Piano World Home Page Forums Our Most Popular Forums Piano Tuner-Technicians Forum The P4 (P19) Window and Pure 19ths on a piano.

I tuned a church piano using the pure 19th check and a P4 window check.

All these were wide: 2:1 octaves, P4ths (very), double octaves, triple octaves, P12ths, but the 19ths were pure. The P4 window and the P19 test create consistent SBI sizes, which help to make this otherwise inappropriate treble temperament, actually sound pleasing.

The musical director said "it sounded brighter".

Here it is:
http://youtu.be/AEkzZ27ztJ8

I just tried it. I liked it very much.

The high treble sounds just in tune with bass notes.

I tuned the pure 19ths aurally by making the m3-M17 test. F3Ab3 and Ab3C6 should beat at the same rate. With the verituner I set it to C6, play F3, stop the blades and then tune C6 to that pitch.

But I don't understand what the P4th window is.

Thanks for the time to use it.

I tune with checks.
So the P4 window is used to tune higher octaves within the P4 window.

Starting with F3Bb3, the test is Db3F3 < Db3Bb3. That's a wide P4. But after a highly accurate ET on the temperament, that window (beat speed difference) should be very accurate. Then I tune F4 and F5 to "fit" in between that window.

Here's how I do it:

First,

Db3F3 < Db3F4, that makes a wide 4:2.
You could just easily tune Db3F3 = Db3F4, pure 4:2.

Then,
Db3F4 < Db3F5, that's a wide 2:1, most techs agree that's appropriate in that range.

Then,
Db3F5 < Db3Bb3, tempered 12th, or
Db3F5 = Db3Bb3, pure 12th, depending.

Put it together, you get:

Db3F3 < Db3F4 < Db3F5 < Db3Bb3, the P4 Window.

Why do you let the piano iH tells you where the "in tune" place is ?

It have not much to do with that in my opinion.

If you want a pure 19th tune a pure 19th, something that acoustically sound as a pure 19.

I am never far of pure 12ths so I tested on a piano that I need to tune again, and yes there are what would be called pure 19ths. AND NO ENLARGED PURE 12th, (it kills all warmness)

But the beats are immediately heard, no need to force the ear, this is in the instrument once and for all. I will record you that (without tuning) if you wish.

Lately I never used such type of tests all is done in regard of the way the octaves stretch. That is direct, not tiring , and more musical in my opinion.

I am not sure the pure 19th can be tuned directly (in octaves) but if they add something they should be.

I dont even use M3 M 17th tests , and if I use them they are right most of the time. I simply do not need them (or eventually to do some fine testing in case of doubt, and even then I am not sure they are not misleading)
If we use our ears to evaluate the amount of consonance in the single unison there is mostly one place where it is optimal.

DO the test later if you wish and see what you get.

Regards


PS The problem is that the more time you pass learning to master such approximate beat comparison the less you listen to the instrument. AT some point the final result have only a meaning for you.

So you tune from A#4 to B5 checking with the P4 window?

If I understand you begin to tune pure P19ths at C6 and up to C8. Don't you?

So what do you tune from A#4 to B5 in order to not have a gap (jump) between B5 and C6?

In otherwords, how do you make the transition from 4:2/6:3 octaves in te temperament octave to pure P19s at C6?

I agree with you here, Isaac. That was well said. There are all kinds of things in the instrument that can only be heard by listening with no formula in mind. A fixed approach often gets in the way of hearing new things.

However, I will say that I think this P4th window test is a good insight on a test tuners have been using a long time: the compromise between the 12th and 15th in the treble.

Those harmonics happen to originate from the 4th below and insight can be gained by realizing their spread is determined by stretch created in the temperament. The wider a temperament is initially created, the more difficulty you will have in finding agreement between the 3rd and 4th partials for a common top note.

The tests mark the distances between the 5th partial of the M3rd below with partials 4 of the M3rd above, 2 of the 8ve, and 1 of the D8ve in relation to the 3rd of the 12th.

It implies that the octave above the base note of the 4th should be a wide 4:2, that the octave above that should be a wide 2:1, with the D8ve being a wide 4:1. Also, that the expected partial structure in terms of sharpness is 4:2:1:3.

This isn't necessarily the optimal or most artistic structure for every tuning, but it certainly is a good benchmark.

Well yes I think it is a good test, then if Mark think he is "on" something, I can tell him the tuning I recorded (one year old) on that vertical piano, have such relations more or less but not with enlarged 12ths in the 5th octave.

But I did not tune that way purposedly. I think I use twelves to double octaves a lot(directly most often, no checks) and that the octaves above have just to be nice and clear, then the 19th is a doubling of the 12th it s not so surprising they fall in the same sheme.

I have noticed that the 19th is a little participating in that high note, not as much as the twelve, it is heard a little so it can be tuned "directly" .

That is just that if the top note is too high, or too low, vs all the notes under it, it will not sound as nice. nor as vivid.

