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Huh!!!

Alfredo, you did not refrain on those champaign bottles, please wait a little Christmas is only in a few days !!

That said, Cheers !

The champaign is still there, promise, it must have been that recent cake...fine patisserie?

Anyway...Cheers!

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Even if there is no wind, an arrow draws a curved trajectory.

Even when I tune a piano very close to my favorite sound whole, say 99%, I never tune Chas on mid-strings, I’ll go for a preparatory tuning, as described above. I always consider the adjustments that will take place, possibly the infinitesimal ones too, and I do everything I can for these adjustments to take place.

If that piano was very very close to my favorite order, say 99.999%, on mid-strings it would (more or less) keep the preparatory tuning I talk about, then it may be a question of unisons. In any case, only in peculiar circumstances do I accept to “repair” my tuning, normally I restart from the beginning.

A piano may look like an ordinary piece of furniture, but in fact, due to the tons of tension it holds, we know that a piano is more an instrument that is constantly “in progress”.

My favorite sound beating-whole can only be the result of a dynamic factor, the piano structure’s adjustments. I determine the premises, and act, so that Chas may result from these premises through the piano’s settling down. Only then can I think of it as a temporary stable condition.

My tuning is causing these factors, determining the premises and driving the adjustments, expecting and wanting them in one, acting and waiting for them to release eventually my favorite sound whole.

a.c.

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Pianos, I only talk to them, with a new one I ask gently if I'll have trouble with him and generally he say no and stay quiet (I've seen that in a movie where the guy comes to jail, the green line, it works).

Sometime only if I put my case near the piano it sound better !

...and if HE'S a SHE does she slap you in the face too?

Nope, once one step on my toe, but as I wear security shoes I smiled and took my hammer, the piano was only badly in need of tuning (that makes them nervous)

Is the grand piano feminine, in English ? (never thought of that).
Here the grand is pretty much masculine, as the vertical.
Special mention to the factory joke about the 3 lid props BTW, (we are in the working class, for most, don't forget even if mention of those terms disappear from common language some years ago)

Alfredo:

I understand that measurements of frequencies of single strings have been compared to a tuned unison with all three strings sounding together. A drop in pitch has been observed. But since a higher partial is measured, I am not sure if it is the fundamental frequency that changes or if it is the effective iH of the strings that change and therefore the frequency of the partials and the beat rate of the tuning intervals. This effect is an argument for tuning unisons as you go and for adding a bit of extra stretch when tuning an octave so that when the other strings of the unison are tuned the pitch will settle where it belongs.

Perhaps this is what you are experiencing rather than the piano’s tension equalizing.

In regards to tension equalization, something I have noticed when doing a preparatory pitch raise is that too much of an overshoot does not seem to matter as much as even a little bit of undershoot.

So how do we setup that CHas preparatory tuning ?

And the real thing ?

These contents were posted on Chas Topic on 5/23/09 (somehow corrected (thanks to Jeff Deutschle)):

I decided to go further my tuning sequence mainly for two reasons: firstly, because hundreds of interesting pages have and are been written about the most original and reasonable sequencies, none of them leading to a solid, reliable theory that could deal with inharmonicity, so leaving tuners in a state of uncertainty. A sequence will always be debatable, a mathematical evidence will not. Secondly, because I do not think the sequence I use is any special, nor time saving or more confortable for listening to or comparing beats. In my opinion, any sequence can eventually work, as long as you clearly know what you can be aiming at and why, and how and where you’ll get it.

The only novelty may regard the overall approach and the interrelation of SBI, i.e. 8ves, 4ths and 5ths beat curves, the research's results that opened to Chas. Chromatic 4ths are not only similar, going up the scale they get tiny little wider. Chromatic 5ths are not only similar, from low notes they first stretch down and get tiny little narrower, in between G3 and G4 they invert and stretch up toward there pure ratio (tuning centre strings), going tiny less and less narrow.

An italian collegue pointed out that SBI are much harder to evaluate than RBI. True, I would also agree in saying that RBI give you the general idea of what you are doing in the shortest lapse of time. Nevertheless in my opinion, anyone truly wanting to achieve excellence in aural tuning, would have to master the maximum control of any interval’s beat. A matter of wrist, both in the figurative and the anathomic sense, and a matter of rhythmics. In my case, SBI control took me to the 7th decimal point (section 4.5).

