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

Overview: A performance of J. S. Bach’s The Well-Tempered Clavier, Book I, No. 1 — Fugue in C Major (BWV 846). The performer designs tone color in two broad directions: (1) overtone-rich brightness for resolved passages, and (2) a “subharmonic-like” (conceptual) ratio viewpoint for minor-like tension. The notes include two notable passages (m. 12; m. 24 to the end) and a simplified explanation of why “major-like brightness” can be associated with overtone-series color, while “minor-like tension” can be heard through a subharmonic-like directional listening framework.

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 — Two “directions” of tone color:
  The piece I worked on is J. S. Bach: The Well-Tempered Clavier I, No. 1 Fugue in C major (BWV 846).
  
  In this performance, I design the tone color in two broad “directions”:
  • In passages that sound bright and resolved, I aim for a sonority in which overtones (the overtone series) rise naturally and richly.
  • In passages that sound minor-like and tense, I use a subharmonic-like, ratio-based viewpoint to create a taut, suspended color.
• Important note — “Subharmonics” as a conceptual tool (not a physical claim):
  By “subharmonics” here, I do NOT mean a physically natural subharmonic series that simply sounds in nature. Rather, I use the viewpoint of just-intonation ratios (mainly 5-limit, and including 7-limit when needed) as a conceptual tool for designing timbre. In other words, the goal is not to “produce subharmonics,” but to steer the sound so that it is heard in that direction.
• Notable passage 1 — Minor-like tension at m. 12 (delayed release):
  A common chord interpretation is: E7 → Am → F → Ddim7 → E7 → Am.
  However, I feel this is one of the most tense points in the piece, where an E-centered dominant-like (E7-like) tension persists across two measures (i.e., the resolution feels delayed). The reason is that the tension around the sonority’s center—especially E and C—does not fully release.
  
  For this explanation only, I treat E as the reference pitch. The sustained C is not meant as “a chord tone of E7” in a harmonic-analysis sense; rather, I use it as a reference tone that fixes the color/tension against E.
  
  In practice, I avoid pedal switches and try to keep the resonance of E and C as long as possible, so that the later E entries rise more sharply. Here I construct the sound while keeping the tension, using a subharmonic-like ratio image. What matters is not “generating subharmonics,” but guiding the resonance and aftersound so that the ear is led in that direction.
• Notable passage 2 — Bright resolution from m. 24 to the end (unique radiance):
  From m. 24 to the end is especially striking to me because it is the only cadence where the major color is major both before and after the cadence. It feels uniquely bright and radiant within the whole piece. For that reason, I design the tone so that overtones rise naturally and the sonority “shines,” aiming for a richly overtone-colored sound.
• Why I associate overtones with major-like brightness, and a subharmonic-like viewpoint with minor-like tension:
  To keep the explanation from becoming too complicated, I describe everything with C as the fixed reference pitch. For other reference pitches, multiply by the 12-tone equal-temperament frequency ratio (the 12th root of 2)^n, where n is an integer. For example, for E♭ we use n = 3 (three semitones above C, with C as 0).
• Overtone series and “major”:
  With C as reference, the overtone series can be viewed roughly as:
  C → C → G (3/2, +2 cent) → C → E (5/4, −14 cent) → G (3/2, +2 cent) → B♭ (7/4, −31 cent) → C
  
  The cent values here are rough offsets when mapping just-intonation ratios (as a guide: mainly 5-limit ratios, and including 7-limit when needed) onto 12-TET. To avoid unnecessary complexity, I stop at the 8th partial here, because within this range the 4:5:6 skeleton already appears and forms the core of a C major triad. (B♭ is included as a 7-limit example.)
  
  As you can see, when the 4th, 5th, and 6th partials (4:5:6) are rounded into 12-TET, the skeleton of a C major chord appears. From this, I think major-like sonorities have a natural affinity with overtone-series color.
• “Subharmonic” viewpoint and “minor”:
  Similarly, if we adopt a subharmonic-like (conceptual) viewpoint with C as reference, we can view:
  C → C → F (−2 cent) → C → A♭ (+14 cent) → F (−2 cent) → D (+31 cent) → C
  
  Within this sequence, the skeleton F–A♭–C (F minor) appears. Here “4:5:6” is not a strict claim about a physical generation method; it means that the same triadic “shape” can be recognized as a directional listening viewpoint.
  
  Also, physical subharmonics do not simply sound in nature. Therefore, I adjust the listening impression by controlling resonance and the damper system through touch and pedaling—such as how deeply I press the right pedal, and whether I avoid pedal changes—so that the sound is steered toward that direction. In other words, rather than “sounding subharmonics,” I use the subharmonic-like ratio image as a framework for designing timbre.
• Aside — reading the score:
  When I was learning this fugue, I was also practicing a four-voice piece from Bach’s 14 Canons (No. 5). That experience made the initial hurdle of reading this four-voice fugue feel slightly lower.
• *This is only the performer’s personal interpretation of the piece.*