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

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

All tuning software systems contain partial ‘changes’.

We can’t use the same partial to tune both A0 and C8.   Different partials are used to tune different parts of the piano.   These different partials used are designed into the tuning software or tuning devices.   A partial change is when the tuning software or device switches from one partial to another within the tuning.

An error is often created when the tuning software or tuning device changes partials during the course of the tuning, an error at that partial change is very likely.   These errors can be small, say less than .3 c. or they can be quite large.   Errors of less than .3 c. aren’t much of a problem.   But errors of .5 c. and greater can easily be heard causing a hiccup or problem with the tuning, not only at the partial change itself, but with intervals that have notes on both sides of the partial change error.

The most obvious errors occur in the tenor and midrange.   Partial change errors in that area of the piano, combined with scaling issues in that tenor area, can really effect the quality of the tuning.

Partial change locations vary from system to system.

Once the partial change locations are known, use your tuning software device to tune across the partial change and then listen to the 3rds, 6ths, or 10ths across the partial change.   If there are ‘hiccups’ in the beating across the partial changes, what you’re hearing is probably errors at the partial changes.   Of course you’ll want to make sure all the notes are accurately tuned.   But if the notes are well tuned and the hiccups are still present, it’s probably an error at the partial change.

The errors are cumulative too.   Most tuning systems will have 3 or 4 or even 5 partial changes in them.   There can easily be an error at each of them.   So, even relatively small partial change errors can end up being significant in the overall quality of the tuning.

The challenge of course, is correcting them.   With an AccuTuner and ‘direct interval’ tuning, it’s relatively easy.  The errors can be measured and corrected.   The process has been made even easier when using an AccuTuner IV.   The SAT IV has a built in feature that easily and accurately corrects all partial change errors.

The AccuTuner is the only tuning device 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.

Here is a link to a video which shows how this new feature works:   (please pardon my singing!  You’ll hear what I mean when you watch the video!)

Since none of the other tuning software or devices can do direct interval tuning, this is a unique feature of the SAT IV.    Some of those other systems may claim their software’s partial change errors aren’t worth ‘fixing’ but that depends on the piano too!   Every partial change is a mathematical ‘guess’ until it’s been checked and confirmed or corrected.

Sometimes the software 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.

My first experience with this was in 2006 or so, 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.   It didn’t take me long 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.

One of the ways to clean up or remove potential errors at partial changes, is to simply have fewer partial changes in our tunings.

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

We’ll start with the AccuTuner’s 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).

Again, the big bang for the buck to fix is the one in the tenor, but the ones in the treble are also worth checking.

 

Here is an example of a “Two Partial Change” Arrangement:

This two partial change arrangement eliminates the use of the 2nd partials.   This two partial arrangement uses the fundamentals or 1st Partials from A#4 – C8.

When we tune A4 @ A440, we are using A4’s fundamental or it’s 1st partial.  So if we can tune A4 using it’s fundamental, we can also
tune A#4, B4, C4 and so on using their 1st partials.  Getting rid of the 2nd partials eliminates any partial change errors above A4 because there are no partial changes above A4.

The partial change locations in the Two Partial Change’ arraignment are also different than what is found in an FAC tuning.

The tenor partial change has been lowered from B2/C3 to G#2/A2.
The treble partial changes has been lowered from B4/C5 to A4/A#4.

This two partial arrangement uses the 6th Partials (green line) for tuning notes A0 – G#2.

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 tuning.

But that’s not the only advantage:  Due to the ‘improved’ location of this A4/A#4 partial change, there will never be an error at that A4/A#4 partial change!

Here’s how that works: When A4 is tuned to A-440, A4’s fundamental (1st partial) is being used.
If the fundamental can be used to accurately tune A4 to A440, there’s no reason why the fundamentals can’t also be used to tune A#4 – and B4 and C5 and so on!

Even though for the tuning itself, A4 is tuned using it’s 4th partial, A4’s fundamental is still @ 0.0 c..  So when using the fundamentals to tune all notes from A#4 to C8, the treble tuning starts @ 0.0.

The setting for A#4 (when using the fundamentals) is going to be either 0.0, 0.1, 0.2,  0.3, or maybe 0.4 depending on the piano of course and the amount of stretch used or called for going from A4 to A5.  There will never be an error at this location grater than .1 or .2 c.   Nothing.  Inaudible.  In fact, the treble tuning when using the fundamentals could all start with A#4 being @ 0.0 just like A4.   But most of the time A#4 will be @ .1 or .2.

The lowered tenor partial change – from B2/C3 down to G#2/A2, provides a full two-octave range (A2 thru A4) with all notes using the same (4th) partials.

