Teaching scales, especially minor scales

[gaer]

Just two weeks ago a lady I teach, who I believe is close to 70 years-old, suddenly wanted me to explain the whole concept of minor scales. She is a very bright lady and actually has a fairly good mind for theory, but she is very impatient and kept bombarding me with a new question before I had a chance to answer the last one.

In another thread I mentioned "bad habits", and perhaps people got the idea there that I think all bad habits come from other teachers and that everything I do is "just fine". In fact, after 35 years of teaching, I feel as though I'm just scratching the surface. And teaching scales has always been a huge weakness for me.

Hannon teaches each scale by showing the major scale then its relative minor. So it shows, in this order:

C Major
A harmonic minor
A melodic minor

The problem with this, for me, is that it reminds me of the rather famous cartoon that shows a horribly difficult mathematical problem on the left, a simple solution on the right and NO idea about how to get there. The caption, I believe is: "And then a miracle occurred."

Here are some problems, for me as a teacher:

1. C Major and the different forms of the C minor scale share the same conventional fingerings. Neither A major nor A minor is related to the C scales by fingering. Therefore I would prefer to teach a major scale with its parallel minor scales.

2. An immediate problem: when a major scale starts on a white note, such as A Major, and it's relative minor starts on a black note (F# minor), then the major and natural minor do use the same fingerings. So now there IS a link. In addition, although the harmonic form of F# minor also uses the A major (and minor) fingerings, when only the third is flatted, conforming to the ascending melodic minor, the fingering switches, and I find that very difficult to teach.

3. I've never been quite sure how helpful it is for students to practice major and minor scales the way they are required to be learned in conventional teaching methods. I have taught them "by the book" only when preparing students for university auditions, because in this case they simply must know them to get in. I learned them all rather quickly in high school and knew them well enough to play them for auditioning, but once I was on the university level, I preferred to study scales as they appear in music, which is usually a very different things from zooming up and down the keyboard for four octaves.

4. I have tried to add at least one extra step. When I do teach the minors, I tell students to being flatting only the third and have them practice going up and down two octaves (to get all the finger turns) and both ways. I call this "simple minor", because "melodic minor", as it is normally taught, is the combination of two scales, using only the flat 3rd ascending but descending with the added flat 6th and 7ty, natural minor. Next I show how flatting the 6th in addition to the 3rd forms the harmonic minor. Finally, I show that adding the flat 7th creates the natural minor and is the only minor scale (not using modes) that does not necessitate accidentals to "adjust it". When I see that these steps are understood, I mention melodic minor uses the "simple minor" ascending and natural descending. But I also mention that it could be quite useful to try ascending with only the 3rd lowered, the descending with the harmonic minor, since composers are like to "mix and match" scales in any way. And I encourage students to try all sorts of combinations, such as ascending with harmonic minor and descending with natural. I don't want students to just learn scales. I want them to understand why we pick certain fingerings to play them and why some are much harder to master than others. I want them to see these scales actually being used and played with in music. This has always been very easy for me to understand. I find it horribly difficult to explain.

I ask my students to practice a scale hands separately until it is really comfortable before putting the hands together. And I ask them to only spend a little time doing this each day, because I would rather that they absorb the overall theory behind fingering and construction of scales, then apply it to pieces.

Suggestions anyone? This is not something I feel I teach well.

Gary

[bernhard]

Here are some threads where scales are discussed in detail:

https://pianoforum.net/smf/index.php/topic,2313.msg19807.html#msg19807
(Speed of scales – the important factors in speed playing - an alternative fingering for scales).

https://pianoforum.net/smf/index.php/topic,2533.msg21955.html#msg21955
(an structured plan to learn scales and arpeggios – includes description of repeated note-groups and other tricks)

https://pianoforum.net/smf/index.php/topic,2619.msg22756.html#msg22756
(unorthodox fingering for all major and minor scales plus an explanation)

https://pianoforum.net/smf/index.php/topic,2701.msg23134.html#msg23134
(Teaching scales – the cluster method and why one should start with B major).

https://pianoforum.net/smf/index.php/topic,2758.msg23889.html#msg23889
(scales & compositions – the real importance of scales is to develop the concept of key, not exercise)

https://pianoforum.net/smf/index.php/topic,2920.msg25568.html#msg25568
(how to play superfast scales)

https://pianoforum.net/smf/index.php/topic,2983.msg26079.html#msg26079
(Best order to learn scales – what does it mean not to play scales outside pieces)

https://pianoforum.net/smf/index.php/topic,2998.msg26268.html#msg26268
(Scales HT, why? – why and when to practise scales HS and HT – Pragmatical  x logical way of teaching – analogy with aikido – list of piano techniques – DVORAK – realistic x sports martial arts – technique and how to acquire it by solving technical problems – Hanon and why it should be avoided - Lemmings)

https://pianoforum.net/smf/index.php/topic,3499.msg31548.html#msg31548
(using scales as the basis for free improvisation)

https://www.pianostreet.com/smf/index.php/topic,2619.msg104249.html#msg104249
(Scaled fingering must be modified according to the piece – Godard op. 149 no.5 – yet another example of the folly of technical exercises)

https://pianoforum.net/smf/index.php/topic,1918.msg15015.html#msg15015
(Thumb under/over – detailed explanation – Fosberry flop)

https://pianoforum.net/smf/index.php/topic,2502.msg21594.html#msg21594
(Independence of the 3rd and 4thfinger – it is impossible, one should work towards the illusion of independence: it is all arm work)

https://pianoforum.net/smf/index.php/topic,3100.msg27113.html#msg27113
(thumb over – hand displacement – practising with awareness – awareness is not thinking – learning by imitation)

https://pianoforum.net/smf/index.php/topic,7226.msg72166.html#msg72166
(Thumb over is a misnomer: it consists of co-ordinating four separate movements).

Most of the questions you address have been covered there, but here is a quick summary:

1.   I always start by teaching the B major scale (it only requires three of the four basic movements), since it is the easiest to play from an anatomical point of view. The next scale is C major, since it is the most difficult (and it requires a further basic movement).

2.   All other scales are covered on an “as needed” basis, in relation to the pieces the student is playing, that is, we only practise the scales present in the pieces – there is no separate study of scales.

3.   I don’t use scales as technical exercises. I use them as irreplaceable resources for the understanding of the concept of “key” and tonal music, so scales are from the beginning tied up with theory and analysis.

4.   I teach scales by isolating the four basic movements (handshifting, forearm rotation, hand slanting and back and forth movement of the arm), and then integrating them the first scale may take up to three weeks to learn properly, after that (see next item) it goes very quickly. Any student should have mastered the 24 major and minor scales in 2 months.

5.   I use an unorthodox fingering, that once understood, will facilitate everything. But we do not stick to this fingering when playing scale passages within pieces, since musical requirements overrule fingering schemes.

6.   Once a student learns the scale and its fingering, the main scale activity will be scale free improvisation.

7.   Minor scales are taught first as modes (so after a major scale is learned we go through all of it modes by free improvising on each mode). The Aeolian mode (natural minor scale) is then isolated and its variants (melodic and harmonic minors) are explained. So really I always work from the point of view of relative minors (C major – A minor), never from the point of view of tonic minors (C major – C minor). These will be discussed much, much later once chords and their genesis from the scale have been thoroughly mastered (by the way, this is by no means the only possibility – working from the tonic minors can be equally effective – it is just not the way I do it).

