This site introduces unknown Emanuel Bach (C. P. E. Bach).
**Just Intonation** is a tuning system where intervals are tuned according to the natural harmonic series. Intervals such as the major third (5:4) and the perfect fifth (3:2) are calculated based on harmonic ratios, resulting in exceptionally pure and resonant sounds. This tuning system is particularly well-suited for instruments capable of flexible pitch adjustment, such as vocal ensembles and string instruments, allowing chords in specific keys to resonate beautifully.
However, Just Intonation has the disadvantage of being poorly suited for modulation. Since it is based on natural harmonics, chords may sound pure in one key but become dissonant when modulating to distant keys. Therefore, for keyboard instruments, tuning systems with "temperament," such as unequal temperament and equal temperament, became necessary.
Just Intonation was mainly used in sacred music and early polyphonic music before the 16th century. However, with the increase in modulation during the Renaissance, it gradually gave way to other tuning systems. In modern times, research and performances focusing on the acoustic purity of harmonics—especially compared to Pythagorean tuning and equal temperament—have brought renewed interest in Just Intonation, particularly in early and experimental music.
I asked ChatGPT4o: "Does using an instrument tuned in Just Intonation to perform a piece in a distant key necessarily go against the composer’s intention?"
Using an instrument tuned in **Just Intonation** to perform a piece in a distant key may not always align with the composer’s intentions. This is because Just Intonation produces beautifully pure chords in certain keys, but moving to distant keys often introduces strong dissonance due to its reliance on natural harmonics.
Just Intonation tunes major thirds, fifths, and other intervals as closely as possible to natural harmonics. This results in exceptionally pure chords in specific keys like C major or F major. However, modulating to distant keys like C♯ or G♯ can cause chords to become muddy and produce unnatural sounds.
When composers use distant keys, they intentionally explore the unique qualities and colors of those keys. For example, Baroque and Classical composers often used distant modulations to create tension and unease. Performing such pieces in Just Intonation may distort these intended tonal colors due to the dissonances that arise.
Baroque and Classical composers often employed unequal temperaments and meantone tuning, which maintained some degree of harmony even in distant keys while giving each key a distinct character. For instance, Bach used "well-tempered" tuning to achieve natural resonance across all keys.
Reference: Daniel Adam Maltz, Mathematics | University of Waterloo.
Using Just Intonation in distant keys can muddy the harmonic clarity, potentially failing to convey the composer’s intended musical effect. Therefore, when performing works that involve distant modulations, historical temperaments (like well-tempered or meantone tuning) or 12-tone equal temperament are often more suitable for accurately expressing the composer’s intentions.
I asked ChatGPT4o: "Since electronic instruments can play in Just Intonation in any key, is it appropriate to use them for pieces in distant keys?"
While electronic instruments can perform in **Just Intonation** in any key, using them for pieces in distant keys may not always be appropriate. This is due to the characteristics and limitations of Just Intonation and how they interact with the musical purpose of distant keys.
Just Intonation offers pure, resonant sounds in specific keys but depends on precise intervals (mainly major thirds and perfect fifths). When modulating to distant keys, these intervals become distorted, emphasizing dissonance. This imbalance can disrupt the harmonic consistency of music performed in distant keys.
Composers often use distant keys to create **tension and dramatic expression**. For instance, Beethoven and Mozart employed distant modulations to introduce contrast and emotional shifts. Performing such works in Just Intonation could alter the intended tonal color and diminish the composer’s intended dramatic effect.
Although electronic instruments can apply Just Intonation in any key, allowing chords to remain pure, the core issue is that modulating to distant keys can still produce dissonance and disrupt harmonic balance. This can compromise the intended musical effects of modulation.
Just Intonation produces beautiful harmonies in specific keys (like the pure major third in C major), but chords in distant keys (such as G♯ or D♯) may lack harmony. This inconsistency can result in a loss of musical coherence when using Just Intonation for pieces in distant keys.
Even though electronic instruments can perform in any key using Just Intonation, it is **not always appropriate** for pieces in distant keys. The tonal shifts and sound effects intended by composers may be compromised. Therefore, it is often more suitable to use tuning systems like 12-tone equal temperament or historical temperaments (e.g., well-tempered tuning) to maintain musical integrity.