Understanding Partial Changes and Correction in Computerized Piano Tuning
Introduction
This section provides an in-depth explanation of the challenges encountered with computerized piano tuning systems, especially focusing on the errors that arise during partial changes. Emphasis is placed on the significance of these errors, their accumulation, and how the Sanderson Accutuner IV’s Partial Change Correction (PCC) feature offers an effective solution.
The Nature of Partial Changes in Tuning Software
All computerized tuning software systems incorporate partial changes. Since tuning the entire range of piano notes—from A0 to C8—cannot be accomplished using a single partial, the software must switch between different partials at designated points. These partials are intentionally designed within the software, and a partial change occurs whenever the system transitions from one partial to another during the tuning process.
Errors at Partial Change Points
Errors commonly arise at each partial change location. These errors can vary in magnitude: while discrepancies less than 0.3 cents may not pose significant issues, errors of 0.5 cents or more are easily audible. Such errors can be detected not only at the change point itself but also within musical intervals—like thirds, sixths, or tenths—that span across the partial change. The most noticeable errors tend to occur in the tenor and midrange sections of the piano. These, combined with typical scaling challenges in the tenor area, can significantly affect the overall quality of the tuning.
Identifying and Evaluating Partial Change Locations
Partial change locations can differ depending on the tuning system or software used. It is essential to identify where these changes occur within the system being utilized. After determining these locations, tuning across the partial changes and listening to relevant intervals for irregular beating helps to detect partial change errors. What is heard during this process is likely the result of these errors.
Cumulative Impact of Partial Change Errors
Partial change errors are not isolated; they accumulate throughout the tuning process. Most tuning systems feature three to five partial changes, each potentially introducing an error. Even relatively minor errors can become significant when compounded, ultimately impacting the overall quality of the tuning.
The Sanderson Accutuner IV and Partial Change Correction
Correcting all partial changes is a straightforward process with the Sanderson Accutuner IV. This device includes a built-in feature that enables users to accurately and efficiently correct partial change errors, a function unique to the SAT IV. While older AccuTuner models can perform these corrections, the SAT IV’s Partial Change Correction (PCC) feature is designed to make the process even more convenient.
Additionally, the AccuTuner is the only tuning device capable of “Direct Interval” Tuning. The PCC feature allows users to check and correct each partial change quickly, regardless of where the changes occur in the tuning range. A video demonstration is available to illustrate the operation of this feature: (please pardon the singing in the video; it will become clear upon viewing!) https://youtu.be/dVmNBPq4C8Q
Comparison to Other Tuning Systems
No other tuning software, application, or device offers direct interval tuning, making the SAT IV’s capabilities unique. Although some competitors claim that their software’s partial change errors are negligible, every partial change inherently involves a mathematical estimation. Therefore, unless each change is checked and either confirmed or corrected, the resulting tuning quality may not be optimal.
The Role of Piano Scale in Partial Changes
The characteristics of the piano itself also influence the impact of partial changes. Long scales are generally more forgiving; however, most technicians regularly encounter pianos with shorter scales. The shorter the scale, the more critical it becomes to check and address partial change errors to achieve the best possible sound. In most cases, there will be an error at each partial change, making careful attention to these points essential.
Reducing the number of partial changes directly reduces the number of potential errors.
Again, the big bang for the buck to fix is the one in the tenor, but the ones in the treble are also worth checking.
Here is an example of a “Two Partial Change” Arrangement:
A Streamlined Piano Tuning Method Using Partial Changes
Introduction
This section describes a piano tuning method designed to simplify the process by focusing exclusively on the 1st and 6th partials. By eliminating the need for partial changes above A4, this approach aims to minimize errors and improve workflow efficiency for piano tuners.
Overview of the Method
Traditionally, piano tuning involves frequent changes between different partials, particularly above A4, which can introduce errors and complicate the process. In this method, the tenor and treble partial change points are lowered, and specific partials are assigned to designated note ranges. This targeted assignment reduces tuning errors and streamlines the workflow.
Two Partial Change Arrangement
The “Two Partial Change” arrangement is central to this method. Unlike traditional approaches that utilize the 2nd partials, this arrangement omits them entirely. Instead, the fundamentals, or 1st partials, are used for notes ranging from A#4 to C8.
When tuning A4 at A440, the fundamental (1st partial) of A4 is used. This same principle applies when tuning subsequent notes such as A#4, B4, and C4, utilizing their respective 1st partials. Removing the use of the 2nd partials eliminates the risk of partial change errors above A4, as there are no changes required in this range.
Partial Change Locations Compared to FAC Tuning
The locations for partial changes in this two partial change arrangement differ from those found in the FAC tuning system. Notably:
- The tenor partial change is lowered from B2/C3 to G#2/A2.
- The treble partial change is lowered from B4/C5 to A4/A#4.
Assignment of Partials by Note Range
In this method, each note range is tuned using a specific partial:
- 6th Partials (green line): Used for tuning notes A0 through G#2.
- 4th Partials (red line): Applied to notes from A2 to A4.
- 1st Partials (blue line): Employed for notes from A#4 to C8.