All of these points are discussed in much greater detail in the thread above.

I hope this helps.

Best wishes,
Bernhard.

[pianistimo]

i use orthodox fingering because i would use the thumb over pattern only in fast playing that is basically non repetitive scales, but harmonically jazzed up runs or arpeggios of various sorts.  playing scales fast doesn't give a beginner time to assimilate the notes in the pattern (major or minor) or take into account the whole and half step patterns. 

of course, bernhards method may be good for someone who's played awhile or an advanced student.

i like what was said about learning C major and then c minor scales (similar fingerings) but i wondered what was meant about point #2.  A major doesn't have a similar fingering to f# minor unless you are doing some radical finger change.  longer fingers on sharp notes make more sense to me (since the thumb naturally drops down on the white note to the left of the black).  it puts your hand at an odd angle to play otherwise.

also, you can't practice block  patterns as easy with 'insane' fingering.  in blocking you can start visualising the 123 1234 (played together as a group) and their repetition.  with 'insane' yet fast fingering (for some bach pieces, a lot of chopin, etc etc)  you have some scales that do not repeat, but go off on some harmonic tangent.  they are leading somewhere different than a repeat of the scale 1, 2, 3, and 4 octaves.  to me, this is where ingenious fingerings and thumb cross-overs should occur.  in fact, i think a book should be written to take some passages of bach/chopin and show where they would be advantageous.

this is just my two-cents.

ps  everyone should know the related minor keys (and learning them at the beginning is quite advantageous - as they seem to store in memory well that way).  maybe if you switch methods with scales it is less advantageous than switching with five finger exercises (where you can play the C major, c minor, and then v/v easily before going on to the D# major chromatically)

[xvimbi]

i use orthodox fingering because i would use the thumb over pattern only in fast playing that is basically non repetitive scales, but harmonically jazzed up runs or arpeggios of various sorts.  playing scales fast doesn't give a beginner time to assimilate the notes in the pattern (major or minor) or take into account the whole and half step patterns. 

of course, bernhards method may be good for someone who's played awhile or an advanced student.

If I remember correctly, that is actually not how Bernhard teaches scales This is how he teaches playing smooth, fast scales.

I think the teaching approach should become clearer if one defines exactly what the purpose is of teaching/learning scales. If the purpose is to do ear training and learn about keys, construction of scales, what notes belong to the scales, how scales are related, etc., i.e. the rather theoretical aspects of scales, then it is completely sufficient to use a single finger to play the notes. This is actually how Bernhard starts out his students (again, if I remember correctly). No need to delve into TO and TU, a basic version of TU, blocked execution of scales, etc. is certainly OK. Because TU is one of the most injury-prone movements in the pianists technical repertoire, it needs to be well-explained and demonstrated.

If, on the other hand, the emphasis is on executing scales in the context of a piece, learning staccato and legato playing, etc., then obviously, one should focus more on the different types of scale fingering, the accompanying movements (anatomy), tayloring scale playing to a certain student and so on, but then it becomes an issue that is somewhat independent of the concept of scales.

[gaer]

i use orthodox fingering because i would use the thumb over pattern only in fast playing that is basically non repetitive scales, but harmonically jazzed up runs or arpeggios of various sorts.  playing scales fast doesn't give a beginner time to assimilate the notes in the pattern (major or minor) or take into account the whole and half step patterns. 

In the rare event that I have to teach scales for auditions, the way I teach them is with what I believe you would call "orthodox" fingerings.

i like what was said about learning C major and then c minor scales (similar fingerings) but i wondered what was meant about point #2.  A major doesn't have a similar fingering to f# minor unless you are doing some radical finger change.

I meant that for the F# natural and harmonic scales, the thumbs are on the same keys as in the A Major scale.

However, in the melodic minor, ascending, the thumbs are on the same keys as in the F# Major scale (since lowing E# to E natural does not change the theoretical fingering):

I'm sure you'll understand what I meant immediately, but in case someone else is confused, let me try to write them out. This is very hard. Writing in letters rather than simply writing something out, in standard musical notation, is very difficult for me.

Right hand:

1. F# natural minor (thumb on A and D, as in the A Major scale)
F#G#A B C# D E F# (G# A)
2   3  1 2  3   1  2 3   (4   1)
(3)(4)

2. F# harmonic minor (thumb on A and D, as in the A Major scale)

F#G#A B C# D E# F# (G# A)
2   3  1 2  3   1 2   3    (4    1)
(3)(4)

3. F# simple minor, or melodic minor ascending (thumb on A and E#, unique fingering, I believe)

F# G# A B C# D# E# F# (#G A)
2    3   1  2  3  4    1    2  ( 3  4  )

Left hand:

1. F# natural minor (thumb on A and E, as in the A Major scale)
F# G# A B C# D E  F# (#G# A)
3    2   1 4  3   2  1  3   (  2    1 )

2. F# harmonic minor (thumb on A and E#, almost as in the A Major scale)
F# G# A B C# D E# F# (#G# A)
3    2   1 4  3   2  1    3   ( 2    1)

3. F# simple minor or melodic minor, ascending (thumb on B and E#, as in the F# Major scale)
F# G# A B C# D# E# F# (#G# A)
4    3   2  1  3   2   1   4    (  3    2)

also, you can't practice block  patterns as easy with 'insane' fingering.  in blocking you can start visualising the 123 1234 (played together as a group) and their repetition.  with 'insane' yet fast fingering (for some bach pieces, a lot of chopin, etc etc)  you have some scales that do not repeat, but go off on some harmonic tangent.

The fingerings I'm talking about are 100% "traditional". But the difference between traditional scales and passage work is night and day. Fingering is an art, not a science, and I believe most of us spend our whole lives trying to come up with better and better solutions to "fingering problems".

Gary

[pianistimo]

thanks, gary for the informative stuff.  i understand what you mean. 

xvimbi,  when you teach younger children it's different than older ones.  i think the more traditional fingering is easier to learn no matter if you are teaching dexterity, fingering, theory, or musicality.  usually musicality isn't learned by scale passages anyway, alone, although you can crescendo as you go up and decrescendo as you go down.  some scales staccato, some legto.  i think i know the point you are trying to get across, yet i still think it's easy for some to criticize teachers before they take a handful of little kids and try to get a concept across.  just the fact that in tradional scales you have different fingerings is almost enough, but with the non-traditional, it is a technique you are working (speed) which imo (which may be wrong, btw) you want understanding.  you can work on speed later.

you know i tried the last fingering for LH as an experiment in 'newer fingering' for the RH f# minor natural scale.  what do you think?  it follows the thumb over idea, but is very comfortable and relaxed if you are quickly gliding your hand across the tops of the keys.  sort of a brush of each finger (like you are dusting each key straight down) and crossing of ALL the fingers.  just an idea.  is it new, or has someone else found it?  i shall be the first to master it, if it is the former. 

[gaer]

thanks, gary for the informative stuff.  i understand what you mean.

I need to make one thing clear though. I was showing the traditional fingering, as in Hannon. I do not use Hannon. In fact, I very much dislike Hannon, at least as it is normally taught. If you are interested, I can give you several reasons why, which I think are logical.

