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#1239096 - 07/28/09 05:39 PM Re: Various issues with pupils [Re: Betty Patnude]
jotur Online   blank
5000 Post Club Member

Registered: 09/16/06
Posts: 5450
Loc: Santa Fe, NM
Originally Posted By: Betty Patnude
You aren't supposed to understand the Circle of 5th going in - it's a result of knowing theory of the 5 Finger Positions, the Major Scale formula of tetrachords, and the theory of how 7 letter names are written as white (naturals) notes, altered to flats and altered to sharps, giving you 21 possibilities for an A - and so on for the B,C,D,E,F G. Exercising your fingers in accurate movement around the keyboard culminates in having a "Circle of 5ths" which is simply a diagram of music logic explaining the theory written about in the 1700's era by Rameau.


What are the 21 possibilities for an A? If I count only the Ab's, A's, and A#'s (not double flats or double sharps) I get 23 possibilities for an A on an 88-key keyboard. Or have I misunderstood what you are counting? Of course, other instruments will have a different number of possible A's, and on some stringed instruments the same pitch can be played on different strings, so one might count something entirely different for the number of possible A's there. I play with a lot of different instruments, and since I started in band, not piano, have always played with lots of different instruments, so my take on music theory isn't piano-centric. I assume you (eventually) let students know that music theory isn't piano-centered, even though they are starting to learn it on a piano.

I also *think* you mean, when you say the 7 letter names are written as white notes that you meant to say "are white keys on the piano" - since they are *written* on lines and spaces on a staff. I assume, again, that although this is a piano-centric viewpoint because you are teaching piano, that eventually you do explain to students that music theory is broader than just piano.

Please note I'm not arguing with your opinions about what constitutes a serious teacher. I'm just attempting to clarify, for my sake, what you meant, from a factual standpoint, in the above-quoted paragraph.

Cathy

PS - I see that this is the "various issues with pupils thread", and not the "serious teacher" thread. However, I'm still simply trying to clarify, for myself, what was being said from a factual standpoint.

Thanks.



Edited by jotur (07/28/09 05:49 PM)
Edit Reason: to add PS
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#1239411 - 07/29/09 03:14 AM Re: Various issues with pupils [Re: jotur]
Betty Patnude Offline
4000 Post Club Member

Registered: 06/11/07
Posts: 4896
Loc: Puyallup, Washington
Cathy,

I'm happy to reply to your questions hoping that the answers I give bring further clarity to what I was trying to express.

Regardless of the number of registers or the total number of keys on the keyboard, my example is that an A can be natural, sharp, or flat. Since there are 7 letters of the alphabet this results in 7 letter times 3 choices for letter name. It is not necessary to duplicate the same information for each register because it is speaking about one set of A-B-C-D-E-F-G that is applied throughout the keyboard.

I did not use double # or double b - because they do not appear in major scales, they appear in music literature by various composers and doubling accidents are not valid in a major scale key signature, they are additional chromatic placements for interest in compositions. Chromatic meaning "color".

Music theory is universally applied to voice and all instruments, however, in my opinion, the piano is the best instrument to express the construction of music theory. Theorists have primarily been piano specific actually earlier keyboards being their focal point of explanations. Music history is full of the development of the evolving keyboards and music theory is the developing knowledge for the learning and playing of the keyboards and the reading of music literature.

Music theory discusses the notation of sound and rhythm and the elements of music. It includes rules which have come to be proven factually through science and mathematics - acoustics, physics, kinesthetics of movement of the human body such as in technique which is the "how to" of producing and controlling the instrument's musical potential. A good music dictionary is a good start toward building the knowledge of music theory, but to really learn what is involved in music learning to the degree that is under consideration in music theory, the best approach is through personal experience in mastering the reading of music, and the ability to present accurately what has been notated on any piece of music written for the instrument by any composer in the various era's of music history.

