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:
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:
In addition to this two-partial arrangement have one fewer partial change than an FAC tuning, the partial change locations are in slightly different locations.
An FAC tuning uses the 2nd Partials from C5/B5 whereas this two partial arrangement uses fundamentals from A#4 – C8. The use of the 2nd partials has been eliminated.
The two partial changes in this arrangement are found between G#2/A2 and A4/A#4.
The partials used in the below chart are the 6th (green line) for notes A0-G#2, the 4th (red line) for notes A2-A4, and the 1st (blue line) for notes A#4-C8.
(Click to Enlarge)
Eliminating the use of the 2nd partials in the tuning, leaves us with one fewer potential partial change error in the treble.
Due to the location of the treble partial change A4/A#4, the tenor partial change is the only one that ever needs to be checked.
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, and B4 and C5, and so on.
Eliminating the use of the 2nd partials in that area, also makes for much more speeding and accurate mapping of A5.
(More on that later in the posts on Mapping.)
Only the tenor partial change in this arrangement needs to be checked and corrected if there is an error.
This particular Two partial arrangement provides a full two-octave range (A2 thru A4) with all notes using their 4th partials. This is accomplished by moving the tenor partial change from B2/C3 to G#2/A2.
No partial changes within that two octave range insures there is never a partial change error in the temperament area.
Another advantage to this A2 -A4 type partial arrangement, is that note 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 from occurring in the 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.
This Two Partial arrangement was what I used 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 we use in the Littau-Conrad Tuning System. This system uses the 4th partials from A0 – A4 and the fundamentals from A#4 – C8.
The only partial change in this arrangement is between A4 (4th) and A#4 (1st). Because of it’s location between A4 and A#4 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 have also eliminated the use of the 6th partials. With this arrangement the 4th partial are used for tuning all the way down to A0.
(Click to enlarge)
The 4th partials are more reliable that the 6th partials for tuning the bass. They, the 4th partials, are more ‘reliable’ than the 8th, or the 10th, or the 12th, or the 7th too!
The SAT has the ability to ‘hear’ the 4th partials all the way down to A2 which is the 4th partial of A0.
There seems to be some confusion regarding stretch and partials.
Some seem to teach and think the only way we can stretch the bass more or differently, is to use a different partial. To ‘switch’ to a different partial. For instance, if we want to stretch the bass a little lower, ‘switch’ to the 8th partial instead of the 6th. Or switch to the 10th instead of the 8th, and so on.
Yes, 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, but a 6:3 can be widened to equal an 8:4 or a 12:6.
But I’m not so sure. Until I measured it, I didn’t know that on some pianos a pure A3/A4 4:2 would 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 have 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 is not necessary to ‘switch to a different partial’ to get more stretch in the bass. In fact, I would go so far as to say that’s probably not such a good way to get more stretch in the bass.
Put simply, the higher partials are less reliable than the lower ones.
The 6th partials on a group of bass notes can vary much more than the 4th partials on that same group of notes. Of course this is piano dependent, but it definitely true 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 (unreliable) the unevenness will show up as uneven beat rates in the intervals that use the lower partials of those notes. That includes the 6ths, 10ths, single and double octaves, 12ths, and so on.
Creating a tuning using a smooth set of 4th partial numbers in that situation makes the intervals using the lower partials sound much better.
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 the 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, were really bad. I went over everything, rechecked the tuning of the notes. re-measured and re-checked the tenor partial change correction, and then re-tuned those notes G#2, G2, F2 and so on. Still awful. Just as awful as it was first time.
But the tuning sounded good above the partial change.
I decided to try to use the 4th partials a little lower down into the bass. I got out my pencil and paper and created a little extension of notes settings all using their 4th partials going down to F2. I tuned them and, Voila! There it was! The intervals checked out down to F2.
But when I started using the 6th partials again @ E2, the problem reappeared! So, I created a tuning using the 4th partials on down to C2. That fixed it again. The 6th partials on that piano were so uneven that when I created a smooth tuning using them, the underlying partials were really off, and that was what caused all the problems.
But when using the 4th partials, even though the 6th partials were still unreliable, they weren’t really causing a problem like they were when I used them to tune. This was a Eureka! moment for me.
We soon got rid of the 6th partials altogether. 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 has absolutely nothing to do with the stretch in the bass. Nothing. On some of my tunings (when using the 4th partials), A0 may be -50 c. and A1 may be -15 c. for the tuning.
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.
Once I know where I want A1 tuned, I set the SAT to A3, play A1 and measure where it’s 4th partial is located. Thats the setting I use for the tuning using the 4th partials.
Same way with A0, actually. I work from A1 and 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. That’s where I start for A0. I check that location with all my other reference notes, and when I find the right placement for A0, I set the SAT to listen to A2 (A0’s 4th Partial), play A0 and stop the lights, thereby measuring the location of A0 using it’s 4th partial.
As you can see, the amount of stretch down there has very little to do with which partials are used. I can get both A1 and A0 where I want them, (the ‘stretch’ I want), get the notes tuned where I want, and measure them with the 4th partial and use that setting for the tuning.
FYI: For the tunings in my LC spreadsheet, the average setting for A0 is -42. But some are -70 c. and some are -20.0 c. My average for A1 is -11.2. Some in the low -7.0’s and others @ -17.
A 5-Partial change arrangement:
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 5-partial change arrangement, used on anything but the longest scales, could be problematical with its partial change ‘hiccups’, compounding on each other.
Many tuners using that system have mentioned that on the shorter scales have to tune the bass by ear. The longer scales are more forgiving of this sort of thing.
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 3 partial changes, without Direct Interval Tuning, it’s extremely unlikely anyone is going to be able to check, let alone correct, any of the partial changes.