Robert Conrad, Registered Piano Tuner/Technician, Tucson, AZ

2. Mapping the Sub-Prime Octave (A2/A3) with a SAT “980” & Templates

Once the prime octave (A3-A4) has been mapped, the sub-prime octave (A2-A3) can be mapped.

The same template is used for mapping both the prime and the sub-prime octaves.

Aural tuning experience is very helpful for all of this.   Technical skills do not exclude aural skills.  But at the same time,  aural skills shouldn’t ignore technical skills.

Whatever is easier for us is generally that with which we are more experienced.   Sometimes tuning the targets aurally and then verifying with technical skills, is the fastest.   Using technical skills to find the targets and then verifying them with aural skills is also a good approach.   In the end both should make sense and compliment each other.   

Sadly, most of us have more experience with aural skills than we do with the technicals.   Even those who use a SAT, often know little more than how to stop the lights, without really knowing anything more about their device.   The SAT can do a lot more than that, and so can we.  

As you may be beginning to see, this approach using mapping puts the technician in complete control of how the piano is tuned.   The technician makes every important decision regarding the tuning.   Combining both aural and technical skills for most of us, requires more work on the technical side rather than on the aural side.  

But as experience with the technical skills grows, they will begin to enhance the accuracy of the aural skills alone, and can be very helpful in the decision making process helping to assure a consistently good sounding result covering the entire keyboard.  And it will make sense both aurally and technically.

D3:
The first note I map in the subprime octave is D3.   Tune D3 using the same template that was used to map the prime.

Now that D3 has been tuned to the template, a few checks are available:
1. D3/A4 12th
2. D3/D4 octave
3. D3/A3 5th

These D3 checks can be made both aurally and technically.   I first listen to everything and go from there.   I eventually confirm the placement of D3 by measuring the upper sub prime 5th’s width (D3/A4).   It’s a good idea to measure that 5th to make sure our ear didn’t put it too close to pure.

1.   The D3/A4 12th:   I like to know where the template places D3 relative to the D3/A4 12th.  With all the talk these days about the ‘whole tone’ or 20th Century Tuning Style having it’s 12ths pure, I will look to see if that’s what I’m getting.   Most of the time this 12th is close to pure.  Most of the time it will be within .5 c. pure.  But at least by my measurements, it is rarely a perfect 12th.
But aurally, this 12th will sound pretty clean.  But rarely is it a ‘pure’ 12th.
This is an easy one to measure:   Simply set the SAT (in TUNE mode) to (A4 @ 0.0), play D3 and stop the lights with the cents buttons.   0.0 means the 12th is pure.  A negative number indicates a wide 12th, and a positive number indicates a narrow 12th.
As far as an exact width for this 12th, I don’t have one.   The final tuning position for D3 can result in this D3/A4 12th being wide, pure and even sometimes narrow.   It just depends on the piano.
But when I compare the placement of D3 using the 12th, I get an idea of direction above or below the template’s setting for D3.  
2. The D3/D4 octave:
   I just listen to this octave.  I don’t measure this octave.   I use it to tweak the tuning of D3 aurally, just to make sure it is in the ball park.   After I’m finished tweaking D3 aurally, I compare the new location of D3 to the template setting.
This bit of information I use in addition to the 12th info.  If both of them are pointing in the same direction I’m probably headed in the right direction since both are confirming each other.   If they don’t confirm each other, I will often check the tuning of the reference notes, and possibly re tune, re listen, and re measure.

3. The D3/A3 5th:   This is the best check for the best location of D3.  Ill tweak tweak D3 aurally while listening to the 5th.  But before I finalize the location, I always measure the D3/A3 5th to confirm.
I don’t have or use an exact width of the D3/A3 5th, but most of the time it ends up being somewhere between -.5 c.  &  -1.2 c. Since we used the -1.5 width for the prime 5ths, the sub prime 5ths are generally a little less narrow (wider) than the prime 5ths.  But the amount will vary from piano to piano.

Working with these 3 interval checks, a good sounding location for D3 can be found.

Once the correct setting for D3 is determined, write it down.

E3:   Once the best location for D3 is determined, finding E3 is a little easier.  Whatever the adjustment to the template setting was for D3, the same adjustment can be made for E3.  

If the new location for D3 required a -.4 c. adjustment to the template setting, simply apply that same -.4 c. adjustment to the template setting for E3 and then tune E3 using that setting.