My point as you "boxed" it, is that it's a huge mass of information and knowing about it is different than being fully versed in it. It is possible to misunderstand many things about theory, and as in math, a small error makes the equation incorrect. It is a huge undertaking to gain complete understanding of music theory and to be able to demonstrate it upon the instrument, write it in notation, or to teach it. It is a long term study, I believe, to totally grasp with accuracy what has been written over the history of music. Like math, the theories of music can be proven.

As in knitting, when one drops a stitch, there is a noticable gap between stitches. In playing music, there is nothing concrete that shows us there was an error that occured here or there. I think this is why music theory seems difficult to understand, if we don't catch our errors in thinking, the error will be forever with us, unnoticed. It takes great diligence and interest to work through theory to the point that I am talking about. Verifying our work is a huge task also. And, remember that the music symbols are basically hieroglyphics and we are reading and thinking in another language - music.

Betty

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#1239413 - 07/29/09 03:28 AM Re: Various issues with pupils [Re: Gary D.]
Betty Patnude Offline
4000 Post Club Member

Registered: 06/11/07
Posts: 4896
Loc: Puyallup, Washington
Aha, Gary!

I couldn't agree with you more than when you say, "They may be little tiny holes, but it is the skill of the teacher that allows the teacher to fill these holes as they appear, and at the right time."

I think many times our individual experiences in teaching bring us to similar conclusions, but it is our own explanations, voiced in words that are comfortable and relevant to each of us, that makes it seem like there is a difference of opinion, when really there is a lot of commonality.

The hoped for outcome is that things will transpire between teacher and student so that progress and success can be enjoyed by both. I think we do that through the logic and understanding we've gained by teaching, I don't think it was all clear and valid when I began. It takes experience and intuition to be able to find a "fix" for a piano student who is having a problem.

But, as in another topic, the serious teacher topic: I think the serious teacher will work very responsibly toward creating the good outcome for the student at every opportunity. Being in an on-going conversation and providing information and effort toward helping a student is what we do. It doesn't happen in a vacuum.

I enjoyed reading your post, Gary!

Betty

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#1239600 - 07/29/09 12:23 PM Re: Various issues with pupils [Re: Betty Patnude]
jotur Online   blank
5000 Post Club Member

Registered: 09/16/06
Posts: 5450
Loc: Santa Fe, NM
Originally Posted By: Betty Patnude
Cathy,

I'm happy to reply to your questions hoping that the answers I give bring further clarity to what I was trying to express.

Regardless of the number of registers or the total number of keys on the keyboard, my example is that an A can be natural, sharp, or flat. Since there are 7 letters of the alphabet this results in 7 letter times 3 choices for letter name. It is not necessary to duplicate the same information for each register because it is speaking about one set of A-B-C-D-E-F-G that is applied throughout the keyboard.


So there's only 3 choices for an A, not 21, I believe, in your conceptualizations? You misstated that the first time?

Originally Posted By: Betty Patnude
I did not use double # or double b - because they do not appear in major scales, they appear in music literature by various composers and doubling accidents are not valid in a major scale key signature, they are additional chromatic placements for interest in compositions. Chromatic meaning "color".


I've reread this whole post a couple of times, and this is the only time in this post I've seen you address "color". So is this when you are addressing my question about the note names being "white"? They're white because they're white keys on the piano? And, pardon me for my obtuseness, but are you saying that A#, Cb, etc., when used as "accidents", are "chromatics" because the piano keys are different colors?

Originally Posted By: Betty Patnude
Music theory is universally applied to voice and all instruments, however, in my opinion, the piano is the best instrument to express the construction of music theory.


Yes, that is your opinion. I think piano is, for some aspects of music theory, a good example, and for some not so good. It is particularly unsuited for understanding intonation, as a major example, since its pitches can't be altered on the fly. Many people never really learn to listen to intonation and can't tell, for instance, that barbershop quartets sing intervals that aren't tuned on a piano (I could give an example from PW if you want), and, IMO, miss a lot of music theory and practice that is rather common. Many good musicians understand that a choir accompanied by a piano has a restricted set of pitches to use. Other people never understand that an orchestra can choose to play at least some pitches in intervals that a piano can't use of the fly. Do you, now, eventually teach that to your students?

