The P4 Window and the Pure Triple Octave

I have been posting in another thread concerning this topic and the suggestion was made that I make a new topic. So here it is.

I use the tests of M3 < M10 < M17 < M6 and m6 below = M17 to create a cohesive and consistent stretch for the mid section and high treble. It uses octaves between a 4:2 and a 6:3 which give clean octaves.

Here is a recording showing how the single, double, and triple octaves and the P12th can all sound clean using these tests.

http://www.youtube.com/watch?v=ys_2vxtEAnw

How does this relate to the P4?

The M10 and the M17 fit into the M3<M6 test, which is the test for the P4. Thanks for the question.

OK I understand you now. I'm not overly familiar with all the checks, so this is pretty interesting for me.

A further question though, sorry to press, but is the P4 window just a name you have for this sequence of tests for consistent stretch, or do you use the 4th in some way to set the stretch?

My technique for the midrange of the piano is to stretch the 5ths as close to pure as possible without allowing the 4ths to beat too fast. This seems to produce the a similar result as this (although I've never used the test for the triple octave).

The fourth has already been set in the temperament. My method for setting the temperament starts with tuning:
A4Fork
A3A4
F3A3 approx. 7bps
F3F4
Then what I call the skeleton which is just contiguous thirds up to A4. Bill Bremmer has a good method but I think mine is better. I will post it next.

But the temperament stretch (not to be confused with the octave stretch) is set by the size of the A3A4 and F3F4 which I tune as between a 4:2 and a 6:3, using checks and just listening to a clean sound. That will also be a future post. Thanks again. Your questions are helping me decide what I should post next.

I'm happy to keep posting questions if it inspires you to write. But if you're going to be writing about how your tuning technique is 'better' then I'm not sure I will. Less of the 'my way is better' please, and more of the 'this is my method and my reasoning'.

Sorry if I gave the wrong impression. Keep posting.

the ladder of 3ds have to be proved right by numerous 4th and 5th, if not it can be progressing too fast and still sound correct.

I gained some ease with the first octave when taking the habit to find the first 3ds with 4ths and 5ths; it is less easy but way less corrections remain.

mistakes are allowed in the temperament, but not too much (my friend Alfredo accepts 2 mistakes or incertitude)

the mistakes are noticed immediately when you tune octaves, whatever test interval you use

on very small pianos it can be better to allow for some huge mistakes in the break region, just favor the interval you prefer.

that is in that zone that the tuners that focus on 5ths have a different result that the one that sticks on fast beating intervals, compromising will differ then

I have also heard nicely tuned grands (S&S mod B) that lower in beat rate near the break, to keep more consonance for the low basses. add a little age to the strings and you raise the iH, lowering the 3ds beats if you keep on focusing on having nice 5ths.

we only have a certain amount of cheat (stretch) allowed, so it is not always the best choice to use it all immediately.

Hi Isaac,

Thanks for posting. When I first started reading your posts, I was like "What is this guy talking about?". Then as your words start to simmer in my mind longer, I start to see your points. Example: tuning the beginning of the note.

Anyway, I will start a new thread about tuning the temperament soon, and then I will discuss that more in detail.

What do you think of my 1/2/3 octaves and tempered P12th?

I tried briefly, but testing so different intervals is now too much hard on my ears

I agree however that 12th cannot be enlarged, sort of stretch limit.

FOr long I had problems with that 3 octaves span, I am very sensitive to that and I hear a too low or high 3d octave note in the 5-6 octave immediately.

I cannot say why my 3 octave span sound right now, but I agree there is a little room yet there.

The main problem is indeed to find the correct amount of stretch that gives you some security for the double and the triple, based on the mediums octaves (and temperament octave of course)

A too large medium octave will make your 3d octave noisy, a too small one also (if you are obliged to raise the dimension of your octave abrubtly)

Some equilibrium have to be find as you try to, with whatever tests. the more the central octaves are enlarged, the more straight the railsback curve.
I tend to like it when the straightness is not too much perceived but not any piano allows it (it sort of bring different registers to the piano, absolutely always at the expense of the global cohesion)

Greetings

Sorry, I hear the M17 as being slower than both the M3 and the M10.