So what happened was, first I empirically calculated the univocal SBI and RBI chromatic proportional order, there I could notice an astonishing euphonic set that would prove how inharmonicity can be made tractable. Then I simply elaborated its essence, to finally construct an updated and comprehensive ET model, reliable in both theoretical and practical terms. Since I know all this comes from practice, simplicity and utmost exactitude, I’m disclosing Chas model with a serene soul.

In tuning, as I have learned, each sound is only temporarly tuned, since every single added sound may indicate the need to correct previously tuned notes. At the end, it is the Chas form that releases me from all doubts and only then I am absolutely certain to have done my best. Anyway, here are a few suggestions introducing and commenting the sequence.

A - do not take this tuning sequence as a must -
B - octaves, 4ths and 5ths shape the skelethon of the entire set -
C - start tuning only middle string, mute from C6 down to strings crossing, dampers up -
D - tuning single strings and unisons, get always the same moderate sound intensity -
E - octaves have a low beat-threshold and a high beat-threshold, this helps me when tuning octaves in middle register -
F - possibly, stabilize middle string frequencies by playing a Forte sound -
G – do not tire your ears, by playing louder you will not hear better nor more -

sharp or flat is referred to the note we are ment to tune. The already-tuned note is in bracket -

Step 1 – A4 – from 440.0 Hz to 442.0 Hz (concert or studio) - from 442.0 to 443.0 (for flat pianos)
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Step 2 – (A4)-A3 - tiny little flat, just on the beating threshold
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Step 3 – (A3)-D4-(A4) - sharp, close to 1 beat/sec. – D4-(A4) faintly beating
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Step 4 – (A3)-E4 - flat
check overlaping 5ths and adjacent 4ths to set up Chas ET EB octave:
A3-E4 about 1,5 beat/3s - sensibly faster than D4-A4
E4-A4 about 2 beats/1s - sensibly faster than A3-D4
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Step 5 – (E4)-B3 – flat - tiny little faster beat than A3-D4, sensibly slower beat than E4-A4
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Step 6 – (B3)-F#4 - flat - little slower beat than A3-E4 since 5ths have already inverted
faster beat than D4-A4 evaluate M6 A3-F#4
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Step 7 – (F#4)-C#4 – flat - faster beat than E4-B3, sensibly slower beat than E4-A4
evaluate two M3’s progression + one M6
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Step 8 – (C#4)-G#4 – flat - slower beat than B3-F#4, tiny little faster than D4-A4
evaluate three M3’s progression + two M6’s progression
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Step 9 – (G#4)-D#4 – flat - tiny little slower beat than E4-(A4), faster than F#4-C#4
evaluate four M3’s progression
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Step 10 – (D#4)-A#3 – flat - tiny little faster beat than A3-D4, tiny little slower than E4-B3
evaluate five M3’s progression
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Step 11 – (A#3)-F4 – flat - tiny little slower beat than A3-E4,
tiny little faster beat than B3-F#4
evaluate seven M3’s progression
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So far, apart from A3-D4, we have stretched "flat" - now we’ll stretch "sharp"
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Step 12 – (D4)-G4 – sharp - tiny little slower beat than G#4-D#4, faster beat than F#4-C#4
evaluate eight M3’s progression + three M6’s progression
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Step 13 – (G4)-C4 - sharp - tiny little slower beat than B3-F#4,
tiny little faster beat than C#4-G#4 evaluate nine M3’s progression + four M6’s progression
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Beats curves are meant to be tuned temporarly. While you are tuning, bear all (few) doubts in mind.
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Step 14 – (A#3)-A#4 – sharp - increase octaves beat’s speed very slowly – 5ths go very, very slowly towards pure – F4-A#4 tiny little faster beat than D4-A4, as for the next 4ths
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From the octave beat threshold, first signs of beating come to us in a shorter and shorter lapse of time, this helps to S-shape octaves stretch
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Step 15 – (B3)-B4 - sharp - increase octaves beats rate very, very slowly - 5ths towards pure
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Step 16 – (C4)-C5 - sharp - increase octaves beats rate very slowly - 5ths towards pure
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Step 17 – (C#4)-C#5 - sharp - increase octaves beats rate very slowly – 5ths start transiting pure - evaluate one M10
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Step 18 – (D4)-D5 - sharp - increase octaves beats rate very slowly – 5ths are transiting pure - evaluate M10’s progression
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Step 19 – (D#4)-D#5 - sharp - increase octaves beats speed very slowly – 5ths are transiting pure - evaluate M10’s progression
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Step 20 – (E4)-E5 - sharp - increase octaves beats speed very slowly –
5ths have transited pure, evaluate M10’s progression –
chromatic M12s, like A3-E5 must be constant and temporarly tuned pure (on normally out of tune pianos) -
Step 21 – (F4)-F5 – sharp
Step 22 – (F#4)-F#5 – sharp
Step 23 – (G4)-G5 – sharp
Step 24 – (G#4)-G#5 – sharp
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Step 25 – A4-A5 – double octaves like A3-A5 must be constant and temporarly beat with a rate of about 3b/2s, or 3/2 bps
increase octaves beats speed very slowly –
5ths are very slowly widening, evaluate M10’s progression –
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Step 26 – (A#4)-A#5 – sharp - check 10ths, pure 12ths, wide 15ths, let 5ths go slowly wider
Step 27 – (B4)-B5 – sharp - check 10ths, pure 12ths, wide 15ths, let 5ths go slowly wider
Step 28 – (C5)-C6 – sharp - check 10ths, pure 12ths, wide 15ths, let 5ths go slowly wider
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Go back down for G#3 to lower notes using SBI, RBI and EB, never lose control of beats progressions for all intervals. 5ths will get slower, so will 4ths. Improve A#4 with F#3 and D#3. Unison all these registers from your left hand moving right, except last muted string on C6, then go up to higher notes. Chas delta-wide 15ths and delta-narrow 12ths beat’s rate is about 1b/3s or 1/3 bps.