Originally Posted By: Betty Patnude
Theorists have primarily been piano specific actually earlier keyboards being their focal point of explanations. Music history is full of the development of the evolving keyboards and music theory is the developing knowledge for the learning and playing of the keyboards and the reading of music literature.


I wouldn't make such a statement as "music theory is the developing knowledge for the learning and playing of the keyboards", but then, as I say, I have always had a wider view of music theory because I interact with many other instruments. But you're entitled to your opinion smile

Originally Posted By: Betty Patnude
Music theory discusses the notation of sound and rhythm and the elements of music. It includes rules which have come to be proven factually through science and mathematics - acoustics, physics, kinesthetics of movement of the human body such as in technique which is the "how to" of producing and controlling the instrument's musical potential.


You have made statements about the mathematics and scientic underpinnings of music theory many times, but I don't remember you ever actually giving an example. On the other hand, I've explained several times, in various posts, the theoretical ratios of the harmonics of a pitch, and where some of the intervals fit in a set of harmonics. I've also explained why one can't tune all the 5ths within an octave in such a way that they all fit the theoretical ratio of a fifth if the octave has a 2/1 ratio. It is my opinion, and I stress that this is an opinion, that if you are going to invoke the mathematics and the science, implying that one needs to know those to be musical-theory literate, that you ought to demonstrate that literacy. To me, and this is my opinion again, it is disengenous to do otherwise.


Originally Posted By: Betty Patnude
A good music dictionary is a good start toward building the knowledge of music theory, but to really learn what is involved in music learning to the degree that is under consideration in music theory, the best approach is through personal experience in mastering the reading of music, and the ability to present accurately what has been notated on any piece of music written for the instrument by any composer in the various era's of music history.


To me, that is a limited definition of what music theory is about.

Originally Posted By: Betty Patnude
My point as you "boxed" it,


I don't know what this colloquialism means.

Originally Posted By: Betty Patnude
is that it's a huge mass of information and knowing about it is different than being fully versed in it. It is possible to misunderstand many things about theory, and as in math, a small error makes the equation incorrect.


Although we do have, in math, ways of indicating that there may be small variances in results, inputs, variables, etc. It's tough to be fully versed in math, as in music theory smile

Originally Posted By: Betty Patnude
It is a huge undertaking to gain complete understanding of music theory and to be able to demonstrate it upon the instrument, write it in notation, or to teach it. It is a long term study, I believe, to totally grasp with accuracy what has been written over the history of music. Like math, the theories of music can be proven.


"Complete", "totally" - what all encompassing words. Are you implying that is a goal for students? That teachers must be at that level? It is, indeed, a "long term study" - I'd be willing to believe that if it includes math, science, and acoustics, as you noted early, that there is much that I, and you, don't yet know smile

Originally Posted By: Betty Patnude
As in knitting, when one drops a stitch, there is a noticable gap between stitches. In playing music, there is nothing concrete that shows us there was an error that occured here or there.


I'm afraid I have to take issue with your grammar here, as I have done sometimes in the past frown The phrase "As in knitting" implies that one is going to cite a parallel example (in music). But you claim an opposite effect in music - you say there *is* something *noticeable* when there's a mistake in knitting, but there *isn't* something noticeable when a mistake is made "playing music."

In addition, I disagree with the universality of the conclusion. I can, often, tell if I've made a mistake when playing music. For me, a wrong note or wrong rhythm is pretty concrete.

Originally Posted By: Betty Patnude
I think this is why music theory seems difficult to understand, if we don't catch our errors in thinking, the error will be forever with us, unnoticed.


And, for some people, when they *have* been noticed, they are still unacknowledged. C'est la vie. smile

Originally Posted By: Betty Patnude
It takes great diligence and interest to work through theory to the point that I am talking about. Verifying our work is a huge task also. And, remember that the music symbols are basically hieroglyphics and we are reading and thinking in another language - music.

Betty


I asked two questions in my original reply: What are the 21 A's? and Are the letter names white because they correspond to white keys on the piano?