Example:   If the template setting for D3 is -.4 c. but the correct setting is -1.0 c.,  the template setting is .6 c. too high.   So, a good starting point for E3 would be to subtract .6 c. from the template setting of E3, and tune E3 to that setting.

Two useful checks for E3 are:
1. The E3/A3 4th.
2. The E3/E4 octave.

The E3/A3 4th is probably the one most useful.  After tuning E3 to the adjusted template setting, I just listen to the E3/A3 4th.   I don’t measure it.   If that 4th is beating to fast, the interval is probably too wide.

[I use both the upper sub prime 4th and the upper prime 4th as a ‘final’ check for the mapping of their respective octaves.   If either octave is not well mapped, it will show up in their upper 4ths.   If either of the octaves (particularly the prime) are not well mapped, or their 5ths aren’t well balanced, it will show up in noisy upper 4ths.]  

If D3 is well placed, using that same cents adjustment for tuning E3 will be pretty close.

Even thought it may be tweaked a bit later, once this setting for E3 is determined, write it down.

A2:
Even thought my average setting for A2 in my finished tunings is around -2.4 c., the default setting for A2 on all my templates is -1.9 c.
But that doesn’t mean every piano’s A2 should be tuned @ -2.4 c.
Some of the tunings in the average had an A2 as high as -1.3 c. and as low as -6.1 c.

I always start by tuning A2 to the template default of -1.9 c.  and then listen to the A2/E3 5th.   This lets me know very quickly if A2 needs to be lowered or if I’m

Sometimes I’ll just tune A2 aurally and sometimes I’ll just put a lower setting  into the SAT and re-tune A2.

My first priority for finding A2 is the A2/E3 5th. 
Once I have aurally placed A2, I measure it’s location and the width of the lower sub prime 5th.   That 5th should still be narrow.   The exact width will vary from piano to piano, but it should still be narrow.   The width of the upper sub prime 5th (D3/A3) can be used as somewhat of a guide.

It would be nice if both the upper and lower sub primie 5ths were the same width, but often times that is not going to happen.   They may be within a few tenths of each other, but I don’t ‘balance’ these 5ths like I do in the prime octave.

The scaling in this part of the piano can make balancing a pair of sub prime 5ths difficult and may not result in the best sounding option.

But the upper and lower sub prime 5ths should both be slightly narrow and probably within .5 c. of each other width-wise.   But both should be narrow.

For instance, if the upper sub prime 5th is -.8 c.,  the lower sub prime 5th can be about that width or maybe a little wider.  But it should still be narrow .

But sometimes, due to the scaling in that tenor area, both D3 and E3 may need to be further adjusted for the best compromise.

this is another reason why each mapped note’s setting is written down.   It’s never a bad idea to re tune or re measure the other previously tuned notes to their correct settings.    Any slippage needs to be corrected as best possible.

The scaling of the piano really comes into play in this area, with the string scaling break (plain wire to wound strings) and the bass bridge/long bridge break.

Most of the time, if A2 is going to be fairly severely lowered, it will start to show up when mapping D3.   The longer scales are easier of course, but on the shorter scales, this area of the piano is full of clever and sometimes not so clever scaling designs.    Sometimes well executed and sometimes not.   But regardless, that’s what’s there and it’s our job to make the best of it.

The above routines will work on every piano.   Good sounding targets can always be found.   Even on the most challenging pianos, a reasonably good sounding compromise can be found.   But sometimes on the more challenging pianos, more trial and error is needed to a decent sounding compromise.   And on those pianos, the combination of technical and aural skills can really compliment each other.   These challenging pianos are a real education and a great teaching tool.   They are also a test of all our skills.

The mapping D3 and E3 give a clue as to how much A2 will need to be lowered.

A poorly scaled piano will generally really expose itself in the sub prime octave.  This expose starts to reveal itself while mapping the prime, but it really shows itself when mapping the sub prime.

Hopefully as you learn this and start doing it, you will be able to learn it and do it on pianos that are more main stream and not too far off the beaten path.

There’s nothing very unusual in having to lower D3 away from it’s template setting to get a good sounding upper sub prime 5th.    A D3 adjustment of  -.4 or  -.7  is no big deal, and it is helpful and does give a clue as to about how much A2 will need to be lowered from it’s template setting.   If you needed to lower D3 by -.5, chances are you will need to lower A2 by about the same amount – from -1.9 to down to maybe -2.4 or so.

Of course, that is just a starting point for A2, and it’s location will need to be checked and verified with the rest of the intervals available for placing A2.

