd above (B—D) .
Now in listening to polyphony the mind can appreciate the parts two at a time; and the i6th century theorists avoid reason ing as if the mind could do more. They were probably right as well as cautious; nor is it necessary that the mind should attempt more. For any fault in the aggregate of the richest polyphony must be a fault between two parts. If it concerns more, then it is more than a single fault; and if there are no faults, the ear enjoys the faultless aggregate whether it can distinguish the parts or not. Accordingly the question arises : Will the ear resent an aggregate which corresponds as such to nothing in nature, but which con tains no intervals that have not already been accepted in the sestina? In other words, can we treat as a concord a triad which puts the minor 3rd below the major? The history of harmony not only answers this in the affirmative, but shows that the contrast between this artificial concord and the major triad is essential to the formation of a flexible musical language. Some theorists, fascinated by the ways in which minor harmonies behave like major harmonies reversed, have invented schemes according to which the "roots" of minor chords are their top notes. The way in which minor chords happen in music does not support any theory which makes Ex. 6 anything other than an artificial alteration of Ex. 5, with the same entirely fundamental behaviour of the same bass-note in every relevant musical con text. The artificiality of the chord is not arbitrary or conven tional ; it is of the very nature of art and is far more self -explana tory than most of the phenomena of spoken language.
Both the major and the minor triad are found in "inverted" positions. An inversion is not a reversal, but a position in which one of the upper notes of the normal chord has become the bass note. When the 3rd of a triad is in the bass we have the chord of the 6th, thus: And now arises a phenomenon wholly unintelligible to acoustics and unpredictable by theory. The once perfect concord of the 4th becomes a discord when taken from the bass. Between any higher parts it is a concord ; but from the bass it will never do except as a passing-note or a properly prepared and duly resolved suspension. The reason for this is purely contingent. It so hap pens that practically every context in which an accented 4th occurs from the bass implies a 5th above it, as in Ex. 4. If instead of the sth you substitute a 6th you will obtain a chord which is theoretically a second inversion of a triad.
But no amount of logic will persuade the ear that this 6th is more than another appoggiatura or "leaning-note" demanding as ur gently to resolve on the 5th as the 4th demands to resolve on the 3rd. The fact is an accident of far-reaching importance, but as unamenable to grammatical logic as the reason why a modern English poet should not apply the epithet "blooming" to his lady's cheek. Find a context for a 4th from the bass which does not imply the a 8 of Ex. 4, and that 4th will cease to be a discord. But it will be some strange and pregnant language, not to be taken in vain ; like the cry at the beginning and end of the Allegretto of Beethoven's seventh symphony. And even there the ear is, at the outset, expecting the true bass and remembering it at the end.
The harmonic materials of i6th century polyphony are, then, the major and minor triads, their inversions as chords of s , and the discords of the end and 7th and (from the bass) the 4th, treated either as suspensions or as passing-notes. The scale in which the flux of polyphony moved through transient discord from concord to concord was the diatonic scale preserved from ancient Greece and handed down. directly from the Greco-Roman or Ptolemaic system to the church-music of the middle ages, doubtless with conflation from Jewish sources.