Your answer to the first one indicated that you meant there are 3 possibilities for each letter name, for a total of 21, but you did not acknowledge that your original statement was in error. You didn't address the second statement, unless you mean for your opinion that the piano is the prime instrument for learning music theory to address that question.

IMHO, a lot of words, not much clarity.

Cathy
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#1239620 - 07/29/09 12:56 PM Re: Various issues with pupils [Re: jotur]
Betty Patnude Offline
4000 Post Club Member

Registered: 06/11/07
Posts: 4896
Loc: Puyallup, Washington
Jotur said: So there's only 3 choices for an A, not 21, I believe, in your conceptualizations? You misstated that the first time?

Here goes my explanation from my point of view:

Well that's 3 times 7 alphabet letters, Jotur.

For Pete's sake, the "color" refers to the sound produced not the black and white key configuration. Chromaticism introduces coloration and interest in a composition.

Originally Posted By: Betty Patnude
My point as you "boxed" it,
This is what I mean when I say you 'boxed' it. The highlighting of the many comments I made that you are going about to undermine. Actually I'm surprized that you found some of what I said to be difficult and that you missed the points I was making.


Students are taught what they need to know and what they are ready for.

When it comes to other instuments of the orchestra (for instance) many were invented after the keyboard which started in the 1600. So the keyboard in my opinion is the foremost best instrument that fully used music theory to it's advantage. The range of the keyboard and the organ alone makes it so, as well as the number of composers for the instrument during the centuries of music. Folk for instance is very often an aural expression, unnotated, and handed down person to person by hearing, seeing and doing. In other words, not read. And very open to improvisations.

I'm going to cut you off Jotur - I will not respond to your postings in the future. You should be aware that antagonizing me by misapplying what I have been saying is the epitome of deceit and bullying on your part when it is used to make me defensive.

You may have your opinion and continue operating from it as it gives you pleasure and one upmanship. Congratulations in your lengthy effort here. I do not appreciate your attack one iota.

Music educators reading this should take a dim view of such tactics to trying to entrap another music teacher in what on my part was a serious attempt to answer your questions. If you are truly stuck on the two questions you asked, and you believe what you wrote, you are the perfect example of the situation I was talking about where the learner does not know they are compounding an error in thinking.

I owe you nothing further in communication.

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#1239682 - 07/29/09 01:51 PM Re: Various issues with pupils [Re: Betty Patnude]
jotur Online   blank
5000 Post Club Member

Registered: 09/16/06
Posts: 5450
Loc: Santa Fe, NM
smile

Cathy
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#1240408 - 07/30/09 03:01 PM Re: Various issues with pupils [Re: Morodiene]
Horowitzian Offline
8000 Post Club Member

Registered: 09/18/08
Posts: 8453
Originally Posted By: Morodiene
Originally Posted By: Horowitzian


Don't pay attention. Jazzed23 is a troll.





:::wonders how Horowitzian got that picture of Jazzed:: laugh


grin

A lovely picture isn't it?

BTW, Jazzed is serving a temporary ban. smile
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#1240460 - 07/30/09 04:28 PM Re: Various issues with pupils [Re: jotur]
Gary D. Online   content
4000 Post Club Member

Registered: 08/30/08
Posts: 4750
Loc: South Florida
Originally Posted By: jotur
[quote=Betty Patnude]

What are the 21 possibilities for an A?

I think from this:
Originally Posted By: BP

You aren't supposed to understand the Circle of 5th going in - it's a result of knowing theory of the 5 Finger Positions, the Major Scale formula of tetrachords, and the theory of how 7 letter names are written as white (naturals) notes, altered to flats and altered to sharps, giving you 21 possibilities for an A - and so on for the B,C,D,E,F G.

The idea was that there are 7 white keys with letter names, repeated over and over again, and each one can be sharped of flatted, omitting the more advanced concept of double sharps and flats.

"giving you 21 possibilities for an A - and so on for the B,C,D,E,F G." should have been "giving you 21 possibilities for an A,B,C,D,E,F G.