I've been reading through Bernard's posts, the ones he recommended (linked), and that's why I have not yet answered him in this thread.

I follow the same "rule of thumb" as he has suggested for passage work. In other words, I finger the LH for the A scale this way:

21 3  2   1  4  3   2  1
AB C# D E F# G# A B

I don't do it for one octave, starting and ending on A, because you have to balance the advantage of a more comfortable thumb turn with the NUMBER of thumb turns in a set of notes. So A to A, in an A scale, using the orthodox fingering, works best for me in most cases, in the LH. It uses only one thumb turn, the C# is comfortable under my 3rd finger, and the 3rd finger moves to F#, which is very comfortable. Perhaps I am just lazy.

But a one octave scale, starting on the tonic and ending on same is a special case. The moment scales begin to start on different degrees of the scale (and end on different ones), the standard fingering immediately becomes slow and uneven for me.

If I started on G#, ascending to B, then I would use:

G# A B C# D E F# G# A B
3    2 1 3   2 1  4   3   2 1

The way I was taught scales was, in my opinion, simply wrong. Or very inefficient. Rather then relearn them as I now think they should be played, I took another approach, which many people may or may not think is wise. For my own playing, I have simply refingered all passage work to follow what I think are sound principles. I never stop experimenting with new ideas, though I throw some of them out very quickly.

In short, I use both the orthodox fingerings and the "unorthodox" ones, exactly as Bernhard has explained them (the unorthodox ones)—and many other variations. In my opinion, those who read and study the info provided in the links in Bernhard's post in this thread (#1) and absorb what's he's talking about will be on very firm ground.

Normally I would be too busy trying to teaching people to be posting so much, but it's Labor Day and I have time off. So I'm here instead.

Gary

[gaer]

Bernhard,

First I want to thank you for taking the time to respond in such detail. Perhaps the only thing I don't understand is this: how do you remember where you have PUT these posts?

Let me respond briefly:

(Speed of scales – the important factors in speed playing - an alternative fingering for scales).

In fact, the fingerings you mentioned are linked to one of the reasons I started this thread. I suspect in the majority of cases, the fingerings I use or recommend are very similar.

When I am explaining how the hand needs to move in scales, I teach the B Major scale for the RH and the Db Major scale for the LH. I have students start with the RH, for instance, starting on third line B in the treble clef then simply "run the scale down", 54321 321 4321 321, two or three octaves. Then, with the LH, starting on third line Db in the bass clef: 321 4321 321, also two or three octaves. (This depends on the size of the person and what I see happening. If I see tension or any movement that I don't like, I change something. If it's right, it looks effortless.)

I ask students to carefully observe what they are doing and watch me closely. I don't describe what I do in words. I never tell people how to do things, in lessons, unless they are doing something that looks wrong to me that I feel will not take care of itself very soon.

I prefer the Db scale for the LH because the movements from F to Gb and C to Db are half steps. I feel that the advantage of "feel" by starting on B, beginning with the 4th finger, is compensated for by the natural half-step crossings of the thumb.

No scale is ever quite as fast or even for me when I am moving "outward", ascending in the RH or descending in the LH. However, by attempting to preserve the relaxation and lack of effort moving in the "hard direction", I am most likely to achieve the greatest speed with the least effort and best possible evenness. When scales are played extremely fast and well, there is one thing I see in all good players: nothing seems to be moving but the fingers. This is, of course, an illusion, but when a student is successful at recreating this illusion, he or she will be relaxed with minimum movement.

We can talk from now until eternity about thumb over, thumb under, lateral displacement, and so on. It's a bit like talking about how people run without being able to see people running. But if I had the courage to try to explain "thumb over", in words, I would be very happy if I could do it as well as you have.

(unorthodox fingering for all major and minor scales plus an explanation)

I use the same fingerings.

(Teaching scales – the cluster method and why one should start with B major).

Self-evident, for explaining many things. I also start with the C scale, but only hands separate, in very little songs I have written myself, always moving towards middle C:

CBAGFEDC/DEFDEFG (RH, all eight notes except for the final note, two bars of common time.

CDEFGABC/B-G-C--- (LH, one bar of 8ths, the next two quarters plus half.)

But this is read and played much more slowly, for other things (mostly increasing fluency of reading).

(scales & compositions – the real importance of scales is to develop the concept of key, not exercise)

Which is why I started this thread. And why I always go over scales hands separately first.

(how to play superfast scales)

I agree with everything you said here, I believe.

(Best order to learn scales – what does it mean not to play scales outside pieces)

You might criticize me for going too far. I prefer not to discuss scales except as they relate to pieces I am teaching. I only see people once a week. I have so little time, and my top priority is showing people how to learn the maximum amount of music in the shortest period of time in a way that will also build a solid technique. I have specific pieces that I like to use to demonstrate how different scales (different modes, major and minor, etc.) are dynamically used. Think, for instance, of the F# minor section of the Mozart's "Rondo alla Turca". The RH is a great example of how F# minor scale patterns are used, doublying back and forth, modulating a bit to A Major then back again to F# minor. Also a great place to show that the dominant triad and dominant 7 chord remains C# Major (C# Maj7)  in both F# Major and F# minor a great deal of the time.

(Scales HT, why? – why and when to practise scales HS and HT – Pragmatical  x logical way of teaching – analogy with aikido – list of piano techniques – DVORAK – realistic x sports martial arts – technique and how to acquire it by solving technical problems – Hanon and why it should be avoided - Lemmings)

In fact, I have mispelled "Hanon" as "Hannon" at least once here, which may give you an idea of how often I use it. I have never taught a Hanon exercise. I think Hanon is mind-numbing, and in rare cases it can even contribute to CTS (Carpal Tunnel Syndrome). The hands should be moved in as many different ways as possible, working for maximum flexibility and strength with no discomfort, and almost all the hand injuries I've heard about have come from students (or competition players) practicing countless hours on the same pieces—or parts of pieces—in a way that is extremely dangerous. To me, Hanon is the first step on the way to a very, very ineffective and potentially dangerous way to practice.

(using scales as the basis for free improvisation)

Very good!

(Scaled fingering must be modified according to the piece – Godard op. 149 no.5 – yet another example of the folly of technical exercises)

Total agreement. On another day I'd like to discuss some editors. For instance, Jossefy's Chopin fingerings are absolutely the most uncomfortable I've ever seen. I think they are insane.

(Thumb under/over – detailed explanation – Fosberry flop)

Good analogy. As I said, I prefer to show the concept rather than to talk about it, which unforunately would not work in this environment.

(thumb over – hand displacement – practising with awareness – awareness is not thinking – learning by imitation)

Very good!

Most of the questions you address have been covered there, but here is a quick summary:

1.   I always start by teaching the B major scale (it only requires three of the four basic movements), since it is the easiest to play from an anatomical point of view. The next scale is C major, since it is the most difficult (and it requires a further basic movement).

I covered that.

2.   All other scales are covered on an “as needed” basis, in relation to the pieces the student is playing, that is, we only practise the scales present in the pieces – there is no separate study of scales.

Then perhaps you would not be unhappy with what I do. I do the same thing.

3.   I don’t use scales as technical exercises. I use them as irreplaceable resources for the understanding of the concept of “key” and tonal music, so scales are from the beginning tied up with theory and analysis.