This structured approach ensures that partial changes are minimized and occur only at clearly defined points, resulting in a more reliable and streamlined tuning process.
Optimizing Partial Changes in Piano Tuning
Introduction
This section discusses the advantages of strategically adjusting the locations of partial changes during piano tuning, with a particular focus on the A4/A#4 range. The methods outlined below are designed to minimize or eliminate errors at critical transition points by utilizing specific partials for tuning. The overall approach enhances accuracy and consistency during aural checks, especially across bridge and string transitions. These improvements are particularly beneficial for pianos featuring 26-bass scales.
Benefits of Adjusting Partial Changes
Eliminating the use of 2nd partials in the tuning process reduces the number of potential errors associated with partial changes. A key advantage of the proposed approach is the improved placement of the partial change at A4/A#4, which ensures that no errors occur at this particular transition.
Utilizing Fundamentals and 4th Partials
When tuning A4 to A-440, the fundamental (1st partial) of A4 is employed. If the fundamental is accurate for tuning A4, it is logical to use fundamentals to tune subsequent notes such as A#4, B4, C5, and those above. Even though A4 is actually tuned using its 4th partial, its fundamental remains at 0.0 cents deviation. As a result, when fundamentals are used for tuning all notes from A#4 up to C8, the treble tuning effectively begins at 0.0 cents.
The setting for A#4, when employing fundamentals, typically ranges from 0.0 to 0.4 cents, depending on the specific piano and the required amount of stretch from A4 to A5. Importantly, any error at this location is negligible—generally not exceeding 0.1 or 0.2 cents, making it inaudible. In practice, the treble tuning could start with A#4 at 0.0 cents, similar to A4, though more often, A#4 is set at 0.1 or 0.2 cents.
Stability in the Tenor Range
The partial change in the tenor region is shifted lower—from B2/C3 down to G#2/A2—resulting in a stable two-octave range (A2 through A4) where all notes are tuned using the same (4th) partials. With no partial changes within this span, the two-octave temperament area is free from partial change errors, enabling more accurate aural checks.
On most pianos, especially those not featuring extra-long scales, A2 is typically located on the bass bridge. By using the same partial across the bridge break, and through the transition from plain wire to wound strings, potential partial change issues in this challenging tenor region are effectively eliminated. This is particularly advantageous for 26-bass scale pianos, where the bridge break occurs between A#2 and B2, with both notes now utilizing their 4th partials.
Transition to the One Partial Change Arrangement
Initially, a two-partial arrangement was used for several years before the 6th partials were completely phased out. The current approach utilizes a single partial change, as implemented in the Littau-Conrad Tuning System.
The One Partial Change System
In this system, there is only one partial change in the tuning process, occurring at A4/A#4. From A0 up to A4, the 4th partials are used for tuning. From A#4 through C8, tuning is accomplished using the 1st partials (fundamentals). This configuration ensures that the only partial change—between A4 (using the 4th partial) and A#4 (using the 1st partial)—is effectively error-free and does not require additional checking.
The use of 6th partials has been eliminated in this arrangement. The 4th partials are consistently used for tuning from A4 down to A0, maintaining simplicity and accuracy throughout the lower range.
The Reliability of Partials in Piano Bass Tuning
Introduction
A common misconception in piano tuning is that achieving different degrees of stretch in the bass requires using higher partials, such as the 8th or 10th, rather than lower ones like the 4th or 6th. This section clarifies that any partial can be used to reach the same pitch, but it emphasizes that lower partials—especially the 4th—are generally more dependable for bass tuning. The reliability of these lower partials contributes to a smoother, more consistent sound, whereas higher partials can introduce inconsistencies, particularly on pianos with poor scaling.
Misconceptions About Stretch and Partial Selection
There is ongoing confusion regarding how much stretch to use and which partials to employ for bass tuning. Some believe—and even teach—that the only way to obtain more stretch in the bass is to use a higher partial. For instance, it is sometimes taught that switching from the 6th to the 8th, or from the 8th to the 10th, is necessary to increase the stretch. However, this belief is not accurate. The note A1, for example, can be tuned using its 4th, 6th, 10th, or 12th partial, and it will reach exactly the same pitch in each case. It may require a wider 6th or 4th to match a pure 8th, but the target pitch for A1 can be attained with any partial.
Reliability of Lower Versus Higher Partials
The main issue with using higher partials—such as the 6th, 8th, or 10th—for bass tuning is their relative unreliability compared to the lower ones, like the 4th partial. The 4th partials are more reliable than the 6th, and this trend continues as the partials go higher: reliability decreases. Poor scaling, especially, can make the use of higher partials for bass tuning problematic. While charts and numbers may appear smooth, if the partials themselves are inconsistent from note to note, the resulting tuning will sound uneven.
It is not fair to simply blame the piano when this occurs. Using higher partials can actually exaggerate underlying problems in poorly scaled pianos. By contrast, relying on the 4th partial for bass tuning can resolve these issues, producing a smoother result even on challenging instruments—and it works just as well on high-quality, well-scaled pianos.
There is no need to switch to a different partial to achieve more stretch in the bass. In fact, doing so can worsen the sound due to the unreliability of higher partials.