Some way of listening that can be learned too. (tuning double open unison seem to be a good start, but tuning the attack is mandatory, it cleans the tone helps to listen to beats and to focus on energy (at attack time, or more precisely slightly later)

Regards

You are not understanding the process. The checks help. The sound proves. All is good. Not stretched. No you cannot have pure 19 and pure 12. Unless 6:3 octave in midrange. It is math. The definitions come from math so if you want to use them, you have to understand them.

I don't tune like this often. This was for show. Only on some concert grands that can take it. The widnesses are much less.

But when I do, I start with pure 12ths at C5.

Keeping 4:2+ in midrange.

Yes, it is a transition.

Often theory is misunderstood.

The birth of theory comes from performance, followed by analysis, followed by theoretical understanding, followed by re-creation by theory, followed by confirmation and adjustment if necessary.

Often people dismiss theory because they think that last step is not performed.

Also, you think you are tuning pure 19ths. How do you know? The P4/P16 window gives a way to know, and compare. I.e. "I tuned pure 12ths but it doesn't fit on this piano" rather than "this piano is not as stretched as I usually tune." Too vague.

Thanks Mark for the video and explanation. I knew that you were just demonstrating how to check and compare the beat speeds, and that all pianos cannot have the same amount of stretch and therefore strict pure 19ths would possibly work better on larger pianos (or if you have a customer who demands a super-bright treble on a smaller piano).

I tune purely by ear so I am always looking for new ways to accurately check my progress outside the temperament area. The high treble has always been the most difficult to accurately compare against something solid. 10ths-17ths are nice but only until the last octave or so. Your P4 window has given me a more accurate assessment as to how much stretch I am giving the piano.

On that particular upright in your video, I might have toned it back a little so that the treble fit more inside your window (rather than at the high extremities of the window), maybe even more narrow so the 19ths were a little narrow of pure. But I realize this was a demonstration and I'm sure you tailor every stretch given the particular piano, customer and use-case.

I appreciate the videos and techniques. Thank you Mark!

-Erich

WHen the treble is using nice 12ths (5-6th octave) all notes above are just in a natural prolongation of that.

Of course I can test with your tests to know what they say in regard of the 12ths, 19ths, inverted 4ths etc. It sound logical I fall there as I use those intervals a lot. I use them to obtain my progression of 10th 17th and doubling of thoses.

Now tuning as you do in the demonstration is just looking for beats speed correspondence , what surprise me is that I dont see you listening to those intervals in octaves and unison.

Anyway as the piano sound this looks not natural, I bet it can be perfectly in the window and slightly off when it comes to the natural consonance of the instrument.

Don't know if the mistake is in the checks (probably) or the way they are listened to.

If I want the 4th to react with the 19th it is just heard, that is a sort of stretch if you prefer.

To tune in the 12-15and why not 1215 19 window, yopu play an inverted minor chord and by memory tune the twelve or the 19th.

The chord is projecting those 2 notes resonance exactly where they can be "naturally"

That is probably me but If I want to know at what pitch to tune that F6, I just listen to it in the tests you do lower. m3d, sixth 5th, fths, etc. The pitch of the note is provided any time and the exat pitch where I can put it is a compromise between the very slight differences that are eventually there.

I hear your F6 as too low from start to the end of the demonstration. I mean t does not line with low mediums or mediums.

May be due to the unison or the piano, also. I am unsure, but I would tune that f6 differently.

Makes me want to say "listen to pitches when tuning" beats are for control only.

Mark, I hope you are not suggesting to tune trebles using exclusively the 12/19th tests. I see these tests only as a valuable tool, not the final arbiter.

I agree with Isaac when he says that the piano's iH guides the level of stretch when listening for good consonance directly across those extended intervals. For me, the best compromise between two or more extended intervals, single or clustered, achieves the most satisfying result. The choice of intervals in this case governs the amount of stretch, but it is always going to be within the level of the piano's natural consonance.

The times when I find the 12/19th-type tests useful is in getting to the ball park under difficult listening circumstances. It also lets us know the direction, too sharp or flat, to a good level of confidence, but I can't say "that's correct now" and then move on. My choice of extended perfect intervals, plus a reasonable clean top octave, governs where the finals tweaks go.

When using RBI's as a tool, I find progressive chromatic 10ths or 17ths to be quicker and less tiring.

Chris, you say let the piano iH tell you how much to stretch. You say the best compromise between two or more intervals is the best sound.

Because I have explained the P4 window multiple times and I still have people asking questions about it, tells me that I have failed to show the benefit if using it.

Ok. Then let me say this. Tuning a piano, using the P4 window allows you to hear the piano iH using many intervals, allows you to tune the piano to the iH of the piano, and allows you to create consistent compromises between not two or three, but four or five intervals for each treble note.

Isn't that good enough?

By the way, the P4 window IS the essence of progressive 10ths and 17ths. They're in there.

