Introduction to Just or Rational Intonation (JI)

By Marc Sabat

JI is an acronym for "just intonation," or, more accurately, "rational intonation," a system of tuning in which every intervalAn interval is the distance between two pitches. It can be measured as a ratio between their frequencies or in cents.Visit the link to learn more is tuned according to a harmonic series. Starting from one reference frequency, called the fundamental, a harmonic series is made of all its whole number multiples, called partials. The intervals between partials are ratios of whole numbers and can all be written as fractions. Whenever frequencies are in a proportion that can be expressed as a fraction of small numbers, the interval they produce is generally consonant and without discernable beatingWhen two tones are very close together, they create a rhythmic pulsing related to the difference in frequency between the two tones. The closer the frequencies are to each other, the slower the tempo of the beating.Visit the link to learn more. Very slight detuning of the frequencies "tempers" the interval by introducing a little beating, perceived as vibrato or "warmth." When intervals are tempered by larger amounts, the beating increases in speed and is perceived as noise or "roughness." The idea of JI is to tune intervals without tempering them, maximizing consonance and blend.

Many historical and theoretical descriptions of musical tunings are based on JI ratios: for example, among many others, Ancient Greek scales described by Ptolemy; early Arabic and Persian oud tunings described by Abu Nasr Farabi and Ibn Sina; modern Indian theorists like Sambamurthy; European tunings described by Boethius, Zarlino, and Rameau. In the 19th century in Europe, Hermann von Helmholtz published his important book On the Sensations of Tone as a Physiological Basis for the Theory of Music in which he argued for just intonation as the basis for chordal harmony and melody. A few decades later, Kathleen Schlesinger published The Greek Aulos, which speculated about ratio-based "subharmonic" scales based on the designs of ancient flutes. These two books influenced the first two modern European composers who took up JI as a new creative possibility, a way to pioneer new harmonic explorations using an infinitude of microtonal shadings: the Australian pianist-composer Elsie Hamilton, and a few years later, the American composer and instrument-builder Harry Partch.

Over the course of the the 20th century, JI composition was pursued by a number of "outsider" composers: Lou Harrison, Ben Johnston, Pauline Oliveros, James Tenney, and La Monte Young, among many others. These days, the field has grown exponentially, including many of the composers and composer-performers of Plainsound Music Edition, among them Wolfgang von Schweinitz, Marc Sabat, Catherine Lamb, Ellen Arkbro, Thomas Nicholson, Idin Samimi Mofakham, and numerous others worldwide working in many classical and popular genres.

The presets in Live 12 (and on this site) offer a tiny window into the infinite world of JI possibilities. These examples can serve as a point of inspiration, but for every new musical project, a JI producer or composer will most likely need to invent their own set of pitches based on musical requirements, instrumentation, style, etc. The scales marked "HS" include subsets taken from a single harmonic series. The two 12 note scales were used by Johnston and Tenney in their JI compositions (the Suite for Microtonal Piano and Diaphonic Trio). The 16 note scale takes all the partials between 16 and 32 (Tenney's In a large open space). Some of the scales are marked with the description "tertial", "quintal", etc., describing the highest prime partial used in making the intervals of the scale. The "LMY WTP" scale was used in La Monte Young's magnum opus The Well Tuned Piano. The undecimal scales of Lou Harrison and Harry Partch include the tuned quartertones of the 11th harmonic partial. The "22 Sruti" are a modern Indian interpretation based on Bharata's ancient description of how the sruti could be derived by ear when tuning a vina. The "Bohlen-Pierce" scale, which also exists in a tempered version, is unusual in not repeating at the octave, instead it has 13 notes in the perfect twelfth. These few curated examples are just a jumping-off point for inventing your own sets of ratios and hearing how they make chords and melodies!

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