## Staying in tune

The equal-tempered scale, where the octave is divided into twelve equal chromatic steps, has dominated western music for over a century. We have been made to believe that its use has been standard since times of Bach, but actually its exact measurement dates back only to the second half of the 19th century, when a new unit of measurement was introduced: the cent. Thus we know now that one chromatic step consists of 100 cents and that 1200 cents make up an octave. But there are several other tuning systems. Let’s take a look at some of them.

Pythagorean tuning. In this tuning the perfect fifth is king because all frequency relationships are based on it. As a result all fifths are pure, but other intervals, like the major third, end up being too large. In equal temperament, the major third consists of 400 cents, while in Pythagorean tuning it contains 407.82 cents. An interesting by-product of this tuning system is the discrepancy between seven octaves and twelve justly tuned perfect fifths; this discrepancy is called a Pythagorean comma. In their quest for new interval and harmonic relationships, some contemporary composers have used this kind of tuning. See Lou Harrison’s Sonata in Ishartum for guitar.

Just intonation. Mathematically speaking, just intonation is based exclusively on rational numbers: the octave is 2/1, the perfect fourth is 4/3 and the perfect fifth is 3/2. The major and minor thirds in the Pythagorean tuning were practically unusable, therefore musicians made some adjustments in order to make them consonant. A Pythagorean major third can be expressed as 81/64 but in just intonation it is rounded up to 5/4. The minor third was also adjusted from 32/27 to 6/5. This was a fantastic advancement but not without its problems. The main limitation being that you couldn’t modulate without retuning your instrument. Modulation therefore was nearly impossible. Listen to Terry Riley’s Land’s End for just intoned piano.

Meantone temperament. In terms of endurance, meantone temperament remained the norm for about four centuries. In it, each key has a certain character. There are several kinds of meantone tuning, but one of earliest and most colorful was championed by Nicola Vicentino in the 16th century. Vicentino divided the octave into 31 equal parts and went as far as building an instrument, called the archicembalo, which made it possible to play in all keys. His research coincides with an increased interest at the time in chromaticism and Greek music theory. His contemporaries had great difficulties in performing his vocal works, so the archicembalo was supposed to serve as an aid. And although Vicentino was convinced that his system would eventually prevail, history took a different turn.

Well temperament. Although most of us have been taught that Bach composed his Well-Tempered Clavier in order to demonstrate the advantages of equal temperament, the truth is he never advocated its use. In fact, for Bach each key had a characteristic sound world and each prelude and fugue was written in order to exploit these differences. There are several kinds of well temperament, but the term refers to a kind of irregular tuning where the octave is divided into twelve unequal parts and where each tone is tuned in such a way that it is possible to play in most keys without them sounding out of tune. Listen to the iconic C Major Prelude from Book I of the Well-Tempered Clavier in well temperament.

Harmonic series. The harmonic series is an arithmetic series that consists of a fundamental frequency and a series of overtones. The equal tempered scale is out of tune with many of the natural harmonics, especially the 7th, 11th and 13th. When an overtone is out of tune it produces inharmonicity. The harmonic series is not a scale or a tuning system in itself, but it generates chords that are not achievable using other tuning systems, at least not with the same degree of accuracy. Partly because of this it has attracted a number of composers, especially those belonging to the Spectral school, who have built their compositions on their analysis of sound spectra. Listen to Gérard Grisey’s Partiels.

Personally I have never ventured beyond the equal tempered scale, and even within it composers have found room for innovation using intervals such as quarter tones, sixth tones and eighth tones, which belong to the realm of microtonality. There are several composers who have made used of microtonality throughout the centuries, but that would merit another article in itself. In fact, some of the tuning systems we discussed here are a window to the world of microtonality, which is commonly understood as the use of intervals smaller than a semitone or one hundred cents.

There are two main hurdles for the performance of microtonal music. First, the instruments that make up the standard western symphony orchestra are generally designed with the equal tempered scale in mind. It is of course possible to bend sounds a little, but not all instruments are capable of doing this. In terms of flexibility, the piano and all keyboard/mallet instruments are the least flexible, while the string instruments are the most flexible. The winds fare somewhere in between, but their construction is such that microtones are at best inaccurate and at worst impossible. There have been several attempts at building instruments capable of producing microtones, but none of them has become standard. Listen to a quarter tone trumpet.

The second reason is music education. All modern western musicians are taught that the semitone is the smallest interval. In addition to this, the vast majority of Western music written during the last five hundred years or so is written with twelve tones in mind. The repertoire of microtonal music is minimal in comparison, so teachers and students alike see no need in incorporating microtones to their vocabulary. What is interesting to note is that most musicians use microtones in the form of tones that are slightly deviated from their originally intended tuning. This happens especially in the case of enharmonics. For example, although a G sharp and an A flat sound exactly the same in the piano, a string musician will most likely bend the sound a little higher or a little lower depending on where the note is going. But these of course are just slight deviations from the equal tempered scale and not a systematic use of microtonality in its own right.

Many composers refuse to be discouraged by these facts and continue writing microtonal music. Some of them out of conviction that microtonality will become the norm in the future while others do it simply because they are interested in the new harmonic and timbral relationships that emerge out of it. I have been in love with the symphony orchestra since my beginnings and, as many of my colleagues know, the symphony orchestra is a very well established institution that doesn’t allow innovation every other day. This is why contemporary microtonal composers have preferred to focus on writing for chamber ensembles. Some notable ensembles are the Ensemble Intercontemporain  and the Nieuw Ensemble Amsterdam.

When I’m asked why I haven’t incorporated microtones into my musical language my first reply is that, so far, I haven’t felt the need to do it. I have experimented with them but they never quite materialized into my compositions. This doesn’t mean I don’t like them; in fact I admire composers like Gérard Grisey and Georg Friedrich Haas who have made extensive use of them. It is ultimately a personal choice, but if a composer does feel the need to use them, he/she should go for it without letting the establishment hinder his/her creativity. Of course we need to make compromises now and then, especially when our ideas turn out to be impractical, but we should not compromise our core values. Us composers should not measure our success based on whether our ideas become standard practice or not, what really matters is the quality of the music itself.