Tuning and Intonation in Fifteenth and Sixteenth Century Polyphony

Early polyphony, from its beginnings in the medieval age was constructed using the modal system. This modal system remained in use into the sixteenth century, during which it underwent changes before becoming the major-minor tonality of the seventeenth and subsequent centuries. It is important to remember that these modes were not based on the white note to white note passages found on the equally tempered piano keyboard, which is an ideal simplification for the student of harmony, but rather they have developed from the Ancient Greek tuning systems of hexachords. Irrespective of the exact method of tuning, all modes can provide a beautiful melody in a monophonic setting. If we were to stick with a precisely tuned scale though, for example that of a keyboard instrument, we would run into problems with harmony.

It would be naïve to think that Ancient Greek music remained stylistically continuous throughout the whole of Ancient Greece, and doubtless the Greeks had many ways of overcoming problems of intonation in tuned instruments, both technical and compositional. Most likely too, there were methods that have not been documented. In fact equal temperament has been known since the time of Pythagoras. Its use however is not continuous. The important thing to remember though is that the voice is free of fixed temperaments and voices combined will react with each other in attempt of euphony and this is true of all music.

The Romans, who acted as a conduit, bringing the Greek modes to the medieval era, adopted these modes. By the time of Guido the modes had undergone changes since the time of Ancient Greeks but the emphasis on melody remained the same, plainsong being the order of the day.

We then move on to early polyphony. Polyphony started with the use of canon and this being simple at first produced simple harmonies. The use of triadic harmony meant that certain notes in the scale would not be fixed so as too keep all harmonies euphonious. This means that some notes (and intervals) must change from one harmony to another, this process is natural and a good singer need not be consciously aware of this. These notes are known as mutable notes and the exact number of them depends on the harmony used and on its complexity. A simple example of this, and that given by Ll. S. Lloyd and Hugh Boyle in their Tuning and Temperament is that of Summer is icumen in. This melody, accompanied by twoPes, is in the Ionian mode transposed onto F and despite being in six parts produces a surprisingly simple harmony:

Sumer is icumen in

Sumer is icumen in

As the Ionian mode is tuned on F the first chord therefore presents no problems of intonation. The second chord is built on the second degree of the scale. If this were to be sung in a way that produces consonance then we should need a perfect fifth between the G and the D, they are however the second and sixth degrees of the mode between which there is not a perfect fifth. Obviously a note has to change. Now it conveniently works out that if we transpose the mode up a minor tone onto a G the sixth degree of the mode on F and the fifth degree of the mode on G are the same note. Therefore if the singer sings the interval F to G as a minor tone as opposed to a major one then (as found in the Ionian mode) there is a perfect fifth between the G and the D. The G that changes pitch is known as a mutable note. A good singer need not be aware of mutable notes, as they will change the notes automatically.

Mutable notes meant that as music developed throughout the sixteenth century consonance could occur in polyphony. As counterpoint became more complex the number of mutable notes increased, although as a natural practice of singing intervals in tune it did not create any technical problems as far as a cappella singing was concerned. As harmonic complexity grew the ability of choirs to adjust the mutable notes also grew; the very nature of the voice allows continual adjustment of pitch so that even enharmonic changes present no problems, and therefore it is possible for a choir to sing very chromatic music, although this does somewhat depend on the ability of the choir.

Whilst modes have a particular scale associated with them in practice they are quite flexible. When performing a melody the modes have a more solid structure but with counterpoint the resultant harmonies insist that the modes attain a certain degree of flexibility. It is also important to note that to the contrapuntal composer the harmonies produced, whilst still significant, were largely the result of a more horizontal approach to composition and therefore melodic progression within the parts was paramount and the flexibility of the modes allows the retention of the melodies.

To the composer working before the baroque era, there would have been no such thing as the heptatonic scale. Rather, the composer would still be thinking in the hexachordal system used by the Greeks. As such the modes would consist of the starting note, the octave above, the five ascending notes to complete the hexachord, an extension above to a seventh note and finally one a semitone below. Thus scales consisted of nine notes. For example in the Aeolian mode the starting on D has in the hexachord: D E F G A Bb. There then follows an extension above to C and a further one below to C sharp. This permits one of the most characteristic harmonic features of the period, that of the false relation, whose use continued into the baroque through the use of melodic minor scales. As far as tuning is concerned these notes are to be sung such that the intervals are sung with consonance and such notes may be mutable.