Ditto.

4.   I teach scales by isolating the four basic movements (handshifting, forearm rotation, hand slanting and back and forth movement of the arm), and then integrating them the first scale may take up to three weeks to learn properly, after that (see next item) it goes very quickly. Any student should have mastered the 24 major and minor scales in 2 months.

I believe I show the same movements. I hope I do. But since there is no way I can teach music that is in all major and minor keys, it takes me much longer to cover the scales. I don't think I spend more time teaching them. I think the timing of WHEN I cover them is different. But my goal, I believe, is the same.

Because of some of your ideas, I may try covering more different keys, or covering them in a more though-out way.

5.   I use an unorthodox fingering, that once understood, will facilitate everything. But we do not stick to this fingering when playing scale passages within pieces, since musical requirements overrule fingering schemes.

I do the same thing.

6.   Once a student learns the scale and its fingering, the main scale activity will be scale free improvisation.

I don't do this. I probably should. There is so much to teach, for me so little time…

7.   Minor scales are taught first as modes (so after a major scale is learned we go through all of it modes by free improvising on each mode). The Aeolian mode (natural minor scale) is then isolated and its variants (melodic and harmonic minors) are explained. So really I always work from the point of view of relative minors (C major – A minor), never from the point of view of tonic minors (C major – C minor). These will be discussed much, much later once chords and their genesis from the scale have been thoroughly mastered (by the way, this is by no means the only possibility – working from the tonic minors can be equally effective – it is just not the way I do it).

I understand your reasoning. My older student did not understand, at first, that a minor scale is not a fixed concept, one solution, one form. I wanted her to understand that while the third generally remains lowered (not taking into consideration modulation, which is another subject), the 6th and 7th degrees are "in flux", one moment lowered, the next not. I specifically showed her that we will see minor scales descending with only the 3rd lowered, and I used CPE Bach's Solfegietto as an illustrationg, since there are numerous examples of the minor scale descending form the 9th in Cm, Fm and Gm. I also wanted her to understand the even the dominant may or may NOT be a major chord, depending on the modality of the composition. I don't know how to explain the appearance of the harmonic or melodic minor in terms of modes unless we consider these alterations of modes.

For theory I prefer to teach the relation of keys in a parallel and relative way, because key changes are so common in both ways.

I hope this helps.

It was a tremendous help, and often because it's helpful to see that you are recommending many of the same ideas that I am!

All the best,

Gaer

[Bob]

I go with 2 8ves major.

Then 2 8ves natural minor.

Then 4 8ves major and 4 8ves medolic and harmonic minor.

When teaching minor, explain the three forms.  Natural is the relative version.  Melodic for melodies.  Harmonic for harmonies and the exceptions of the seventh step.

[gaer]

I go with 2 8ves major.

Then 2 8ves natural minor.

Then 4 8ves major and 4 8ves medolic and harmonic minor.

When teaching minor, explain the three forms.  Natural is the relative version.  Melodic for melodies.  Harmonic for harmonies and the exceptions of the seventh step.

The specific question my student asked me was this:

"Where is the missing information?"

She had brought in one of the early Thompson books and was stumped by the explanation of scales in the book. I don't use Thompson, but I had promised to try to explain anything that she asked, from any source if I thought she was ready to understand it.

Thompson took the traditional approach and was showing the natural minor and harmonic minor related to the keys of C, F and G, so the explanation involved Am, Dm and Em.

I explained that the information was correct, although the fingerings used were traditional. However, I had started with only one key, C Major, and I had showed that it is only necessary to change one "note" to form what we call the "melodic minor", which is actually the combination of two scales, since as it is usually taught, it is shown to descend as a natural minor scale.

My point was that only one degree of the scale must be lowered for the sound of the scale we associate with the melodic minor scale. So instead of presenting C minor with the conventional key signature, I used Finale to print out the C Major scale, two octaves, on one line, the same scale with only E flatted on the second, adding Ab on the third, and finally adding Bb on the forth, arriving at the natural minor in three steps. But no flats in a key signature. Bad idea, because it was not clicking for her. (It has worked very well for others. Everyone is different.)

My purpose in doing this was to show the 6th and 7th degrees of the scale vary, one moment being flatted, the next not, all according to the chord structure and countless other factors.

The problem was that she could not make the mental "jump" to seeing these scales without a key signature. The solution was to simply "turn on" the key signature for C minor, then show her the same thing in reverse. This time I showed her that although the natural minor follows the key signature of three flats, the harmonic "turns off" the flat on the Bs, and the "melodic" then turns off the flat on the As. I wanted her to understand that the frequency with which naturals occur, as accidentals, in a minor key has a great deal to do with the fact that the 6th and 7th degrees tend to "morph" back and forth, one moment lowered, the next not. I did not dare go beyond that explanation at this time.

Once I had added the conventional key signature, although I had not really changed anything she got it. Then I did the same thing with the key of A Major, showing the three forms of the scale in A minor. Then, when I gave her the two pages I had just created and printed out, a light went on, and she got it.

She also understood, for the first time, why the triad built on the fifth of a minor key may be either a minor or a major chord, although it is usually shown as only major and taught together as a V chord, linking it to the V7 chord and thus showing these chords to be the same as the parallel major key.

If you've followed this so far—music is so easy to talk about with a keyboard handy and so hard to talk about without one—this lady, almost 70, largely self-taught and VERY bright was unable, at first, to realize that I was simply explaining the same thing in a different way. Once she did, which happened in the last lesson, she said it was crystal clear.

Now, this gave me the courage to do something I have never done before. Following the logic of what I had just done, I wrote all four scales (major, melodic minor, harmonic minor and natural minor) two octaves with all scales descending first for the RH and ascending first for the LH (moving in the more natural direction first), then put in the scale fingerings I prefer to teach—which I believe are the same as what Bernhard uses.

[I use, for in stance, for the D Major scale, LH ascending:
21 4321 321 4321 32, with "21" shown at the end as a superior fingering to end with, especially when reversing direction without stopping, the thumb falling on E and B…]

Also, since I prefer to teach the RH descending first, because I believe this is a much more natural direction to move in, I had to redefine what I was showing as the "simple minor scale", a term that does not really exist, right? Otherwise, following the traditional approach, I would have to show this as the same as the natural minor, since the melodic minor scale, as shown in traditional books, is shown as a descending natural minor scale.

But I wanted to make it clear to you and others that I was using scales to explain what was happening in music this lady was playing, not teaching them separately as exercises or as only theoretical information. In addition, she more or less "forced me" to introduce this info ahead of time. It's very hard to pull rank on someone who is older than I am, especially someone who is also exceedinly nice and truly interested.

I'm sorry to make this sound so complicated. I have over three decades experience teaching people. I have zero experience trying to explain what I do in this manner, without actually working personally with a student and having a keyboard to demonstrate. This is hard. <whew>

Gary

[gaer]

The specific question my student asked me was this:

"Where is the missing information?"

She had brought in one of the early Thompson books and was stumped by the explanation of scales in the book. I don't use Thompson, but I had promised to try to explain anything that she asked, from any source if I thought she was ready to understand it.

Thompson took the traditional approach and was showing the natural minor and harmonic minor related to the keys of C, F and G, so the explanation involved Am, Dm and Em.

