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

Working with the Prime 5ths

After learning the 4th A4 Number, it is fairly easy to make a general guess as to the location of A3.  If it (the 4th A4 number) is a high number – above 3.0 or so, I will often start with a template that results in a pure 4:2 width, using that template to tune A4, A3, D4, and E4 and then measure the prime 5ths.

The combined widths of the prime 5ths will let me know if I need to expand or contract the prime octave.

At this point, look for a combined width of the prime 5ths to be -3.0 c.  It doesn’t matter at this point if one of the 5ths is -2.0 and the other -1.0, simply add the widths together and if it is -3.0 c., the prime octave width is about right.

If one of them is -1.5 and the other is -2.3, that total is -3.8.  This combined width tells me the octave is .8 c. too narrow, (-3.8  vs. -3.0).   I then find another template in the SAT with an A3 setting .8 lower and using that template, re-tune A4, A3, D4, and E4 and re-measure.

While working with the prime 5ths, keep an ear and eye on the width of the prime octave’s 2:1.   As long as it stays < 2.8 c. wide, and at this point the combined width of the prime 5ths is -3.0 c, the octave is about right, and once the 5ths are balanced, all should be well.

Most pianos will allow for that relationship too.   But some don’t.  Some pianos need more compromising.   I have ended up with prime 5ths as narrow as -2.2 and as wide as -1.1 c.  It just depends on the piano.

Hopefully your first few times trying some of this, you won’t be on a piano that is too much out of the ‘norm’ so to speak, if there is such a thing.

Remember, until the 5ths are balanced, all that is needed here is for the combined width of prime 5ths, to be -3.0 c.   Balancing will be done later after it is certain, that the combined width of the 5ths is -3.0 and the width of the prime octave is < 3.0 c.

If however, when the combined width of the prime 5ths is -3.0. but the prime octave is 3.6 c wide and beating too much, some compromises will need to be made.   Those settings would probably cause me to try a combined 5th width of -3.4 which would put the 2:1 octave around 2,8 or so.

{Hopefully the first times you try this you will not be on a piano that requires that degree of compromising.    This routine works great on all those pianos too, but it does take some experience (and patience) with everything involved.  Those pianos are often noisy and false, and will often have wound bichords well up into the 3rd octave.  But I have actually come to enjoy working with these exception pianos.   Those are the teachers for me now.  I’m constantly wanting to confirm that this system will work on every piano and help me do a great job, every time. 

Doing this keeps teaching me, and each time I make one of these challenging pianos sound really pretty good, I find it rewarding.   I am also surprised at how many of my customers hear it and appreciate it too.   I get, ‘My piano has never sounded that good!”  After all, it’s their piano, and if they play it, they will hear it.   The tuning takes me a little longer, but our LC spreadsheet has a database in it too.   Their piano’s tuning is now stored and ready for me to use next time I tune their piano – without all the measuring and mapping and so on.}

Start with the 5ths while keeping an ear and eye on the prime 2:1 width.   Once a combined width for the 5ths is -3.0, I don’t really care if the resultant 2:1 is 2.6 c.  or 1.8 c. or 1.5 c. wide.  The octave will sound good and after the prime 5ths are balanced they will sound good too.

The resultant prime 4ths come into play here as well.

Before the prime 5ths are balanced, the easiest ‘out of balance’ tell will probably be heard in the resultant 4ths.   Since the 4ths beat faster than the 5ths or the octave, the most noticeable beating will probably be in the upper or lower prime 4th.   Which 4th beats the most depends on  the direction the mid point of the octave will need to be moved to balance the 5ths.

If I can get the prime octave’s 2:1 width < 2.8 c.  with a pair of -1.5 prime 5ths (combined width of -3.0), the resultant 4ths will sound good too.

Prime 5ths more narrow than -1.5:

On pianos with a high 4th A4 Number, i.e. a really wide 2:1, one might think the prime 5ths would be too wide as well, and simply contracting the octave using a template with a higher A3 would remedy the situation.  But that’s not how it works.

I know it sounds strange, and I’m not sure of the why of it, but I’ve found that the prime 5ths on those pianos just won’t let me shrink the octaves all that much.    In fact, sometimes the prime 5ths, will be pretty close to the -1.5 c. width, while the prime octave is 4.0 c. wide!

So when contracting the prime octave to clean up a little of the beating in the 2:1, the prime 5ths, will be made narrower than -1.5 c. each or have a combined width of -3.5 or -4.0.

And since the 4th A4 number is the width of the prime octave’s 2:1 after the prime octave has been tuned as a pure 4:2,  on these pianos the A3/A4 4:2 will actually be narrow!

****Every time I come across one of these challenging pianos, I think about how aural tuning is most often taught.  Invariably it starts off by tuning A3 from A4 as a wide 4:2, with the F3/A3 M3rd beating slower than the F3/A4 10th.   On these pianos that require a narrow 4:2 instead of a wide 4:2, the correct beating is just the opposite:  The M3 should beat faster than the 10th.    Sadly, most beginner tuners are practicing on a poorly scaled spinet or console – a piano very likely needing a narrow 4:2 rather than a wide one.*****

It’s a balancing act.  What needs to happen is a good sounding compromise between the beating in the prime octave and the beating in the prime 5ths.

When I first started doing this I didn’t have any ‘guidance’ as to a good width for the prime 5ths or the prime octave’s 2:1.   My starting point of -1.5 c. for the 5ths was purely the result of tuning a lot of pianos, doing a lot of listening and noticing the widths of what I was preferring.   Empirical data, I guess it’s called.

I found myself ending up with a width of -1.5 for the prime 5ths.   I liked the way the 5ths sounded on most pianos at that -1.5 c. setting.