I think that the beat comparison method is flawed because the global tone is not really taken in account, only partials and partials can be flawed as a tool for justness.

Then only one element of the perceived tone is heard.
When listening in the mediums and not focusing on a particular level of beating I suppose a better compromise is attained because more partials are active in intervals.

Once that "ramp" is in place the treble (at last) is on its way. and probably does not need too much testing as long as the FBI stay progressive and /or not screaming)

The high treble stretch is decided in mediums, more or less, if you see what I mean.

Isaac,

Once again we have a situation where two tuners agree and tune in similar way, yet one sees only what they want to, it seems, in order to present their view as somehow juxtaposed.

The video is about one tenth me using checks to correct a note and the rest; listening not only to octaves, but 12ths, 19ths, unisons, all musically.

I find some people tend to dismiss any mathematical approaches to musicality as invalid, which of course they can be, just not necessarily.

Mozart was know to use two dice and compose melodies by rolling them to create a sequence of notes within an octave. (From memory. Anybody else ever hear that story?)

So, I do not know what you mean. Of course I was listening to the octaves. And the other intervals as well, in a musical context, to check the "sound" as a whole, prepared to override what the math says at any time.

Let me know, if I misunderstood you.

Hello Mark

possibly it is due to the video quality, and the room , but that is about the way you tune the F6

when you play the test intervals, the pitch of F6 is heard ,then you tune it lower and have to raise it twice.

I think I would have listen to the pitch provided by the beats , an not the beats themselves,

Possibly we listen in a different mode, I have read something about that lately. This does not mean I do not use tests also, but probably I give them less importance now.

I think I "enter" in the piano "in tune" mode by listening to the piano as a whole , may be only musical memory is at work there.
I recorded those intervals tests but not on a tuned piano, on one that have an old 1 year old tuning, so I will send that privately if you dont mind. I will do another record on a tuned one asap

I remind I was using those 4th window test, and sometime I may do if the consonance is unclear.

Now probably just listening directly to double and triple octave is enough to know if the top note is in place (which is somehow high in stretch , the 12th and 19th are very tolerant,even in their "tempered" window; they hardly can be tuned directly, but their effect in the octaves is noticed (as in 6:3 where the coupling at that level projects the twelve tone strong in the octave)

I did not take in account the reverberation in your recording. not the best situation to listen quietly be it to beats or to the piano consonance.

Regards

PS I like to listen to ghosted notes, playing the top one and noticing how good the bottom ones react to that impulsion.

1st inversion of the minor chord show the level of activity of the upper 12th (and 19th ?)
It is clear when the top note is not in the window that something is dull , at the note itself level, and when ghosting, the bottom notes do not react as good nor as vividly.

Yes. There is a definite difference to where a note sounds in tune melodically, compared to harmonically. Is that what you are saying?

The P4 or P19 window tunes intervals harmonically. They may not sound in tune melodically, but I distrust that more. Not measurable. Go down that road and you could end up with a can of worms at the end, unless you have highly practiced ears.

Note that my passion is getting beginners tuning at a high level early on. Once they can get good at harmonic intervals, I'll send them on to you. Deal?

Also, let's not ignore one of THE most powerful tools in the P4 window; catching the drifters.

When I tune in octaves 5 and 6, I am using the P5 window.

E.g. Starting at C5: Ab2F3 > or = Ab2C5. (Tempered or pure 12th) and
Ab2C5 > Ab2C4 (wide 2:1)

Together:
Ab2F3 > or = Ab2C5 > Ab2C4

Notice C5 fits into Ab2F3 > Ab2C4 (narrow fifth)
In engineering, we call this "elegant".

Now, tuning C6 with the P4 window,
Ab3C4 < Ab3C5 < Ab3C6 < or = Ab3F4

Here, if C5 has settled at all, due to Weinreich or bridge tilting, it won't fit in the window.

This technique allows me to confidently say "I can't tune a piano until it is in tune". It is that precise at catching drifters.

Notice that I am not saying tuning by beats is the way to go for the best sound. I'm only saying that it allows such a high degree if precision, I'm not claiming accuracy, that you can easily tell if something has drifted.

Look, don't you think I would rather not get through half a tuning and find that octave 5 and 6 have settled when I was only raising the pitch one or two hertz?

But I can't just leave it like that. You once wrote some thing like "flatness is more perceived than sharpness". I agree. I can't leave a note I know is flat re: one test unless I have a good reason.

Not using the P4 test would allow me to set the notes and move on.

Sure, my ear might alert me to some settling if I used Bill's mindless octaves, for instance, but from my experience, the naked ear is not as precise as when using a check. Why else is F2 so accurate at setting A4?

And to end on agreement. I concede the practised naked ear may be able to create more art than these tests but I am not there yet.

I do not want to go there, because then, I would not be able to quantifiably teach others how to tune.

Natural performers make the worst teachers for me. I.e. I find them frustrating.

I study, so I can teach younger "me's" to tune.