On the benefits of thinking "harmonically" about the piano

[danny elfboy]

Just a quick consideration and I'd like your opinions

I think the majority of teachers teach the piano the wrong way
Not only wrong because it makes harder to play to understand technique in its context but also wrong because it create individuals who can play very hard pieces robotically but lack any musicality and skill in improvization.

I think the approach of considering piano just a tool where you play what you decipher is wrong. It's embarassing how so many pianists don't understand the music they play at all but robotically follow the sheet music and if you remove the sheet music they are lost

I think and have experienced myself that when the piano as an instrument and the piece you can play at the piano and the playing of the piano itself is considered withing an "harmony context" then not only music makes more sense, but playing becomes easier
and it easier to make it sound good

What I mean is that usually piano teaching is approached in this way

1) The teacher tells the student that each key produces a note and that for some time is better to focus on the black keys
2) The teacher tells the student that you play the piano with two hands but for some time is better to focus on the right hand
3) The teacher tells the studet that there are two cleffs but that for some time is better to focus on the treble cleff
4) The teacher has the student playing little melodies for the right hand
5) The teacher has the student learning the treble cleff as second nature
6) The reacher tells after a lot of time that it's time to learn the bass cleff and it's like to play the treble cleff but you must think two notes below of the note you see
7) The teacher tells the student it's time to add the left hand
8.) The teacher has the student playing A RIGHT HAND MELODIES to which LEFT HAND NOTES are added
9) The teacher tells the students there are notes that go beyond the cleff lines and you have to add little lines
10) The teacher has the student playing always more complicated pieces that are just a RAMIFICATION of the same concept of having a right hand melody and a left hand added notes

It seems banal but these short instrunction and approach at the piano lay the foundation for a musical disaster.

This approach leads to a sort of "disorientation in the keayboard" which make subconscious to consider the keyboard as the central part and make it hard to incorporate big movements and jumps
This approach leads to very hard sightreading and many year of frustration and hand watching
This approach leads to poor coordination between the two hands and make it impossible to grasp the coordination, it is simply memorized by the muscles repetition after repetition
And worst of all this approach leads to "unawareness of the piano"
It produces people who are sitting at an instrument they don't know, they don't undestand just following mindlessly the instructions seen on a paper
It leads to poor musicality, unability to improve, unability to understand why the music we're playing is in that way and how it should sound

What I mean by "thinking harmonically about the piano" is laying very few basic harmonical and musical foundation that becoming inconscious would make a lot easier to learn technique, feeling orientated in the piano, sightread, improvize, playing musically and understanding why music is like that

As much as laying the simple wrong foundation can cause disasters, laying the right foundations at the very beginning would, I'm sure, bringing huge benefits we cannot even imagine

(if your teacher was so good to teach from the very beginning about the piano harmonically then you're lucky, believe ... this is not the usual approach)

The simple foundations are these:

1) The basics of music are in the voice; voice is the most natural and better example we have
2) There are several pitches in the kind of voice we have and the extention of these pitches creates the "parts"
3) Music (except from single melodies) is comprised of these parts playing notes that are in harmony one with each other because there's a relationship based on the overtones
4) When we have four parts playing a C, E, G, C we have a chord
5) The keyboard is a rapresentation of the voices pitches and the parts in harmony. The lower you're in the keaybord the lower voices/parts you're playing, the higher you're in the keyboard the higher voices/parts you're playing
6) The foundation of a four part piece for voices is the bass
7) It's not about treble cleff or bass cleff (this nonsense should be ignored) it's about starting from the harmonic foundation and going up from there. Cleffs are just a synbolic practical labelling of the parts/voices of the piano we're playing but they don't explain anything at all.
8.) it goes by itself that any kind of sightreading and any kind of first-practice at the piano should always begin with the bass, the foundation of the whole piece
9) it's not about playing right hand and adding the left hand when ready, it's about learning the piece by reconstructing it the way it was composed understanding how each note is actually the one line melody of one voice/part
10) The bass is the foundation of musical playing and good technique not the high voice/right hand melody. Every pianist should first of all become second nature with the bass, with how the notes are the bass are creating the whole nature of the mood, attitude, musicality of the piece, the kind of intensity and force it should played being a bass
11) The orchestra is just a chorus of different pitches voices where the voices are substituted by instrument. Again, every pianist should focus on this specular rapresentative link between the chorus, the orchetra and the piano starting from understand the nature of the bass. This will make what we play so senseful that any kind of technique needed to play the piece will not be "awkard" as in trying to do something that you know you should do because it's written so .. but you really don't understand it, but will come naturally ...

