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If you tune the middle section in equal temperament, and then tune the rest of the piano via beatless octaves, will it be in tune? What is stretching and when does it come into play? Is this something that has to be consciously done every time?

Stretching is needed on acoustic pianos because of their inharmonicity.

Tuning the temperament involves tuning the F and A octaves. Tuning them "beatless" results in stretched octaves; wide 4:2, narrow 6:3, usually.

Then, tuning all other octaves "beatless"; same thing. The result is wide 2:1 and sometimes wide 4:2. I.e. Stretch.

Stretch is a byproduct of good octaves, not something you force on a piano.

Stretch is not something you do, it is something that happens. When the piano sounds good, it is stretched to it's optimum.

I learnt aurally at first. Some 30 years ago. At that time I did not even have a machine to tell me how "stretched" my tuning was. I just thought it sounded good.

Now I use tunelab all the time. I still test myself to see if tunelab agrees.

tunelab relies on partials.... and if the partial does not register, you can switch to another. Or move your unit a few inches.

I don't bother. I use my ears. In those cases. Which happen around the break and false beats etc. And the extremities.

Now that I use tunelab, I am less and less surprised that C88 can be anywhere from +20 cents to +50.

Stretching is trying to have the octaves crisp and not only shining.
Often done by using partial matching as a reference for the opening of the octave, which is not as accurate that using its ears in my opinion (but implies a different training)

Stretching the octaves can be understood in the treble and high treble (depending of the scale of the piano)

But is not appropriate in mediums, where it sort of "fix" the "life" of the octaves.

Still many techs use an expanded octave as a start for the temperament.
It is easier to tune as all 5ths are slower an larger then.

I belive that something goes with the listening of the tuners, age tends to give a preference for warmer (more calm) octaves.

The basses are also tuner with enlarged octaves,

Enlarge mediums gives some security to keep the fast beating M3, 6ths an 10ths, etc , progressive, while limiting the amount of stretch usable in treble and basses.

Stretch is also the condition of the wire under tension.
More stretch favor stability of tuning, as the wire is then more elastic, less sensitive to impacts and variations in soundboar shape.
The stretch is anyway limited, must not be more than 4 mm in mediums.
The longer the string the more it will stretch (long backscales an front duplexes)

Ye there are 2 sort of stretch - to simplify- Natural stretch an the one that is added by the tuner to help the ear, in treble (sometime expressedly asked by the pianist to have a crisp tone in arpeggios in the high treble region.)

In my experience it does not mean extreme stretch , just a hair more than usual.

The "natural stretch" is only apparent when using tuning checks relating to partial match ( names of octaves tehn 2:1 4:2 6:3 etc) this is just a trick , the aural tuner just "hide" the most annoying beatings between thos impure partials.

regards

Actually the term "stretch" is a machine-centric term that only came about after the development of the Strobo-Conn -- one of the first tuning machines. Those machines work by listening to pitch and indicating a value of "sharp" or "flat" based on an internal programmed calculation. The first machines simply used the theoretical mathematical location of the partials as the standard from which to evaluate "sharp" or "flat". Because the actual partials on the string are sharp to the theoretical location -- primarily due to wire stiffness -- it was necessary to "stretch" the octaves wider from the machine's point of view to really be in tune. But actually, the machine was compressing the octaves out of tune.

So, if a piano is aurally tuned to beatless octaves (no such thing, really, but the ideal we all strive for) it is not actually stretched, it is simply in tune. Early machines did not account for that and compressed the octave.

Comment here on one difference between aural tuning and machine tuning. . .

When a piano is "in tune", we mean that when we compare one note with another (or strings in a unison), they are in a satisfying relationship to one another. We are not concerned about the particular pitch of a given note (although we may be sensitive to overall pitch level). So being in tune is about comparison and relationship. Aural tuners deal with this directly -- simply by putting notes in relationship with one another directly as they can best determine by comparing them with one another. We do not somehow pull a pitch out of our heads and apply that pitch willy-nilly to a given note.

Machines, on the other hand, know nothing of relationship or comparison. What they do is measure pitch of a note and compare it to someone's best guess of what the pitch should be for correct relationship among the notes that has been previously input into the machine. (The term "algorithm" is commonly used by the ETD folk because it sounds more impressive than "best guess".) Then the machine --through a display -- indicates whether the pitch it is measuring is sharp or flat to that internal "best guess" standard that was given at manufacture (or latest program upgrade).