Me too, but it is possibly because of the compression that steal us some high partials.
then all Major intervals sound too slow

There is no much raise in speed between M3 10th and the 17th sound slower , (the M3 also sound slow) the high F sound also too low to me but this is possibly due to the recording

I believe that the way I "open" the unison raise the speed of the FBI during the dwell. if not (flat sounding unisons) I noticed the pitch tend to lower after the initial dwell so to have the good beating speed we tend to enlarge too much everything if we listen too late . Actually when I tune, the speed of FBI I use is good for a really short moment, may be less than 0.25 seconds, afterthat I dont consider it fiable.

I have a vertical I made similar check just now , and I really feel the unisons (with external strings tending high) help to keep enough life in the beats.

I will try to record that. It is very difficult to place that top note, and anyway it will pitch differently in arpeggios and notes played together

Would you mind spelling out what these intervals are for say an example of F3F4F5F6. For example I think M3 is probably C#3F3, M10 C#3F4, M17 C#3F5. But I can't figure out which interval you mean by M6 and m6 below.

A second question: If you talk about 4:2+ do you mean equal beating 4:2 and 6:3 are more generally something in-between 4:2 and 6:3?

Thanks,
Kees

Kees,

Mark is using C#4/F4 (M3) < C#4/F5 (M10) < C#4/F6 (M17) < C#4/A#4 (M6), and then F3/C#4 (m6) = C#4/F6 (M17).

I use a similar "window" of RBI tests, although somewhat reduced, which allows me to get equal-beating 12ths and 15ths (ie "mindless octaves"):

M3 < M17 < M6

I start using that test as soon as I have two full octaves tuned. I use a F3-F4 temperament, so I go by fourths and fifths up to C5, and down to C3, respectively. From then on i go by the "window" method.

When Bill tunes his "mindless octaves", he uses SBI's (4:1 and 3:1, and higher in the treble 8:1 and 6:1). I had troubles separating the SBI's from false beats and such, so I started using RBI's. They give the same end result. I always finish by running the 12's and 15's chromatically up and down the piano, which catches possible mistakes and drifts.

I also do a "window" moving down through the bass. The latter I picked up from Ben Gac, RPT, who also uses and endorses the aforementioned "treble window" method.

One more thing regarding the octave stretch. I support Isaacs writing earlier, where he mentioned that jazz gets warmth from a narrower approach, whereas (among others) Ravels music might benefit from wider octave sizes.

Now, Ravel's music can certainly be played on a "narrower" piano, too, and vice versa can jazz be improvised on a "wider" piano. It is all down to the preferences of the piano player.

A narrower tuning gives less busy fourths. It is often appreciated by jazz pianists because they feel the piano is warm-sounding, compact, together. Fourths are arguably the most important interval in jazz piano voicings of today.

Likewise, in music with cascading, arpeggiated intervals spanning several octaves, it's nice if the top note is as high as possible

So, at least I myself tune differently for different contexts and players.

Thanks Pat.

Not being used to thinking in terms of tests would you mind correcting my homework, which is to interpret the meaning of these tests? Here's my work:

C#4/F4 (M3) < C#4/F5 means F4F5 4:2 is wide
C#4/F5 (M10) < C#4/F6 means F5F6 2:1 is wide
C#4/F4 (M3) < C#4/F6 means F4F6 4:1 is wide
C#4/F6 (M17) < C#4/A#4 means A#4F6 3:1 is narrow
C#4/F5 (M10) < C#4/A#4 means A#4F5 3:2 is narrow
C#4/F4 (M3) < C#4/A#4 means F4A#4 4:3 is wide
F3/C#4 = C#4F6 means F3F6 8:1 is pure

Correct?

But what about F3F4 4:2 and 6:3? Are these presumed to be tuned equal beating?

And what about F5F6 4:2? It could come out wide or narrow, or not?

Nice to have you back here Pat.

Kees

This sounds like a clever test group, Mark. In all cases, the 5th partial of the root note is tested.

Example set:
F3(5)A3(4) < F3(5)A4(2) < F3(5)A5(1) < F3(5)D4(3)
A2(8)F3(5) = F3(5)A5(1)

The only part that I don't understand is the comparison to the M6th at the end. This assumes that the iH measurement between the 5th partial of F3 and the 3rd partial of D4 yields a positive result to the difference between partial 5 and 1 of the M17th pair. I can see this as going either way on different pianos.

It's interesting also the comparison between the m6th below and the M17th. Where do you find this equivalency gets the stretch set on most pianos?

I like the organic nature of these tests, but another thought I had is the beat speed between the M3rd and M6th test for the P4th is very close. To make all these others fit in between proportionally would be quite a challenge in patience.

Thanks for sharing your thoughts and technique.

