What I’m calling ‘The A4 Numbers’ are the locations of the 2nd, the 4th, and 8th partial of A4 when A4 is tuned to A440.
These A4 numbers tell us a lot about the piano.
First, we’ll know the target setting for A4. Since this system uses the 4th Partial of A4 to tune A4 @ A440, we’ll know the setting for A4 that will be used in the tuning.
Second, the 8th partial number is the setting to use if the technician wants to use a triple octave for A7.
Third, the 2nd Partial setting is the setting for A3 if a pure 4:2 octave width is desired for the A3/A4 octave. If an A3/A4 4:2, 1/2 bps wide is desired, simply subtract 1.0 c from the 2nd partial setting. Adding 1.0 c. to the width of the pure A3/A4 4:2 will add 1/2 bps. to the A3/A4 4:2 octave. The resulting A3/A4 octave will be a 4:2, 1/2 bps wide.
To measure A4’s 2nd Partial:
Tune A4 to A440.
Set the ETD (AccuTuner) to listen to A5, play A4, and stop the lights (with the cents buttons).
The cents setting is the location of A4’s 2nd P.
To measure A4’s 4th Partial:
Tune A4 to A440.
Set the ETD (AccuTuner) to listen to A6, play A4, and stop the lights (with the cents buttons).
The cents setting is the location of A4’s 4th P.
To measure A4’s 8th Partial:
Tune A4 to A440.
Set the ETD (AccuTuner) to listen to A7, play A4, and stop the lights (with the cents buttons).
The cents setting is the location of A4’s 8th P.
These “A4 Numbers” should be used only as a guide, or a reference. They are the locations of the 2nd the 4th and the 8th Partials of A4, but that does NOT mean A5, A6 and A7 should be tuned to those ‘pure’ locations.
For example, tuning A5 to the location of A4’s 2nd Partial will be tuning A5 too flat!! Guaranteed! That’s also true if tuning of A6 as a pure double octave from A4. That setting will also probably be too flat.
A7: High treble tuning (A6 – C8) is quite subjective. Some say, a triple octave is too sharp, others say it’s too flat. This is where the experienced ear of the technician is essential! A triple octave may be good for C7 but not good enough for F7? or A7?
However, knowing these A4 numbers for every piano can be very helpful.
Many technicians may like (or teach) tuning A3 as a 4:2 octave, 1 c. wide, which is a 4:2 octave, 1/2 bps. wide.
Knowing the location of the 2nd P of A4 makes that a snap. Simply tune A3 as a pure 4:2 and then lower it by 1 c. That may be a good starting point for A3, but on some pianos it’ll be too wide, and on others that won’t be wide enough. There are some pianos where that A3/A4 4:2 will need to be narrow!! It depends on the piano.
Mapping involves gathering as much information about the piano as possible so the best decisions can be made how to tune it to best match it’s particular inharmonicity. Information helps removes guesswork and can reduce some trial and error.
Effective mapping routines enable an experienced technician to identify from the outset the necessary steps for achieving the optimal piano tuning.
Measuring the A4 numbers is a great place to start.
With some experience, the technician will quickly recognize both ‘normal’ and ‘abnormal’ A4 Numbers.
Mapping like tuning, has to begin somewhere, and just as we learned with our aural tuning skills to start at A4 and work our way outwards, that’s what’s happening here. But instead of just tuning A4 we can use some technology to take a look at how that string is vibrating, what it’s inharmonicity is as seen by the locations of its 2nd, 4th and 8th partials.