It may seem like an exaggeration but I DO believe that approaching the piano from a "learning right hand melody and add the left hand" point is a disaster and that approaching the piano from a "learning the specular link between the chorus, the piano and the orchestra and focusing on understanding, mastering, making second nature the bass foundation of the song and adding the left hand voices to the already ingrained structures" is a god-send for piano students that are having and hard time

If you think about it, the typical ridicolous and stupid approach to piano learning (especially with young children) makes as sense as building an house starting from the roof, while the harmonic approach does makes sense as buiding an house from the foundation, from the concrete laid basement of the building

When I joined a choir I was given every day different sheet music with the four parts and I have just to study mine (I'm a tenor) But beginning to see music from this point of view, to see the notes in the parts moving and the foundation of the bass I suddenly realized how I had to think the same about my piano playing. When I did not only the piece I'm practicing makes musically sense but a lot of problems I was having just disappeared and I not longer feel so little in front of a big giant piano and of playing at the extreme of the keyboard as stretching. I consider the piano the miniature of the choir I play with and I feel a sense of coordination and a sense of directon and orientation I've never felt before

Suddenly I know what I play, why I play, why what I'm playing is written like that, and I think of the piano as a whole, and me and the piano as a whole and this is making playing and sightreding so damn easier, not only that but improvization too

I hope piano beginners are reading this as I do believe this is the most important thing they will ever need to know about their piano piano playing
For the others: what's your opinion?

[overscore]

I think you could solve the whole problem just by learning improvisation and composition. You can't do that by rote - you *have* to understand music to be able to do it.

From what I've read it seems that these two disciplines were an essential part of a piano lesson up until the early 20th century, where for some unfathomable reason they died out.

As has been said elsewhere, you can learn to recite a poem perfectly in French, but unless you can actually understand French it's all rather pointless!

[danny elfboy]

I think you could solve the whole problem just by learning improvisation and composition. You can't do that by rote - you *have* to understand music to be able to do it.

From what I've read it seems that these two disciplines were an essential part of a piano lesson up until the early 20th century, where for some unfathomable reason they died out.

As has been said elsewhere, you can learn to recite a poem perfectly in French, but unless you can actually understand French it's all rather pointless!

But, if composition and improvisation, are to be learned as part of piano training, that should happen before the wrong concepts (melody + left hand, treble cleff + two notes below - bass cleff, reading the melody first and the left hand later) are ingrained

I tried to explain the foundation of harmony applied to piano as an instrument and piano playing to the 6 years old cousin of a friend of mine who is taking piano lessons and is learning little pieces with sinple figured bass like Silent Night, Away in a Manger, Oh Holy Night. She was having problems with coordination and beats subdivision and as soon as she understood that THE BASS LEADS and the MELODY FOLLOWS and the piano is just a rapresentation of the orchestra and the choirs (but in this case the same person can play for all parts) all her problems disappeared soon and she began playing even these little pieces with more ease and musicality

I agree that studying harmony should be an important part of piano training but it's possible to begin the piano training with just THESE fundamental basics of harmony as they describe the piano as an instrument and the playing at the piano within the context of music itself, without waiting after the wrong ideas has been ingrained (that's why I believe bass cleff and treble cleff (grand staff) should be taught at the same time as a whole)

[preludium]

With the harsh language you're using you probably won't get too many answers. Basically I think the same way, though. As a child I had instrumental lessons and theory lessons separately once a week and I just can't understand how people get by without this. Harmony reveals at least half of the composer's intentions to you. I have no idea how music sounds to people who don't know the rules by which it was written.

