The A4 Numbers: Mapping and Tuning Insights for Piano Technicians

Understanding the A4 Numbers

The term “A4 Numbers” refers to the specific locations of the 2nd, 4th, and 8th partials of the A4 note when A4 is tuned to A440. These numbers provide valuable information about the piano’s tuning characteristics and serve as reference points for achieving precise intonation.

Significance of the A4 Numbers

The A4 Numbers offer several key insights for piano technicians:

  • Target Setting for A4: By focusing on the 4th partial of A4, technicians can determine the exact setting for A4 when tuned to A440, guiding the tuning process for this crucial note.
  • Triple Octave Reference for A7: The 8th partial number indicates the setting to use if a technician wishes to create a triple octave for A7, providing flexibility in high treble tuning.
  • 4:2 Octave Width for A3/A4: The 2nd partial setting serves as the target for A3 when a pure 4:2 octave width is desired between A3 and A4. Adjustments can be made by subtracting or adding 1.0 cent to achieve a 4:2 octave with desired beats per second (bps) width. Specifically, subtracting 1.0 cent yields a 4:2 octave that is 1/2 bps wide, while adding 1.0 cent will widen the octave by 1/2 bps.

Measuring the A4 Partials

Accurate measurement of the A4 partials is essential for effective mapping and tuning. The following procedures utilize an Electronic Tuning Device (ETD), such as an AccuTuner:

  • 2nd Partial: Tune A4 to A440. Set the ETD to listen to A5, play A4, and use the cents buttons to stop the lights. The resulting cents setting indicates the location of A4’s 2nd partial.
  • 4th Partial: Tune A4 to A440. Set the ETD to listen to A6, play A4, and stop the lights with the cents buttons. This gives the location of A4’s 4th partial.
  • 8th Partial: Tune A4 to A440. Set the ETD to listen to A7, play A4, and adjust the cents buttons until the lights stop. This reveals the location of A4’s 8th partial.

Guidelines for Using A4 Numbers

It is important to note that A4 Numbers should be used as reference points, not as absolute tuning targets for higher octaves:

  • Tuning A5 to the location of A4’s 2nd partial will result in A5 being too flat.
  • Tuning A6 as a pure double octave from A4 will also likely yield a setting that is too flat.
  • High treble tuning (A6–C8) is highly subjective. Some technicians find a triple octave too sharp, others too flat, making the technician’s experience and judgment crucial. A triple octave might work for C7 but may be unsuitable for F7 or A7.

Despite these limitations, knowing the A4 Numbers for each piano can be extremely helpful in guiding the tuning process.

Practical Applications in Tuning

Many technicians prefer tuning A3 as a 4:2 octave, 1 cent wide—equivalent to a 4:2 octave 1/2 bps wide. The location of A4’s 2nd partial makes this process straightforward: tune A3 as a pure 4:2, then lower it by 1 cent. This method serves as a practical starting point, though the ideal width may vary depending on the piano, with some requiring a narrower 4:2 octave and others a wider one.

Mapping for Optimal Tuning

Mapping involves gathering comprehensive information about the piano to make informed decisions that best match its unique inharmonicity. This approach reduces guesswork and minimizes trial and error, enabling the technician to develop an effective tuning strategy from the outset. Measuring the A4 Numbers is an excellent starting point for this mapping process.

With experience, technicians will quickly learn to recognize both typical and atypical A4 Numbers, enhancing their ability to tailor tuning to each piano. As with traditional aural tuning that begins at A4 and expands outward, this system leverages technology to analyze the vibration and inharmonicity of the A4 string by examining the locations of its 2nd, 4th, and 8th partials.