No partial changes within that two octave range insures there is never a partial change error in the two octave temperament area.  This makes for much more accurate aural checks in that area.

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.

The one partial change arrangement

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

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

The 4th partials are used 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), and it never needs checking.   There will never be an error at this partial change between A4/A#4.

The use of the 6th partials has also been eliminated in this one partial change arrangement.

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

(Click to enlarge)

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

Some seem to think (and even teach) that the only way we can get different amounts of stretch in the bass, is to use a different partial.  They teach that if we want more stretch in the bass, we need to use a higher partial – use the 8th instead of the 6th or use the 10th instead of the 8th or the 12th instead of the 10th.     That’s just not true.   A1 can be tuned using it’s 4th or 6th partial, and be at exactly the same pitch as if it were tuned using it’s 10th or 12th partial.   It may be a wide 6th and an even wider 4th to get it to be at the same pitch as a pure 8th, but A1 can be tuned to the same exact pitch using any number of partials.

But the problem with using high partials (the 6th, 8th, 10th, &c.) for bass tuning is their relative unreliability compared to the lower partials like the 4th.

The 4th partials are more reliable that the 6th partials for tuning the bass – and the higher the partials used, the less reliable they are!

Put simply, the higher partials are less reliable than the lower ones.  Scaling, poor scaling especially can be devastating when using a smooth set of 6th or 8th partial settings for bass tuning.   Yes, the numbers may be smooth, nice chart and so on, but if the partials on those strings is jumping up and down from note to note, the tuning will sound pretty bad.

Blame it on the piano?   Well, the piano may be poorly scaled, but using those higher partials just exaggerates the problem.   Using the 4th tuning for the bass is a solvent for those type of wild bass tunings.   And if using the 4th Partials on those problem pianos is better, they are also a better choice for the better scales.

It’s just not necessary to ‘switch to a different partial’ to get more stretch in the bass, in fact it can often be a way to make the piano sound even worse due to the unreliable nature of the higher partials in the bass.

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

Reliablethe quality or state of being fit to be trusted or relied on

Reliability is when the location of the partials,  over a range of notes in this case, are reliably equal going from one note to the next.   For instance, the 6th partial of G2 is the basically 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 sounding tuning.  Chances are if they are reliable for the 6th, they will be reliable for the 4th, and the partials below that.

But oftentimes the height of the 6th partials from one note to the next can vary quite a lot.  Especially on the shorter scales.   And if the 6th Ps are unreliable, the partials above that (8th, 10th, 12th, &c.), will probably be even more unreliable.

On the other hand, the 4th partials on those pianos – over that same group or range of notes – will mort likely be more reliable than the 6th or higher partials.   Of course on the poorly or shorter scaled pianos, the 4th partials may not be perfect either, but they will be a much better choice for tuning because they bounce around less than the 6th.   The locations of the 4th partials of those notes will not be as varied than their higher partials.   And therefore will be more ‘reliable’ for tuning those pianos.

The 4th partials are better for the challenging pianos and they can also be used very nicely for the longer scales as well.

Every tuning software device basically tries to use a reasonably smooth set of number for tuning the bass.  That smooth set of numbers is found between the partial changes.  For instance if a system uses the 4th partials from A0 – A4, the chart will generally show a ‘smooth’ curve from A0 – A4.  If the system uses the 6th partials from A0 – B2, it’s chart will generally reveal a relatively smooth curve from A0 – B2.   If the system uses say the 12th partials for tuning A0 – A1, and the the 8th partials for tuning A#1 – A2, the chart of that tuning will show two separate curves – one for each partial, and most of the time those ‘curves’ will be reasonably ‘smooth’ in appearance.

So it’s really just a matter of which partial’s smooth set of numbers, which smooth curve, will result in the smoothest sounding tuning?

The higher the partials used for that smooth curve, and especially when there is a partial change between the use of those 2 high partial choices, the less likely the result will be a smooth sounding tuning.  The upper partials of bass strings are simply less reliable than their lower partials.

Using the higher partials n the bass 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 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 all 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.

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

How do I know this?

I discovered it quite by accident when tuning a piano.   It was a Eureka Moment for me.   I was just trying to find out why nothing was working to get even beat rates in the tenor area of this piano.   Across the tenor partial change in particular.

This experience caused us to on all this eliminate the use of the 6th partials for tuning the bass.  That was a big deal and has made a huge difference in our ‘One Partial Change’ tuning arrangement.

I was made aware of this on a 4’6″  Tokai ‘Sherman Clay’ piano.   This was ‘the’ piano that caused us to

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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