notes that are in harmony one with each other because there's a relationship based on the overtones

Just to comment on this - overtones are a myth, or better a theoretic approach. The possibility to express frequencies as ratios of small whole numbers is the foundation of harmony. The frequency of a tone corresponds to the 0th overtone. This one is real, because it can be seen on the screen of a oscilloscope. Higher orders don't exist physically. Every function, periodic or not, can be expressed by a complete system of orthogonal functions. Trigonometric functions can make such a system, and this is the foundation of the myth of overtones. There are other systems made of Legendre polynoms or Bessel functions. The sole reason why trigonometric functions are used often is the fact that they can be handled easily when expanded to complex numbers. Especially on the piano the higher orders of "overtones" are heavily off the target, i.e. they are not harmonic, and they even change with time. For swinging membranes of drums a system of Bessel functions is even more suitable, though kettle drums give the impression of a well defined tone, which again is the 0th order of a system of trigonometric functions aka Fourier series.

[pianistimo]

preludium, i beg to differ.  why then do we have sopranos and basses who can switch into falsetto?  this is a form of overtone.  why do we have instruments - when pressing similar keys can blow differently and obtain overtones?  how about birds that chortle two and three notes out at a time?

i think cats and dogs have the capability of hearing more sounds than we do.  and, just because we can't hear all the overtones doesn't mean they don't exist.  it is a mathematical concept, yes.  but, with the 'well-tempered' piano we just don't think sometimes as a vocalist or a violinist.

about PURITY of sound.  you can have tone.  but sometimes is 'flat.'  not flat flat - but just DEAD.  add some overtones and voila.  listen to renee fleming and you'll hear a swirl with her notes.  now - to get this on the piano is kinda difficult without doing a completely different type of tuning for a particular piece that you want to achieve this effect with.  i'd say if you pick the keys that mozart did (basically 1/2 the keys) and don't worry about the others.  you have the keys that build on the overtone series of the others going up the scale - and getting sharper going up and slightly flatter going down.  this makes for a really beautiful emperor concerto or something where you want to hear some 'swirl' in the music.  mozart concertos, too.

haven't you ever been extremely frustrated by the lack of consistency between the bass range, the middle range, and the treble range with 'well tempered' tuning?  i think this was the bane of my entire childhood music education.  centering everything around the center of the piano.  come on people...there are more notes out there.  even for kids.

sorry.  now i will switch into apologetic mood.  i know that not all students really care.  but, those that are interested in tuning differences might!  for instance - i liked to hear true bass - and finally found it when i heard barry douglas play pictures at an exhibition.  now, the true love of music is not just found in playing a piece - but also getting a tuning on your piano that matches the music.

[danny elfboy]

With the harsh language you're using you probably won't get too many answers.

Sorry it's just frustration

Basically I think the same way, though. As a child I had instrumental lessons and theory lessons separately once a week and I just can't understand how people get by without this. Harmony reveals at least half of the composer's intentions to you. I have no idea how music sounds to people who don't know the rules by which it was written.

Okay but it's important not to take a certain direction with the piano lessons and the opposite direction with the theory lessons. I think more credits must be given to the students, even the very young ones, and in my experience there's no such a thing as being too young to understand something or too unprepared to know the whole story
Most of nowadays teaching for beginners is based on some sort of "condescending attitude". For example I don't agree that young children should be given books with just pictures as a beginner, I don't think there's anything good in having watered down pieces or stories. It's true the challenge of learning something difficult but complete and in context that we learn not trough patronizing watered down step-by-step.

What I think is important is to remove this silly idea that it's best for a beginner to think of the piano in a totally different manner than what it really is by watering down all the info and starting with the treble cleff and the right hand and then telling you have to add the left hand which is two notes below the treble cleff and so on
I think from the very beginning the student must be trusted when coming in contact with complete information

I think the whole education system has it all wrong
Because the first things you teach are the foundation, the ones that become second nature ... and it makes even more sense to have more complete, complex and not-watered-down information at the beginning rather than later
The foundation must always be solid and there's nothing solid in silly right hand only pieces, simplified versions of virtuoso pieces, mnemonic tricks ...