When it comes to my < 3.0 c wide width for the prime’s 2:1, that too, is a personal setting.   I just generally find that when a prime octave’s 2:1 starts to get much > 2.8 c., it starts to sound too beaty, or too noisy, or too edgy for me.

So, I just began to start using those two guidelines or guideline combinations to help me get started and get things in the ballpark.   I was surprised, and I guess I still am, at how many pianos those guidelines fit.

In fact, they worked so well, when I would come across a piano where they wouldn’t, I was taken aback and really had to do some extra work trying to figure out why not.   It took me a while to figure it out too, because those pianos where it didn’t work, were really the exception, and I just didn’t come across them every day.   But eventually I figured it out and now I know just what to do.  But those first few times I kept trying to fit a square peg into that round hole.  I’d walk away thinking I was missing something somewhere.

What’s also interesting when putting all this together, is how few technicians I asked, knew any of this.   With Al being gone, I really had no one to go to to confirm or deny what we were doing.

A few years ago, while talking to Rick Baldassin about some of this stuff and I asked him what he thought the width of a 5th in this part of the piano should be.   He said -2.0 c..  He knew the theoretical answer straight away.   But when I asked him if he used that in any of his tunings, he said, “No.”

But of course, theoretical can be very different that what we do when tuning pianos for real.   My target width for the prime 5ths is about .5 wider than theoretical.   -1.5 c. rather than -2.0 c.   What that means is that ‘in practice’ is that I’m not only tuning a slightly wider prime 5th, but I’m probably also tuning a slightly wider prime octave.   But I’m fine with that.  As long as the octave is good, less beating in the 5ths is good.

I have come to believe that there is more ‘variation’ in the prime octave than there is in the prime 5ths.   By that I mean that I have use the -1.5 c. width for the prime 5ths and that width has resulted in a prime octave’s 2:1 being anywhere from 1.2 – 3.0 c. wide.   I would say the range of the widths of the prime 5ths, I’ve tuned are in the -2.2 to -1.2 range.

What that has told me is that there is no given width for the octave or the prime 5th that is right for every piano.   My data indicates there is no ‘perfect width’ for any interval that works every time on every piano.   There is so much talk about the perfect 12th these days, and how it is the best way to make pianos sound their best.   My data doesn’t confirm that at all.

The easiest P12ths for me to check or anyone else for that matte is the D3/A4 P12, or the A2/E4 P12th.   Those can be checked after mapping the midrange.   And with all the talk about the P12th, of course I started checking my work against the talk.   the easiest one for me to quickly check is the D3/A4 12th.   It was so rare that it was pure, I eventually quit checking it.   Sure it was close, but most times I found my placement for D3 at least .5 c. away from the pure setting.   And it could be either sharp or flat of the pure setting.

My approach to midrange tuning is minimal beating.   I don’t want to stretch any more than necessary to get a pair of good sounding prime 5ths contained within the prime octave.  And I don’t want the prime octave’s 2:1 to be any wider than about 2.8 c. unless absolutely necessary.

But others feel that the best sounding tuning is as wide as tolerable in the midrange.   Trading 5ths almost for octaves, and letting the 4ths, beat on the edge of objectionable.   Giving up noisy octaves for cleaner 5ths.

Those amounts of ‘stretch’ are now being built into some tuning programs as a tuning option.

There was a series of articles in the PTJ Journal a year or so ago.   In one of them some numbers were given which I found interesting, helpful, and useful.   In the article the width of a 5th was given as -1.2 c.   I now had 3 numbers for the width of the 5th:
-1.2 c.from the article,
-2.0 c. theoretical number I got from Rick Baldassin
-1.5 c. my own personal number of -1.5 c.

I felt confirmed in what I was doing.   In fact, I think generally speaking, in the real tuning world, on most pianos, the theoretical values don’t consider inHarmonicity.

Here is where I use the -2.0 theoretical value:

Whenever I come across a piano like the Baldwin Hamilton that has a 4.2 wide 4th A4 Number, I can shrink the octave until I get an OK sounding 2:1 and a pair of 5ths, that are as narrow as -2.0 c. each.

In fact I have even left those 5ths, as narrow as -2.2 on a piano or two.  And on those pianos their relationship between their prime octave and the prime 5ths needed compromising.

But what really helps those pianos sound as good as they can, is having their prime 5ths balanced!  That’s so important on those pianos.   If the prime 5ths are balanced, the resultant 4ths will also be balanced and sound better as will all the other intervals contained within the prime octave on those challenging pianos.

If you are curious about this, start measuring the prime 5ths in your own tunings.  See if they are balanced or not.

Depending on how out of balance they are,  you may be able to hear a difference in the 5ths.  Hearing a difference in the resultant prime 4ths, can be easier than listening the the prime 5ths.

Most computed tunings are consistent curves in the prime octave.
Even though the starting and ending point – say A3 and A4  – may vary, the ‘shape’ of the curve between those notes will probably be fairly consistent in virtually every tuning system or software.   It will also probably be the same for every combination of A3 and A4 settings.   Tuning software is designed to be consistent so that it will work on most pianos, but it will really only work on ‘some’ pianos.

Careful listening and measuring will expose a mis-fitting template or tuning to the piano itself.

The piano’s scaling will often, and I could say most of the time, not be a good fit for that computed tuning’s curve.    The pianos are just not that consistent.   This is particularly noticeable with less than well scaled pianos – which I know I can say, is most of them.  But it can show itself on any piano.  Simply measuring the prime 5ths after tuning A4, A3, D4, and E4 using the template being used for the tuning will tell you all you need to know.

Again, it’s easy to check.   Just tune A3, D4, E4, and A4, and measure the widths of the prime 5ths.   If they are the same width, they are balanced.  If they are not balanced, the piano could sound even better!

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