Thanks for all the comments. I will be responding to those who had a question as soon as I have more time. And thank you those of you who took the time to answer some of the questions for me.

Thank you, Kees, its good to be back Fall was crazy, I felt like a hamster thrown into a wheel. Better now, anyways.



Yes, absolutely. But I would assume that Mark doesn´t check the 2:1, 3:2 and 4:3 per se (neither do I). The idea would be to step through it like this:

1) check C#4-F4 (listen for beat speed)
2) check C#4-F5, this should be faster than the previous one,
3) check C#4-F6, this should be faster than the previous one,
4) check C#4-A#4, this should be faster than the previous one.

This would give you a wide 4:1 and a narrow 3:1 with F6 as the upper note. Which is, just as you mentioned earlier, what Bill's mindless octaves and CHAS aim at.

Now, one could argue that Mark's method doesn't place the 4:1 and 3:1 equally beating, but the difference is small if not even negligible. Fact is, I end up closer to equal-beating 4:1/3:1's using these RBI's than if I listen to the SBI's. That might be just me, but if there is a difference between the "direct interval" method and "Mark's window", it is indeed very small.

I use pretty much the same method, only that I skip the 4:2 test (second step) and just check the 4:1 and 3:1. That is, I play C#4/F4, C#4/F6 and C#4/A#4. The checks should speed up progressively, then I get the stretch I desire.



I would assume (from reading Mark's writings) that he aims for a 4:2+ octave (again, not maybe exactly "in between" 4:2 and 6:3, but close enough for all practical purposes.) This he does when he sets the temperament initially, and thus the F4, from that point on, is a set note of reference, not something that are to be moved to "fit the window frame", so to speak



From my experience using this system, the 4:2 come out just or wide. At least that is what the checks tell me when I move up through the treble. Now, I have to admit that I do practically all my aurally based tuning on good instruments, and almost always attack the scale-challenged high IH pianos with an ETD, so I am not sure how IH affects the "window". If I go aurally on the latter kind of instruments, I accept equal instead of speeding up, that is:

C#4/F4
C#4/F6, not slower than the previous one,
C#4/A#6, not slower than the previous one.

->Mark: If I give misleading information as to how you go about this, please forgive me and correct me. My assumptions are from my own experience of using a very similar method, and there might be deviations.

Hello Patrick , nice to read you too !

Did nobody find how much equal beting is almost automatic ?

Just have to avoid confusion between too large 12th and tempered twelve, then when tuning the twelve the resonant spot is clearly audible, it is a large spot (inclueding resonnaces coming from many intervals lower) so not very precise, that is why I believe there is some acoustical effect that push the notes into balance.

Beginning with a pure 12th on a tuning type +2 cts, the things fall in place without any effort.

I am not saying the beat speed of the 12th is always perfectly progressing , when the tuning evolve in time often the original "perfection " is disturbed.

But strangly the equilibrium 12th 15th seem to stay solid.

Find me a good reason, please, that will make me happy !

I will try a few recordings ...


I admit your comment on challenged pianos, but I also believe that as the model is added on the scale of the piano, it will apply on any piano. (with indeed different final results, for instance some customers that play much with close harmony and music using only 5 octaves, may admit that the piano is more sonorous, but can be less enthusiast about the raised activity of FBI - as on moderately low iH pianos, Yamaha U1 U3 for instance)

I finally understood that is a sort of maximum for the stretch.

AFter using it for a few years I now recognize how a given tuning is acting vs that equilibrium, it is particularely noticeable in the diskant section, That is in my opinion, where it is the most useful, as it reduce the time it takes for other notes to be exited , the enghancement of the played not is then a characteristic that is noticed once you are used to it.

That is funny, I knew how to perceive if the stretch was not enough in 5-6 zone, but I never thought it could be noticed by the way the attack is enghanced.

I agree, Isaac - the 12th/15th relationship seems to work whether the piano is tall, short, nicely-scaled or not.



-> everybody else: If/when Isaac posts recordings, these are well worth digging into - he is a very skilled tuner/technician, one of my mentors (so is Bill, Jeff, and BDB. There are of course other IRL and web mentors, too, but this quartet has been particulary helpful in getting me where I am at right now.)


I agree. Most of the jazz/pop/studio work i do will compass about 5 octaves, with an occasional arpeggio. I feel that under these circumstances, it's better to keep the mid-range harmony "tight", possibly sacryficing the uppermost treble.


I agree on this, too, and I share your conception of the maximum stretch.