This applies to other things as well.
For example why my father grew so much better with real living since a very young age, from listening real dark fables based on real life events both happy and sad, with real newspapers, with real experience compared to the kids who grow nowadays with all this nonsense of the "age appropriate" books that are just watered-down and censored version of what the real world is like ... and isn't it absolutely clear that all this stuff is doing no good, serve no purpuse if not and do only harm (except giving money to the ones creating them)

Just to comment on this - overtones are a myth, or better a theoretic approach. The possibility to express frequencies as ratios of small whole numbers is the foundation of harmony. The frequency of a tone corresponds to the 0th overtone. This one is real, because it can be seen on the screen of a oscilloscope. Higher orders don't exist physically. Every function, periodic or not, can be expressed by a complete system of orthogonal functions. Trigonometric functions can make such a system, and this is the foundation of the myth of overtones. There are other systems made of Legendre polynoms or Bessel functions. The sole reason why trigonometric functions are used often is the fact that they can be handled easily when expanded to complex numbers. Especially on the piano the higher orders of "overtones" are heavily off the target, i.e. they are not harmonic, and they even change with time. For swinging membranes of drums a system of Bessel functions is even more suitable, though kettle drums give the impression of a well defined tone, which again is the 0th order of a system of trigonometric functions aka Fourier series.

I haven't researched this myself and english is not my native language but I can reply to this with the article by a physicist and musicist that claims that harmony is not just human made but based on natural relations of the overtones and that certain relations (like the fifth) are found in every musical system known ... even the tribal hunter-gatherer ones totally immune to western influence. He says that overtones create this natural relations and that they are what brought the scale into existence

The Natural Forces Bringing Do, Re, Mi Scale

He wrote one of the most comprehensive book on origin of music and acoustic phenomena I've ever seen

[pianistimo]

that was explained really well.  i tend to believe as dr. fink does - that it didn't happen this way by chance.  that our ears pick up dissonant and consonant sounds even as babies because of this overtone phenomenon. 

let's not talk about the glass harmonicas yet.

[counterpoint]

"The Natural Forces Bringing Do, Re, Mi Scale"

Okay, you can explain it like that. But noone ever could explain me, where the minor third does come from. Why there is a minor triad. There is no minor triad in overtones.

[preludium]

preludium, i beg to differ.  why then do we have sopranos and basses who can switch into falsetto?  this is a form of overtone.  why do we have instruments - when pressing similar keys can blow differently and obtain overtones?

Overblowing wind instruments or falsett voices have nothing got to do with overtones. Every vibrating system has a whole bunch of partial vibrations. On a string you can see them with the blank eye. It is wrong to call them overtones, since overtones are sine/cosine functions by definition, whereas partial vibrations are rather complex by themselves. On stringed instruments you can prevent some orders of partial vibrations by touching the string in different places. These tones are called flageoletts and have
a frequency spectrum themselves, so they cannot be overtones.

Another example which shows that overtones are not real is the fact that you can create complex vibrations other than by adding sine waves. One way to do this is called frequency modulation. One sine wave modulates another and if you do a Fourier analysis of the result you get a lot of "overtones". Where do they come from? They shouldn't be there because they weren't put in.

harmony is not just human made but based on natural relations of the overtones and that certain relations (like the fifth) are found in every musical system known

When saying the reason for harmony cannot be found in overtones I didn't mean that there is no foundation. On the contrary, I wrote that ratios of small whole numbers are the foundation. Thus they must be observed in other tonal systems than the western. An octave is 1:2, a 5th 2:3, a 4th 3:4, and so it goes on to the more dissonant intervals. A 5th and a 4th make an octave, since 2/3 * 3/4 = 6/12 = 1/2.

The Fourier series describes the sound of a tone, not its relation to other tones. When you want to derive intervals from the Fourier series you have to ignore the measurable fact that the spectrum of strings is not harmonic. Otherwise you get different intervals for different instruments. You cannot define any intervals for sine tones from sythesizers, since they don't have a spectrum. If there was only one type of instrument in the world and it would produce only sinoidal waves, do you think there would be no harmony, just because the tones have no spectrum? All this overtone thinking is flawed. It's an attempt to find a relation between things that are not related. Like if you try to predict the number of babies based on the population of storks in that area.