As a matter of fact, the algorithms that have been developed in recent generations of machines are getting to be very very good. But machines are not actually "tuning" the piano in the sense of directly comparing notes and establishing on-the-spot, real-time optimization of the relationships between notes. To the extent they get there, it is by a round-the-back-of-the-barn approach. Computing horsepower and refinement of algorithms have developed to the point where ETDs generally do a pretty good job of getting the piano in tune.

So, back to the question about stretch. If a piano is tuned normally by ear, it will be "stretched" by exactly the right amount to compensate for the "compression" that early machines applied.

Now, there is another level of finesse: since one set of partials is out of tune with all other partials due to inharmonicity, one can "select" (either by machine or by ear) which set of partials will actually be in tune. Or, since the actual function of listening may or may not assign more importance to one set of partials, if we tune by ear, we can tune for the most pleasing partial "blend" or aural effect of the entire tonal envelope. So, in that sense, there can be greater or less stretch depending on which partials (or blend of partials) one has determined to use in a particular tuning scenario.

But basically, if you are starting to tune by ear, don't worry about stretch. Nothing is written about stretch before the 1940s because it was never a problem with aural tuning and only became an issue when people began using the early ETDs.

If you have some experience and want to refine your work, start paying attention to the partial envelope.

Am I correct to assume that the meaning of tuning to a 2:1 octave means that my ear should be hearing first partial of the higher note sounding against the second partial of the lower note?
When I tune my piano I hold down the lower note of the octave ( without letting it hit the strings) and then strike the upper note of the octave.
If I hear this upper note on the open lower strings I assume that my tuning is good?
I read that the term first partial means the actual/desired frequency of the note.

I have repeatedly asked for a definition of the pitch of a piano note, or barring that, a explanation of what is being measured, and never received a comprehensible answer.

Goof, as a non-tuner, that seems to be the case as the lingo is different between a tuner and a musician. It would be interesting to hear from the pro-tuners on the matter.

If I understand correctly, the 1st. Partial = the Fundamental Pitch (note).

What a musician refers to as the 1st. Harmonic or 1st. Overtone, would be the 2nd. Partial.

Ghosting does not really show you, unless you hear beats in the non played note, the leeway is large.

BUT, ghosting can help to focus on the secon note, and also the "speed at which the ghosted note reacts gives some clue as to the efficiency of energy transfer between both.

For instance, I play a high note and hear the bottom ghosted note "jumping" out clearly, it tells me I am lining well.

The same the other way, but treble notes always react well so it is less significant, to me.

Tuning basic octaves you perceive a reinforcement of tone, probably both ways, without ghosting, just playing.

The twelve (beating very slowly) is hear but faint and not coloring the octave. clearly heard but not very present.

for ghosting, I suggest you play a strong but ery short note, and listen how the other one reacts. it must be fast and present, not reacting slowly.

Olek YES as you write so I do! - that is how I tune the higher note to the lower more as a final check.

cool ! then you can detect the same thing happening without ghosting.

with some experience, you even can detect the loss of resonance in a single note (particularly in the 5th octave and above, but if concentrated, it can be perceived lower as well)

Well, there we have it. ETDs are not scientific instruments, they are tools (and, quite useful to the folk that choose to use them). As I understand it, they are listening to the fundamental -- whatever it is that a frequency counter would pick up. At least mostly. Some previous models would listen to partials in the bass because they couldn't accurately pick up or process the fundamental. I'm not sure if the latest models listen to the fundamental all the way down or not. Maybe a person more knowledgeable about ETDs would know.

Keith, as far as the Sanderson Accu-tuner is concerned, it is designed to pick up any selected frequency in the air when used in it's basic mode, and that is irrespective if it happens top be a fundamental or not. However, because of the practical difficulty in actually detecting lower frequencies, the lower notes of the scale are typically determined by listening to their higher partials. When using the FAC mode, it only listens to fundamentals from about C6 upwards. For all the rest it listens for certain partials of the notes.

What is interesting is that when tuning A4 in FAC mode, Accu-tuner is not listening to 440Hz, it is listening to the frequency at A6 with a modelled offset to account for an assumed inharmonicity. Then, A4 is supposed to land about right!

