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

Partials, Partial Changes, Partial Change Errors, & Partial Locations

Because we can’t use the same partials to tune A0 and C8, there must be at least one partial change in every tuning software system.

Different partials are used to tune different parts of the piano.   The partials used are designed into the software.
Therefore, all tuning software systems contain partial ‘changes’.

A partial change is the ‘switch’ from one partial to another within the tuning.

Whenever the software switches from one partial to another during the course of the tuning, an error at that partial change is very likely.   Small errors of less than .3 c. are not much of a problem.   But errors of .5 c. and greater can easily be heard and can cause problems with the tuning.

The most obvious errors occur in the tenor and midrange where everything is really easy to hear.   And those partial change errors, combined with the other scaling issues contained in that tenor area, can really effect the quality of the tuning.   Partial change errors effect all the intervals ‘spanning’ the partial change.

The location of these partial changes will vary from system to system.

Listen for yourself:  Once the partial change locations are known, after tuning, listen to the 3rds, 6ths, or 10ths across the partial changes.   If there are ‘hiccups’ in the beating across the partial changes, what you’re hearing is probably errors at the partial changes.

The errors are cumulative in the tuning as well.   Depending on how many there are, and where they are located, these partial change errors build upon each other as the tuning is expanded.  So, even relatively small partial change errors can end up being significant in the sound of the tuning.

Partial changes are a universal issue.  Every piece of tuning software has them.  Using an AccuTuner and direct interval tuning, the errors can be measured and corrected.   And now the AccuTuner IV has a built in feature that can be used to easily and accurately correct all partial change errors.

The AccuTuner is the only piece of tuning hardware that can ‘do’ Direct Interval Tuning.

This new Partial Change Correction (PCC) feature on the SAT IV is specifically designed for checking each partial change and making any correction needed quickly and easily at any or all of the tuning’s partial changes.   This feature also works regardless where the partial change is in the AccuTuner’s tuning.

Since none of the other software only systems do direct interval tuning, this is a unique feature of the SAT IV.

Partial change locations are important and which partial used is also important.   But even more  important to the sound of our tunings, is for all of those partial changes to be correct and error free.

Sometimes the designers get lucky and will guess right at a partial change.   But 99% of the time, there will be an error at each partial change.

The first time I checked this was years ago on a Yamaha C7.   The biggest culprit on most pianos is the tenor partial change, so that was the one I checked.   But on that piano, and with the tuning I was using, no correction at the tenor partial change was necessary!   Someone made a good guess somewhere along the line, and the tuning I was using was a good fit for the piano.

But from what I know now, that was pure luck, because it happens so infrequently.   Sometimes we get lucky, like a broken clock being right twice a day.

It didn’t take me long at all to realize how unique it was to not have any correction needed at that tenor partial change.  All I had to do was keep checking.

Since every partial change is a potential tuning issue, the fewer the partial changes the better!

Here are some partial arrangements found in some of the different tuning software systems:

FAC partial change arrangement:
The FAC tuning partial arrangement is as follows:
The 6th partials are used for notes A0-B2
The 4th partials are used for notes C3-B4
The 2nd partials are used for notes C5-B5
The 1st partials (fundamentals) are used for notes C6 – C8.

FAC Partial Change locations:
1.  B2/C3,
2.  B4/C5,
3.   and B5/C6.

Here is a graph of an FAC tuning with the partial changes circled in red:
(Click graph image to enlarge).

 

A Two Partial Change Arrangement:

This two-partial arrangement has one fewer partial change than an FAC tuning because it eliminates the use of the 2nd Partials in the tuning.

The partial change locations are also in slightly different locations than an FAC tuning.

The two partial changes in this arrangement are found between G#2/A2 and A4/A#4:

The 6th Partials (green line) are used for notes A0 – G#2, and the fundamentals or 1st Partials (blue line) are used for notes A#4 – C8.

Using the fundamentals or 1st Partials from A#4 on up, eliminates both the use of the 2nd Partials, and the associated treble partial change.

An FAC tuning uses the 2nd Partials from C5/B5.   So, the FAC treble partial change is between B5/C6, where it switches from the 2nd P to the fundamentals.

The other FAC partial change above C4 is found between B4/C5.   At that point it switches from the 4th P @ B4 to the 2nd P @ C5.

This two partial change arrangement changes that partials location to between A4 and A#4, going from the 4th P @ A4 to the fundamental @ A#4.

The partials used in the below chart are:
the 6th P. (green line) for notes A0-G#2,
the 4th P. (red line) for notes A2-A4,
and the 1st P. (blue line) for notes A#4-C8.
(Click to Enlarge)

Eliminating the use of the 2nd partials results in one fewer potential partial change error in the treble.

Due to the ‘improved’ location of this A4/A#4 partial change, the tenor partial change is the only one that ever needs to be checked.

And here’s why:  When A4 is tuned to A-440, A4’s fundamental (1st partial) is being used.
If the fundamental can be used to tune accurately tune A4 to A440,  there is no reason why the fundamentals can’t also be used to tune A#4!

The treble tuning (A#4 – C8) can then start @ 0.0 for A#4.