[stephen.hazel]

6) The foundation of a four part piece for voices is the bass
7) It's not about treble cleff or bass cleff (this nonsense should be ignored) it's about starting from the harmonic foundation and going up from there. Cleffs are just a synbolic practical labelling of the parts/voices of the piano we're playing but they don't explain anything at all.

Well, I'm a beginner, so bear with me...

But when somebody composes a song it doesn't necessarily have to be all about the harmony, right?  It can be more about the melody in some places and more about the harmony in others, right??
I mean, they have to go together, but one takes the foreground at any particular instant, right?

Pop songs seem to be all about the melody, and the harmony mostly just tags along, right?
Whereas with classical the harmony supports most everything and the melody is much more based on it.

So keep in mind that i'm new to all this...

Am I way off base?

...Steve

[pianistimo]

preludium - you are a mathematician if you call overtones 'sin and cosine.'  but, i think i understand what you are saying.  in the 'well tempered' piano - we don't have the purest of systems and it is not like a 'mean-toned' piano.

speaking of 'mean,' i realize most people consider the 'golden mean' a figure of speech for proportion - but it also indicates a certain replication of patterns from the smallest sized creation to largest.  the overtones are similar in that they follow this pattern infinately.   if you do follow the golden mean (with anything - overtones, whatever) it DOES go on forever.  who better than you should know this?

just because you don't hear sound in space - doesn't mean it doesn't exist.  we can't HEAR it!  energy doesn't evaporate.  or does it?  i think the energy goes on and breaks down into smaller and smaller waves.  we may not hear them - but i think they hit middle and then get bigger again somewheres out in space.  you know - like a tin can to God's ears.  the same elements that went into creation - come out of it don't they?

how would one explain radio waves or microwaves or those waves that are not heard but we know they exist.  what if they actually did have sounds and we couldn't hear them yet.

in sleep we have patterns too.  brain waves.  they aren't random. 

there are two approaches.  everything is random.  things are created out of chaos into order.  a highest order, if you want to call it that - on planet earth.  unlike the other planets we know.  and there are patterns everywhere that replicate.  take a leaf on a tree - same pattern as was there - 6000 years ago.  (some say more).  and, your last comment about babies - IS actually somewhat a predictable pattern - being that families in different generations have varying degrees of beliefs which either promote or do not promote 12-13 children (or more).  for instance, if you are catholic and marry young -you are likely to have a lot of children.  that is somewhat predictable.  what isn't predictable nowdays is when people use birth-control.  of course, you can't predict because someone/thing is stopping a natural action/reaction from occuring.

[pianistimo]

a little i found about the 'golden mean' in relation to overtones:
https://cellphonesafety.wordpress.com/tag/golden-mean/
https://saphierartworks.com/golden.html

[zheer]

    On the benefits of thinking "harmonically" about the piano  


  Harmony and music theory has been created by music theorists and not composers. Music theorists created music theory to understand and make sense of music, and so that we can understand music better ( thats what i was tought)
    When a Dr of music told me this i was vey happy, since my first composed sonata, etude and prelude  (i composed) , i had no knowledge of music theory. So basically a composer does not decide to compose in D minor harmonic scale, but simply compose.
     As pianist i agree that knowledge of music theory is essential in learning a piece of music on an intellectual level, however as i have recently discoverd (thankfully). human-beings have a sixths sense, through which we can understand music on a higher level  ALL MUSIC LOVERS HAVE THIS.

[clavicembalisticum]

Attempting to perform without minimal composer skills may be possible for simpleton stuff. But it will never get you any further since you will not be able to understand the music.

Pick a piano sheet, any piano sheet. If you can "understand" it, you can play it.