But if you find yourself needing to lower D3 by a couple cents or more,  flags should start going up.   Some pianos are so pooly scaled that their strings start to get too short quite high up in their scale.   Maybe even up to A3 and above?   I’m not saying there is a single string length all the scale designers use for A4 on up, or anything like that, because I don’t know.

But I do know that the inharmonicity of the notes in the sub prime octave can take a real leap.   Sometimes the scaling breaks and the too short strings can really make for a very challenging tuning situation.   Compromises need to be made right there in the middle of the piano, that are sometimes quite broad.   Not nice little compromises, but great big compromises.

This system of mapping exposes them.   They are just there for us to do the best we can.   And I’m convinced mapping is by far the best way to deal with them.    At least with mapping, we can set the specific octave widths and tweak the shape of the curves within the octaves in the prime and sub prime octaves.   That is just not possible with any other system.

This system gives us the tools to first analyze the situation, and then we get to make the decisions as how we want to deal with it.   Which compromises are the best sounding.

We can make an attempt to ‘cater’ to the scaling of the piano as best we can, or we too, can simply ignore the scaling issues breaks and use a ‘straight’ calculated curve and tune it like it’s problems aren’t even there.

We can do it either way.   But we are the only system that can also tweak that curve to maybe get a better compromise and a better fit custom tuning.

One more thing that makes this system superior is how we have no partial changes in this area at all.   None.   From A0 – A4 the 4th partials are used throughout.   In the other systems the will be at least 1 partial change, and in some systems 2 or even 3!!   Add partial change errors to a piano like this and you might as well just try tuning the lower half of the piano by ear.

Our mapping routines gives us the information about the piano we need to map it and then create a custom tuning for it that will sound surprisingly ‘OK’.

So just be aware, that when D3 needs to be lowered 2.0 c, or something like that, flags should go up!   Hopefully you won’t run into one of these problem pianos until you’ve had enough experience to deal with it.  These are really great learning experiences.

Aurally tune A2 and then compare that setting to the template setting. 

The lower sub prime 5th (A2/E3) should still be slightly narrow.   It shouldn’t be pure.  If it’s pure, something is not as good as it should be.   It might only be -.5 or so, but it needs to be at least a little bit narrow.   Even on the pianos I’ve tuned where I’ve placed A2 @ -5.8 c. that lower sub prime 5th was at least a little bit narrow.

***  A few notes about a small Chickering Grand from the early 1960s I service . . . . . Both D3 and E3 were plain wire, low tension, high iH notes.   To get a decent upper sub prime 5th, D3 needed to be lowered much more than usual.  My average D3 settings is -.9 c., but D3 on this piano was -4.0 c.!   My average setting for E3 is -.2 c. but on this piano E3 was -2.5 c.!   So the excessively necessary stretch started happening in in the top end of the sub prime octave.   The A3 setting was 1.6, which is more in the normal range for my A3 numbers.   But what was happening in this scale, was the strings started getting way to short very early and the sub prime octave took a real dive from A3 down to A2.
In fact, I have 2 of these in my clientele, both mfg. between 1960 – 1965.   The other one has an A2 of -6.1 c.!  Of course the mapping targets are not exactly the same, but both of these pianos are from the same ilk, and both have similar issues in this subprime octave, and both of them are really hard to get to sound good.
What’s also interesting on both of these, and all the others that require some extra work during the mapping process is, once they are tuned,  when they are played, they really don’t sound all that bad.   They are what they are of course, but I think they sound surprisingly ‘OK’ considering what a mess their scales are in there.   ***

The same basic relationships should still exist once the subprime mapping is complete:
The upper sub prime 5th (D3/A3) should be narrow – generally somewhere between -.6 c. and -1.2 c.
The D3/D4 octave should be slightly wide, but not be beating too much.*
The D3/A4 12th should still sound pretty good, but of the 3 intervals here, it is the one that will be beating the least.

The upper sub prime 4th should beat slightly faster than the lower sub prime 5th, but not beating too fast as to be objectionable.*
The E3/E4 octave should sound pretty good as well.

*As far as the D3/D4 and E3/E4 octave widths are concerned, when mapping the prime octave, the width of the A3/A4 2:1 is  known, or can be easily calculated.   That width can be used as a guide for the widths of the D3/D4 and E3/E4 octaves.   If the width of the prime octave is 1.3 c., the width of the D3/D4 and the E3/E4 octaves should probably be at least that wide or slightly wider.

Once the best location for A2 is determined, write it down.

Once the settings for D3, E3, and A2 are known (and written down), the sub prime octave is mapped.

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