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For many years now I have been frustated by not being able to find an easy, intuitive way to get across the idea of keys and traditional key signatures.

I've been looking for something that works without memorization.

For instance, I mention that if you play:

C B A G -- F E D C, with the right rhythm, it produces "Joy to the World". I haven't yet found a another tune that follows a major scale this way, this obviously. I may be overlooking something obvious.

But then I play F to F descending one octave and have people hear that it sounds wrong without B flat. Same thing with G major, showing that it doesn't sound right without the F sharp.

That seems to click for most people. But then the next question comes: how do you know what key you are in, any key, without memorizing all the rules for key signatures?

In the last couple years I've been suggesting simply finding the last bass note on the page, assuming that it is the key, then identifying if the composition sounds major or minor. This seems to almost always work for simple music, and it is not too bad for a lot of more difficult compositions. In addition, it can be a major clue to determining the key of a large section of a composition that is not in the same key as the signature.

Has any one else tried this? I've used every traditional trick to teach the rules, but it horrifies me that some people only learn the rules and never understand the principle behind the rules.

Gary

I explain to students that the keynote is the "home base" of the piece (or section of a piece). There are several clues which, when put together, will tell where the "home base" is:

--Key signature

--Highest note and lowest note

--First and last note

--Most frequent note

--Harmonic structure: where do most cadences end?

Taking a look at all the "clues" usually results in a specific note being definitely identified as "home base".

But using the key signature to determine what the key signature should be is circular!

Let me try to explain in more detail. Suppose I choose to write a song in C minor and then print it out with all flats written in as accidentals. Immediately a student is going to say, "How could I know it is C minor?" My answer would be: "Let's look at the end of the piece. What's the bottom note? It's C, isn't it? Now, does the song sound happy or sad, light or heavy, serious or non-serious?"

And in most cases, people who are still learning will process that. Then I explain that although I will later print out the same compostion with a key signature, it is not the signature that tells us for sure. I also point out that in long compositions, we may be in a key for pages that is different from the key signature.

I don't think the highest note is very helpful. In a simple composition in C Major, it is equally likely that the highest note will be G or E. Too complicated.

First note is even less reliable, because it assumes that the first note will be part of the "tonic" chord. First base note might be more reliable, but if we start with an inversion, oops. The final chord is more likely to be in root position.

Most frequent note is a good idea, but that involves a lot of analysis. And the might lead quickly to ideas such as dominance, looking for the dominant chord, but that is still way too advanced.

Most of my students are not going to process "cadence" either. You know what you mean, and I know what you mean, but that is another technical term that is going to go right over their heads.

I like the idea of "home base" much better, but if I'm going to talk about home base, I'd rather have a student make a reliable "guess" at a letter. Than at the "quality" (major or minor).

That was what I was getting at. Starting with something very simple and rather dependable as a start, then moving towards some of the things you mentioned later.

Gary

Does this help anyone?

In sharp keys: the 7th degree of the scale is the sharp, therefore the 8th tone (a half step above) is the same as Tonic (octave). F# shows you are in the Key of G.

I don't teach minor keys to students until they have begun to play in minor keys. When a student has been through 12 major keys, and found the root position chord, I then teach minor, diminished and augments as small adjustments.

In flat keys: the next to the last b in the key signature is the name of the Key you are playing in. (The flat is placed on the 4th degree of the scale).
F (Bb)
Bb (Bb, Eb)
Eb (Bb, Eb, Ab) etc.

For cadences, after teacing all 12 root position Major Chords, it is easier to teach I, IV, V chords and to voice them in their closest proximity with an extention of the thumb while the 2-3-4-5 are stationary, and another extension of the 2-3-4-5 away from the thumb which is stationary.

Teaching two tetrachords with fingering is also easy because the C Major shows the distances between notes (whole step/half step well).

1-2-3-4-5-6-7-8 degree of scale
5 4 3 2-2 3 4 5 (LH to RH)

All white note starts (7)/then all black (5)
or, Chromatically written,
or, Circle of 5ths written (insert * at degree 5 and RH 2)
Circle of 5th teaching can be done at this time.

First they need to understand the pattern of the Major scale using whole and half steps:

whole, whole, half, whole, whole, whole, half

I break that down into two tetrachords to begin with:

eg. C D E F followed by G A B C

The tetrachord is half of the scale.

