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CHAS is an equation that describes a well-stretched piano using the balance between a stretched 15th and a narrow 12th. This is what many of us habitually try to tune anyway. It has merit in the way the equation allows you to see what happens to the beatrates of other intervals if this stretch is maintained consistently - specifically the way the 5ths and 4ths behave. If I remember correctly, the fifths reach a minimum beatrate close to pure somewhere below the temperament region (depending on the scaling) and get progressively narrower as you move upwards and downwards from that minimum. This is the consequence of semitones being the size that they are supposed to be in this system. It also has progressive 4ths.

Alfredo's tuning technique attempts to incorporate these progressions into the tuning, but the accuracy required is very high, with diminishing returns.

There's no denying that this size stretch results in a beautiful tuning. But there's a massive disconnect between the theory (which is actually very simple, it just suffers from a lot of obfuscation and bad communication) and the practice, and unfortunately that gap has been filled with alfredo's own tuning philosophy. (I'm not saying your tuning technique is bad, alfredo, it's just separate from the model you have presented, yet you treat it as the same. Slow-pull technique and pin 'charging' is nothing to do with CHAS)

There's also space within his maths for other 'delta' values, amounting to different stretch patterns. I find it an adequate model for a theoretical 'good' tuning on a theoretical piano. I believe if it was programmed into a dedicated ETD then it would produce good results similar to StopperStimmung.

Not so. Are intervals remain the same size everywhere in chas as chas doesn't take inharmonicity into account at all, hence it has no relevance to piano tuning.

Kees

Hey Phil, how do you see this?

It's not in the original paper, Tunewerk, but it came up in the discussions, so it'll be buried somewhere in the many threads. The derivation would be tedious but you can see how it might be done.

Inharmonicity is not taken into account in the equation, Kees, but he compares his values to the railsback curve, which is an idealised inharmonicity model of a piano, and it compares favourably.

As I said, an idealised model for an idealised piano.

Thanks for the reply, Phil.

No, I don't see how this could be done. Reversal of 5ths and 4ths was an inharmonicity artifact first discovered by Fairchild. No math will predict or model this, unless you are talking about finite element analysis of soundboard loading and scales.

CHAS too easily becomes a Shopsmith talisman for answering everything piano. I think this is a problem that leads to its discredit.

He just states that it compares favourably, without ever showing the CHAS and Railsback curves together. The CHAS "curve" which is supposed to be like the Railsback curve is actually just a straight line. It does not "compare favourably" at all.

Kees

I've never understood how 4ths and 5ths "reverse". When and where on the keyboard does this supposedly occur? Aren't all 5ths supposed to be narrow and all 4ths wide, no matter the register?

Well I just took his word for it really, so I'm happy to be corrected.

erichlof, it wasn't that the 5ths become wide, it was that the fifths become less narrow, and then more narrow. So the direction of the change of narrowness reverses.

Good question, Erichlof. This is something I'd really have to pull out the data for, which I don't have around at the moment.

To the best of my memory, increased soundboard loading causes negative inharmonicity on 3rd partial of most pianos, around the 5th-6th octave. This causes the 5th to be pure with less stretch and, at the same time, the 4th to be pure with more stretch (neg. iH acting on both sides of these complimentary intervals).

Very rarely is there a crossover. It has been documented and is possible with extreme negative iH, but it is rare.

The real world outcome of this effect is you'll notice it is easier to get both 4ths and 5ths pure as you rise out of the temperament region.

This is an excellent point to post here, because tuning models never represent variable partial fields on a real piano. When partial fields fluctuate, the rules of tuning fluctuate.

Phil - glad to hear, and to know that all together we can clear up misinformation!

Ahh... thank you Phil and Tunewerk for the explanations. I think I understand a little better now. I guess it's kind of like in physics when you can have negative acceleration. This concept always tripped me up in High School and here I am many years later encountering it again with a completely different system!

Thanks!
-Erich

Many intervals exhibit anomalous behaviour. All aural tuners who use all the test intervals in the whole piano must have noticed them, particularly how single octave size and double octave size change places on several notes in and around the top octave, even in the best pianos..
This is maybe the most readily apparent of them, at least it's the first one I ever noticed as an ardent student of all this. It's only about 30 years ago that I started to choose the single octave to tune to instead of the double octave when the alternatives were too noisy in the smaller intervals. That was the time I started working in more recording studios and spending more time listening to playbacks with other musicians than tuning. (1 hour tuning/3hours listening).

Bass strings exhibit even more random exchanges but that's to be expected even in the largest pianos. Far too random to try to marshal them into some sort of order.

ETD's never pick up on them or pick up on the wrong ones.

A wizened old tuner once told me, don't listen too hard, you'll go crazy. Maybe that's what's happnin'.

Hi,

Posted in the "Sample" thread:



rxd, when you mention "..the emotional content carried over from other threads..", do you mean this thread? Or is it the "How long should it take?", where you wrote:



What I am saying, rxd, is that your insinuations do not help, and in the Sample thread I was not concerned about me, but Isaac.

Sure, I cannot say I am happy to read that I would be a charlatan, or an amateur, or one that would try to take you hostage, or... crazy, as you last wrote in this thread.

Let me suggest: take it easy, be respectful and filter your thoughts and fantasies three times before you post.

About theoretical and practical/technical contents... later on.
.

Sorry, everyone, I appear to have picked up another self obsessed stalker in the above post who, not content with insulting us all and being censured for it, has chosen to mix up the content of two different threads for their own ends.

I apologise to you all for any inconvenience or confusion this has caused.

IMO, there is little to be sorry about, when we try to be clearer.

You confirm your attitude again, rxd. BTW, do you have a name and surname?

Hi pinkfloydhomer,

Unfortunately I do not know what the user can do with TL, and I am not familiar with recent ETD's; I guess Robert Scott may say, perhaps it is worth a PM?

As for the Chas maths, which is the point you do not get?

Regards, a.c.
.

No he does not have a real name. He is a robot from a Boy Scout project that went horribly wrong. rxd is just a model number.

Oh no, he found it..

This thread, even though already resolved, is about to become extremely confusing. And long.



This is great advice that you should follow yourself, Alfredo.



It always is later on, even if unsolicited. And when you do explain, you never do really explain.

Yes, I think it is clear to everyone that CHAS is more about your own personal show than presenting something of worth.

Xd is the original model designation but it all went horribly wrong.
Started to exhibit human traits and developed attitude problems so the R prefix stands for "rebuilt". Now the attitudes are just right.

Some in the piano profession in a few parts of the world know exactly who I am. Some even know who I used to be, still fewer know what I used to be.

Nobody knows why.

And NOBODY, oops, nobody knows what you will become! (Or are you becoming?... naaah)

I am becoming very becoming.

Thanks for a good belly laugh, Jeff

Oh, the original Xd couldn't laugh at itself.