Eliminating the use of the 2nd partials in that area, also makes for faster and more accurate mapping of A5.
(More on that later in the posts on Mapping.)

Only the tenor partial change in this two partial change arrangement needs to be checked and corrected.

The locations of the partial changes contained in this two partial arrangement provides a full two-octave range (A2 thru A4) with all notes using the same (4th) partials.

This is accomplished by moving the tenor partial change from B2/C3 down to G#2/A2.

No partial changes within that two octave range insures there is never a partial change error in the two octave temperament area.

Another advantage to this A2 -A4  type partial arrangement, is that A2 is generally found on the bass bridge for all by the longer scaled pianos.   Using the same partial across the bridge break, and through the plain wire to wound string break, on all but the longest scales, eliminates any partial change issues from occurring in that already challenging tenor area of the piano.

This works well for 26-bass scales, whose bridge break is between notes A#2/B2 – with both A#2 and B2 now using their 4th partials.

I used this two partial arrangement for a few years before dropping the use of the 6th partials altogether.

 

A one-partial change arrangement:

This single partial change arrangement is what is used with the Littau-Conrad Tuning System.

There is only one partial change in the tuning: A4/A#4

This system uses:
the 4th partials from A0 – A4 and
the 1st partials (fundamentals) from A#4 – C8.

The only partial change in this arrangement is between A4 (4th) and A#4 (1st).

Due to this location and the partials used,  this partial change never needs checking.   There will never be an error at this partial change between A4/A#4.

We’ve also eliminated the use of the 6th partials.

The 4th partials are used for tuning from A4 all the way down to A0.

(Click to enlarge)

The 4th partials are more reliable that the 6th partials for tuning the bass – more ‘reliable’ than the 8th, or the 10th, or the 12th, or the 7th too!

Put simply, the higher partials are less reliable than the lower ones.

There seems to be some confusion regarding stretch and partials used for bass tuning.

Some seem to think (and even teach) the only way we can get different amounts of stretch in the bass, is to use a different partial:
For instance, if we want to stretch the bass a little lower,we need to ‘switch’ to the 8th partial instead of the 6th.   Or switch to the 10th instead of the 8th, and so on.

Even though a pure 6:3 will probably not be as wide as a pure 8:4, and a pure 8:4 will probably not be as wide as a 12:6,and so on, there may be times, on some pianos, when that a pure 6:3 down there may be the same with as it’s pure 8:4.

It depends on the piano.

The same thing can happen in the midrange too.    I didn’t know that on some pianos a pure A3/A4 4:2 could result in a pure A3/A4 2:1.

So, I wouldn’t be surprised if sometime on some piano, a pure 6:3 might result in a pure 8:4?    I’ve never measured it so I don’t know for sure, but I just wouldn’t be surprised if that might happen on some piano out there somewhere.

It’s just not necessary to ‘switch to a different partial’ to get more stretch in the bass.

In fact, given the upper partials lack of ‘reliability’, I would go so far as to say that’s probably not such a good way to get more stretch in the bass.

Here’s what I mean by ‘reliability’ of the upper partials for bass tuning:

Reliable is when the location or height of the partials are all pretty much equal going from one note to the next.  Chromatically.   For instance, the 6th P of G2 is the same height as the 6th P of G#2, and the same height as the 6th P of A2 and so on.

If all those 6th Partials are the same height, a smooth set of number using those 6th partials will create a smooth tuning for not only those intervals using the 6th Partials, but also those intervals using the 4th partials and so on.   Chances are if they are good for the 6th, they will be good for the 4th, and the partials below that.

If the 6th partials are relatively ‘even’ or ‘reliable’ a smooth set of numbers in the tuning will probably result in a good smooth sounding tuning.

But, the 6th partials in the bass can vary quite a bit!   Especially on the shorter scales.   And the partials above that (8th, 10th, 12th, &c.), even more so.

On the other hand, the 4th partials on those pianos – on that same group of notes – will be more reliable.   The differences in their widths will just not be as great, and therefore more ‘reliable’.  Of course on the poorly scaled or shorter scaled pianos, the 4th partials may not be perfect either, but they will be a better choice because they will at least be better and will bounce around less than the 6th.   They will be more ‘reliable’ for tuning those pianos.

And if they are better for the challenging pianos, they can also be used very nicely for the longer scales as well.

It’s really just a matter of whether to use a smooth set of numbers using the 6th partials or a smooth set of numbers using the 4th partials.

If the 6th partials are used for that smooth set of numbers, the 4th partials may bounce around and cause issues with the intervals that use them.

If the 4th partials are used for the smooth set of numbers, even though the higher partials may bounce around as bit, their unevenness won’t cause nearly as much of a problem.

Using the higher partials down there will make the situation even worse on all but the longest scales.

In addition to the use of those higher partials, additional partial changes in the bass will also cause extra issues.    Switching partials down there introduces additional partial changes that need to be checked for errors (and then corrected) if the tuning is to sound smooth.

Of course this is piano dependent, but is obvious to the listener on the shorter scales with lower quality bass string design and/or manufacturing, and uneven string lengths.