Understanding Partial Reliability
Reliability, in this context, means that the location of a partial remains consistent across a range of notes. For example, if the 6th partial of G2, G#2, and A2 are all at the same “height,” then using the 6th partials will yield a smooth-sounding tuning. If the 6th partials are reliable, the 4th partials and those below are likely reliable as well. However, on many pianos—especially those with shorter scales—the heights of the 6th partials can vary significantly from note to note. When the 6th partials are unreliable, higher partials such as the 8th, 10th, or 12th are likely to be even more inconsistent.
By comparison, the 4th partials over the same range of notes tend to be more reliable. Even on poorly scaled or shorter pianos, the 4th partials are usually a better choice for tuning because they fluctuate less than the higher ones. Their locations are more consistent, making them more trustworthy for accurate tuning.
Thus, the 4th partials are preferable for challenging pianos and are equally effective for those with longer scales.
How Tuning Devices Use Partials
Tuning devices aim to create a smooth set of numbers for tuning the bass, and this smoothness is typically found between partial changes. For example, if a system uses the 4th partials from A0 to A4, the resulting chart will show a smooth curve over that range. Similarly, if the 6th partials are used from A0 to B2, a smooth curve appears over that span. If the system switches from the 12th partial for A0–A1 to the 8th partial for A#1–A2, there will be two separate curves, each smooth in appearance.
The true question is which partial’s smooth curve results in the smoothest-sounding tuning. The higher the partials used, and especially when switching between high partials, the less likely the result will be smooth. Additional partial changes in the bass introduce further complexity and potential for errors, which must be checked and corrected to ensure a smooth-sounding tuning.
These issues are most pronounced on pianos with shorter scales, uneven string lengths, or poor bass string design and manufacturing. Creating a smooth set of numbers using unreliable partials, such as the 6th, will result in uneven beat rates and an uneven tuning. Using the 4th partial numbers in such situations produces intervals that sound much better.
A Practical Discovery: The Eureka Moment
This understanding arose from a personal experience while tuning a piano. After struggling to achieve even beat rates in the tenor area, particularly across a partial change, it became clear that using the 6th partials was causing problems. Despite repeated attempts to correct the tuning, the intervals across the partial change remained unsatisfactory.
To solve this, the 4th partials were extended lower into the bass, and the tuning improved dramatically. When the 6th partials were reintroduced below this point, the problem returned. Extending the use of 4th partials further down resolved the issue again. The 6th partials on that particular piano were so unreliable that trying to create a smooth tuning using them resulted in poor-sounding intervals, but using the 4th partials produced a much better outcome.
This was a pivotal moment, leading to the decision to eliminate the use of 6th partials for bass tuning. Subsequent experience showed that if the 4th partials worked well on a small piano, they would also be effective on a concert grand—and that proved to be true.
Using the 4th Partials: Method and Rationale
It is crucial to note that using the 4th partials in the bass has nothing to do with the amount of stretch. For example, the pitch location for A1 is initially found using its 6th partial. Once the desired location is determined, the position of the 4th partial is measured and used for both creating and performing the tuning. This approach eliminates the reliability concerns associated with higher partials and avoids troublesome partial changes in the bass.
The same method applies to A0. After tuning A1, the location for A0 is determined using intervals such as the 8:6 4th and the 6:4 5th. The final setting for A0 is then measured using its 4th partial, and this value is used for tuning.
Ultimately, the amount of stretch in the bass is not dependent on which partials are used. Good pitch locations for both A1 and A0 can be found, tuned accordingly, and then measured using their 4th partials, which serve as the settings for the tuning.
A 5-Partial change arrangement:
Challenges of a Five-Partial Change Arrangement in Piano Tuning
Introduction
This section examines the specific challenges encountered with a piano tuning arrangement that incorporates five partial changes. The focus is on the problematic nature of this system, particularly when applied to pianos with shorter scales.
Overview of the Five-Partial Change Arrangement
The arrangement under discussion utilizes five distinct partial changes. Notably, three of these changes occur in the lower half of the piano. According to current understanding, such a configuration is generally undesirable. While this arrangement might function adequately on some long scale pianos, it tends to be problematic on anything but the very longest scales. The potential for five partial change “hiccups” can result in compounding tuning difficulties.
Impact on Tuning Shorter Scale Pianos
Tuners who use this five-partial change system have frequently reported challenges when tuning the bass of shorter scale pianos. In many cases, they find it necessary to rely on their ear for bass tuning rather than systematic methods. This is because longer scale pianos are somewhat more forgiving of such arrangements, but only to a certain extent.
Significance of Partial Selection
The issues are not limited solely to the number of partial changes; the choice of which partials to use is also crucial. The selection of specific partials can either exacerbate or mitigate tuning challenges, especially in the lower registers.
Limitations Without Direct Interval Tuning
Even if a tuner were able to identify the most likely errors at any of the five partial changes, the absence of Direct Interval Tuning makes it extremely unlikely that these errors could be reliably checked or corrected. Thus, the combination of multiple partial changes and the partials chosen creates significant obstacles in achieving precise tuning.
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