I explained that the information was correct, although the fingerings used were traditional. However, I had started with only one key, C Major, and I had showed that it is only necessary to change one "note" to form what we call the "melodic minor", which is actually the combination of two scales, since as it is usually taught, it is shown to descend as a natural minor scale.

My point was that only one degree of the scale must be lowered for the sound of the scale we associate with the melodic minor scale. So instead of presenting C minor with the conventional key signature, I used Finale to print out the C Major scale, two octaves, on one line, the same scale with only E flatted on the second, adding Ab on the third, and finally adding Bb on the forth, arriving at the natural minor in three steps. But no flats in a key signature. Bad idea, because it was not clicking for her. (It has worked very well for others. Everyone is different.)

My purpose in doing this was to show the 6th and 7th degrees of the scale vary, one moment being flatted, the next not, all according to the chord structure and countless other factors.

The problem was that she could not make the mental "jump" to seeing these scales without a key signature. The solution was to simply "turn on" the key signature for C minor, then show her the same thing in reverse. This time I showed her that although the natural minor follows the key signature of three flats, the harmonic "turns off" the flat on the Bs, and the "melodic" then turns off the flat on the As. I wanted her to understand that the frequency with which naturals occur, as accidentals, in a minor key has a great deal to do with the fact that the 6th and 7th degrees tend to "morph" back and forth, one moment lowered, the next not. I did not dare go beyond that explanation at this time.

Once I had added the conventional key signature, although I had not really changed anything she got it. Then I did the same thing with the key of A Major, showing the three forms of the scale in A minor. Then, when I gave her the two pages I had just created and printed out, a light went on, and she got it.

She also understood, for the first time, why the triad built on the fifth of a minor key may be either a minor or a major chord, although it is usually shown as only major and taught together as a V chord, linking it to the V7 chord and thus showing these chords to be the same as the parallel major key.

If you've followed this so far—music is so easy to talk about with a keyboard handy and so hard to talk about without one—this lady, almost 70, largely self-taught and VERY bright was unable, at first, to realize that I was simply explaining the same thing in a different way. Once she did, which happened in the last lesson, she said it was crystal clear.

Now, this gave me the courage to do something I have never done before. Following the logic of what I had just done, I wrote all four scales (major, melodic minor, harmonic minor and natural minor) two octaves with all scales descending first for the RH and ascending first for the LH (moving in the more natural direction first), then put in the scale fingerings I prefer to teach—which I believe are the same as what Bernhard has posted elsewhere and what I'm sure many other people here use.

[I use, for in stance, for the D Major scale, LH ascending:
21 4321 321 4321 32, with "21" shown at the end as a superior fingering to end with, especially when reversing direction without stopping, the thumb falling on E and B…]

Also, since I prefer to teach the RH descending first, because I believe this is a much more natural direction to move in, I had to redefine what I was showing as the "simple minor scale", a term that does not really exist, right? Otherwise, following the traditional approach, I would have to show this as the same as the natural minor, since the melodic minor scale, as shown in traditional books, is shown as a descending natural minor scale.

But I wanted to make it clear to you and others that I was using scales to explain what was happening in music this lady was playing, not teaching them separately as exercises or as only theoretical information. In addition, she more or less "forced me" to introduce this info ahead of time. It's very hard to pull rank on someone who is older than I am, especially someone who is also exceedinly nice and truly interested.

I'm sorry to make this sound so complicated. I have over three decades experience teaching people. I have zero experience trying to explain what I do in this manner, without actually working personally with a student and having a keyboard to demonstrate. This is hard. <whew>

Gary

[omnisis]

Here's a trick for learning your melodic minor scales.  The melodic minor is just the first four notes (tetrachord) of the natural minor + the last four notes of the parallel major.  Let me explain.

Take  C minor for instance
====================
Related Major = Eb Major [Bb,Eb,Ab]
Parallel Major = C Major   [ no # or b ]

1) Take the first four notes of the natural minor (same notes as related major Eb): C,D,Eb,F
2) Add the last four notes of the parallel Major (in this C major): G,A,B,C

so the C minor melodic scale is: C,D,Eb,F,G,A,B,C

Another way to think of the melodic minor is as a parallel major with a flattened third. 

~omnisis

[abell88]

Here's a trick for learning your melodic minor scales.  The melodic minor is just the first four notes (tetrachord) of the natural minor + the last four notes of the parallel major.  Let me explain.

Take  C minor for instance
====================
Related Major = Eb Major [Bb,Eb,Ab]
Parallel Major = C Major   [ no # or b ]

1) Take the first four notes of the natural minor (same notes as related major Eb): C,D,Eb,F
2) Add the last four notes of the parallel Major (in this C major): G,A,B,C

so the C minor melodic scale is: C,D,Eb,F,G,A,B,C

Another way to think of the melodic minor is as a parallel major with a flattened third.

Those are both fine, as long as you realize that descending is different...

[omnisis]

oh yeah, of course...you have to revert to the natural minor for descending...the previous was just a trick to learning the melodic minor ascending....sorry should have said that....

~omnisis

[gaer]

Here's a trick for learning your melodic minor scales.  The melodic minor is just the first four notes (tetrachord) of the natural minor + the last four notes of the parallel major.  Let me explain.

Take  C minor for instance
====================
Related Major = Eb Major [Bb,Eb,Ab]
Parallel Major = C Major   [ no # or b ]

1) Take the first four notes of the natural minor (same notes as related major Eb): C,D,Eb,F
2) Add the last four notes of the parallel Major (in this C major): G,A,B,C

so the C minor melodic scale is: C,D,Eb,F,G,A,B,C

I would not explain it that way. Too many steps. Of course I understand what you mean.

Another way to think of the melodic minor is as a parallel major with a flattened third. 

That's the only way I would teach the concept.

But first, a question:

Why is the melodic minor important, as it is tradionally taught?

Why do people persist in hammering on the strange idea that it's very important to play a scale ascending in one way and descending in another?

This is why I refer to the "melodic" minor as the "simple minor". There is absolutely no reason not to teach the minor scale with only the 3rd lowered in both directions. Why instill the idea that a scale, in any form, should be and is only played in one direction? That is illogical to me from both a technical and a theoretical standpoint.

I want my students to understand the construction of scales and how they appear in music. I'm not concerned with them playing scales over and over again, in some theoretical form. This is a great way to bore people, and it takes time away from reading—or working out musical problems.

I want to go straight to music and explore how scales are used, how they are modified, and how fingering needs to be adjusted to the context in which scale patterns occur.

Here is an excellent example of how the "simple minor" scale is used in music. I'm sticking with the term "simple" because of the traditional insistence upon calling a scale melodic when it descends as a natural minor scale. By definition, a scale can not be melodic when it descends with only the lowered 3rd—if we stick rigidly to the normal use of this word as applied to a scale played according to audition or "skills" requirements.

In CPE Bach's Solfeggio—or Solfegietto—this scale, with only the lowered 3rd, appears in three keys, descending. The first time it is in C minor:

D C B A G F Eb D Eb.

Quite obviously this contains a G7 chord, the dominant 7th.

