Piano World Home Page Forums Our Most Popular Forums Piano Tuner-Technicians Forum Frustrating temperament problem. Advice please

Dear tuner techs,

Yesterday I tuned a console upright (my wife's teaching piano at a creche). I've tuned it before, but hadn't paid as much attention to the temperament. Previously I had used ET via Marpurg. [Edit: not meaning that one method is superior; just that I hadn't worked as meticulously, and happened to be using that method at the time.]

For the last few tunings I have started to use the U3U3D5 sequence, and found it quite fast, with little need for large corrections. So I used this sequence yesterday, too.

Details of the instrument's scale breaks: bass-tenor break is at C3/C#3, wound bichords change to plain trichords at D3/D#3. Many of the wound bichords are badly matched, e.g. I had some difficulty in choosing one string of C#3 for checking the F3F4 4:2 octave. [Edit: when tuning both strings into a "unison", it was difficult to hear a clear beat with F3 or F4.]

I soon ran into problems, and I'd appreciate your advice.

1) A4 to fork, using F2 as check.
2) A3 to A4, aurally as wide as possible while still beatless, which checked out as hardly even a 4:2, and significantly narrow 6:3. I made it an exact 4:2, even though it rolled slightly. For me, this was the first red flag.
3) CM3s from F3 to A4: I could only get an even progression by setting F3A3 quite slow (5 to 6 bps). Second red flag. Just like the A octave, the F octave rolled, even though it was only 4:2, and noticeably narrow at 6:3. Third red flag.
4) F#3 to C#4: I tried to give the P5 the slightest tempering, but invariably the F#3A3 m3 turned sour. The only way to get a half-decent m3 was to tune F#3 on the wide side of beatless. Fourth red flag.
5) A#3 to F3, using F#3 as check: I had to temper the P4 quite strongly, more than 2 bps, to even get F#3A#3 to beat as fast as F3A3. If I wanted F#3A#3 faster than F3A3, the P4 became much too busy. Red flag no. 5.
6) D4 to A3, using A#3 as check: even worse than the previous case. In order to have A#3D4 at least as fast as A3C#4, I had to temper the A3D4 P4 to more than 2 bps, closer to 3 bps. Sixth red flag.
7) G3 to D4, using A#3 as check: as before, as soon as a started to temper the P5, the G3A#3 m3 would become unbearably busy / sour. Seventh red flag.

And so it continued. The RBIs forced me to keep the P5s pure, and to over-temper the P4s. I've never experienced this type of problem. It's not the sequence; I've used it before.

Please, if anyone can shed some light on this, I'd be really grateful!

Thanks for a great forum.

I am not a tuner tech, I hope you take my words accordingly.

If I were in your position, the first thing I would try would be to change the progression of CM3s and sacrifice a bit. Maybe just flatten the C#4, and keep F3A3 faster than 6 bps. Yes a progressive M3s M6s are important, but octaves, fifths and fourths would be more disturbing and easily recognized by the pianist.

Mark R.,

I tune many small consoles very often. The main issue I have to tune them is that there is a huge jump in iH when going from plain strings to wound strings, and the another (lesser) big jump when going from treble bridge to bass bridge.

If you tune a smooth progression of M3s, then you'll have a jump in fifths from nearly pure in plain strings, to highly tempered (narrow) in wound/plain strings.

If you tune a smooth progression of fifths, or equally tempered fifths, then M3s will be too tempered for wound/plain strings.

What I've found better in those pianos is to tune a smooth progression of fourths, letting the 5ths and M3s to jump at the passage from wound to plain.

By doing so you'll minimize the damages!

So what I suggest you is to tune CM3s as usual and then tune the Sanderson-Baldassin sequence, which works on P4s.

Tune:

A4-A3-F3-F4-C#4 CM3s as usual.