This will help explain why certain scales need certain sharps or flats. They must conform to this pattern.

You need to teach about harmony and cadences if you want your students to grasp the concept of being 'in a key'. Do plenty of work on chords I, IV and V in the key of C Major to start with. I use listening, composition and improvisation to get this through. Add chord VI for the interrupted cadence (you guys call this something else I think).

When they fully understand what is meant by being in the key of C Major you can teach the cycle of 5ths to show how to find all 12 Major keys. To find the next key go up a 5th and raise the 7th. Get them to work this out on paper as well as on the keyboard.

You have to take it step by step. Like Betty said, it's best to leave the minor keys until Major is understood.

I don't talk to students much about finding key signatures, but finding keyNOTES (as in, "what's the most important, central pitch?") Knowing the keynote is "key" to figuring out good fingering patterns and listening skills.

I find that looking at the last (or lowest final) note can be unreliable, especially for Impressionistic or jazz pieces. And I'm always surprised to see how many teaching pieces (including folk songs & Christmas carols) are in neither major nor minor, but modal keys.

So I give students an "arsenal of weapons" they can use to help them discover the central, home base pitch. And once that is discovered it's usually easy to figure out the scale structure.

OK. This has been a bit frustrating. Quite obviously if you are talking about something written by Debussy, simple conventional rules of any kind are going right out the window. Feuilles mortes (Dead Leaves) ends on B, lowest note, right by middle C. Scarboro Fair, starting on a Dm chord, may or may not be notated with a Dm key signature (Bb), and is likely to end on a D Major chord—and it most certainly can be played on all white notes, using Dorian minor using the set of keys we know of as C Major. And yes, folk songs and many Christmas carols are modal.

For us this is all elementary. So is the fact that jazz is going to be harder to analyze, for similar reasons.

However, if you go through a lot of literature, even you might be surprised how often the final bass note clue works. It's pretty accurate for most Baroque, Classical and Romantic compositions (including those of Rachmannov). Now, if something I teach does breaks this elementary rule, I'm either going to say that it is an "exception" or make a quick attempt at an intuitive answer. (Any thing that uses a standard blues structure is going to be problomatic, because of the lowered 7th. Usually something that is shown in C will not notate a Bb, but most Bs will be lowered, and certainly sharper students will notice that and ask what is going on.)

When I'm teaching more advanced students, I think you'd find that the tips and suggestions I give are probably very similar to what you teach. Finding anything new on an advanced level would literally be reinventing the wheel.

I was talking about students asking questions very early in their exploration of how music works. I tend to introduce scales in pieces first, because I put such a huge emphasis on reading. You may not agree. I use Arkansas Traveler, in G Major, to introduce the G Major scale:

(G, F#, G, D, E ***G, F#, E, D, C, B, A, G***)

I prefer to always teach scales moving inward (moving left for the RH, right for the LH) before I teach moving in the other direction, since the inward movement is more natural, producing fewer unnecessary wrist and elbow movements. A student will, at that case, ask me why the key is G Major, because I have at the top of the page: Key of G Major, F# is the key signature.

That's when I will say, "Well, eventually you need to know all your scales in all keys, and then you will simply know. But for now, the final bass note is G, the song has a rather upbeat sound to it, so Major would be a better guess than minor), and once you know that you are playing something that is in G Major, because I have told you, you may start to associate one sharp, F#, as standard for that key. And for a bonus, know that even if there is no key signature, those F#s will still be indicated with accidentals."

(I actually use much simpler language than that, again something that is absorbed more intuitively, since I get the same questions from adults and fairly young children.)

At that point, most students will ask what these things mean, and as I'm having them read the music, they will successfully play it (once I stress the F sharps and highlight them) but will not yet grasp what is going on. It is at that point that I will show them the descending G scale, point out that for such simple, conventional songs, they can count on knowing that it is G Major by the final bass note, by the fact that all F's are sharped, and that there are no other sharps or flats.

Again, WE know that such examples are special cases. I'm not suggesting that simplistic tricks are a cure for later problems, just that they allow complete beginners to get their feet in the door, so to speak. I always warn students: "I'm giving you something simple that works a lot of the time, mostly in the beginning. Later, when you get to more advanced music, I'm going to give you tools that are much more powerful, but I don't want to jump the gun by analyzing problems before they occur."

