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rolex67 Offline OP
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hi every one,
I m new on this forum, and a beginner on piano.
Proud owner of an acoustic Kawai NS10 , I 'have decided to buy an electric one for an apartment where I live part time.
The forum was very helpful to guide my choice.
I had the opportunity to test the Kawai ca 67, Roland hp 603 and a Yamaha ( don t remember 545 or 575 ) .
The Kawai won, just due to the key action, sound, which from my point of view were better.
( I prefer the roland' s cabinet, thought )

First conclusion:
When proceeding for a test, always check the settings of the piano prior to give an opinion!!
( the key action of the Roland at the beginning was set " heavy" , the one of the Kawai " normal " . Of course, the first one felt very weak before reset) .

Second : Noooooooo ! never, Jamais ( I m French..) an electronic piano will compete with a REAL one!!!
My NS 10, which is not a " grand " but 48 or 49 ( 123 cm ) is beyond , in all domains !! Key action, resonance of the cabinet, harmonics, feeling to be with a partner )
Perhaps if we talk about " bass" ok, the 67 is impressive, but... Realistic?.... Don t have so much experience to conclude on that point.


Now, my issue:

While playing ( acoustic EX grand, which I prefer, didn't do the test on the other acoustic ones) let's say the middle " DO " or C and at the same time the "mI" or E at the next octave ( perhaps even the following middle E don t have my piano to check right now), there is a kind of totally unrealistic vibrato ( like the sound of an electronic piano) that comes following the
Note.
My virtual technician is set on temperament "Equal" .
If I change to " mean tone " now the sound is correct , for the chord C and E But I could eventually find that strange vibrato with a particular different chord. Apparently, the pure major or minor seems not to affect any chord, but I do't want to set "major "or "minor " each time I have to play major or minor.

Could the specialist give me more info on the different temperament settings to be applied, the virtual technician nor the paper booklet are very clear on that.

Furthermore, for the CA67 owners, do you experience that kind of vibrato on this specific chord ?
Thank you and best regards to all

Last edited by rolex67; 03/06/16 03:32 PM.
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What you hear are the beats of intervals in equal temperament. This is perfectly OK, and in fact such beats are unavoidable in tuning a piano. Equal temperament distributes the beats evenly over the octave, the older temperaments (such as mean tone or Werckmeister) distribute them unevenly so some intervals of the scale sound purer than others (thirds and sixths are OK in the major scale of the base key, whereas fourths are a little too large and fifths a little too narrow). Probably you hear this on your digital piano more than on the acoustic piano because you are used to how the acoustic sounds, and digital pianos are always a bit more static in their tone, which implies that you hear beats between notes even more clearly. Usually you can hear these beats in your acoustic piano in a similar way just after it has been freshly tuned.

Congratulations by the way that you are aware of and can hear these unavoidable beats of intervals in a piano temperament. Many people never pay attention. There are tables on the web telling you how many beats per second you should hear in an equal temperament third, fourth, etc.



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If you want to tune the piano perfectly, you will have to tune the octava with a ratio 2/1, fifths : 3/2 and thirds: 5/4. Try and calculate the notes frecencies from a A440Hz, you will quickly find that this doesn't match. Then there is multiple way to tune the piano. Equal temperament tunes fifth with ratio of 1.4983 instead of 1.5. Then after the whole circle of fifths, you can go back to the same note frequency. Because of the differnece between 1.5 and 1.4983, fifths have some beats. With thirds, that is even worse, the ratio is 1,2599 instead of 1,25.

This is why the Meantone has bean created : the fifths are altered in order to make thirds purer. The drawback is that if you try and tune all the notes trough the circle of fifth, you won't go back to the original frecency : One of the fifth will not be tuned correctly and sound badly.


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Sounds like you're talking about some exaggerated programmed harmonics.


Started playing in mid-June 2007. Self-taught... for now. :p
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rolex67 Offline OP
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Thank you so much for your very accurate answers guys !

You have exactly catch the " problem " .

Well, honestly, Laurent, I m not so " pro " to change all the features as you suggest ;-)
( prefer to be concentrate on what is doing my left hand while the other tries to play !! )

No, I really don't hear that kind of vibrato ( like a " ouin ouin ouin " electro like ) with my acoustic. The 2 notes are perfectly mixed . ( but I will try again to be more focused on it )

And apparently, the " pure major " or " pure minor" seem not to feature that kind of issue, whatever the notes played together.
I say " seem " because I didn't try all the combinations yet.

Last edited by rolex67; 03/06/16 08:07 PM.
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These beats emerge most when the two keys are perfectly tuned... in an AP, these beats will be most prominent immediately after the tuner is done with their job.

A DP is always perfectly tuned, so you will hear the beats... and chords that are supposed to sing will always sing for you. (Something I love about my DPs... also, I used to tune my own pianos.)