A#3 <- F3 up a P4 F3A#3 about 1 bps (to be refined later)
F#3 <- A#3 down a M3 A3F3>=F#3A#3
B3 <- F#3 up a P4 F#3B3 same tempering than F3A#3 (to be refined later)
G#3 <- C#4 down a P4 G#3C#4 same tempering than the previously tuned P4s (to be refined later)
C4 <- G#3 up a M3 F3A3<F#3A#3<G#3C4<A3C#4
G3 <- C4 down a P4 G3C4 same tempering than the previously tempered P4s (to be refined later

Check: G3B3 to fit in the M3s progression: F#3A#3<G3B3<G#3C4
Refine: if G3B3 is too fast then your P4s are too wide. If G3B3 is too slow, then your P4s are not enough wide. Adjust the P4s as needed retuning A#3, F#3, B3, G#3, C4, G3. Check again if G3B3 fits in the M3s progression and repeat until it does fit.

Now you have the correct size for P4s and M3s for this piano, and you have completed the tuning of the mini-temperament from F3 to C#4. Expand this to complete the temperament from F3 up to A4.

Now you can go down by prioritizing the eveness of P4s and the eveness of 4:2 octaves which must be getting wider as you descend in the scale.

In this kind of pianos, there is a lot of iH in the lower plain strings, so it is normal to have to tune narrow 6:3 octaves with almost pure and in some cases slightly narrow 4:2 octaves for F3F4 and A3A4.

The usual 6:3/4:2 balance does not work fine for these highly inharmonic pianos in which there is a huge difference between 6:3 and 4:2 octaves.

I hope this helps.

Hi Mark,

If you heard rolling in the octaves when tuning a pure 4:2 but narrow 6:3, you may be able to widen it a bit and put it exactly in the 4:2/6:3 window. Whenever I do this, I always hear an improvement in the quality of the octave.

This may give you more room in the lower 3 CM3 to get more difference in the beat speeds.

Thanks for all the responses.

Hakki:
Yes, I actually played around with the placement of C#4. It did help to even out some of the SBIs somewhat.

Rafael:
Yes, the problem seemed to lie mostly in the lowest plain strings. I use the Harvey chord as a first approximation for expanding the temperament, e.g. tune E3 to A3, B3 and E4. Using this approach, the M3s in the plain strings were quite slow, but as soon as they spanned the "steel to copper" break, they became faster. The P5s in the plain strings were basically pure, but as soon as they included a wound string, they were noticeably narrower. (Which confirms what you wrote.)

Thanks for the tip with the Sanderson-Baldassin sequence. Next time I tune the piano, I'll use it to determine the correct width of P4 for this piano. (It does seem a bit cumbersome to repeat 6 steps until I've found the correct width - but if this is the price I have to pay...)

Mark:
I tried widening the octaves, aiming for an equally beating 4:2/6:3 compromise, but anything wider than 4:2 sounded progressively worse. The best sound was actually somewhere between 2:1 and 4:2. I was wondering whether I should have used that as the basis for my temperament...

In reality it's faster than shooting in the dark and then having to fight with the piano to make things fit together.

A fourth has no much tolerance in where it sounds correct, maybe less than 1 cent, so in general two to three rounds will suffice to get a good G3B3. Once you get it, you'll see it's easier and faster than you imagined.

Thanks, Rafael, I'll certainly try this. The pianos that I work on are mostly consoles...
[Edit: the P4 is an interval that I could consider more seriously... I haven't done so previously. In the case I described above, the P4 was a victim of the process.]

On smaller instruments, when I must to go by ear because the ETD isn't giving me satisfactory results, I find it easier to do 2 things:

1) Forget about octave types. Just play the octave and get it clean sounding in its totally without over-analyzing. Maybe use the 3rd/10th test. Or, even the 4th/5th test. But, be prepared to compromrise if you find a problem with beat speed progression as you begin expanding the temperament outwards.

