This site introduces unknown composer Emanuel Bach (C. P. E. Bach). This English version was translated from Japanese one by ChatGPT.
**Just Intonation** is a tuning system where intervals are tuned based on the natural harmonic series. Intervals such as the major third (5:4) and the perfect fifth (3:2) are calculated according to harmonic ratios, resulting in a very pure sound. This tuning method is particularly utilized in instruments capable of flexible pitch adjustments, such as vocals and string instruments, offering the advantage of chords resonating beautifully in specific keys.
However, just intonation has the disadvantage of being weak in modulation. Since it is based on natural harmonics, while chords may be pure in one key, they can become out of tune (resulting in dissonance) when modulating to distant keys. Therefore, keyboard instruments required tuning systems with “temperament” adjustments, such as unequal temperament or equal temperament.
Just intonation was primarily used in religious music and early polyphonic music before the 16th century, but as modulation increased during the Renaissance, it was gradually replaced by other tuning systems. In modern times, however, there is renewed interest in pursuing the acoustic purity based on harmonics, compared to Pythagorean tuning or equal temperament, in fields such as early music and experimental music.
I asked ChatGPT4o: "Is it true that using an instrument tuned in just intonation for a piece in a distant key might not align with the composerʼs intentions?"
When performing a piece in a distant key using an instrument tuned in just intonation, it may not always align with the composerʼs intentions. This is because, while just intonation creates very beautiful chords in specific keys, it tends to produce strong dissonance when modulating to distant keys.
Just intonation tunes major intervals like thirds and fifths as close to natural harmonics as possible. As a result, very pure chords can be achieved in specific keys like C major or F major. However, when modulating to distant keys like C# or G#, the chords in those keys can become muddled, resulting in unnatural sounds.
When composers create pieces using specific distant keys, they are often conscious of the characteristics and sounds of those keys. For example, Baroque and Classical composers frequently used modulation to distant keys to create tension or unease. Therefore, performing in just intonation, which can result in dissonance in distant keys, may not accurately express the tonal colors intended by the composer.
Baroque and Classical composers often used “unequal temperament” or "meantone temperament." These tuning systems maintained a degree of harmony even in distant keys, giving each key its unique character. For instance, Bach used “well-tempered” tuning to ensure natural sounds in all keys.
References: Daniel Adam Maltz,Mathematics | University of Waterloo.
Using just intonation for distant keys can result in muddled tonal sounds, potentially failing to fully express the musical effects intended by the composer. Therefore, when performing pieces that use distant keys, tuning systems that can accommodate all keys, such as historical temperaments (well-tempered or meantone) or 12-tone equal temperament, are often more suitable.
I asked ChatGPT4o: "Is it appropriate to use just intonation for performing pieces in distant keys if electronic instruments can play in just intonation in any key?"
While it is possible to perform pieces in distant keys using electronic instruments capable of playing in just intonation in any key, it may not always be appropriate. This is because the characteristics and limitations of just intonation can affect the intended use of distant keys.
Just intonation provides very pure tones in specific keys, but its sound depends on specific intervals (mainly major thirds and perfect fifths). When modulating to distant keys, these intervals can become distorted, emphasizing dissonance. As a result, performing distant keys in just intonation can disrupt the acoustic balance between keys.
Composers use distant keys to create tension and dramatic expression. For example, Beethoven and Mozart often used distant keys to introduce contrast and change in their works. Performing these works in just intonation can alter the “color” and “instability” of the keys, potentially undermining the composerʼs intentions.
With electronic instruments, it is technically possible to apply just intonation in any key, ensuring that specific chords always have a pure sound. However, the fundamental issue with just intonation is that when moving to distant keys, other chords become impure, disrupting the overall harmony of the key. This can result in the loss of the musical effects of distant keys.
While just intonation creates beautiful sounds in specific intervals (e.g., the major third C-E in C major), it often lacks harmony in distant keys like G# or D#. Such musical inconsistencies can result in a loss of musical consistency and intention when using just intonation for pieces in distant keys.
Even if it is technically possible to perform in just intonation in any key using electronic instruments, it is not always appropriate to use just intonation for pieces in distant keys. Since the intended changes in key and acoustic effects by the composer may be lost, it is recommended to choose appropriate tuning systems, such as 12-tone equal temperament or well-tempered tuning.
I asked ChatGPT4o: "Is it appropriate to use just intonation for performing pieces in distant keys if electronic instruments can modulate to any key while maintaining pure intervals?"
While electronic instruments can maintain pure intervals (pitch) even when modulating to any key, whether this is appropriate for pieces in distant keys requires consideration from a musical perspective. Below are considerations regarding its appropriateness.
Just intonation provides very pure sounds for specific chords (especially major thirds and fifths), but it has the characteristic of subtly changing other chords when modulating. This results in different pitches for each key, emphasizing musical tension and color in specific keys.
Composers use changes in key to intentionally create tension. For example, Baroque composers used unequal temperament to give each key its unique color and sound.
If distant keys are performed in just intonation, the instability and sound changes unique to those keys may be lost. To accurately express the intended “contrast of colors” and “emotional changes,” using 12-tone equal temperament or unequal temperament may be more appropriate.
Modern 12-tone equal temperament provides uniform sounds in all keys, allowing for consistent chords regardless of modulation. In contrast, just intonation results in different sounds for each key, potentially altering musical effects in unintended ways.
For example, composers like Beethoven and Mozart used distant keys to express instability and drama. Performing these pieces in just intonation may result in the loss of musical effects, potentially failing to convey the intended emotions and intentions accurately.
While electronic instruments can use just intonation in any key, resulting in consistently “correct” sounds, musical consistency and differences in key may be diminished. For example, the tension and instability of distant keys may be lost, resulting in a flat overall sound. This may prevent the dynamic expression and emotional intensity intended by the composer from being accurately conveyed.
While the technology to use just intonation in any key with electronic instruments is attractive, caution is needed when applying it to pieces in distant keys. Especially when composers intentionally use changes in key, using just intonation may undermine their intentions. Therefore, when performing pieces in distant keys, using 12-tone equal temperament or historical tuning systems is often more appropriate for maintaining musical consistency and expressiveness.