Tune as you know, middle string first, then unison previous note’s right string (C6), next left (C#6), tune next middle (D6), unison previous right (C#6), next left, tune next middle and so on, checking also M17ths progression. While tuning, do not stop evaluating strings and sound-board rigidity/elasticity, so you’ll be able to conveniently tune centre strings.

a.c.

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Thanks so much ALfredo,

What a huge job to describe and theorize on that ! I said esoteric not because of the method but the way you present it, but I suppose I can get used to your way to express things.

I believe I'll have a better picture of what you are doing while doing it myself.

I'll ask my Brother, which is violonist, what he think about large fifths (and small ones ! )
He plays very just, and with many pianists (or even an organist once)

Hopefully he also have some humour ! Ill let you know what he say.

http://www.amazon.com/Bach-parodies-transcriptions-Johann-Sebastian/dp/B00166GMGS

Thank you and please post other recordings if possible (with voiced piano) Best regards.

May I respectfully suggest that you are not familiar with modern temperament directions, which contain much specific detail not included in your directions.

Many sets of directions have been published. I myself have published a set of directions for some decades; my directions are known to have been helpful to many learning piano tuning.

My directions are presently somewhat out-of-date, but remain useful.

Pending a needed update, the latest version of my directions may be seen at:

files.me.com/kentswafford/0p8fok

I hope my directions will provide at least one example of a modern set of temperament directions.

Thanks Kent, I very much appreciate the chance you offer me. That address do not seem to work though, what can I do?

a.c.

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Hello Alfredo !

I could not be there for some days, but I'll give you news soon !


The kind of thing that makes the explanations may be not precise enough is for instance "first octave barely beating"

To know how much I may know what kind of "proof" to be used and how many beats differences. for instance, 1 beat in 5 seconds for M3d/10th (or4:2 if expressed differntly)

That said, on a Fazioli concert grand for instance, (from memory ) you cant have a noticeable difference between 6:3 and 4:2 , iH is simply too low there so the trade of is not the way to have the best temperament octave.

I approach that this way :
I tune 2 doublets unisons that "speaks"
Octave may speak the same, I only may be careful with the tendency to have too little stretched octaves that way.

Your method of pulling one string higher than the final wanted pitch is also a "guess and hope method" , or you count of the energy blend coming from the instrument to "lock" the octave (which is certainly possible but difficult to prove, we are now in "artistic tuning" and not following a model.

I have no particular problems with rolling octaves, as long as the roll is not out of phase , or perceived, but depending of the output I'll lessen that ( if FBI begin to raise speed too much).