2) Try to incorporate at least one or more of the wound strings into the temperament octave. I almost alway use a D3 - D4 as the temperament octave. The 3rds and 6ths are a little slower. So, I find it less taxing to get a good progression going.

The advantage to this is you have already taken the change in inharmonicity of some bass strings into account as you set the temperament. You won't have a radical change when you hit the wound strings. You've already compensated for the transition.

Expand the temperament down towards the bass at least one octave to D2 first. (Check A2-A3 AND A2-A4 as you work your way down to check fo possible problems.) Check and tweak the temperament for good beat speed progession. You want a smooth progression as you leave the temperament.

You now have a 2 octave temperament with good BSP (Beat Speed Progression). Check D3 - D4. Also, check D2 to D3 and D2 to D4. Don't be afraid to slightly alter the width of the D3 - D4 octave and retweak the initial temperament if necessary... even the relationship between D3 and D4 to A3.

Then, start progessing upwards above the temperament. The correctly tuned bass octaves will prevent you from tuning the treble octaves too wide. We don't want them too wide so we don't have certain over-energized intervals when we play certain chords there.

Then, tune up to D5. Check BSP. Check D5 to D4 and D3 and D2.

You now have a 3 octave temperament.

Check the other octaves and double octaves in there, too.

Tweak accordingly, even back to the initial temperament if necessary.

Then, go down some more, go up some more, go down even more, go up even more. All the while, keep checking single octaves, double octaves, triple octaves, etc. Keep checking BSP. 3rds, 6ths, 4ths, 5ths, etc.

Usually, I'll start

A4-A3

Check F3-A3 F3-A4. F3-A3 usually beats a little slower than F3-A4. But, the amount of difference can vary. Sometimes, though not often, then can even seem to be beating the same speed. Do what the piano wants as you begin setting the temperament and expanding it. Use your judgment and experience.

D3-A3

D3-D4

Check A3-D4

G3-D3

Check G3-D4

Set your ladder of 3rds

D3-F#3-A#3-D4

D#3-A#3

Check BSP D3-F#3 and D#3-G3

and so on.

I'm sure everyone gets the idea.

Thanks, Joe, lots of stuff to mull!

Right, this is what you must use as the basis for your temperament. An octave set to its best sounding spot.

The 6:3/4:2 balance works fine for large pianos, that is full uprights and medium or larger grands.

For vertical studios and baby grands a pure 4:2 octave is all that can sound good, if you tune a larger octave it will have a roll.

And for small pianos like consoles and spinets a 4:2/2:1 balance is the better width for the A3A4 octave.


I know of tuners that do not tune pianos anymore other than their own piano, then they tend to believe that what works for their piano is the best for all pianos. But that's not true.

In my case, I tune spinets (numerous), consoles, studios, uprights, baby grands, medium grands, large grands and concert grands (rarely) and I am aware of the differences in the way of tuning them.

It may sound contradictory that a spinet should be tuned with a 4:2/2:1 temperament octave and a concert grand with a 6:3/4:2.

Stretching the tuning is needed to compensate for iH then:

The smaller the piano, the more iH
The more iH, the more stretch.
So: the smaller the piano, the more stretch

Isn't it?

In fact yes! The smaller the piano, the more stretched its tuning will be.

The stretch is the difference in cents between the actual tuned frequences and their theoretical values.

If we measure in cents the stretching of a 4:2/2:1 octave in a spinet we'll confirm that it is wider (in cents) than the 6:3/4:2 octave in a concert grand. That's all.

In other words a 4:2 octave in a spinet is more stretched than a 6:3 octave in a concert grand.

So, do not be afraid of tuning 4:2/2:1 octaves in small pianos. If that's what sounds good that's what you should tune.

The only advice it to tune the temperament octave as wide as this piano will allow.

Mark,

What you have encountered is what any technician would and it is also the reason that an ETD calculated program is never quite right. If anything, the fact that you find the dilemma means that you are very discerning. A lot of tuners wouldn't care.