Next the piece modulates to F minor, and the pattern is transposed:
G F E D C Bb Ab G Ab, containing C7

Next the piece modulates to G minor, and the pattern is transposed:
A G F# E D C Bb A Bb, containing D7

In music, we may ascend in any scale and descend in a different form. Ascending in "simple minor", then descending in harmonic minor is quite common:

C D Eb F G A B C, D C B Ab G F Eb D, C

Now, what are we going to call that? Are we going to make up a new name everytime we ascend one way and descend another? A "meloharmonic" scale?

Although I do explain the term "melodic minor", I think it is a strange name, and we would be better off without it.

In fact, if you do the same thing in F minor:

F G A Bb C D C E F, G F E Db C Bb Ab G, repeat

you have the 2nd ending before the coda of the last movement of Beethoven's "Appassionata". But now it's a nine note pattern, not an eight note (set of seven), so you have to use a fingering such as:

up 1234 1234 down 54321 4321

Or how would you explain to a student why Chopin, in bar 18 of the "Revutionary" Etude, starts on Bb on beat two, descending with what appears to be C natural minor (starting with Bb) but then "morphs" into what finishes up as a C harmonic minor.

These things are probably all obvious to you and most of the people who read these threads, so my reason for starting this thread was to address the problem of trying to help students understand such elementary theory.

Gary

[bernhard]

Ok. Brace yourself and sit comfortably, this is going to take a while.

What exactly is a scale?

Quite simply it is a sequence of intervals leading in steps from one pitch to another – hence the name “scale” which is Italian for “ladder” or “staircase” (Scalla).

So one way to go from C to C one octave higher is by playing (on the piano) every single note (black and white keys) until you get there. This is the chromatic scale, and the “size” of the step is a half-tone. On the piano, this is the “ladder” with the smallest possible step. You could also try to get there with steps one-tone in size (C – D – E – F# - G# - A# - C) which is the whole tone scale. One interesting fact about these two scales, is that there is really one chromatic scale – no matter which note you start, it is always the same notes. With the whole tone scale, you can only have two possibilities (C# - D# - F – G – A – B being the other one). However, if you have an unequal pattern on the size of steps, like for instance in the major scale (tone – tone – halftone – tone – tone – tone – halftone), you will have 12 different scales  - that is each note of the piano generates a different major scale.

Does this mean that by altering the specific pattern of tones semitones I get different scales? Exactly.

Now let us go back in time. In Medieval times there were no black keys. The only scale around was C-D-E-F-G-A-B-C. It was not called C major either. This came much later. All that musicians knew was that the peculiar sound they got out of that scale was due to the peculiar sequence of tones and semitones. So they had seven “scales”:

CDEFGABC – with pattern – 1 – 1 - ½  - 1 – 1 – 1 – ½ (Ionian)
DEFGABCD – with pattern – 1 - ½  - 1 – 1 – 1 – ½ - 1 (Dorian)
EFGABCDE – with pattern – ½  - 1 – 1 – 1 – ½ - 1 - 1  (Phrygian)
FGABCDEF – with pattern – 1 - 1 – 1 - ½  – 1 – 1 – ½ (Lydian)
GABCDEFG – with pattern – 1 – 1 - ½  - 1 – 1 – ½ - 1 (Mixolydian)
ABCDEFGA – with pattern – 1 - ½  - 1 – 1 –  ½ - 1 - 1  (Aeolian)
CDEFGABC – with pattern  ½  - 1 – 1 – ½ - 1 – 1 - 1  (Locrian)

To our ears, these “scales” – or to give their proper names “modes” – do not sound like scales at all. In fact they sound like nothing, just some random melodic fragment. Yet, in medieval times, a mode like the Dorian (from D to D) would have been far more familiar than the C major scale (Ionian mode).

For several reasons that are not important for this issue, by the end of the 16th century, most of the modes had fallen into disuse, except for the Ionian (our major scale), and the Aeolian, which is formed by playing the notes of the major scale, but starting and finishing on the sixth degree (the submediant). Hence, if you have a C major scale and play it but starting and finishing on A, you have the Aeolian mode, or natural minor scale. Even though it has all the notes of C major, it sounds very different because the sequence of tones and semitones (the steps of the ladder) has been dramatically altered:

CDEFGABC – with pattern – 1 – 1 - ½  - 1 – 1 – 1 – ½ (C major scale)
ABCDEFGA – with pattern – 1 - ½  - 1 – 1 –  ½ - 1 - 1   (natural A minor scale)

In comparison, a scale like Gb major which has no notes in common with C major except for the F will sound exactly the same because the pattern of tones and semitones is exactly the same:

GbAbBbCbDbEbFGb -  with pattern – 1 – 1 - ½  - 1 – 1 – 1 – ½ (Gb major)

Natural as the Aeolian mode may be, it presented a serious problem: the distance of its leading note (7th degree) to the tonic was a full tone, when compared to the Ionian (major scale) mode, whose leading note was just a semitone away from the tonic. This is important in terms of melody, because the strong feeling of movement from B (leading note) to C (tonic) in C major, is basically a consequence of how close they are. On the A minor natural scale, on the other hand, the leading note (G) is a full tone away from the tonic, creating far less of a pull towards the tonic.

By the 17th century, musical theoreticians decided to sharp the leading note of the natural minor scales to create the desired attraction between its leading note and the tonic. And since this “sharpening” was completely artificial and had no grounds on the genesis of the scale (form the Aeolian mode), it was considered an “accidental”, and therefore was not included in the key signature of the piece. So now we have:

CDEFGABC – with pattern – 1 – 1 - ½  - 1 – 1 – 1 – ½ (C major scale)
ABCDEFGA – with pattern – 1 - ½  - 1 – 1 –  ½ - 1 - 1   (natural A minor scale)
ABCDEFG#A – with pattern – 1 - ½  - 1 – 1 –  ½ - 1+1/2  - ½ ( modified A minor scale in order to create a semitone between leading note and tonic)

This solved the problem of the distance between the leading note and the tonic, but created another problem: by pushing the leading ntoe towards the tonic, they increased the gap between the submediant (6th degree) and the leading note, which was now 1 tone and a half. So again – and promising never to meddle with it again – seventeen century theoreticians sharped the submediant, and that produced a satisfyingly uniform pattern:

ABCDEF#G#A – with pattern – 1 - ½  - 1 – 1 –  1 - 1  - ½ ( Melodic A minor scale, ascending)

Now in the 17th century, European music was mostly concerned with polyphony, that is, the weaving together of several melodic lines. So the aim here was melody. Hence the criteria to change the scale were melodic (providing a strong pull between leading note and tonic, creating a pattern of intervals with more or less regular intervals without large jumps and so on), and so this modified Aeolian mode was called a “melodic” minor scale.  And because the priorities were melodic, these modifications were important only when ascending the scale (it is important that the leading note “leads” to the tonic, but there is no such importance the other way around: the tonic is not required to “lead” anywhere). Because of that, the Aeolian mode was modified only when going from leading not to tonic. When going down (descending scale) from tonic to leading note, they just left the Aeolian mode unmodified (that is the natural minor scale):

CDEFGABC – with pattern – 1 – 1 - ½  - 1 – 1 – 1 – ½ (C major scale)

ABCDEFGA – with pattern – 1 - ½  - 1 – 1 – ½ - 1 - 1   (natural A minor scale)

ABCDEF#G#A – with pattern – 1 - ½  - 1 – 1 – 1 - 1  - ½ (Melodic A minor scale, ascending)

AGFEDCBA – with pattern – 1 - ½  - 1 – 1 – ½ - 1 - 1   (Melodic A minor scale descending = natural A minor scale)

Since all these modifications were completely artificial and had nothing to do with the scales and their derivation proper (as modes), these sharps are not represented in the key signatures. This means that a major scale and its relative minor scale – that is the Aeolian mode (or mode derived form the sixth note of the major scale), have exactly the same key signature, because originally (before 17th century theoreticians started meddling with them) they were the same scale, just starting and ending on different notes.