If the composer were to stick with just the notes of the mode it would be hard work to keep the listener engaged. Colouring the notes or chromicising them is an important part of the composing process, its usage ever growing with the development of contrapuntal technique. When tuning these notes the singer will adopt the same practice as with the mutable notes and will adjust the pitches so as to provide concord. This also accounts for the increasing use of dissonance, in the form of our suspension. When a singer sings the preparation of a suspension they are singing a consonance and tuning should present no difficulty, then the note is simply held for the suspension and the dissonance occurs. Finally the singer falls to the resolution and will once more be at a consonance. With the flexibility of tuning in the modes, how does one sing a particular dissonance, especially if more than one person is singing the same note? Therefore the practice of preparation-suspension-resolution overcame the difficulties of singing dissonances, and explains why there are so few unprepared dissonances in fifteenth and sixteenth century counterpoint.

Problems do arise when accompanying singers with other instruments. On a modern day violin the performer is allowed the same freedom as a singer to play an infinite number of pitches, now although the violin did not exist at the time, stringed instruments did in various forms. The bowed precursors to the violin family were allowed the same freedom of pitch, or else like the lute were fretted. Now, supposing one were to put frets on a stringed instrument baring more than one string and it were not to be tuned in equal temperament, then the frets would be in different places on different strings; such a system would be devastatingly complex and therefore fretted instruments have always been tuned in equal temperament.

This does not mean however that the same issues we have today with equal temperament do not occur. The third would still be too large and the fifth too small, but it provides convenience for the instrument builder, performer and composer.

Whilst the problems involved in harmonic changes provide no hindrance to the a cappella choir, with the strings and lute (with regard the ensembles technical ability) there are several reasons why more exotic keys weren’t used. Firstly, if you were to write a piece of music in the Dorian mode on F, you are going to stay within certain pitch parameters of the mode. If one were to start the mode on F sharp instead, you would be using the same pitch parameters, but tuned up a semitone, which would produce the same result, but would require a lot of extra notation driving printers of the day crazy! The second reason is one of acoustics; the stringed instruments resonate better when then pitches used allow sympathetic vibrations with the harmonics of the strings that are not played, especially with the lute, which has unplayed strings for that very purpose. This resonance is achieved when the mode is transposed onto the pitches that instruments are tuned to. Thirdly, just as playing in F sharp major on a modern guitar is extremely difficult, the same is true of the lute and composers were aware of this.

Not all polyphony was accompanied by lute and strings but any combination of these and a cappella was used. The real difficulty in tuning is when instruments with fixed pitches come into play, i.e. those with keyboards or early woodwind such as the recorder. When keyboards accompanied vocal music or simply when polyphony was written for keyed instruments there would have to be several compromises made. To allow the player to play more than a monophonic melody in a fixed mode the musicians of the day had to develop a way of tempering these intervals. In more chromatic music of the era, such as Gesualdo’s work, this would still present problems. The sixteenth century saw some very exciting and unusual attempts to solve this problem.

The fourteenth century saw the development of meantone tuning. Meantone tuning allows for perfect major thirds and sacrifices the fifths. Four fifths cover the same interval as an octave and a major third, in reality though the four fifths are a comma sharper than the major tenth, and as we have to keep thirds true, we flatten each fifth by a comma, hence “Quarter-comma meantone.” The greatest misconception relating to meantone tuning is that it only allows the performer to play in certain keys. This is true, but is a bi-product of the origins of its conception, in reality meantone tuning developed in a modal context before the development of tonality.

As the sixteenth century progressed the use of modes began to transform. The tendency towards the leading note grew ever stronger and at the close of the century the development towards major-minor tonality was becoming much more progressive, leaving the music with a modal inflection that would continue into the baroque through the influence of ecclesiastical music. As the systems of scales developed into the tonality of the baroque a new methods of tuning began to emerge.

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