The above people are right. What you have is a wild mix of inharmonicity rather than any kind of smooth curve. The lowest plain wire will always have the highest inharmonicity. That is why you can't make the A3-A4 octave sound right with an interval test or the interval test has to be a narrower one (closer to 2:1) than would be good for finer instruments.

So, I think Joe is right, just make that octave sound "pure" and go from there. What you will also hear from 5ths that fall among the lowest plain wire is two sets of audible coincident partials: 3:2 and 6:4. The difference between the two will be large enough that you cannot seem to reconcile it. Again, just go for the "whole" sound as Virgil Smith put it.

Frankly, that entire problem was one reason why I began using a Well Temperament on such pianos 30 years ago. Well Temperaments "eat" poor scales! They really do make the kind of music that most people would play on such a piano sound more harmonious.

If you insist on tuning ET (and I am glad you seem to like the "Up a 3rd..." sequence), don't worry if 5ths sound a little narrower than you would like them to be among the lowest plain wire. There is virtually no music that has exposed 5ths in that area. All music would be chords of some type and that will conceal the narrowness of 5ths. If you have the whole middle a little more narrow than you would on larger pianos, it will sound more harmonious.

It is a compromised scale, so whatever you do with temperament will be compromised as well. To lean in favor of "cleaner" sounding 5ths is not the best compromise. You can get fairly smooth M3s, however and those, in my opinion are the intervals to favor if you have to make a choice about which kind of interval you want to make sound the most correct.

Mark, here is my advice:

I think that your first A3-A4 octave was too wide for the piano and that is why the octave and the 4ths rolled too much.

One way to establish a better first octave is to precede the CM3rd "skeleton" with an outer skeleton, ie, Tune a smooth D3-A3-D4-A4 skeleton so that all the perfect intervals sound as smooth as possible separately and altogether.

Do not worry about what kind of octave type you are ending up with. The M3/M10 and M3/M6 tests are useful to help establish the octaves and 4ths, but not to be used as a measuring stick to set the intervals since their increase in beat rates can vary too much.

Mark, I would not worry with a short octave an slow M3 on a short piano.

Why not listening at 2:1 and forget the high partials beating ?

if strengthened enough at 2:1 you will have the 4:2an 6:3 that will balance out and be quietened.

Then I do not complain of having slow M3 ,as long as 5ths and 4ths are good (the 5ths are very easily almost "pure" (dont like that improper term) on those high iH pianos.

If you focus on the amount of consonance from the 2:1 to higher, you will be way less annoyed.

and the tone will be warmer even if of course somehow nasal.
Lot of stretch installs naturally by itself then..

Just try to reinforce the bottom note with the fundamental of the upper one , not focusing on all the tinkling from above.

I think it is a different way of listening, not much in use when you learned with 6:3 4:2 balance.

Ok, I'm missing something here.

I just tuned a spinet with wound strings in the tenor. I bisected the 4:2/6:3 and the octave was acceptable, even cleanish. A little beating at the 4:2 and a little beating at the 6:3. If I made it a 2:1, holy cow, that would have sounded horrible.

Also, as I use P4 and P5 window when building up through the treble, 2:1 octaves in the middle would destroy it and forget about having a good compromise between 12ths and 22nds.

I have never had a problem using the 4:2/6:3 window with any size piano and getting the temperament to fit. Mark R. states he did that; made the octave narrow from the one I'm mentioning, and the CM3's didn't work out.

Wouldn't a wider octave create some more difference in the CM3's? Like I said, I've never experienced a 2:1 octave that sound better than a 4:2+.

What am I missing?

I know M3 don't move well across the break on small pianos, but I'm more concerned with getting octaves and fifths and fourths to sound good there; chords don't sound great there anyway.

I will also look for triple octaves fitting a little lower as the iH starts to reverse direction there and can tend to match that of the triple octave above.

