Piano Tuning Using Prime 5ths and Octave Widths
Introduction
This structured guide explains the process of tuning a piano by focusing on the combined width of prime fifths and the prime octave. It highlights a recommended approach where achieving a combined fifth width of -3.0 cents generally indicates a well-tuned octave. The guide acknowledges that compromises may be necessary due to the unique characteristics of individual pianos, and encourages patience and experience in order to achieve excellent results, even with challenging instruments. The value of storing custom tunings for future use is also noted.
Locating A3 and Initial Tuning
After determining the fourth A4 number, estimating the location of A3 becomes straightforward. If the fourth A4 number is high—above 3.0 cents—begin with a template that produces a pure A3/A4 4:2 interval. Using this template, tune A4, A3, D4, and E4, then measure the prime fifths.
Assessing Prime Fifths and Octave Widths
The combined width of the prime fifths reveals whether the prime octave needs to be expanded or contracted. The goal is a combined width of -3.0 cents for the prime fifths, regardless of individual values (e.g., one fifth at -2.0 cents, the other at -1.0 cents). Add the widths together; if the sum is -3.0 cents, the prime octave width is likely correct. While this guideline works for most pianos, exceptions do exist.
If, for example, one fifth is -1.5 cents and the other is -2.3 cents (totaling -3.8 cents), this indicates the prime octave is 0.8 cents too narrow. In such cases, select another template with an A3 setting 0.8 cents lower, then retune and remeasure.
Monitoring the Prime Octave’s 2:1 Width
While tuning the prime fifths, pay attention to the width of the prime octave’s 2:1 interval. As long as the 2:1 stays below 2.8 cents and the combined prime fifths’ width is -3.0 cents, the prime octave is likely tuned correctly. Most pianos will accommodate this relationship, but some may not, requiring further adjustments.
All that is required at this stage is for the combined width of the prime fifths to be -3.0 cents. The fifths will be balanced later by adjusting the mid-point (D#4) of the prime octave.
If the combined width is -3.0 cents but the prime octave is 3.6 cents wide and produces excessive beating, compromises must be made. In such cases, a combined fifth width of -3.4 cents, resulting in a 2:1 octave around 2.8 cents, may be a suitable compromise.
Dealing with Challenging Pianos
Some pianos, especially those with noisy or false scaling, may require more significant compromises, such as narrower fifths or wider octaves. These “exception” pianos offer valuable learning opportunities. With experience and patience, excellent results can still be achieved, and customers often notice and appreciate the improvement. Custom tunings for these pianos can be stored for future use, saving time and ensuring consistent quality.
Balancing Fifths and Observing Fourths
Begin tuning with the fifths while monitoring the prime octave’s 2:1 width. If the 2:1 is less than 3.0 cents, the octave should sound good; once the fifths are balanced, they will sound good as well.
Before balancing the fifths, listen for “out of balance” cues in the resultant fourths (A3/D4 and E4/A4). Since fourths beat faster than fifths or octaves, the most noticeable beating may occur in the upper or lower prime fourth, indicating the direction in which the mid-point should be adjusted.
If the prime octave’s 2:1 width is less than 2.8 cents and the prime fifths are balanced at -1.5 cents, the resultant fourths will also sound good.
Narrow Prime Fifths and Special Cases
On pianos with a high fourth A4 number, the prime fifths may need to be narrower than -1.5 cents. Sometimes, setting the fifths at -1.5 cents results in a prime octave’s 2:1 interval as wide as 4.0 cents. In these scenarios, to reduce beating in the 2:1, the prime fifths should be narrowed further, potentially reaching a combined width of -3.5 or -4.0 cents.
Because the fourth A4 number represents the width of the prime octave’s 2:1 after tuning as a pure 4:2, some pianos will require a narrow A3/A4 4:2 interval.
Contrasting Aural Tuning Methods
Traditional aural tuning often begins by tuning A3/A4 as a wide 4:2, where the F3/A3 major third beats slower than the F3/A4 tenth. However, on pianos needing a narrow 4:2, the correct beating is reversed—the F3/A3 major third should beat faster than the F3/A4 tenth. Many beginners practice on spinets or consoles that require a narrow 4:2, a point often overlooked in standard teaching.
Finding the Best Compromise
Tuning a piano with a prime octave that demands more beating in both the octave and the fifths is a balancing act. The objective is a pleasant compromise between beating in the octave and the fifths. Knowing the width of the prime octave’s 2:1 (the fourth A4 number) and the widths of the prime fifths is a significant advantage.
Personal experience led to a starting point of -1.5 cents for the fifths, based on empirical observation. This width typically produces pleasing fifths and octaves on most pianos. Similarly, keeping the prime 2:1 width below 3.0 cents usually avoids a sound that is too “beaty” or noisy. These guidelines serve as effective starting points.
Addressing Exception Pianos
Occasionally, pianos will not conform to these guidelines. In such cases, remeasuring and retuning are necessary, but often the piano simply cannot accommodate the usual settings. These exceptions are rare but require an individualized approach.
Consulting with experts, such as Rick Baldassin, reveals theoretical widths (e.g., -2.0 cents for the fifths), but practical tuning often uses slightly wider intervals (e.g., -1.5 cents). More variation is tolerable in the prime octave than in the fifths. In practice, prime fifths typically range from -1.2 to -2.2 cents, with the prime octave’s 2:1 width spanning 1.2 to 3.0 cents, and sometimes wider if compromises are necessary. The most critical aspect is balancing the fifths, especially when both are at the edge of acceptability.
Ultimately, there is no universally “perfect” width for any interval; it depends on the piano. The pursuit of a perfect twelfth (P12th) is often touted, but empirical data shows that the twelfth is rarely pure, and the piano’s characteristics often dictate the actual settings.
Evaluating Prime Fifths and Tuning Consistency
Most computed tunings use consistently shaped curves in the prime octave, regardless of the starting and ending points. While tuning software strives for consistency, it only works well for some pianos; most instruments require more individualized attention.
Measuring and balancing the prime fifths in your own tunings helps identify mis-fitting templates or tunings. A piano’s scaling often mismatches computed curves, especially in less well-scaled pianos, but this issue can arise in any instrument.
To check, tune A3, D4, E4, and A4, and measure the widths of the prime fifths. If they are balanced (the same width), the piano will sound better. Hearing differences in the resultant prime fourths can be easier than in the fifths. When the fifths are balanced, the instrument’s sound improves noticeably.