[danny elfboy]

    On the benefits of thinking "harmonically" about the piano 


  Harmony and music theory has been created by music theorists and not composers. Music theorists created music theory to understand and make sense of music, and so that we can understand music better ( thats what i was tought)
    When a Dr of music told me this i was vey happy, since my first composed sonata, etude and prelude  (i composed) , i had no knowledge of music theory. So basically a composer does not decide to compose in D minor harmonic scale, but simply compose.
     As pianist i agree that knowledge of music theory is essential in learning a piece of music on an intellectual level, however as i have recently discoverd (thankfully). human-beings have a sixths sense, through which we can understand music on a higher level  ALL MUSIC LOVERS HAVE THIS.

But my point was specifically about "knowing your instrument"
Maybe it's true theory is not necessary but I still think it's necessary to put the knowledge about your instrument in a "wider music" contest

I think that to believe the piano is "an instrument with hammers that hit strings that make sound" is not enough as it since to put piano without any context in which it can make any sense. What it makes sense is to understand what music context the piano belongs too.

After all the first form of music ever and the one we understand instinctively better is human voice. And the theory about the human voice is pretty sixth sense based and logical. There are lower voices and higher voices and together they form harmony.
Lower voices are more solid like the foundations of houses and high voices are more volatile like roofs of houses, hence the important of the foundation

It makes sense to remember how the piano is a ramification of this universal concept how it belongs to a musical context as old as time and it's not just a "tool" coming from nowhere and contextless which tends to make the whole concept of piano playing very abstract in a kind of robot-like manner (you don't understand, you don't see the context .... you just follow instructions)

[zheer]

It makes sense to remember how the piano is a ramification of this universal concept how it belongs to a musical context as old as time and it's not just a "tool" coming from nowhere and contextless which tends to make the whole concept of piano playing very abstract in a kind of robot-like manner (you don't understand, you don't see the context .... you just follow instructions)

   I believe my piano tuner made the same point a few months back (intresting)

[zheer]

But my point was specifically about "knowing your instrument"
 

   so why call your thread   
On the benefits of thinking "harmonically" about the piano 

[danny elfboy]

   so why call your thread   
On the benefits of thinking "harmonically" about the piano 

Because knowing the nature of the piano as a musical instrument allows to realize its harmonical nature ... even without knowing what "harmony" is all about
But you're right that may I should have called this thread "know your instrument" or "realize the musical context the piano belongs to"

[pianistimo]

perhaps we should not limit our thinking according to age so much?  sometimes the guidelines and 'prescriptions' for what a child of a certain age is able to do - might not be true for every child.  say you have a three year old that has gone past the idea of melody alone - and actually sings harmony on purpose.  that child, imo, understands the concept.  normally - this doesn't happen (does it) until a much older age 7-8.  i think.  basically i am hypothesizing according to what my own children and some students have been capable of.  the higher level of continuous harmonization (by sight-reading choral music) probably happens in jr. high and highschool.  the kids ultimately understand the concept of using harmony and it's principled methods (when taught).

now, back to the young child.  normally, in my lessons - i stick to tetrachord 5432 2345 scale forms and melodies - but ALSO add in the chords.  using the thumbs again (lh 531 = I chord) (rh 135 = IV chord) and moving the hand up one whole step (rh 135 = V chord).  now they know how to play these three basic chords in a hand position which can go anywhere's within the circle of fifths.

don't you think usually in piano methods - they leave out harmonizing for the very young child because of hand size and dexterity?  (playing right and left hands separately)  but, as one develops a bigger hand and more dexterity and sight-reading - it isn't as difficult.

now, what i think (and i am presuming here) dannyelfboy is saying - is that don't stop with a method book.  create your own methods of teaching beyond what the books say.  if they do not incorporate harmony - create something (might not even be at the keyboard) to teach the child more and more about harmony.

i never really thought about this in depth - but it makes a lot of sense.  mozart would listen to his father's friends when they came over to jam on the violins and violas.  he was used to hearing LIVE jam sessions and not just the radio.  i think live music is more invigorating to children.  they would then pick up the idea of harmony by watching and playing occasionally.  sometimes adults throwing out a challenge - handing over the violin and letting the child make up some kind of harmony.  same with singing in choirs.  who does this today at a young age?  hardly anyone.  but, in bach's day - all the children were in church singing.  at least the boys.  although girls choirs could be a 'thing' too.

kodaly has some interesting concepts - but they stick mostly with melodies at young ages, i think.  somehow the child's brain is able to start with that the best (intervals and melodies) BUT don't you think some children with the aptitude and talent - if give the opportunity (jamming and jazz and improv) would learn very very quickly at much younger ages.  they just need the time and place to do it every week.

