Best-Practice Overview

When refining FAC tunings, start by setting the A Multiplier Default to 0.8. This usually places A4 very close to the A440 standard.

Next, lower the tenor partial change from the FAC default of B2/C3 to G#2/A2.

Check the A2/A4 Double-Octave Width

After the tenor partial change is lowered to G#2/A2, both A2 and A4 use their 4th partials. That makes the A2/A4 double-octave width easy to read directly from the A2 setting:

  • -3.5 indicates a 3.5-cent-wide double octave.
  • -4.0 indicates a 4-cent-wide double octave.
  • -4.5 indicates a 4.5-cent-wide double octave.

Reference Point from Appendix E

In Appendix E, “The Two-Octave A Temperament,” Al Sanderson describes a direct-interval tuning routine for the AccuTuner that “exactly simulates the way fine aural tuners tune by ear.” In step 2, he recommends checking the A2–A4 octave and narrowing both octaves if the span is more than 4 cents wide.

In practical terms, this suggests that an A2/A4 double octave wider than 4 cents may be too wide.

Even with the A Multiplier Default set to 0.8 and the partial change lowered to G#2/A2, some FAC tunings will still produce an A2/A4 double octave wider than 4 cents.

Adjust the A2/A4 Width with Double Octave Beat

The SAT IV’s Double Octave Beat (DOB) feature lets you expand or contract the tuning while keeping A4 fixed:

  • A positive DOB value increases stretch by raising the treble and lowering the bass.
  • A negative DOB value contracts the tuning by raising the bass and lowering the treble.

In either direction, the tuning changes above and below A4 while A4 itself remains unchanged.

If A2 reads lower than -4.0 after the tenor partial change has been lowered—and the A Multiplier Default is already set to 0.8—use DOB to narrow the A2/A4 double octave so it is no more than 4 cents wide.

Use Your Ear as the Final Guide

Pianos vary, and every tuning guideline has exceptions. In my experience, the A2/A4 temperament range usually sounds best when the A2/A4 double octave is less than 4 cents wide. Because the SAT IV is highly adjustable, small changes are easy to test. Listen carefully, compare the results, and let your ear guide the final decision.

Before changing the width with DOB based on the numbers alone, first listen to the result produced by the lowered partial change and the 0.8 A Multiplier setting in the FAC tuning. Whatever the A2 setting is, tune a small group of reference notes: A2, D3, E3, A3, D4, E4, and A4.

Although scaling issues may appear in this part of the piano, listening to these notes in several combinations will usually reveal if the A2/A4 double octave needs adjustment. For example, if A2 reads -4.5 and the single and double octaves both seem to beat too much, the numbers and the sound are pointing in the same direction: the temperament will probably sound better with slightly less stretch.

In most cases, the DOB change in this area will be small—usually 0.1 or 0.2 in either direction. A positive DOB value, such as +0.1, adds stretch; a negative DOB value, such as -0.1, removes stretch.

If the need for adjustment is not obvious at first, use DOB to test a few different widths in the A2–A4 temperament area. The SAT IV command for DOB is Blue Shift + Cents Up/Down.

Each 0.1 DOB changes A2 by about 0.4 cents. For example, if A2 starts at -4.0, a +0.1 DOB setting will move A2 to about -4.4, while a -0.1 DOB setting will move A2 to about -3.6. A -0.2 DOB setting will move A2 by about 0.8 cents. To test a slightly narrower double octave, enter -0.1 DOB, check the new A2 setting, retune the reference notes, and listen again.

When evaluating the best width, listen primarily to the larger intervals: the A2/A4 and A3/A4 octaves, followed by the A2/E3 and A3/E4 fifths. Also check the twelfths in this area, especially A2/E4 and D3/A4. These larger intervals usually provide enough information to choose a suitable A2/A4 double-octave width and, by extension, a workable A2–A4 temperament width using DOB.

To compare DOB settings, use a few simple listening checks:

  • Play A2, E3, A3, E4, and A4 together, then listen.
  • Play A2, D3, A3, D4, and A4 together, then listen.
  • Play softly with the pedal to reduce extra noise.
  • Compare the A notes with the E notes, and then compare the A notes with the D notes.

It is better to retune a small group of notes a few times with two or three DOB settings than to move forward with a width that is not convincing. With practice, this comparison becomes faster and more reliable. If needed, deliberately add or subtract a little too much DOB, then work back toward the middle until the best stretch and DOB setting are found. Once a good A2–A4 temperament width is established, move on to the partial correction.

My typical target for A2 is approximately -3.3 to -3.8, though exceptions are common. Once a promising width is found, tune additional temperament notes, including thirds, to confirm the result. Be cautious, however: major thirds can expose scaling problems, especially on short-scale pianos, and those problems may not be fully correctable. For that reason, use the larger intervals as the main guides.

Avoid sacrificing the larger intervals simply to improve the smaller ones; the tuning will usually sound better overall when the larger intervals remain balanced. In general, the octaves should beat less than the fifths. On difficult pianos, aim for a reasonable compromise between the beating of the fifths and the beating of the octaves, rather than sacrificing octaves for fifths.

Taking time to find a good temperament width with as few notes as possible, before continuing, will usually produce a better overall tuning for the piano.

Apply DOB Before Correcting the Tenor Partial Change

If a DOB setting is needed, keep it active while tuning the bass. Decide on the DOB setting before checking and correcting the tenor partial change, so the correction is calculated with the DOB effect already in place.

For example, after lowering the tenor partial change, you may decide that the best A2/A4 temperament width uses a DOB setting of -0.1. In that case, apply the partial change correction while the -0.1 DOB setting is active.

Recommended Starting Targets

  • A Multiplier Default: 0.8
  • Tenor partial change: G#2/A2
  • A2/A4 double-octave width: less than 4 cents wide, when appropriate*

*Less than 4 cents wide is common, but not universal. Some pianos require a different compromise. Difficult scaling situations often call for what Al Sanderson described as “the least bad sounding solution.”