By the 18th century however, harmony – which before was simply a consequence of having more than one melodic line at the same time – started acquiring a life of its own. Chords were codified and the very important step of realising that an inversion was still the same chord had happened. While before intervals were the important concept now chords and chord progressions became all the rage. Counterpoint and many of its demands and rules on melodic lines gave way to a single melodic line and an accompaniment  (the “gallant style”). From that point of view, it does not really matter if there are large or small gaps from one note to the next to the scale, but rather which chords can we form from each note of the scale. While the fifth degree (dominant) of a natural minor scale will produce a minor chord (in A minor natural, the 5th degree E, will produce the E minor chord: EGB), the fifth degree of a modified minor scale will produce a major chord (in A minor: E major: EG#B). I will leave for you on homework to work this out to the melodic minor scale, but you probably can predict that several different chords will be produced depending on its being ascending or descending. This complicates harmonic thought, no matter how useful it is in terms of melody. And since by the 18th century harmony was more and more prevalent, the modified version of the A minor scale was reintroduced as an “harmonic” form:

ABCDEFG#A – with pattern – 1 - ½  - 1 – 1 –  ½ - 1+1/2  - ½ (Harmonic minor scale: the same ascending and descending).

This is the form prevalent in most piano music, simply because polyphony took a different course in the 17th century. Musicians who play medieval and renaissance music are of course thoroughly familiarised with modes and melodic minors. Of course you can still see them in much piano repertory, but who bothers to do an analysis of a piece showing the underlying scales and the modes being use by the composers? In fact, much post-romantic and contemporary music (especially against minimalists, Satie, Debussy, Hovhaness, and so on use modes and alternative scale systems extensively)

So, we have the major scale, the natural major scale (the old Aeolian mode - exactly the same notes of the major scale but starting and finishing on the 6th degree), the harmonic minor scale (a modified form of the natural minor scale where the leading note is sharped) and the melodic minor scale (a modified form of the natural minor scale where both the 6th and 7th degree are sharped when ascending, but which reverses to the natural minor scale when descending – all this for melodic considerations). These scales sound very different because the pattern of tones and semitones are different – contrary to major scales which sound all the same because they share the same pattern of tones and semitones albeit with different notes.

And that is pretty much it. But where does that leave the C minor scale? I am afraid nowhere. The C minor scale is unrelated to the C major scale. The fact that they have many notes in common and most of the chords is a pure coincidence (although expected mathematically if you bother to do the homework). The C minor scale is the relative minor of Eb major, a scale with 3 flats in its key signature, and therefore quite far from C major (which has none). The natural C minor scale – like Eb major – has the same three flats (in fact all the notes are the same). It is only when modified artificially by the sharping of its 6th and 7th degrees that most of the notes become common, and only when ascending. Check it out:

C – D – E –  F – G –  A –   B –  C – (C major)
C – D – Eb – F – G – Ab – Bb – C (C minor natural or melodic desc.)
C – D – Eb – F – G – Ab – B -  C (C minor harmonic)
C – D – Eb – F – G – A – B – C (C minor melodic ascending)

Why do people then relate both of them? C minor is what is called a tonic minor meaning that both C major and C minor start on the same note (share the same tonic). This has many implications in tonal music, including a frequent modulation from C major to C minor. Everything that is used often soon becomes well known even if people don’t quite know why. It is a bit like a C6 chord (CGA). Of course, properly speaking there is no C6 chord. What there is, is an inverted, incomplete A minor 7th chord (ACEG). But try telling that to your pop musician friend strumming his C6 in the guitar. It becomes a mnemonic which is mostly mechanical without much real relationship to the historical evolution of the musical structure.

So, personally I always teach minor scales as relative minors, never as tonic minors, and I always show the derivation from the modes. Part of the scale work should include free modal improvisation, since there is no better way to get oneself acquainted with all these concepts.

I hope this helps.

Best wishes,
Bernhard.

PS: In regards to your musical examples, remember that theory always comes after composition. Most likely CPE Bach and co. were not aware that they had to conform to this or that scale form! (Or they were aware and were deliberately “breaking the rules” a favourite past time of Beethoven )

[gaer]

Ok. Brace yourself and sit comfortably, this is going to take a while.

It was interesting.

Now, brace yourself, because I have as much to say.

As you mentioned, there are only two whole-tone scales. For the same reason, there are only four augmented chords, each using three of the possible 12 "notes" in an octave, using our modern system and assuming equal temperament.

Then there are only three diminished chords. The diminished chord is one of the first chords I teach, pointing out that that if you play all four notes in the chord in the most "condensed" form, you end up skipping exactly two keys between each finger.

Then there are so many scales that can be constructed by continuing a pattern, such as:

C D D# F F# G# A B C
B C# D E F G G# A# B

Here again there are only two.

I have heard them called "artificial scales", but the name is unimporant. They make great effects. Bartok loved to play around with such scales.

Now, so far we are talking about scales coming from scales (whole tone comes from "half-tone" (chromatic) and chords formed by ommiting notes in scales (diminished, augmented)

Now, modes: I simply teach that there are 7 modes and that none comes before all others, although some were used more often. Many jazz musicians teach the modes for a different reasons. They try to describe which mode is most useful for improvising over a chord. They might, for instance, describe the Locrian mode as being perfect for a half diminished chord.

Composers such as John Williams are very fond of using the Lydian mode because of it's slightly "exotic sound". Something that is obviously using C as the tonal center will often end: C D E F# G. It's a very "ET" thing to do.

Scarboro Fair uses Dorian. I'm sure you could add many other famous examples.

Now let us go back in time. In Medieval times there were no black keys.

I have a picture in my mind of someone carrying around a keyboard with all the black notes ripped way.

But seriously, I use the same explanation with children. "Imagine this piano, with the black keys taken away. Now, imagine that we can make the sound go higher or lower." I then play some modal tunes, using an electronic keyboard, transposing with a button, then resetting to standare pitch and playing the same tunes in the key the keyboard was just transposed to. I explain that this is much like what happens when singers use one set of notes but make the set higher or lower. (I have to keep my terms simple, at least at first.)

I use for major or Ionian:

CB     AG          FCDA. Joy to the world, the Lord is come…

It's the only piece I can think of that uses a major scale that is instantly recognizable to most people. I wish someone would give me another, and I could use one that is ascending.

Blues tunes use a bastard form of Mixolydian, since the seventh degree of the mode, in its pure form, is raised when a V chord is used. Blues is a subject all of its own.

The end of Debussy's "Brouillards" (Fogs) always reminds me of Locrian, although it is ambigious, since there is Ab "hanging around", just to make things more interesting.

To our ears, these “scales” – or to give their proper names “modes” – do not sound like scales at all. In fact they sound like nothing, just some random melodic fragment.