If we create a smooth set of numbers using the 6th partials, and if the 6th partials on a group of notes are uneven, that unevenness will show up as uneven beat rates in all the intervals that use the lower partials.

Creating a tuning using a smooth set of 4th partial numbers in that situation makes the intervals using the lower partials sound much better.

My Eureka Moment on all this:

I was made aware of this on a 4’6″  Tokai ‘Sherman Clay’ piano.   This was ‘the’ piano that caused us to eliminate the use of the 6th partials for tuning the bass.

At the time, my tenor partial change was G#2 (6th)/A2 (4th).   The tuning sounded good down to A2 using the 4th Partials.

After making my standard tenor partial change correction, I began tuning down into the bass, going down from A2 to G#2, to G2, F#2 and so on.   But my aural checks  were awful!   The 3rds, the 6ths, the 10ths, 4ths, and 5ths, across that partial change were terrible!

I went over everything again, remeasuring the correction needed, rechecking the tuning of the notes, and then re-tuned and re-listened to those notes G#2, G2, F2 and so on.   Still awful.  Just as awful as it was first time.   At least I was consistent.

The problem was at that partial change.   The tuning sounded good above the partial change.

So not knowing what else to do, I decided to try to use the 4th partials a little lower down into the bass.  Using a pencil and paper method, I created an ‘extension’ of 4th partial notes going down to F2.   I tuned them and, Voila!   There it was!   The intervals checked out down to F2.  Everything now sounded good down to F2.

I then made another tenor partial change, but this time it was between E2/F2.

But when I started using the 6th partials again @ E2, the problem reappeared!   My aural checks and the smooth progression of intervals stopped @ F2.

So, I then, using the pencil and paper method, created a tuning using the 4th partials on down to C2.   That fixed it again.

The 6th partials on that piano were so uneven or unreliable, that when I created a smooth tuning using them, the underlying partials ended up being really off, and that was what caused all the problems.

But, when using the 4th partials instead, even though the 6th partials were still terribly unreliable, they (the 6th Partials) weren’t causing a problem like they were when I used them to tune.   This was a ‘Eureka moment’ for me.

A smooth set of 4th Partial numbers worked fine, where as a smooth set of 6th Partial numbers was terrible, awful, unusable.
(I admit that when I was finished with this piano, I was smiling.  Not only did it sound really pretty good for what it was, I had learned a huge lesson that I would use from then on.)

We soon got rid of our use of the 6th partials for bass tuning.   We figured if they worked this well on a Tokai 4’6″, they would work just fine on a concert grand.   And they do.

Using the 4th partials in the bass has absolutely nothing to do with the stretch in the bass.    Nothing.

In fact, I map (find the pitch I want it to be in the tuning) A1 using it’s 6th partial.  But once I’m happy with A1’s location, I measure where the 4th P is of A1 and that’s the number I use for creating the tuning and the actual tuning.  The 4th P not the 6th.   Creating a set of numbers using their 4th partials from A0 – A4 eliminates all those reliability issues of the higher partials.  And I have no partial change down there to worry about and cause problems.

For finding the location for (mapping) A1, I start by tuning A1 as a 3.0 c. wide 6:3 (from A2).   It may end up being a little higher or lower than that, but it will generally end up pretty close to a 6:3 octave, 3 c. wide.

But I use a 6:3 to find where I want A1 to be in the tuning.

Once I know where I want A1 tuned, I measure where it’s 4th partial is located.  That’s the setting I use for the tuning using the 4th partials.

Same way with A0.   My routine for finding what I think is a good location for A0 is pretty convoluted.   Working from a properly tuned A1, I use a 8:6 4th, and a 6:4 5th.

I tune E1 as a 8:6 (4th + octave) 4 c. wide, and then I tune A0 from E1 as a 6:4 (5th + octave) 5 c. wide.

I check that A0 location with all my other reference notes and checks, and when I’m happy, I then measure the location of A0 using it’s 4th partial.

That 4th P setting then becomes my setting for A0 when creating the tuning in the LC spreadsheet.

As you can see, the amount of stretch down there has very little to do with which partials are used.   I can find good locations for both A1 and A0,  Tune them where I want, and measure them using their 4th partials,which will be their setting for the tuning.

A 5-Partial change arrangement:

This last chart is the partial arrangement is in use and contains 5 partial changes:
(Click to Enlarge)

From everything I know, the above is just what you don’t want.   This 5 partial change arrangement has three of them in the lower half of the piano.

Even though this partial arrangement might work on some long scale piano somewhere, this arrangement, used on anything but the longest scales, could be problematical with its potentially 5 partial change ‘hiccups’, compounding on each other.

Many tuners using that system have mentioned that on the shorter scales they have to tune the bass by ear.   Now we know why.   The longer scales are more forgiving of this sort of thing.   But only up to a point.

It’s not only the partial changes, but its also the partials being used.

Even if someone were to pick up on the most likely errors at any of those 5 partial changes, without Direct Interval Tuning, it’s extremely unlikely anyone is going to be able to check, let alone correct,  the partial changes.

 

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