[danny elfboy]

perhaps we should not limit our thinking according to age so much?  sometimes the guidelines and 'prescriptions' for what a child of a certain age is able to do - might not be true for every child.  say you have a three year old that has gone past the idea of melody alone - and actually sings harmony on purpose.  that child, imo, understands the concept.  normally - this doesn't happen (does it) until a much older age 7-8. 

kodaly has some interesting concepts - but they stick mostly with melodies at young ages, i think.  somehow the child's brain is able to start with that the best (intervals and melodies) BUT don't you think some children with the aptitude and talent - if give the opportunity (jamming and jazz and improv) would learn very very quickly at much younger ages.  they just need the time and place to do it every week.

That's the point: giving the opportunity
There is actually no real direct link between age and skill, intelligence or maturity
Piaget believed to have showed there was but he has been disproved a billionth of times by almost everyone who could make a serious research. The consensus is that Piaget and all the others like him didn't actually proved a connection between age and mental skills or perception but between "the opportunities that a certain culture gives or deny to certain ages" and their results skills and perceptions of lack of them.

This became very very obvious by looking how children of the same age but from different cultures responded completely differently to tests and analysis to determine their level of perception, abstract thinking and skills

The bottom line was that unlike what Piaget believed, that there's a strong correlation between age and the ability of a child to have perception of certain things, the truth is that the only connection was being between the ability of a child to perceive or not certain things and it's being allowed or denied to be exposed to them by its culture

Abstract thinking that was considered by Piaget impossible before the age of 11-12 have been observed in most 5-6 years old. When it was not it came out they were segregated into a non-abstract cultural environment of parental limitations

As a Supreme Court said in a famous circumstances also after checking "scentific evidences"

"The court's analysis is premised on differences in the aggregate between juveniles and adults, which frequently do not hold true when comparing individuals. Chronological age is not an unfailing measure of psychological development."

'Nough said

There's a wonderful quote by Holt that says it all and sums up nicely the huge flaws of western psychopedagogy:

"The words "expect" and "expectation" are on the whole badly misunderstood and misused by most people who write about children. Most people use them as synonyms for "demand" or "insist" or "compel." When they say we should have higher expectations of children, they mean that we should demand that they do certain things and threaten to punish them if they do not. When I speak of expecting a lot of children, I only mean that we should not in our minds put an upper limit on what they may be able to do.
The fact of being a "child," of being wholly subservient and dependent, of being seen by older people as a mixture of expensive nuisance, slave, and superpet, does most young people more harm than good."

[ail]

Hi all,

unfortunately, I've not read the whole thread in depth, but I wanted to tell you of my experience. I took my first piano lessons early, when I was 7 to 9, and for the most part, they followed danny's outlining. Some years later, I learned electronic organ, and I must say that here, from the very start, the left hand is an accompaniment that is merely playing a harmony. It plays whole chords, then adds a pedal that does more melody and eventually it begins to arpeggiate and break chords. I never got that far, but it was the organ that taught me all chords I know today, and in a very intimate fashion. I find that having studied the organ was a very efficient way to learn music harmonically, and to know the chords and their inversions from inside out almost without noticing. Now, when I play the piano, I recognize the harmonies I am playing because I remember those chords from the organ, even if they were all simply memorized without much explanation at that time.

Of course I know how to build chords now, but many times I find that if something is explained to you after you have been exposed to it somehow, even when you work with it without understanding the concept (and this has happened with me with derivatives of math functions when I had physics in high school but only calculus in the univ.) then the whole explanation is better understood and stays in your head for much longer and in a more coherent manner.

Just my two cents.

Alex