I do have to give some kind of answer to minor when asked, because I teach people to play a few basic pieces in Am, Dm and Cm long before I've gotten to cadences or had people memorize scales.

I taught brass for many years, and when I taught brass, scales were a very different thing. My brass students were faced with constant scale tests, which usually were a large part of what rewarded them with first chair. Since I had to drill the scales every week, my students had no choice but to absorb key signatures and the scales. If you have to use scales in this way, they get into your muscles. You and I and all the other teachers here can see a whole scale at once, and it is elementary for us to see any major scale as two tetrachords.

To sum up, when working with more advanced students who have at least an average aptitude for theory and who are willing to work hard, theory is not a problem. I was specifically mentioning clues or partial explanations for people who are curious but who do not yet have skills yet to understand more sophisticated explanations.

Sorry if I was unclear.

Gary

Chris,

I misposted to you instead of to Betty and can't find a way to delete, so I'm editing this. The short answer: yes, I do all the things you mentioned, all good advice. Once again, I was specifically mentioning things I do very early, before I have gotten to the stage you are talking about.

Gary

Betty,

Again, you are talking about teaching on a much higher or more advanced level than what I had in mind, but yes, I most definitely use the ideas you mentioned, among others.

When I was very young, I learned that the taking the last sharp and going up a half step gives you the major key. No exceptions.

And that F major (Bb) has to be memorized, but for all other flat keys, the second to last flat gives you the name of the key.

I teach people to play a few elementary pieces in Cm, and not in fixed hand positions, before I teach cadences and scales. At the top of each page, it says: "C Minor, Eb, Ab and Bb". Now, some students and perhaps even most don't care what is going on at this point. They just want to play the music, and that's fine. But if they ask why, I will mention that minor keys conventionally add three flats (or subtract three sharps, etc.) and then say that more explanation is just not possible at that time without learning scales and chords (cadences).

For those who are interested in learning one chord in all keys, I teach them by color:

C, F, G, all white. D, E A black in middle. Db, Eb, Ab white in middle. Gb, unique, all black. Bb, B, oddballs, the only two major chords where the root and fifth are not the same color.

Because my mind works very mathematically, I at least try to point out that by counting the keys between each finger, you can see the pattern. I do this for people who have not yet learned scales well enough to visualize a I chord as 1 3 5 in the scale. Obviously if you teach scales first, you can use them to explain chords. If you teach chords first, the logic is a bit different. I do both, according to the student.

I also teach minor and augmented as a half step movement of one key (finger), but I absolutely refuse to teach a diminished chord as a three note chord, so I have a different way of introducing that chord.

All of your suggestions are good and in line with what I teach to more advanced students.

Gary

GaryD,

I found a lot of your posting to be a very interesting subject.

1) One of the things you mentioned was: "C B A G -- F E D C, with the right rhythm, it produces "Joy to the World". I haven't yet found a another tune that follows a major scale this way, this obviously. I may be overlooking something obvious."

If you will include melodies moving in conjunct movement not just 8 notes of C Major scale, you will find other carols in scale like progressions with very few skips.
The First Noel
Deck the Halls with Boughs of Holly

Another feature of carols is that there are many repeatable parts of melody and rhythms, making it easy to remember. Repeated notes are very dominant. Minor songs exist readily. And ancient carols are easily introduced, as well as hymn carols, natural carols, secular music, folk music, music by country, and popular music.

I think the holiday season (including winter titles here in the US)round out the many, many choices. The good news about songs learned in elementary level, are that they can be played again in the future with a more challenging version as the players skill goes up. By the time a student has experienced the holiday season at the piano, he will have the makings of a large repertoire.

I'm glad you mentioned the Joy to the World's relationship to teaching C Major scales. I'm a little off topic by relating the other good news about seasonal songs and their contribution to development.

So in my studio we make an analysis and study of them - what does each song contain...and we answer in a simple format.

As I have said before, I break theory and technique into small tidbits of formative knowledge, not trying to "feed" too much all at once, but adding some more as seems appropriate.

2) I think Chris's tetrachord formula might say * W W H + W W W H (to show 8 degrees)

* represents the key note (starting/ending note)
W - whole step (2 half steps)
H - half step (1 half step)
+ - continue adding next tetrachord which is a Whole Step away.