If I ever find a piano where the temperament doesn't work out with a 4:2+ octave, I'll certainly try a 2:1, but only if it sounds better than a 4:2+, but as some if you are saying, it will sound better, so maybe I've just been lucky.

Also, let's not forget that if the 4:2/6:3 window is small, a 4:2 octave will be very close, if not virtually identical, to a 4:2+. And if the 2:1/4:2 window us small, you could tune 2:1 and they also would be close to the 4:2+. But isn't that a more pure iH? Shouldn't we expect larger differences in octaves sizes on smaller pianos? In which case, a 4:2 or 2:1 will be screaming at the 6:3. Is this really a better sounding octave?

A recording of a good sounding 2:1 here would be great.

It is listening to 2:1 I do not really check the 4:2 6:3, but the 6:3 beat get faint when balance is more between 2:1 and 4:2

I also aim to acceptable 4th and 5th, but I not see why a medium range that avoid stretch would cause problems higher.

I do not tune much very small pianos anyway. But think that 2:1/4:2 is yet much "stretched" on some of them.

Many helpful answers! Thank you all.

Gadzar:
What you write about stretch, makes perfect sense to me. When expanding the treble, I ran into rolling octaves when I tried to make P12 and double octave as pure as possible ("mindless octaves"). In order to prevent badly rolling octaves, I had to make the P12s narrower than I like them (musically). On my own studio upright, I find the compromise between octaves, P12s and double octaves much easier.

Bill:
Thanks for chiming in. Yes, I do try to be discerning in my tunings. I don't insist on ET only, but at this stage, I would like to tune it, because it trains the aforementioned discernment. I am, however, quite open to mild well temperaments. When first I tried to tune EBVT-III, I was much more inexperienced than I am now, and I was disparaged by one or two keys that came out "sour". Rest assured, I have not written off well temperaments. My own pianos are both overdue for tuning, so there's room for experimentation. And when I next tune my wife's teaching piano, I'll probably try a well temperament (it's only used for beginners and easy accompaniments anyway). Thanks for confirming what I was wondering, and what others here have written: that a narrower middle will keep things more harmonious. By the way, my problem was not so much in the fifths, but the overly wide fourths. I hope that a cleaner temperament octave would sort this out.

Chris:
What you advise, seems to resonate with Joe's post. I often check treble notes by playing them together with ladders of octaves and fifths. It makes sense to me to do the same thing in the temperament area.

Isaac:
Listening to the consonance "without all the tinkling" - I like that. This is how I try to listen to octaves. I only become aware of 6:3, 4:2 etc. if I do the physical test. When I first set the octaves, as wide as possible while remaining consonant, they tested slightly narrow of 4:2.

Mark C.:
It's not that the CM3s didn't work out. They just had a very strong increase in beat speeds. Regarding octaves: see what I wrote to Isaac above. I tuned the octaves aurally, as wide as possible, while retaining the "whole sound envelope" as calm as possible. Only then did I test them. The 4:2 test turned out slightly narrow, and the 6:3 test decidedly narrow. When I widened the octave to get an exact 4:2 test, the whole sound envelope started to roll, while 6:3 was still quite narrow. When I widened the octave even more, to compromise between 4:2+ and 6:3-, the whole sound envelope was quite objectionable. So I returned more or less to 4:2, thinking that I needed this stretch. You write that octaves narrower than 4:2 "scream" at 6:3. This was not my experience. Yes, the sound envelope was "busy", but the point at which it was the least busy was slightly narrow of 4:2. Regretfully, I was pressed for time. I did have my recording equipment with me, but alas...

Mark R,

English is not my native language and I often experience troubles to say what I mean clearly and accurately. But you've got it and you've explained it better than me.

I bet the next time you tune a small piano you are going to solve the tuning puzzle successfully and with confidence.

BTW this way of stretching the temperament octave is valid in any kind of temperament be it ET, Well, Victorian or any other UT.

