Piano Tuning and the Implications of Low 4th A4 Numbers
Understanding Low 4th A4 Numbers in Piano Tuning
The concept of the ‘4th A4 Number’ plays a significant role in piano tuning, particularly when considering the flexibility available to technicians in stretching the midrange without risking excessive beating in octaves. A low 4th A4 Number typically indicates that when the prime octave is tuned as a pure 4:2, the resultant 2:1 is also pure or nearly pure. This characteristic provides the technician with greater freedom to stretch the midrange, as the 4:2 interval can be widened further before the 2:1 interval becomes too wide and starts to produce objectionable beating.
Impact on Tuning and Tonal Quality
Careful adjustment of the prime octave and fifths is crucial in achieving a pleasing sound, especially given the unique characteristics of each individual piano. Both low and high 4th A4 Numbers often require slightly narrower prime fifths to maintain tonal quality, underscoring the variability and individuality inherent in piano tuning. Pianos featuring low 4th A4 Numbers generally do not present significant problems, and the resultant tuning allows for a more controlled stretching of the midrange.
Practical Observations
Instances of a 4th A4 Number measuring 0.0 cents are rare. Although some sources suggest this measurement is a sign of a well-scaled piano, practical experience shows that not all highly regarded pianos exhibit this trait. For example, while a pure 4th A4 Number was observed on a Yamaha Studio Console, such a result has not been found on long scale models from Steinway, Yamaha, Kawai, Mason & Hamlin, and similar manufacturers.
Guidelines for Tuning
From a stretching perspective, a low 4th A4 Number provides technicians with more leeway for midrange stretch. However, caution is advised to avoid tuning the prime octave too wide. Using prime fifths as a guide can help, but it is important to recognize that the commonly used width of -1.5 cents for fifths may be too broad for pianos with a pure or very low 4th A4 Number. In such cases, the prime fifths may need to be set closer to -1.8 or even -2.0 cents.
It is also helpful to remember that a 1 cent wide 4:2 interval produces approximately 0.5 beats per second. Stretching the 4:2 to 2 cents wide results in one beat per second, which is generally considered too fast for most tuners. For personal preference, keeping the 2:1 interval less than 2.8 cents wide is ideal. Stretching the octave to -2.8 cents also makes the 4:2 interval close to 2.8 cents wide, which may be too much for the piano’s midrange.
Achieving a Balanced Sound
By understanding the relationship between the prime octave and prime fifths, it becomes easier to find an optimal compromise for a pleasant sound. On pianos with a low 4th A4 Number, it is often necessary to tune the prime fifths slightly more narrowly than the typical -1.5 cents starting point.
Interestingly, mapping a piano with either a low or high 4th A4 Number often results in the need for slightly more narrow prime fifths. Ultimately, each piano is unique, with its own individual inharmonicity characteristics, and the tuning process must be tailored accordingly to achieve the desired tonal quality.