3) It would be interesting to me to see how you introduce the augmentation of a chord.

This is a document I designed that leads one through: Major/Minor/Diminished/Augmented Chords

http://www.sailwave.com/betty/chords.pdf

It's nice to get to know you!

PS: And, I hope by your "address" that you come through the weather demands of the next week just fine. Be prepared!

Betty

Absolutely. I also mentioned Arkansas Travel. I was sticking specifically to a major scale, tonic to tonic, either ascending or descending. And things that are very famous. I'm thinking right now of a Bach Prelude that does from D to D, all white keys, so that is a perfect example of both natural minor and dorian minor, but it's not a major scale and it's not something most people would recognize. The First Noel is a good use of the scale. Deck the Hall I don't like as well, since there is no 6th until later, and by that time F sharp has been used. Same problem with "Do a Deer", since F# and Bb are added before the end of the tune.
In fact, I wish at times I could use carols all year around, but I think it would drive me mad in the long run. Hanukkah songs are less well known, but they are fascinating, since many are modal.
Because there is no "right" arrangement, there is also no end to how creative you can be, much like Twinkle Twinkle Little Star, the first tune I use to introduce the 6th, but also a wonderful set of variations by Mozart.
BINGO! I talk about "teaching on the fly". I like to answer questions as they come up, because that is when students are most likely to listen. That's why I also have "simplified answers", because I don't like saying, "I can't explain this to you at all. You aren't advanced enough."
I've used this for decades (literally), but I find that it clicks for some people, while other explanations seem to click faster for others. Theoretically smashing down all 8 notes with both hands, not using the thumbs, is a wonderful way to visualize a whole scale as a "thing". Have you found that some people count keys well, but others are "challenged"? The best adult student I ever worked with became one of the best sightreaders I've ever taught, but to the very end, she was weak in theory, chord structure. She hated math and tended to follow rules exactly but was not good at generalizing.
About the same way. I use "raise" and "lower", since the idea of "flatting" a "sharp" throws some people off. Or sharping a flat, going from minor to major.

I also teach augmented in another way though. I teach it as a magic modulating chord, and show that C E G#/Ab can move right to C, Ab or E with one single half step movement.

In the same way, I teach a diminished chord as a four note chord, showing that there are only three diminished chords (spelled enharmonically), and show that what we might call a C diminished chord can move equally well to B7, D7, F7 and Ab7, a favorite trick by composers like Liszt. And that the key that is lowered forms the root of all four possible dominant chords. This also shows that by using any diminished chord and either modulating it up one 1/2 step or down 1/2 step allows you to instantly set up any key, which is a typical organist's trick.

But that's pretty advanced for most people, and this is probably drifting way too much towards another topic. If you ever start one on diminished chords, I have a LOT of ideas!

(And yes, we are worrying about Hanna now, which we hope will be far enough off the east coast of South Florida so that we escape losing work and facing things like high winds and flooding.)

Gary

I teach key signatures by first teaching scales. I explain that songs are built from a scale, and they learn the C Major scale. I simply tell them that's the name because it starts and stops on C. Once they can do this well enough, I ask them to try playing the scale starting on G. If they don't automatically notice that there's a problem when they get to F, I'll ask them, didn't that sound a bit weird? Then I'll have them play it again and try to figure out where the problem is. Then we figure out it's F that needs to be different, and then I explain that they need to play F# instead of F natural. I call this the G Major scale because it starts and stops on G.

Once they work on that for a week or so, then I ask them to play the first 5 notes of the G major scale to find the next scale (D). Then we figure out what our new sharp will be. We do a similar approach to flat keys, except we play down 5 notes to find our new key.

As far as finding a key when all the accidentals are written out, all they need to do is look at the sharps or flats that occur regularly in a given section and list them. They need to know the order of flats BEAD-GCF (the reverse is the order of sharps) and then they can begin to arrange the sharps or flats in order. This is really the best way I think to figure out the key. Looking at the last note can be deceiving in some pieces, because of key changes that can occur. However, it is good to help determine whether it is major or minor (along with finding the leading tone in the minor scale in the piece).

Gary, I am not sure I understand what you are asking.