That may be incredibly obvious, stated that way, to you and other people who play, but for beginning students it is not. For instance, the idea that there is an E# and a B# is difficult for many people to understand. They read them as Eb and Bb, or as Ex (double sharp) or Bx, thinking that a sharp must be a black key.

A point I keep making is this: some of the best teachers you will ever meet do not always write concepts out, on the fly, in public forums, with the same logic and clarity as they teach them.
Quote:

I also *think* you mean, when you say the 7 letter names are written as white notes that you meant to say "are white keys on the piano" - since they are *written* on lines and spaces on a staff.

I often talk about the "white and black notes on the piano". I TRY to be consistent about saying "keys", but I suspect I often don't notice when there is not miscommunication. smile

While it is true that theory goes far beyond piano or keyboard or keyboards, I do believe the for pianists (beginners and intermediates), at least, it is logical to concentrate on theory as it applies to the piano unless these students are studying other instruments.

As I've said before, when I was in theory courses, the pianists generally found such courses easier than those playing other instruments. Who was better? Probably excellent pianists who also sang or played other instruments that further develop the ear.
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#1240468 - 07/30/09 04:55 PM Re: Various issues with pupils [Re: Gary D.]
J Cortese Offline
Full Member

Registered: 07/20/09
Posts: 357
Loc: Los Angeles, CA
This is interesting enough to me that I'd like to try getting a good basic textbook on music theory. I can't even remember learning a lot of this stuff; I was so young. I don't ever recall anyone -- although my teacher must have -- telling me explicitly that a sharp or flat was simply a half-step up or down from wherever you happen to be at the time. I don't recall absorbing the circle of 5ths, or being told that you add sharps one at a time as you hop up until the flats show up, and you pick them off one at a time until you're back at C. The only things I recall her telling me outright was that you hop down a minor third to get the minor key that corresponded to a given major key, and that there are three types of minor scales. And I recall her telling me about diminishing and augmenting chords on minor and major. Everything else, I can't recall when it hit me. It's like trying to remember when I learned to read.

Other oddball things, like the fact that equal, just, and meantone temperament even exist, are things that I didn't encounter until very, very recently. I guess they are harder to avoid if you play a stringed instrument where you have to go looking for the notes and each string does triple and quadruple duty. Weirder things like how an Eb and a D# aren't necessarily the same note still makes my head cramp up -- I suppose that comes from playing an instrument that has a diatonic scale sort of built into it.

Pianos come with a lot of Western music theory built in, while guitars and violins seem to have a lot of acoustic physics up for grabs -- tuning two strings that play well together until you hop up by an octave, that sort of thing.

I need to find a good book on music theory so I can start in on this stuff. It's really interesting.
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#1240486 - 07/30/09 05:48 PM Re: Various issues with pupils [Re: J Cortese]
Gary D. Online   content
4000 Post Club Member

Registered: 08/30/08
Posts: 4750
Loc: South Florida
Originally Posted By: J Cortese
I don't recall absorbing the circle of 5ths, or being told that you add sharps one at a time as you hop up until the flats show up, and you pick them off one at a time until you're back at C.

The circle of 5ths is one of the most elegant and useful principles we have in music.

However, there is no completely right or wrong way of teaching it. That's the point. People who see patterns everywhere see patterns. People who are very good at math see something else. People who are good at both will have yet another view.

Here are several ideas that help.

1) Practice writing the key signature for C# major and Cb major. The forces you to learn all the sharps and flats, but you also feel the pattern in your hand as you write them. For instance, with sharps you realize you put a sharp on F, then move to C, then to G, eventually completing the pattern of FCGDAEB. All with sharp symbols.

2) You can then play that same sequence of letters, but using white keys, going straight up the piano, and you are clearly playing all perfect 5ths. You can also start way up high, playing down, and you notice that you are playing all perfect 4ths.

3) The flats are just reversed.

These things are probably all obvious to you now, but it's the matter of putting it all together and using it that eventually absolutely imprints the sequence in your brain.