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rolex67 Offline OP
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I would never have imagined an acousic piano could Sound like that, so unatural....

We always learn, thanks to the forum !
;-)

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For a fun experiment, on either a well-tuned acoustic or on a DP, play a major third and listen for the beats. After you hear them, play the next major third up a half step... and then another... and then another... on a well-tempered instrument, the beats will go faster and faster as you go up in pitch, and will become steadily slower as you come down in pitch.

If middle C to E should have somewhere around 10 beats per second, then C to E on the next octave up should be more like 20. It's an excellent test of whether you've put the temper in properly. If there is a third where the beats are faster than the next third up, then some note is out of tune.

The slowest beats will happen when playing a fifth (C and G), but they will also become faster as you move up the keyboard. Middle C to G will beat just under once per second. (You're unlikely to notice it unless you know, in advance, that it will be so slow! Wah, wah, wah, wah...) It may help you to hear the beats if you know that when you play C4 and G4, you will hear the beating at the pitch of G5 (the next octave up.)

Same is true for playing the third of C4 E4... the beating will be heard an octave or two above the two notes being played.

Octaves, themselves, are usually tuned very slightly "open," or "stretched," to mitigate inharmonicity, and some people can hear the beat there (especially on uprights, which have more inharmonicity and so need more stretching)... and if the piano has open octaves and you play C4 E5 (Octave plus a third), you'll hear a faster beat than C4 E4.

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rolex67,

The CA 67 has the ability to tune notes individually (see page 98 of the manual), so you could try small increments/decrements on one of the affected notes rather than changing temperament.

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I've just learnt a lot too :-)

One big difference I noticed from going AP to DP, is that the notes are much purer. I imagine this is because the 3 strings (or 2 as you go lower down) aren't quite in tune with each other. So I would actually hear beating on my old AP just playing single notes on their own. With a DP i've never heard that happen. Maybe a AP which is even very slightly out of tune in this way, masks you being able to hear the beats between intervals clearly, and why the OP hadn't noticed them on an acoustic before. (And why another poster says you can best hear them on an AP when its just been tuned)

One question posed on here a while ago, that I don't think someone answered. The notes are all sampled from a perfectly tuned Grand piano, however, was that grand Piano tuned normally or stretched. If it was the latter, then does that mean the notes are digitally processed to remove the stretch if you choose normal, and plays them as originally sampled when you choose stretch. Or worse is normal actually stretched, and stretch is double stretched. If that makes sense.

I guess someone who understands how to listen for those beat frequencies would be able to answer that, can't imagine Kawai would make that mistake.



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tabber, the Stretch setting has 3 options: Off, Normal and Wide.
I once tested them all with a tuner app on my phone. There surely is a difference. If I remember correctly, with the stretching turned off, each note was perfectly in tune.

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I thought the normal tuning is a stretch tuning : the tuner tunes octavas such that there are no beats. Because of the inharmonicity, the frequency ratio is slightly higher than 2, then the tuning is "stretched".

Edit: using some higher ratio could detune octavas but make fifth purer, this could explain the "wide stretched" tuning.

Last edited by Frédéric L; 03/08/16 08:42 AM.

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Kawai's default tuning is stretched, and so I assume are the samples

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Originally Posted by tabber
The notes are all sampled from a perfectly tuned Grand piano, however, was that grand Piano tuned normally or stretched. If it was the latter, then does that mean the notes are digitally processed to remove the stretch if you choose normal, and plays them as originally sampled when you choose stretch. Or worse is normal actually stretched, and stretch is double stretched.


A perfectly tuned grand is necessarily stretched. An octave doesn't sound "best" when the root note is tuned to a perfect octave, because the harmonics don't fall into a perfect octave, and the harmonics will beat and make the octave harsh.

A very slight stretch mellows the harmonics nicely. On most pianos, you can barely hear the beats in an octave, and only if you're skilled at hearing them. On a grand, which has less inharmonicity, the stretch can be so slight that you can't hear the beats in single octave... but if you play a double octave, you'll be able to find the beats.

This happens because the harmonics are a function of the string length AND the string weight AND the string tension. If the next octave up had the exact same string weight and exact same string tension but the length were exactly half, then you'd have a perfect octave, perhaps with no inharmonicity. But in actuality, we can't cut the length in half for each octave, or else, over the course of the seven-plus octaves of the keyboard, we'd either have a bass string impossibly long, or a treble string impossibly short. So compromises are made, and different weight strings are made for different ranges of the piano... and different string tensions are used as necessary to get the notes in order. Also, if the bass strings were not heavier, they would not produce enough volume of sound, so those are extra-heavy; they're wound. Again, this changes the nature of their harmonics.