The things I mentioned I would not see as being in any way advanced. Tetrachord patterns would be played on any note quite early on. This is the first step towards understanding scales and therefore keys/key signatures.

It sounds like you might be looking for quick ways to explain concepts if a student asks. But I am not sure why a student would be analysing music to see if it were in a particular major/minor key before knowing what a scale is. Am I missing something obvious (it wouldn't be the first time )?

I really wasn't asking anything. I was attempting to share my experience. But I can understand your confusion. Let me see if I can explain.

I teach my own materials as the core of what I do. Rarely do I get a student who can afford more than a 1/2 hour per week. Teaching in this area is ridiculously competitive, since a whole number of people who have very little training advertise themselves as teachers. If I am unable to get people to a much more advanced level than most other teachers, I will lose my students to someone who lives down the block from my students.

They key to what I do is that I get people reading very well much faster than most teachers are able to. I use a three step system, and it takes up most of my time. I wish I had unlimited time to cover all the things that other teachers here seem to suggest they cover, but I put off everything else but reading until I'm absolutely sure a solid reading foundation has been established.

It's not that I don't care about other things. I do. But I seem to get to them later, and get to more advance pieces sooner.

In short, I'm a fanatic about the importance of solid reading. It doesn't mean that I don't think other things are important, and I'm certainly aware that there are marvelous musicians who don't read at all, but people who want to play be ear, without being able to read, are not part of the group I teach. I refer them to other teachers.

I use a three step system, my own. First, using a keyboard chart I made some time ago in Corel Draw, I have pictures of what each note looks like behind each key. On each panel I have the most common key word used. Going right from middle C: C, D, Every, Face F, Good, Face A, Boy, Face C, etc.

Left, from Middle C: C, B, Animals, Grass, Fight, Eat, Dogs, Cows.

Students are free to use letter only, but in the beginning I suggest linking to the word. I teach each piece with the chart up, at first, but I review all pieces in two more steps.

First, I have my students play each piece with the chart off, and I test them at random in each piece, in each hand, checking on key words. With really sharp students, I'll move right to letters, if they prefer.

Second, I review again, this time making sure that every single piece is counted correctly.

This allows me to zoom ahead, since they are able to play out of positions, leap from place to place, pick up scale patterns, etc. Without my having to cover the theory of what is going on.

It's an intuitive process. And by following up with the chart away and then with strict rhythm, I'm able to accelerate much more quickly to more sophisticated music, which is what my students (of all ages) want. They really don't care as much about the style of what they play as they do about if the music sounds interesting to them. So I'm trying to "sell them on" the music I like, although I will introduce many styles, because if they are convinced that what I have just played is what they want to play, that's about 90% of the battle for me.

And of course, the critical step is making sure that my students are able to play what they like, because if they like something but can't play it, it turns into frustration and sometimes even hatred for a piece/composition.

Please don't think that I don't think theory is important. Even for people who only want to perform but who are not interested in improvising, arranging or composing, it's my believe that a thorough knowledge of structure not only accelerates learning but more importantly makes memorization SO much easier.

The bottom line: I teach people to play things first and analyze them later. You may not agree, but it has worked very well for me.

This is why some of my more curious and successful readers may ask me questions that seem elemntary to you. It's chicken/egg thing. Their reading is ahead of their theoretical knowledge.

Please don't think that I don't teach keys, tetrachords, circle of 5ths, scales and so on. I do. I have no disagreement with any comments here about how other people teach these things.
I would have to take away from time I'm spending on things that I consider more important, in the beginning, to start on tetrachords so early. I was a "precocious reader", so to speak. I grabbed every piece of music I could lay my hands on, any style, and tried to play everything. I feel that the reason that theory was so easy for me was that I already had so much music in my fingers by the time I was still quite young. I didn't know what a tetrachord was until I was in a college theory class and I witnessed a professor trying to use that system to get scales into the minds of non-keyboard players, especially singers, who simply did not know scales.

My second teacher just asked me to learn all the scales when she thought I was ready. She gave me a book of Hannon, told me to study the fingerings, then be able to play all major, natural minor, harmonic minor and melodic minor for an exam. I found most of them quite easy because most of the scales were already in my fingers, although I had not analyzed them.