Seem to me that on low iH instruments, as harpsichords, tuning models that allow beating octaves leave no place for the inherent acoustic of the instrument, it scream, it catch the ear, eventually musically but not in its most natural way. Some like that impression of constant suspense and it clean minor harmony, but I've seen very negatives reactions from musicians with some comments as " Bontempi tone"
(not talking of your particular method here, that is more in the Cordier reaction)

It could be cultural, why not, anyway a taste affair.

Till next time, and have a nice end of 2009 !

All of the following are correct paths to the file:

files.me.com/kentswafford/0p8fok

http://files.me.com/kentswafford/0p8fok

http://www.kentswafford.com/EWW/ewwt.pdf

Thanks Kamin, I'll reply asap, it will be 2010!!

Thanks Kent, they are correct paths indeed, I'll study your paper and reply to you too. To All

-(----------------------- 20 * HAPPY NEW YEAR *10
.

Happy new also, , sorry it is just to have my name on the whole front page !!!

Best regards '(no reply needed !!!)

Chas Preparatory Tuning is referred to centre-strings-tuning and it comes out to be mindful tuning:

Chas ET octaves are progressive.

Chas 4ths are progressive. The 4ths beat rate progression invert on C3.
Chas 5ths are progressive. The 5ths beat rate progression invert on E4 (tuning centre strings).

Octaves beat-rise-time – Propensity to beat

------------------------TIME
I-----I------I--------I----------I--------I------I-----I---I
A0...A1.....A2........A3...........A4........A5.......A6...A7..C8


In Chas preparatory tuning, octaves are wide and progressive. In order to distribute the octaves progression I evaluate the “propensity to beat”, in other words I calculate the TIME needed for the beat to rise. Midrange octaves do not beat, though octaves swell towards beating.

So I set the A3-A4 octave on the edge (or soil) of the beat (on centre string) and, little by little, this stretch is to be chromaticaly widened. Then, going towards high and low notes, the octave’s beat gets more and more defined, i.e. it rises in a shorter and shorter time, as shown above. Only for the highest octaves I can count progressive beating around 1/bps or little more.

The octave’s beat rate is always relative to all the other intervals beat rate, as in a system of levers, so I draw the form with SBI and RBI. To evaluate the stretch-curve in practice, I use 12ths as a reference (on centre strings). In fact A3-E5 - on centre string – has to be apparently beatless (3:1 ratio). So will be the next chromatic 12ths, when tuning centre strings upwards.

This will produce constant wide 15ths, beating at about 3/2 bps, on centre string. Just unisoning left and right strings will correct these intervals and gain the Chas ET form in stable terms, with the form’s constant and opposite equal beating 12ths and 15ths all along the keyboard.

a.c.

Hello ALfredo,

You are welcome to Paris, of course, thanks for proposal.

Thank you for your clearing , it begin to comes thru my slow mind !.

What I am not exactly understanding is why there is any interest in having the piano tuned as if it was a single chord, it probably misses some movement along the keyboard harmonically then, as to me the stretch evolving gave that , and pianist most probably play with it while improvising.

I see tuning as a reproduction more or less precise because of the piano iH, of a temperament, it can be based on an octave or include yet corrections in prevision of the highest and lowest regions, it can be more tonal or more based on the inharmonic spectra of the notes (inharmonicity is low in the medium range but yet perceived, hopefully, if not the tone is not as crisp as a piano tone.)

I have yet tried yesterday with your inversion in mind, and finishing with the 12th 15th evening so 4th 5th temperament with that inversion gives strange results, no harshness but one have to get use to that.

I had not time to record the piano, it will be done later (may be , aint my instrument)

I may say that my first impression is that 12th 15th evening will correct any kind of temperament and make the piano then playeable by reconciliation of the medium tweaks and the treble and bass (hopefully on pianos we have often much room for cheats !)

second impression is that 12th 15th is a very valuable and quiet method to raise in the treble
Also very comfortable to find pitches in the low basses when the wires are dumb (old)

I tuned that 122M Grotrian (while "listening" to the concerto "the Emporor' so to be sure to not tune as usually) and it had a nice resonance in the end (despite a slow third in the middle of temperament).

But I did not came near any of the slow beats of the tenths and 17th of the begin of your recording, the medium octaves are not 2:1 to my ears they need a little more stretch so the beginning of the treble sticks out more easely.

May be compromizing the 12th and the double octave is a good way to determine the size of the octave while going up and down but I am unsure it is the same for the temperament or the low medium range.

