Performance Record of J.S. Bach – WTC I No. 1 Prelude in C Major, BWV 846

Overview: A performance of J. S. Bach’s The Well-Tempered Clavier, Book I, No. 1 — Prelude in C Major (BWV 846). The performer analyzes local sonorities as just-intonation ratios organized “in relation to C,” discusses the syntonic comma as a theoretical mismatch that can arise in chained pure intervals, and describes interpretive choices in tone color and harmonic hearing—especially around measure 28 (F♯ vs G♭ interpretation).

Note: All content on this page is originally explained by Reiji in Japanese. The English version is translated by AI and structured by a parent, with Reiji's final approval.

Reiji's Words and Ideas

• Performer’s Comment — “In relation to C” as a reference point:
  When I look at this piece from the perspective of fixing C (Do) as a reference point and organizing the notes as ratios on the overtone series or the undertone series, I feel the entire prelude can be understood as a structure “in relation to C.” Here, C does not mean the root of each chord; it is simply a reference point for describing ratios.
• Opening measures (m. 1–3) — Ratio mapping (local sonorities):
  
  Measure 1: C–E–G–C–E (CEGCE). Using C as the reference, it can be organized as the ratios 1, 5/4, 3/2, 2/1, 5/2 (overtone-like ratios).
  
  Measure 2: C–D–A–D–F (CDADF). Here, keeping C fixed as the reference, if we prioritize consonance within the sonority and tune F–A as a pure major third (5/4) and A–D as a pure perfect fifth (3/2), then D becomes 10/9. As a result, relative to C the measure can be organized as 1, 10/9, 5/3, 20/9, 8/3 (because of register, the same pitch can appear an octave higher, so D appears as both 10/9 and 20/9).
  
  Measure 3: B–D–G–D–F (BDGDF). Relative to C, it can be organized as 15/16, 9/8, 3/2, 9/4, 8/3.
  
  In this way, when I view local sonorities through just-intonation ratios, many places in the piece feel naturally “well-aligned” with overtones (or undertones), and I sensed an overall consonant overtone relationship throughout the prelude.
• Drift and the syntonic comma — A theoretical mismatch in strict just intonation:
  However, if we try to keep “perfect consonance” continuously in just intonation, there can be a phenomenon where pitches drift downward little by little over time. What I describe here is not the claim that this phenomenon is literally happening inside the score; it is an explanation of the theoretical mismatch that can arise when we interpret progressions in strict just intonation.
  
  To illustrate how such a discrepancy can accumulate when we connect intervals as a chain, I take as an example a progression found around measures 9–11 (A → D → G). For instance, if we connect A → D as a pure perfect fifth and D → G as a pure perfect fourth, then there is a difference of 81/80 between G as a reference (3/2) and G obtained as the result of the chain (40/27). This 81/80 is called the syntonic comma.
  
  Because this piece is written in equal temperament, the “accumulation of mismatch” that would occur in strict just intonation does not proceed inside the work as-is; instead, pitch is held stable by the equal-tempered framework.
• Performance approach — Overtone richness and undertone color:
  Based on this, in performance I aimed to let overtones resonate richly overall, and in more minor-sounding passages I tried to bring out a more undertone-oriented color (darkness and weight).
  
  Also, around measure 28 I felt the color of the sound shifts noticeably. The set of notes there can be interpreted either as a chordal sonority or as part of a flowing texture including passing/ornamental tones, depending on context. I chose to treat it as a more “chord-like” sonority, because it can be heard with a diminished-like tension that stands out in this piece. In performance, I paid special attention to tone color and overtone production so that the character of this moment would come through clearly.
• Example (m. 28) — Ratio mapping if treated as a chordal collection (F♯ vs G♭):
  Below is an example of how the ratios can be mapped if we temporarily treat the notes in that measure as a single chordal collection. To keep the explanation simple, I assume that up to this point the pitches have not drifted downward (without this assumption, we would have to track the drift through the progression, which becomes very complicated). I also fix C as the reference because the piece is in C major.
  
  Since the mapping changes depending on how we interpret enharmonic spellings, as an example, if we take the sonority in measure 28 as G–E♭–A–C–F♯ and interpret the last note as F♯ (Note 1), then replacing each note with just-intonation ratios gives: 3/8, 3/5, 5/6, 1/1, 45/32.
  
  If instead we interpret the last note as G♭ (Note 2), then the ratios become: 3/8, 3/5, 5/6, 1/1, 36/25.
  
  I believe this difference can affect the performance approach. If we interpret it as F♯, the color leans more toward the overtone side; if we interpret it as G♭, it leans more toward the undertone side.
  
  The reason is as follows:
  45/32 can be understood as starting from C (1/1), moving to the 9th partial (9/1), then to the 5th partial (45/1), and finally bringing it back into the same octave by dividing by 32, yielding 45/32.
  36/25 can be understood as starting from C (1/1), moving to the undertone 5 (1/5), then to the 6th partial (6/5), then to the undertone 5 again (6/25), and finally moving to the 6th partial, yielding 36/25.
  
  In other words, the former follows an overtone-oriented pathway, while the latter follows an undertone-oriented pathway. In this performance, I interpret it as G♭, because it feels more strongly like it functions as a dominant-like sonority.
  
  Note 1: If D is taken as a major whole tone 9/8, then multiplying by 5/4 gives F♯ (9/8 × 5/4 = 45/32).
  Note 2: 6/5 × 6/5 = 36/25.
• Closing note:
  Overall, I feel this prelude has relatively little “chaos” in its overtone structure; for that reason, I tried to shape the entire performance with an awareness of rich overtones and changes of color.
• *This is only the performer’s personal interpretation of the piece.