Then she asked me to learn a I, IV, I, V7, I cadence in all keys along with the scales, and I did that too. Very quickly. I'm convinced that a great deal of what made theory and ear training so automatic for me was the fact that I could play a great deal of music and that I also played brass, which is great for developing the ear.
No. I think I did a bad job of explaining, and I've probably made it worse. Frankly, if I had the opportunity to watch you teach, I'd probably be impressed.

Although you might not agree with all the things I do, again, you might at least have a more positive impression if you could see me at work.

That's the frustration of this medium. So much of teaching is a matter of feel, reaction to what is happening at the moment, intuitive understanding of what each student is lacking, etc.

By the way, I can go very much in the other direction. A year ago I had a student who was a weak reader who was only interested in composing. He wrote things, learned to use Finale (the program I use), then brought in his compositions for my ideas. I liked some of his work, but it was SO frustrating because of his lack of playing experience. I found it about 100 times harder to teach the kind of foundation (theory. structure) I wanted to give him because he was such a slow reader. I wrote out different kinds of circle of 5ths exercises (C7, F7, Bb7 etc.) going around the whole circle, of course, and I covered both roman numberals and conventional pop notation. I hate teaching such things by endless repetition (watch me and copy), and it took him forever to read anything I wrote, for illustration.

Sorry if I have left you more confused!

Gary

Thanks for the clarification Gary. I am more intrigued than confused now. For me, developing those reading skills which we both know are so important has more to do with solid understanding of theoretical concepts than it does about playing the piano. It's how you get them to understand the theory that is important. Most of my piano students learn theory and music literacy before playing a note. This might sound as strange to you as you feel your methods might seem to others. I run musicianship classes for 4-6 year olds which feed into my piano teaching practice. By the time they start playing they have a good understanding of rhythm, pitch (including standard notation), harmony and composition. This means that when they start playing the piano we are able to focus on the physical aspects of controling the instrument. Progress is swift. I started teaching in this way because, like you, I was sick of plodding through easy pieces for months on end trying to teach it all at once which in my opinion is overload on the senses and confusing.

Of course there are so many ways in which we can teach music. It's most important to use methods which you believe in and feel confident with. If it works then that is all that matters.

Chris, I was a lightning-fast reader long before I knew much at all about theory or structure. At age 14 I auditioned for a job accompanying a voice teacher in my area and got the job. I remember he "threw at me" something I had never seen from The Messiah. It was my ability to get very close the first time that got me the job, plus the fact that I read so fast, it was very easy for me to look at my part, follow, and know everything that was going on.

Strangely, it was my lack of theory and structure that lead to a severe memorization problem, and filling in those gaps took care of that problem. I also love theory, so it was hardly a chore to catch up. Perhaps my story is highly unusual. I really don't know. I played by ear in high school without having the faintest idea of how I was doing it. No knowledge of chords beyond major, minor, diminished, augmented and dominant seven chords. I began arranging a few things and memorizing them on the fly without any plan.
That's obviously the key. When progress is swift, you can do just about anything want. Although theory was miserably neglected in my education until college level, I certainly don't think that's a good thing. I also had miserable technical training, with next to NO help with fingering, and that I look back on as a crime!
We may be trying to reach a similar goal with a different path. Regardless, here is a bit of what I wrote yesterday about key signatures, in a PM:
==========

Here are a couple tips I give to my advanced students that are obvious to me but not to them.

1) Key pairs. The always add up to 7. F is 1b, F# is 6#. No exceptions. This even works for C.
C=0, C#=7#, Cb=7b.

2) Enharmonic keys: they always add up to 12.
F# and Gb, 6+6. Db and C# 5+7. This even explains theoretical key signatures that are not notated. D# Major, if it existed, would have 9# (12-9=3).

Such concepts are important, because even though the key of D# minor has 6 sharps (relative minor of F# Major), the dominant chord remains the same as what it would be in D# major (theoretical), so when ever a melodic line traces a diatonic scale over the dominant 7 chord, which is indeed A#7, you will get:

A#, B#, Cx, D#, E#, Fx, G#, A#
(Bb, C, D, Eb, F, G, Ab, Bb)

The 9 sharps result because of the enharmonic spelling of the "dominant scale", which is over a A#7 chord or V7 in the key of D# minor. This occurs in at least one Bach prelude, for instance.

Gary