Summary
This document explains how to use an Accu-Tuner to accurately tune specific piano notes by selecting an appropriate template after determining key reference values. It outlines the process for tuning the prime octave and related intervals, focusing on achieving a balanced combined width for the prime 5ths. Adjustments are made by choosing templates with different A3 settings, ensuring the prime octave and its intervals are tuned to the desired specifications.
Establishing and Balancing the Prime Octave and Prime 5ths
This system is based on the relationships among the prime octave (A3/A4) and the prime 5ths (A3/E4 and D4/A4) to determine the optimal widths for both intervals. These relationships are identified using the A4 Numbers, the 4th A4 Number, and templates stored in the Accu-Tuner’s memory. Once the A4 numbers and the 4th A4 numbers are established, a template for Mapping A3 is selected. This template is then used to tune the notes A2, D3, E3, A3, D4, E4, and A4.
Tuning the Prime Octave
The process begins with tuning the prime octave: A4, A3, D4, and E4 are tuned according to the selected template. The A4 Number provides information about the prime octave’s width, but the widths of the prime 5ths (A3/E4 and D4/A4) must also be measured directly.
Measuring and Adjusting Prime 5ths
After tuning A4, A3, D4, and E3 to the template, it is common for the widths of the prime 5ths to differ—one might measure -2.2 cents and the other -1.2 cents. At this stage, the focus is on their combined width, not their individual equality. The goal is for the combined width of the two prime 5ths to total -3.0 cents (for example, -1.5 + -1.5 = -3.0).
If the combined width is greater than -3.0 cents (e.g., -4.0 cents), the prime octave is too narrow by roughly 1.0 cent. If the combined width is less than -3.0 cents (e.g., -2.0 cents), the octave is too wide and should be narrowed by 1.0 cent. Adjusting the octave is straightforward using templates: simply select a template with a slightly higher or lower A3 setting by the necessary amount, then retune A4, A3, D4, and E4. After this adjustment and retuning, remeasure the prime 5ths; their combined width should now be close to -3.0 cents.
At this point, it does not matter if the prime 5ths are not equally wide; balancing them comes later. The primary objective here is to achieve a pair of prime 5ths whose combined widths equal -3.0 cents. On most pianos, the prime octave should sound quite satisfactory at this stage.
Listening to the prime 5ths and the resulting prime 4ths (A3/D4 and E4/A4) can reveal slight differences in the beating of the 5ths. When the prime 5ths are unbalanced, these differences often manifest in the 4ths, as 4ths are slightly faster-beating intervals than 5ths. Comparing the upper and lower prime 4ths can confirm both the difference in the widths of the prime 5ths and indicate which direction the midpoint of the prime octave should be adjusted to balance not only the 5ths but also the 4ths.
Balancing the Prime 5ths
Once the difference in width between the prime 5ths is known, it is simple to determine the necessary adjustment to make them equal. For instance, if the lower 5th is -2.0 cents and the upper 5th is -1.0 cent, lowering both by 0.5 cent results in both being -1.5 cents, achieving balance. This is done by lowering the setting for D4 on the template by 0.5 cent and retuning D4, then doing the same for E4. After retuning both, the prime 5ths and their resulting prime 4ths should sound considerably improved.
As long as the prime octave 2:1 is not wider than about 2.8 cents, the octave’s sound should be pleasing as well. With these adjustments, accurate locations for A4, A3, D4, and E4 are established for this piano. These settings are used for the remainder of the mapping process and for creating the tuning with the Littau-Conrad Spreadsheet. While these guidelines work well for most pianos, some may require further adjustments. The ability to tune and measure precisely is essential, and although it is challenging, consistent practice and experience contribute to improved accuracy.
Considerations for the Prime Octave
On most pianos, if the prime octave’s 2:1 width is less than 3 cents, the beating will be tolerable. In certain cases, a wider prime octave is necessary, but as a general guideline, keeping it “no wider than 3.0 cents” is a good starting point. The prime octave’s width is largely determined by the widths of the prime 5ths, making these intervals crucial to the overall sound.
Some subjectivity is involved, as preferences for wider octave widths vary. The piano itself should guide the process, with the goal being minimal beating. The prime octave should not be wider than necessary, but must accommodate a pair of good-sounding prime 5ths. Since every piano is unique, there are no universal rules; each instrument may require a tailored approach. However, the basic procedure outlined here provides a reliable starting point and helps quickly determine if a piano fits the “most pianos” category.
Occasionally, a pure 4:2 (prime octave) may result in a 2:1 that is too wide and fast-beating, while narrowing the octave excessively can make the 5ths beat too quickly. Thus, compromises are often needed for challenging pianos, possibly resulting in a prime octave’s 2:1 wider than 3.0 cents and prime 5ths narrower than -1.5 cents. The aim is to find the best-sounding, or at least the “least bad-sounding,” compromise for both intervals.
A balanced pair of prime 5ths, regardless of their absolute width, generally leads to a satisfactory overall piano sound. The process involves iterative adjustments to achieve the most harmonious balance between the octave and the 5ths.
With experience, it becomes clear that some pianos, especially with shorter string scales, require this nuanced treatment to sound their best. If the combined width of the 5ths is -3.0 cents and the prime octave’s 2:1 is less than 2.8 cents wide, the Mapping of A3 is considered complete.
Final Balancing: The Prime Octave and Sub-Prime Octave
For the prime octave and prime 5ths relationship to be optimal, the prime 5ths must be balanced, which also brings balance to the resulting prime 4ths (A3/D4 and E4/A4). Balancing involves adjusting the midpoint of the prime octave, which, while technically D#4, is determined using the settings for D4 and E4. The midpoint (D#4) is found by averaging the settings for D4 and E4 and is displayed in the spreadsheet for reference.
The spreadsheet also provides settings for D3, D#3, and E3 in the third octave, allowing for midpoint adjustment in the sub-prime octave. While this adjustment can help balance the sub-prime 5ths, its primary function is to adjust the curve shape within the sub-prime octave to better fit the piano’s scale—especially important where transitions occur between string types and bridges.
The same template used for the prime octave is applied to the sub-prime octave, which is an extension of the relationship established in the prime octave. Typically, sub-prime 5ths are not as balanced as those in the prime octave, with the upper sub-prime 5th often being slightly narrower. As tuning extends into the bass, the 5ths generally become less narrow.
This midpoint adjustment helps achieve good-sounding sub-prime 5ths (A2/E3 and D3/A3), octaves (D3/D4, E3/E4, A2/A3), double octaves (A2/A4), and 12ths (A2/E4, D3/A4). All these settings are utilized by the Littau-Conrad spreadsheet to generate a tuning that passes through all key target and mini-target notes.
Having the ability to adjust the midpoint in both the prime and sub-prime octaves is a unique feature of this system. For example, if the lower prime 5th is -2.0 cents and the upper is -1.0 cent, raising the midpoint (D#4) by 0.5 cent balances both at -1.5 cents. This minor adjustment not only improves the 5ths but also cleans up the resultant 4ths and other intervals, such as major thirds, within the prime octave.
The capacity to shape the tuning curve in both the prime and sub-prime octaves, and have these adjustments reflected in the tuning generated by the Littau-Conrad spreadsheet, is a distinctive and valuable aspect of this method.