The A Targets in the Littau-Conrad System
Every A on the piano, from the lowest A0 to the highest A7, is systematically mapped and used in the LC spreadsheet for creating the tuning. Once the targets have been entered into the LC spreadsheets the tuning using those settings is created for all the notes from A0 – C8. In addition to the main targets, secondary or “mini” targets—specifically, the D and E notes in the third and fourth octaves – are also used for creating the custom tuning.
The secondary targets are used for additional tuning curve balancing, shaping and refining. These secondary targets play a crucial role in ensuring that the prime fifths are balanced, aiming for the widths of all prime fifths to be exactly the same in any given tuning.
Balancing the Prime Fifths
Understanding the Tuning Curve and Its Limitations
Electronic Tuning Devices (ETDs) often generate a tuning “curve” that appears smooth and visually appealing. However, this curve may not actually suit the unique characteristics of every piano, especially within the Prime Octave (A3-A4). It is frequently necessary to modify the shape of this curve to achieve a more accurate fit for the specific instrument.
Unique Flexibility of the LC Tuning System
One of the most distinctive features of the LC tuning system is its ability to adjust the shape of the curve within the Prime Octave. The LC spreadsheet lets tuners alter the midpoint of the Prime Octave (D#4) to balance the widths of the prime fifths (A3/E4 and D4/A4), leading to a more tailored and precise tuning.
Balancing the Prime Fifths
Computer-generated curves in the Prime Octave often result in the prime fifths (A3/E4 and D4/A4) having different widths, which causes unequal beating between the intervals. Through the LC spreadsheet, these prime fifths can be adjusted so their widths match and their beating is equalized. This adjustment is incorporated into the final tuning, ensuring the curve in the Prime Octave fits the piano more accurately.
Measuring and Correcting Fifth Widths
To determine the necessary adjustments, the initial widths of the prime fifths must be measured. For example, if the ideal width for the prime fifths is -1.5 cents each, it is common to find the lower fifth (A3/E4) at -1 cent (narrow) and the upper fifth (D4/A4) at -2 cents (narrow). This results in the lower fifth’s beat being too slow and the upper fifth’s beat being too fast, making them unequal and audibly distinctly different.
The standard smooth curve produced by ETD software does not accommodate these subtle differences. The piano, therefore, requires an adjustment to the shape of the tuning curve in this region.
Implementing Curve Adjustments in the LC Spreadsheet
By lowering the midpoint (D#4) by 0.5 cents, both D4 and E4 are also lowered by the same amount. This change makes the lower prime fifth (A3/E4) more narrow and the upper prime fifth (D4/A4) less narrow, both now measuring -1.5 cents. The curve in the Prime Octave remains smooth but has a slightly deeper dip, which better suits the piano. This correction also improves the sound of the major thirds (M3rds) and all intervals within the Prime Octave.
Exclusive Precision of the LC System
Adjusting the location of the midpoint (D#4) of the Prime Octave’s curve is a feature unique to the LC system with mapping and the LC spreadsheet. No other tuning system offers this level of flexibility and accuracy for shaping the Prime Octave curve. While a skilled aural tuner might intuitively adjust for optimal sound with a more correct curve in the prime octave area, ETD software does not provide this degree of precision and control.
The Role of Prime Fourths
Prime fourths play an important role in piano tuning, exhibiting a distinct characteristic in their beat rates. These intervals naturally beat somewhat faster than prime fifths. When the prime fifths are not properly balanced, the difference in beat rates between the fourths and fifths becomes even more pronounced, especially in key intervals such as A3/D4 and E4/A4. Even when the fifths are well-balanced, the upper prime fourth tends to beat slightly quicker than the lower, a phenomenon attributed to inharmonicity. This subtle increase in speed is actually desirable, contributing positively to the overall tuning structure.
Secondary Targets in the Sub-Prime Octave
The A2-A3 range is known as the ‘Sub-Prime’ octave. Within this octave, certain secondary targets—specifically D3 and E3—serve a unique purpose. Unlike other intervals, these notes are not typically leveraged to balance the sub-prime fifths. Instead, they are used to precisely locate A2 and refine the tuning curve to better accommodate the sub-prime octave’s scaling complexities. In this section of the piano, the pair of sub-prime fifths (A2/E3 and D3/A3) are close in width but rarely identical, a tendency that is especially pronounced on pianos with shorter scales and greater scaling challenges.
The placement of D3 is primarily influenced by its relationship with A3, E4, and A4, with the width of the D3/A3 fifth also taken into account. Typically, the D3/A3 fifth is only about half as narrow as the D4/A4 fifth. For instance, if the prime fifths are set to -1.5 cents, the D3/A3 fifth will often fall within the range of approximately -0.7 to -1.1 cents (narrow). The lower sub-prime fifth (A2/E3), while still narrow, frequently ends up less narrow compared to the upper sub-prime fifth. However, this outcome is highly dependent on the specific piano and is determined during the mapping process.
Using Secondary Targets to Shape the Tuning Curve
Employing secondary targets within the sub-prime octave allows for more accurate tuning curve adjustments. Once optimal settings for D3 and E3 are identified, these values are incorporated into the LC Spreadsheet tuning. For example, on some pianos, D3 may be a wound bichord and E3 a plain wire trichord. By using both sub-prime and prime octave mini targets, the tuning can be made to fit the instrument much more effectively.
Mapping both main and mini targets in the prime and sub-prime octaves allows for the creation of highly customized midrange tuning for any piano. While exceptions to this approach are rare, they do exist.
Challenges in Tuning Shorter Scales
A common scenario involves tuning pianos with shorter scales and poor scaling. Achieving the best possible balance in the midrange area makes a significant difference in the sound quality of these challenging instruments. The balancing process must include a wider area of the keyboard, especially in the midrange. This system is well suited to handling these complex situations, as it requires a blend of technical expertise and aural skills. Successfully navigating these compromises is essential for optimal results.
Conclusion
Although these scenarios can be demanding, they offer rewarding learning experiences and lead to surprisingly improved piano sound. The combination of technical and aural skills is necessary, and relying on only one is insufficient for achieving the best outcome.