It is very difficult to precisely define 'pitch' , as it is a psycho-acoustic phenomenon, and is thus a subjective term.

You could say that the pitch of a piano note is 'what that particular person hears when that particular note on that particular piano at that particular moment in time is struck in a manner causing that particular amplitude'.

For a person using an ETD, pitch is what the ETD's best guess is about the sound it senses during a given interval of time.

All of which means that tuning is an approximation. It cannot be defined to any particular degree of exactness.

the small eventual pitch change during sustain is not something really important, the mind still consider the pitch as stable.

the softwares have more difficulties with that, I suppose the display is somehow averaged for a better stability.

Even when seeing a pitch change on it, the ear do not hear it (mine anyway), in a 0.4 cts range I cannot see how it makes a significant difference.
I also have the gut feeling that the global consonance of the tuning "maintain" the pitches and notes stability, as if the energy was drawn in channels that "straighten" the pitches.

For a long time I was tuning with the idea that strengthening the fundamental (for a rounder and mellower tone) sort of "drives" the partials, rule them.
It seem to be the case indeed but their revenge is a moaning that appears if the note is played strong. (audible by tuners, I am unsure it is so bad when playing)

I seem to obtain that sort of unison tone with a "reverted smiley" the initial pitch is given by the center string, then iH "fight" by the 2 outside strings, a hair low, that pull the partials down (the opposite happens with the smiley, and the Weinreich effect is probably nil with that shape, as the outer strings sustain the top of the spectra.)

The first style is as tuning an octave with the second partials lining with fundamental, but on a single note, while the smiley shape is giving an "open" tone with clear partials, and possibly the pitch tend to rise during sustain.(I still have to check those with a spectrum analyser or a good ETD)

Anyway in all or most unisons, the tuner uses the full available spectrum fundamental and partials.

I also wonder of the "reconstruction" effect done by the ear of listener, as it happens in the basses to hear a fundamental that is absent, in reality, - and how those partials coupling and management influences the pitch impression in the end.

May be with a clean lining of partials a sort of phantom fundamental is perceived

clearly the way to go in high treble (most tuners do that I think) waiting for the 'ringing' of the octave below (or/and other notes as the 12th,...

it is possible to tune high treble without mutes, just base on the strenght of the resonance. A trap exists if you get caught too high and make an octave that rubs with extreme stretch more than it couples
I have read that the human ear likes to have a 1/4 tone rise on a 3 octave span - 25 cts - no surprise extreme stretch may sound in tune when listening "musically" (not that 25 cts at A88 is so much, but 1/4 tone is where the ear seem to like the high treble octave when listening to energy spread.

Yes, but any approximation is, by definition, a degree of exactness.

It is my opinion, not based on the precise details of the algorithms used by various EDTs, that they do not provide a level of exactness that is expected by the novice ETD user.

Well, that's interesting. In the practical world, it's certainly "good enough" for most purposes. But, good grief! -- The approach to establish A-49 from A-73 -- whatever else one might want to say about how close it is -- is clearly a "best guess", not a definitive absolute.

And, I didn't mention before, but compared to a scientific instrument, the ETD reports its output in plus or minus cents. That report is in comparison to an internally installed standard -- not objective reality. In contrast, a freq. counter simply counts the hertz and reports them. Its output cannot be gainsaid. One must understand, perhaps, that its output is within a certain range of tolerance -- but within that tolerance, it is providing a valid report of external reality that it is attempting to measure.

In contrast, the ETD is not providing an objective report on the state of reality but rather instructions of a "this is what you need to do" nature to achieve something that will sound good (or, at least, OK). Anytime you have a machine saying "should" or "ought" it's not scientific -- there's a human opinion in the box somewhere.

Well , the best ones are MORE exact than what is expected but that is based on things we do not really use for tuning aurally. More compromising than what is available to us for instance.

When the ear begins to listen the way the ETD does (for instance with RCT listening to the 3 partial when tuning in octave 5-6, there is some loss of the "normal" tuning perceptions, they are then very slightly flawed, in a so imperceptible way, it is difficult for the tuner to realize.