They most definitely do sound like scales to me, but I will agree that to our ears, they tend to sound very exotic. Perhaps most people don't pay attention…

For several reasons that are not important for this issue, by the end of the 16th century, most of the modes had fallen into disuse, except for the Ionian (our major scale), and the Aeolian, which is formed by playing the notes of the major scale, but starting and finishing on the sixth degree (the submediant).

But several others, or at least three, have regained popularity from roughly the time of Debussy and continue to be used a great deal in film scores. Dorian is used a great deal in jazz improv.

By the 17th century, musical theoreticians decided to sharp the leading note of the natural minor scales to create the desired attraction between its leading note and the tonic. And since this “sharpening” was completely artificial and had no grounds on the genesis of the scale (form the Aeolian mode), it was considered an “accidental”, and therefore was not included in the key signature of the piece.

One question: do you think it was theoreticians who were dictating this change, or do you think they were describing what was already being done? To me it seems that those who attempt to explain "the rules" are always several steps behind (or decades behind, or centuries behind) those who are gleefully breaking them.

Now, I see where you are going. You are describing the logical evolution of the scales we teach today, showing that the harmonic minor came first, followed by the medolic minor (ascending) since it alters two degrees of the scale. I would merely suggest that from a practical standpoint, it is logical to teach the melodic minor as a scale that simply lowers the third of a major scale and leaves the rest alone. But the natural minor (or Aeolian if you prefer) is the logically described as a mode going from the 6th note of a major scale to the next 6th. Harmonic is closer to natural minor, since it only requires the change of one note.

Now in the 17th century, European music was mostly concerned with polyphony, that is, the weaving together of several melodic lines. So the aim here was melody. Hence the criteria to change the scale were melodic (providing a strong pull between leading note and tonic, creating a pattern of intervals with more or less regular intervals without large jumps and so on), and so this modified Aeolian mode was called a “melodic” minor scale.  And because the priorities were melodic, these modifications were important only when ascending the scale (it is important that the leading note “leads” to the tonic, but there is no such importance the other way around: the tonic is not required to “lead” anywhere). Because of that, the Aeolian mode was modified only when going from leading not to tonic. When going down (descending scale) from tonic to leading note, they just left the Aeolian mode unmodified (that is the natural minor scale)

If you are considering a scale in its most pure form, descending, no skips, then I would agree with you. And I'm not disagreeing. But it is interesting to examine how often Bach descends to the raised 7th, leaps up to the 6th, then descends again. If you take the last four 16ths in bar one and the first of the next up one octave (Invention 2, Cm, 2-part), you then have a descending harmonic scale. Now, I would not be at all surprised to see something like this from Bach:

C D Eb F G A B C B (leaping) Ab G F Eb D C B C.

This is cheating, because there is a leap, and it's also cheating to use Bach as an example, since he took the existing system and pushed it to the absolute limit, but it is important to mention that Bach used scales melodically but also to sketch intricate harmonies. Already we see a tendency to use at least the set of notes we know of today as the harmonic scale to descend when there is either a dominant chord or an implied harmony of that nature, and we are now using the concept of melodic ascending and harmonic descending.

Now, in bar 15 of the 7th two-part invention, E minor, there is no scale there in terms of something clearly ascending step-wise, but the movement is ascending in the way a melodic minor would, C# D# E because the implied chord structure is B7, and then he comes straight down from F# to G in with the same set of notes, 6th and 7th still raised, but again because the implied chord structure is the dominant 7th. In Invention 11, Gm, 1st measure, he goes up and down with a minor scale, but what do we call it? It can't be melodic, by definition, because it does not lower the 7th and 6th descending. Only the third is lowered, and again it's a combination of melody and harmony. The feel, again, is a V7 chord, implied.

This is the problem with the term "melodic". It is taught as being applicable only to an ascending scale, and it is furthermore locked into combination with the descending natural minor. This is useless for describing what composers actually do, and I see zero technical value. It pens in the mind.

Scales should be taught as sets of notes, not formulas only applicable in one direction. This is clearly absurd and totally misleading.

What determines which set of notes is used is largely determined by the first note that starts a downward movement, when there is a dominant feel. So if the first note is the 6th, it will usually start with Ab, in the key of C minor, descend to B natural, then either double back, ending on C, or continue downward. A harmonic scale pattern is then set in motion. If it starts with the 2nd (or 9th, if you prefer), both the 6th and 7th degrees are often raised, exactly as in the CPE Bach Solfeggio. No rules are broken unless you consider the rules so often stated as valid. CPE is following JS.

Obviously when the implied chord is the tonic, then the natural minor scale will be used to descend by Bach. There is probably some exception, but I can't think of one at the moment.

This is the form prevalent in most piano music, simply because polyphony took a different course in the 17th century. Musicians who play medieval and renaissance music are of course thoroughly familiarised with modes and melodic minors. Of course you can still see them in much piano repertory, but who bothers to do an analysis of a piece showing the underlying scales and the modes being use by the composers?

I do, and I assume you do to. The problem is that few pianists today compose, arrange, trascribe and spend a great deal of time studying notation. They spend too much time listening to each other and too little time thinking for themselves. Yes, you can learn a ton by listening to great players, but it can also become an incestuous thing, with too much blind acceptance leading to copying for no reason other than laziness.

Of course, properly speaking there is no C6 chord. What there is, is an inverted, incomplete A minor 7th chord (ACEG).

But try telling that to your pop musician friend strumming his C6 in the guitar.

Jazz guitarists and pianists, who will consider a C6 chord as C E G A, would argue that this chord, voiced any way you wish but with C in the bass, is going to produce a different feeling in the mind of the listener than the same chord, played with an A in the bass. I understand your point, but saying that a C6 chord is nothing but an inversion of an Am7 chord is misleading. No one is going to write a C6 chord as Am7/C. It just isn't done, for the same reason that Cm6 is not going to be written as A7(b5)/C (also notated with a small circle with a line through it to indicate "half-diminished".) Certainly you can analyze a Cm6 as the first inversion of a half-diminished chord, but it is extremely impractical. You'd have to re-write the changes in almost every jazz chart ever written.

So, personally I always teach minor scales as relative minors, never as tonic minors, and I always show the derivation from the modes. Part of the scale work should include free modal improvisation, since there is no better way to get oneself acquainted with all these concepts.

I think that we need to know modes, how music moves from major to relative minor and parallel minor. These things are all important. The only critical matter when working with students is to find a way to get the ideas across. I may end up using exactly your method, if I find out the way I am teaching these things right now are not working. But my only goal is to get the idea across that these different scales exist more as sets of notes to be played with than as a set of 7 notes only to be played on one direction or the other and rigidly fixed in some way.

PS: In regards to your musical examples, remember that theory always comes after composition. Most likely CPE Bach and co. were not aware that they had to conform to this or that scale form!

True, but remember that CPE was only doing what his father did, and JS Bach probably did it much better. They were all rule-breakers. How many people know that young Bach nearly got fired for trying to introduce "new music" into the church? He was just as rebellious as Beethoven in his own way, but much quieter about it later on, because in his time he could not have survived othewise. And I don't think for a moment that any of these great composers were unaware of breaking rules. Rules and creativity mix as well as oil and water.

Gary