You say that ih is poor in the medium. do you have the numbers ? I just checked and it looks like even on a concert grand the ih of the A3 is around the iH of the lowest plain wires, anyway my experience have been that iH change your first octave as any other note on the piano, even on a concert grand you cant reconcilite all intervals, there is a differnece between 6:3 and 4:2, and the speed of intervals vary depending of the piano.

If your method have to be matheamtically valid you cant say "it is low so does not matter" because it is a variable and the primarly goal of tuning is to make an interesting use of the iH of the piano.

By evidence the piano is driving the beats speed, but I relate to that thoses too slow 10ths I hear in the beginning of the recording.

That said you certainly have find a way to have a nice resonance within the instrument.
I may respectfully ask you : do you play piano ? I know some very talented concert tuner which is unable to play and to check the harmonic behaviour of a piano (hense stick to what he learned and then please most pianists)

I was lucky enough to grow within a musician family so it sort of sharpen my ears (that have been a little beaten by my tuning days but I stay acute I guess!)

When I say that contrast is necessary I mean that it may be too much perceived if a tuning is based on one interval only (while it is highly pleayeable to have progressive RBI, they may progress in speed not to slowly so to pealse the musican's ear)

Your last explanations give me material, so Ill write again after having tried with that method too.

I'll answer on the preparatory tuning, I guess you have some part of mysticism that makes you believe that the piano will "self tune" in some way after you tense the middle string. I believe you may be right in that case but probably only if the piano is yet not far from final pitch.

It would be interesting to do your tuning with the right pedal engaged and see how the pitch evolve.

If not there are % that can be used to ascertain where the final pitch will be (some EDT have good solution to that problem, but based on an unison tuning as we go, so your approach make sense , but I see no maths at that point, for instance how do you deal with piano which is 4 cts low how do you evaluate the necessary raise).

A customer , piano teacher that was math teaching in a precedent life, told me when I showed her the debate on your presentation of CHAS, that once you look for mathematic proof of something you had find by trial, you always find a way for justification.

Being not at a sufficient level of maths to say so I would not comment, but that seem to be what most have say on the forum
while I believe it should be less sterile in the discussion if my colleagues directly try to tune with your recipe, then discuss later.)


Best regards.

Hello Kamin, you kindly write:

...“What I am not exactly understanding is why there is any interest in having the piano tuned as if it was a single chord, it probably misses some movement along the keyboard harmonically then, as to me the stretch evolving gave that , and pianist most probably play with it while improvising.”...

I tune centre strings – the way I was taught – mainly for distributing strings load on the bridge and, while the piano is settling, for correcting (in case) only one string.

...“I see tuning as a reproduction more or less precise because of the piano iH, of a temperament, it can be based on an octave or include yet corrections in prevision of the highest and lowest regions, it can be more tonal or more based on the inharmonic spectra of the notes (inharmonicity is low in the medium range but yet perceived, hopefully, if not the tone is not as crisp as a piano tone.)”...

In my experience, iH can influence my tuning form very very little, much less than usually lamented. In any case, I could draw the qualities of Chas form and get its symmetric properties out, even on very small pianos.

...“I have yet tried yesterday with your inversion in mind, and finishing with the 12th 15th evening so 4th 5th temperament with that inversion gives strange results, no harshness but one have to get use to that.”...

Yes, most probably it will be strange at the beginning.

...“I may say that my first impression is that 12th 15th evening will correct any kind of temperament and make the piano then playeable by reconciliation of the medium tweaks and the treble and bass (hopefully on pianos we have often much room for cheats !)”...

Well, if one uses it to correct any kind of temperament, a part of the smoothness of the overall progressions will be lost, together with a part of the beats synchronism, what effects the overall resonance. In any case, one could still have a precise reference given by Chas Theory's Delta rule for 88 tones ET tuning.

...“second impression is that 12th 15th is a very valuable and quiet method to raise in the treble
Also very comfortable to find pitches in the low basses when the wires are dumb (old)”...

I agree. When I tune, I find very confortable having precise checks and control opportunity. Chas Pre-form's tuning displays the curves for all intervals, so I get plenty of chances to check this Pre-form and to know what I'm doing.

...“I tuned that 122M Grotrian (while "listening" to the concerto "the Emporor' so to be sure to not tune as usually) and it had a nice resonance in the end (despite a slow third in the middle of temperament).”...