When the display show a partial only, I think the ear will tend to focus on it.
The multiple partial displays (VT100 for instance) get rid of that defect probably, but I often could not "understand" what the display was looking for, while tuning. This is not comfortable, particularly when you hardly catch the ETD in defect/fault. I finally thought that it was taking too much care of the extremes of the scale and that was modifying the center in a more or less effective consonance depending of the notes.

Beginning to tune with more attention to consonance was a delivery, and re-conciliates me with tuning

Having worked with frequency counters for some decades, I can say that they are fine for counting up the periods of a given signal over a given time, but need a single frequency, not a complex waveform to produce an output. They get confused when there is more than one frequency involved. Which one does it count, the strongest? In that case, it would capture the second or third partial of A0, not the first. In the real world , an FFT algorithm is the only method to tease out the structure of a complex waveform. One can also use a lock-in amplifier if the desired frequency is known in advance within narrow limits and achieve a very high level of acurracy.

CERN uses the same type of FFT analysis as I use for their experiments ( I read a paper published by CERN in 2004 on the preference of Gaussian windowing and interpolation over parabolic interpolation ) whose frequency range is similar to the audio spectrum.

I think more specifically, a frequency counter can cope with complex waveforms but providing they are regular and periodic at the fundamental. What gets confusing is when inharmonicity rears it's ugly head because then the complexity changes progressively for every successive period of the fundamental. Regularity becomes very poor. Fortunately, FFT can cope because it looks at individual frequencies at a fine resolution across a specific spectrum without regard to whether it is seeing fundamentals or otherwise. Every frequency of the partials in an inharmonic waveform still exists in their own right and their presence will be more or less captured when the loop in the FFT at their particular frequency come around.

True, a frequency counter will easily work on square, triangle, sawtooth waves. But the catch is that the fundamental frequency amplitude must be >\= the harmonics.

The way I think of stretch these days really comes down to the quality of the 10ths and 17ths. These intervals are quite sensitive to small pitch changes - more so than octaves. These intervals are the vibrato of the piano, and if they are too fast the piano sounds "edgy", like its had too much caffeine. To slow and the piano sounds lazy. There is a "just right" range that comes down to the good taste of the tuner.

I like that imagery. Thanks.

It's true that small changes in interval size result in more noticeable changes in RBI (10ths, 17ths, etc) than SBI (octaves, 12ths, etc).

What some technicians don't understand, is that the RBI's are just mirroring the temperament and are smooth when the SBI's are consistent. There is very little "taste" involved here. If you tweak those RBI to suite your taste, you risk creating uneven SBI's and inconsistent treble temperament.

Yes but assuming your temperament is smooth, a wider stretch will still result in faster beating 10ths and 17ths and narrow stretch will result in the opposite. The question is how fast is too fast? That's where musical taste must prevail.

The effect of stretch on RBI's is relatively very small, changing something like 8.7bps to 8.8bps for example. I doubt anyone could notice that.

Kees

I suppose you computed that, but I di not find it was the case in reality.

Stretching the temperament octave influences the RBI clearly, to me.


While I used for a long time the basic ladder of M3, I was not really happy with the guess for the first octave.

It is more precisely setup with 5ths an 4th control, I do not find discrepancies in the color or beat of those slow intervals as it could happen when using the M3 as a proof.

That is generally admitted that the FBI are "more precise" for tuning, while in the end the slow intervals are much more.

the FBI then "reflects them".

Ryan, I know what you mean about musical taste with the faster 10th and 17ths. There is a limit beyond which you just know it is too much stretched from the sound. However, I prefer to limit the stretch by using compromised expanded SBIs that are as beatless as possible. i.e., the bounds of the 10th and 17th beat speed progression is guided by 8ths, 12ths, 15ths and/or 19ths that are as cleanly compromised as possible. In other words - mindless octaves I think.

The beatings will become more frequent until the stretching stops.

hidden secret message !
"stretch" I see more as a crutch, providing some security against the contraction of intervals (due to whatever reason (Weinreich, bridge motion, soundboard settling) .

It is difficult to learn how to avoid stretch when tuning mostly small pianos, that provide a lot naturally.

Agree that the FBi will signal if you are deviating , while using the octave +12 node is also a good focus point to judge of the amount of "overpull" (some training is necessary as 12ths have a large leeway, but the 5ths quality can be recognized in them IMO.