The end result is that we can tune the correct root notes, but the harmonics are slightly off... and to keep them from being harsh, the octaves are stretched slightly. The amount of inharmonicity in a piano dictates how much stretch is needed, and an expert tuner adjusts to each piano. Sometimes, a particular pair of notes will have a lot of inharmonicity - perhaps because of a big difference in string weights or tensions - and an expert tuner will do their best to tweak one or both notes every so slightly out of "proper" tune to make them sound "better" in the given piano.

As far as the sampling... the Kawai sample should be, as you say, of a perfectly tuned piano, but I'm not sure which of three approaches they took...

a) tune a perfect piano, stretched, and sample that as a "stretched" setting; then digitally stretch that to make the "wide" setting and digitally contract it to make an "off" setting

b) tune perfect intervals, unstretched, sample that as "off," and then stretch a little for "stretched" and a lot for "wide."

c) tune the piano three different ways, sampling each!

I doubt they did option c. I suspect they'd go with a, since most people will play in the normal "stretched" mode, and they expect it to sound like a normal "stretched" fine piano.

Funny side note: you CAN, if you want, use piano modeling software to design an absurd piano with ludicrously long strings and, in so doing, carefully engineer a piano with very, very little inharmonicity... but when you listen to it, people will say, "it doesn't sound like a piano!" It will sound too aritificial! You see, we've accepted the particular sounds and harmonics and inharmonicities of a piano as being what a piano sounds like!

Last edited by Mental Nomad; 03/08/16 03:43 PM.
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Originally Posted by Mental Nomad
If the next octave up had the exact same string weight and exact same string tension but the length were exactly half, then you'd have a perfect octave, perhaps with no inharmonicity. But in actuality, we can't cut the length in half for each octave, or else, over the course of the seven-plus octaves of the keyboard, we'd either have a bass string impossibly long, or a treble string impossibly short.


It is not the reason of the inharmonicity. The inharmonicity is due to the stiffness of the string which causes the ratio of frequencies of the first 2 partials a little higher than 2. Then octavas needs to be stretched according to such a ratio if we want to get rid of beats.

The inharmonicity depends of the length (higher when the string is shorter), this is why concert grands have less inharmonicity than little uprights and the inharmonicity is higher in treble than in medium. The inharmonicity is also higher in the bass, but I suppose (not sure), that it is because we tune the bass strings not with the 1st and 2nd partials, but with the 2nd and the 4st partials which are more audible.

With a null stiffness string, the partial frequencies are

[Linked Image]

The frequencies are proportional with the number of the partial (n) : no inharmonicity.

In reality, the formula of the partial frequencies is :

[Linked Image]

where B depends of the stiffness and the length. We see that when the number of the partial (n) is high, the Bn² term is higher, so 2:1 octavas are less stretched than 4:2 octavas.

The diagram of the resulting stretching is like :

[Linked Image]

Last edited by Frédéric L; 03/08/16 06:04 PM.

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Merci beaucoup!

I'd often heard that the longer strings reduce inharmonicity, but nobody exposed me to those formulae for the harmonics or your exact arguments... so now I have to find time to dive down that rabbithole to see what I learn next...

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The formulaes are from the French wikipedia page of inharmonicity (the english one doesn't go so deep).

But the following article could be interesting : http://www.21harmony.com/blog/illuminating-inharmonicity (you will have the B values which varies with the square of the length... Which explains why the length is so important).

Last edited by Frédéric L; 03/08/16 06:07 PM.

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@Mental Nomad: Thanks for doing a wonderful job in explaining some basics of (equal) temperament here! thumb


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I now understand that inharmonicity is inherent in a single piano string, I thank you for pointing me in this direction.

I'm still working through the formulas and implications, but I'll note that my initial supposition is not entirely off the mark... mass is relevant to my thoughts.

The formula for the partial frequencies includes the factor of the B variable, the inharmonicity coefficient, which is a function of the cross-sectional area of the string (and Young's modulus and radius of gyration)... so a lighter-gauge string used on the top half of an octave will still be made of the same steel, but will have a smaller cross-sectional area, changing the inharmonicity coefficient, and changing the progression of the harmonics.

If, on the other hand, the top string of the octave were the same weight string, at the same tension, but at half the lenght, then the two notes would have the same inharmonicity curve - instead of the usual situation, where the inharmonicity curve of the lower octave is less steep than the inharmonicity curve of the upper octave. I do not, however, see that this is ameliorated in any way by stretch-tuning... so, as you said, stretch-tuning is solving the basic problem of tuning the octave above to the harmonic of the string below, when the harmonic of the string below is actually sharp of the true octave.

Thanks, again!

So, when considering the sound of the interaction of the harmonics when playing an octave, I believe differences in tension and weight can worsen the mismatch between the tones beyond the effect of the inherent inharmonicity of a single string.


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Thank you so much to share your deep knowledge with us.
I couldn't have imagined that at at the beginning of the post
;-)

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