Good, I’m glad.

...“But I did not came near any of the slow beats of the tenths and 17th of the begin of your recording, the medium octaves are not 2:1 to my ears they need a little more stretch so the beginning of the treble sticks out more easely.”...

Is not immediate to evaluate how much the piano is going to “take back” and where, in terms of stretch and load. In a way, it remains an unknown variable, but you certainly know about this.

...”May be compromizing the 12th and the double octave is a good way to determine the size of the octave while going up and down but I am unsure it is the same for the temperament or the low medium range.”...

Chas Pre-form favours 3:1 ratio (for 12ths) and 3:2 or even wide 5ths, up the scale on centre strings. Never had problems in mid or mid-low range, I keep progressive octaves, 3rds, 6ths, well related and progressive 4ths and 5ths, and check with, 10ths, 17ths ecc. as usual.

...“You say that ih is poor in the medium. do you have the numbers ? I just checked and it looks like even on a concert grand the ih of the A3 is around the iH of the lowest plain wires, anyway my experience have been that iH change your first octave as any other note on the piano, even on a concert grand you cant reconcilite all intervals, there is a differnece between 6:3 and 4:2, and the speed of intervals vary depending of the piano.”...

In my opinion, setting with 6:3 intervals may expose you to the iH’s effects.

...“If your method have to be matheamtically valid you cant say "it is low so does not matter" because it is a variable and the primarly goal of tuning is to make an interesting use of the iH of the piano.”...

Ohi, I would not like to be extreme, I do not tune with a calculator. Chas Theory is mathematically impecable, Chas Pre-form tuning must consider all variables. Then, in my experience, defining the beats order with basic ratios, may limit iH’s influence.

...“I may respectfully ask you : do you play piano ? I know some very talented concert tuner which is unable to play and to check the harmonic behaviour of a piano (hense stick to what he learned and then please most pianists)
I was lucky enough to grow within a musician family so it sort of sharpen my ears (that have been a little beaten by my tuning days but I stay acute I guess!)”...

I’m not dedicated to piano playing, but I play the piano as a preparer’s routine. As for the rest, playing is not a passion for me, it is more of a chronic disease and a family inclination.

...“When I say that contrast is necessary I mean that it may be too much perceived if a tuning is based on one interval only”...

Chas Pre-form is drawn with all intervals, with slow and fast beats checks and proportions.

...“I'll answer on the preparatory tuning, I guess you have some part of mysticism that makes you believe that the piano will "self tune" in some way after you tense the middle string. I believe you may be right in that case but probably only if the piano is yet not far from final pitch.”...

More than faith or personal belief, it is a question of phisics. Not only for pitch-raising but always, when I charge the piano’s structure, change tensions and load the bridges, I must expect some degree of settling. I like evaluating the smallest one.

Say you play bowls, you throw the bowl and let it go towards your target. It is the bowl that gets it. Same if you shoot an arrow, you stretch your bow and let your arrow get your target. Same with tuning, I evaluate and stretch Chas Pre-form and let the piano gain it. For me this is very much realistic and respectful of how things go.

...“It would be interesting to do your tuning with the right pedal engaged and see how the pitch evolve.”...

I do not know this technique and I’m very curious about it.

...“If not there are % that can be used to ascertain where the final pitch will be (some EDT have good solution to that problem, but based on an unison tuning as we go, so your approach make sense , but I see no maths at that point, for instance how do you deal with piano which is 4 cts low how do you evaluate the necessary raise).”...

The lower (in pitch) the piano, the more approximated the tuning, then experience helps but you well know that.

...“A customer , piano teacher that was math teaching in a precedent life, told me when I showed her the debate on your presentation of CHAS, that once you look for mathematic proof of something you had find by trial, you always find a way for justification.”...

Well, I do not have research experience in other fields but, if you can, ask her how she likes the mathematical proofs and justifications adopted for any medical equipment, when she needs it.

...“Being not at a sufficient level of maths to say so I would not comment, but that seem to be what most have say on the forum
while I believe it should be less sterile in the discussion if my colleagues directly try to tune with your recipe, then discuss later.)”...

For what I’ve seen – also in other fields - when it comes to accuracy, exatitude, reliability or else related to self control, product and performance’s quality, many people prefere to talk about artistics, but I like it this way...Vive la diversité!

Best regards,

a.c.
.