All the other rules for remember key signatures, or reading them, are just using those principles. In my experience most students memorize rules but never grasp the patterns behind the rules.

Does this make sense to you in writing? I can show this SO easily, when I am working directly with someone, but here, in this medium, simple things seem hard and hard things seem (in a totally illusionary manner) simple.

I have other ideas but first want to find out whether what I just wrote connects with anyone who is learning…
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#1240500 - 07/30/09 06:22 PM Re: Various issues with pupils [Re: Gary D.]
J Cortese Offline
Full Member

Registered: 07/20/09
Posts: 357
Loc: Los Angeles, CA
It makes sense to me, but like I said, I feel like I took this in without even realizing it. It's like explaining the word "the" to me at this point.

I'm definitely a pattern-searcher, though. What must have happened is that my teacher explained a bit to me, and I raced off and started transposing like mad to see how it worked with every key, then once I saw the pattern, I just figured I'd cracked it.

The weakness of being a pattern-happy learner is that I never developed anything near perfect pitch and have a hard time seeking out keys to things sometimes. Every key is exactly equivalent to every other key, so my head stopped trying to tell them apart.
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#1240534 - 07/30/09 07:08 PM Re: Various issues with pupils [Re: J Cortese]
Gary D. Online   content
4000 Post Club Member

Registered: 08/30/08
Posts: 4750
Loc: South Florida
I get it. I don't know how I absorbed the circle of 5ths. I learned it and understood it so early, I have NO idea what it felt like not to know it. It's almost like trying to remember what it felt like not to know how to walk.

I would forget about perfect pitch. Most people work out things relatively. I have what I call "imperfect pitch", meaning that it is not always accurate but usually is, so much so that I can't play any instrument like trumpet that has different "sizes" so that the written notes and fingerings remain the same but the pitch changes, relatively.
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#1241259 - 07/31/09 09:24 PM Re: Various issues with pupils [Re: Gary D.]
Betty Patnude Offline
4000 Post Club Member

Registered: 06/11/07
Posts: 4896
Loc: Puyallup, Washington
In the most of simplicity, I was trying to say: there are 7 alphabet letters from which to name notes on the music staff or on the keyboard.

ABCDEFG are repetitions on both the music staff and the keyboard and they can move (be read) in either direction - ascending/descending up/down.

On the piano keyboard there are 3 possibilities of notating each letter name (regardless of which register they appear).


1) ABCDEFG
7 natural white key names

2) Ab Bb Cb Db Eb Fb Gb
7 flatted key names a half step down from the natural key

3) A# B# C# D# E# F# G#
7 sharpened key names a half step up from the natural key

The above is the 21 to which I referred. (7 times 3 = 21)

I did not want to do double flats (bb) or double sharps (x).

The purpose of identifying these being to show the Circle of 5ths.

The Circle of 5th ASCENDING from Middle C with # names:
(C) - G-D-A-E-B-F#-C#

The Circle of 5ths DESCENDING from Middle C with b names:
(C) - F-Bb-Eb-Ab-Db-Gb-Cb

In a one on one lesson in person, the misconceptions and wrong turns in logic could be handled easily to make corrections to help a student become adept at writing and playing the (12)Major Scales for complete understanding. And, afterward, to organize all of the Major Scale in order of their appearance by starting with the Key of C which has no accidentals, and adding one new # in ascending by 5ths, or adding one new b by descending by 5ths from the keynote of the previous scale.

As in math, one simple error will create miscalculation within all scales. It is important to learn the C Major Scale first and completely before moving on. This is not to be a read only exercise, it is at the piano with correct notes, correct fingering (standardized) and a steady, slow tempo until it is absolutely clear in your mind. Some teachers would also want you to take a blank manuscript paper to draw your own notation to represent the scale.

The experience of learning scales and organizing them into the Circle of 5ths is a high level logic requirement, in my opinion. The capacity to recite the theory is one thing, the ability to play them accurately without stumbling is another. This is not a novice activity, it takes patience, diligence and intelligence.

If you like puzzles and games and patterns, you will probably thrive on this!

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