The Twelve-Tone Temperament
The twelve-tone temperament, also referred to as equal temperament, constitutes the most widely employed tuning system in Western music. The following overview delineates some of the principal twelve-step temperaments:
Equal Temperament:
In this system, the octave is divided into twelve equidistant semitones, such that each step represents the same proportional frequency ratio. This temperament forms the prevailing basis of tuning in modern Western musical practice.
Just Intonation:
Here, intervals are defined by simple integer ratios. Although such intervals yield highly consonant and acoustically pure sounds, the system presents significant difficulties in transposition and renders modulation between keys problematic.
Pythagorean Tuning:
The Pythagorean system constructs the octave from successive pure fifths. While this ensures the purity of fifths, it concomitantly produces imperfect thirds owing to the accumulation of tuning discrepancies (known as comma drift or beating).
Werckmeister Temperament:
Developed during the Baroque era, this temperament represents a hybrid system that combines pure and tempered intervals to favor specific key areas.
Kirnberger Temperament:
Closely related to Werckmeister’s approach, the Kirnberger temperament also belongs to the Baroque tradition and was conceived to privilege certain tonalities. Kirnberger’s method emphasizes the preservation of pure intervals—particularly fifths and fourths—in order to enhance harmonic purity and overall sonority.
Meantone Temperament:
This system seeks to achieve just major thirds, thereby producing acoustically pure thirds within certain keys. However, this is achieved at the cost of rendering other intervals and keys comparatively dissonant.
Silbermann Temperament:
A historical temperament employed by the German organ builder Gottfried Silbermann, this system combines features of both equal temperament and Werckmeister’s approach, reflecting a transitional stage in the evolution of Western tuning practice.
It should be noted that many of these temperaments emerged under specific historical and technical conditions and have largely been supplanted in modern performance contexts by equal temperament. The selection of a tuning system depends upon various factors, including musical repertoire, instrument design, and aesthetic preference.
Tunings for the Present and Future
Microtonality and the Concept of EDO
In recent years, goldenwhale has undertaken extensive research into alternatives to the established systems of tuning. Within his work on the C15 synthesizer, developed by nonlinear labs, he has explored numerous approaches to dividing the octave into proportions differing from the conventional twelvefold division.
The term “EDO” (Equal Division of the Octave) refers to the subdivision of the octave into equally spaced steps. The following brief descriptions outline selected contemporary tuning methods, alongside representative examples and potential applications in future music composition and performance practice:
15 EDO (Equal Division of the Octave):
In 15 EDO, the octave is partitioned into fifteen equal parts, thereby expanding the available pitch palette relative to traditional twelve-tone equal temperament. This system allows for a more diverse harmonic spectrum and novel timbral possibilities.
16 EDO:
Sixteen-step equal temperament extends both harmonic and melodic capacity, offering composers and performers access to new realms of intervallic subtlety and expressive nuance.
17 EDO:
By dividing the octave into seventeen equal parts, 17 EDO introduces additional intermediate pitch steps between the conventional semitones. This expansion enables the articulation of microtonal melodic gestures and unconventional harmonic relationships.
18 EDO:
Eighteen-step equal temperament provides a yet finer gradation of pitch, facilitating heightened control over intonational nuance and color. Such systems may significantly enrich the expressive potential of music through subtle variations in tone and sonority.
19 EDO:
Dividing the octave into nineteen equal intervals produces an even denser pitch network and affords an extension of harmonic and melodic resources. In contemporary and future contexts, 19 EDO is particularly suited for innovative harmonic experimentation and expanded tonal vocabularies.
Prospective Applications in Future Music
- Microtonality: These systems facilitate the exploration of pitches between traditional semitones, thus broadening the perceptual and compositional scope of harmonic and timbral expression.
- Nuanced Expression: The refined subdivision of the octave permits enhanced precision in the articulation of melodic contour and emotional shading.
- Experimental Sound Worlds: Alternative temperaments provide fertile ground for the creation of new sonic environments and textural innovations unattainable within conventional tuning frameworks.
- Expansion of Harmonic Vocabulary: The additional pitch materials enable the conception of complex harmonic structures and unconventional tonal relationships.