Just to chime in for a moment about the width of the initial octaves...

One piano I tune regularly is a certain Jasper Kimball. This thing is something.

When I tune the A4-A3 octave with the Verituner, the octave beats wildly. It doesn't just roll... it: TWANG TWANG TWANG!

Just a mess.

The only way to tune this octave is by ear. It needs to be tuned much narrower than the VT wants it. Oddly enough, the other octaves seem to not have this problem.

I've tried cycling through all the different styles discussed on the VT forum.

I've tried using different octave types as well. They are all too wide.

Some instruments respond well to the theoretical approach; some don't.

Some pianos will give you the best result by using the octave type approach. Some will repsond better if you just listen to the octave in its totality without over-analyzing.

Some pianos's unisons will respond best to listening to the various partials. Some will repspond better by listening to the sum total of the unison.

It really does almost require a shift in consciousness or perspective or something to go back and forth between these two approaches.

Then, there are false beats. There can be other junk and distortions in the note as well on these small pianos. We can tune an octave that is theoretically correct, but sounds bad.

Everything is open to compromise except A4 in most circumstances. Then, that compromise should be compensated for by retempering as necessary.

Every tuning is a custom tuning for that unique piano.

Every piano really is just a great big puzzle to be solved

THANKS, just excellent !

regards

Mark, opinions are like, er, noses. Everyone has one and they all, er, "smell." Take ALL our responses with "heavy doses of salt."

So far, so good. And why as wide as possible? Because somebody said so? You made a wise choice by being narrow of 6:3. Narrow of 4:2 would have been wiser yet... And another octave that should be narrow of 4:2. Your ears told you so, but there was still that advice from "on high" saying that octaves should be wider than 4:2. This seems to be confirmed by the slow F3-A3 M3. But in reality, the CM3 progression above the break on a small piano should have slower than normal beatrates the further you go down the scale. This is due to the higher than ideal iH in the unwound strings above the break. Well, narrower octaves will help when you want narrow intervals to beat faster, such as a P5, but not when you want them to beat slower, like a m3. But when you think about the m3/M6 test for the 6:3 octave, you really don't have a choice but to have the m3s beat faster when the octave is narrow of 6:3, right? So the choice of pure/wide P5 or fast m3 should go along with what the octave width that was chosen: narrow of 6:3 = faster m3s. OK, to get the RBIs to work you are finding that the P5s AND the P4s need to be wider than you like. Again, this points to an octave that is too wide. Octaves too wide? Yep. Again the choice is between the wide P5 to make the m3 right, or a fast m3 to make the P5 right. The fist choice is appropriate with wider octaves, the second with narrower octaves.

Mark, I haven't read the other posts and of course you will have to make your own choices. Everything you wrote points to octaves that are too wide, and the only advantage is to try to make the m3s and M3s beat at their theoretical rates and their theoretical progressions.

Of course if it is decided to use a narrower octave, how do you decide how narrow? (Yes, most will guess where I am going with this.) Tune a P12 and see how you can get the P4s P5s and P8s to fit. Expect the octaves to be quite narrow, (2:1) above the break and more normal (4:2) when straddling the break. Likewise, the beatrate of the RBIs will show they are narrow from theoretical above the break and wide from theoretical across the break. It is not unusual to have a pair of CM3s equal beating in such a case. But the SBIs will be about right.

There are some that will say, "But how do you know the P12 is right? A pure P12 is already wide of theoretical!" My answer is: try it and find out. If a pure P12 is too wide, the P4s, P5s and P8s will tell you. I have never found a pure P12 to cause a tuning, especially on a small piano, to be too wide.

The main point is, don't expect a good tuning on an atypical piano by using typical octaves. There are other ways (I suppose) of determining the best octave before "running the bus into the ditch" when trying to get the RBIs to work, but first fitting P4s P5s and P8s into a P12 makes a lot of sense to me.