Friday, July 21, 2006
Lesson-37 : Harmonic Minor - Flat List
By this time, you are familiar with the Harmonic Minor Scales and similarity with the Major Scales.
Such a kind of similarity we have already seen regarding Harmonic Minor Scales w.r.t. Sharps. (Of course, some slight adjustment about the additional sharping the leading note is already clear in your mind).
If so, you can easily guess the sequence of Harmonic minor scales with Flats also.
The steps are just repeated to recall the procedures :
Such a kind of similarity we have already seen regarding Harmonic Minor Scales w.r.t. Sharps. (Of course, some slight adjustment about the additional sharping the leading note is already clear in your mind).
If so, you can easily guess the sequence of Harmonic minor scales with Flats also.
The steps are just repeated to recall the procedures :
- Start with the A-Harmonic minor
- Proceed in terms of Perfect 5th downward each time from the previous minor scale.(or perfect 4th upward)
- Omitting the sharp required in the Leading note (7th note) , we can see the addition of flats each time which is similar to major scales in the same sequence and in numbers
- We can represent these flats in the key signatures in the same way that of Flat Majors, but in addition to that, the leading note is sharped (raised) every time separately in front of the note in stave wherever it occurs.
- Also, we can establish the equivalent Major and Minor scale relationships, in terms of the key signatures, which is separated by an interval of Minor Third. Thereby proving again that, for any Harmonic Minor Scale, there is an equivalent Major Scale (in terms of number and sequence of flats/sharps) whose tonic is a minor Third above the tonic of minor scale.
- Remember and be careful, using the proper accidental before the leading note every time.
With the above, our Harmonic Minor Scales sequence with flats are as follows :
[you can also check each scale with the standard pattern required for the Harmonic Minor Scale which is (Whole+Semi+Whole)+Whole+(Semi+One&Half+Semi) ]
Our standard sentence for flats sequence (reverse sentence of sharps),
“Battle Ends And Down Goes Charles Father” holds good.
Hope, now you can realise that, the system of forgetting the leading note first, helps us in getting a uniform system, similar to major scale approach and then adding back the effect of leading note separately, which is the simple task.
Caution :
While writing the notes in score sheet for Harmonic Minor, Please remember these:
· When you are using key signatures all the flats are taken into it and only the sharp or natural symbols are added in front of the leading note.
· If you are not using the key signatures, then all the notes shall be added with corresponding flats or sharps, but there is no need to add separate natural symbol for a leading note which is raised to normalcy (from presumed flatness).
That is to say, write a normal note as normal note only, and no need to add a flat and sharp symbol simultaneously in front of the leading note !
As done before for sharps, if we compare the Major & Minor scales equivalent in terms of flats for each of these scales, we get the confirmation that the tonics of each are separated by the interval of Minor 3rd !
Remembering these equivalence tables will help in undertsanding the Modualtion aspects later.
Yes….where have we reached now…?
15 Major scales and 15 Harmonic Minor scales….
We have travelled a long …long….way….!
Try to consolidate that ! In your mind and in your feeling !
Monday, July 10, 2006
Lesson-36 : Harmonic Minor - Sharp List
Let me repeat the two harmonic minors discussed last time viz A & E Harmonic Minors.
A – B – C – D – E – F – G - A ( but G is Sharped separately ) – All White notes equivalent.
E – F# – G - A – B – C – D – E ( but D is sharped separately) – Single sharp equivalent.
As we know, E-Minor was arrived at by going Perfect 5th upward from the starting A-Minor.
In the same way, if we proceed with the balance keys also, as we used to do for Major Scale, ie going upward in terms of Perfect 5th every time from the previous scale tonic,
we get the following complete table of Harmonic minor scales of
B-minor (2-sharps)
F# minor (3-sharps)
C# minor (4-sharps)
G# minor (5-sharps)
D# minor (6-sharps) and finally
A# minor (7-sharps)
in that sequential order.
Also, we know that, the leading note shall be separately sharped.
If the leading note happens to be a sharp note already, then it becomes double sharp !
[Double sharp is usually written using a x-mark (cross mark), before the notes].
This double sharp business is little but confusing in the beginning, but you can understand easily with key board in front of you, and try to locate the exact key and everything looks very logical.
For example,
F-Double sharp is equivalent to G, and
C-Double Sharp is nothing but D, and finally
G-Double Sharp is again nothing but A !
So that’s simple !
So, in case of Minor scales, we are now having the method similar to Major scale; similar in approach as well as the number and sequence of sharps etc.
Making our life a lot easier!
Only additional thing to remember is to Put a sharp before the leading note every time without forgetting!
That’s a relatively smaller simpler additional effort compared to our simplified learning…Isn’t it !
Our same old sentence of “Father Charles Goes Down And Ends Battle” helps us in identifying the sequence of sharp notes getting added each time.
Another important observation is :
If we compare the Major & Minor scales equivalent (in terms of sharps) for each of these scales, we get the confirmation that they are separated by the interval of Minor 3rd !
Refer the following equivalent table :
You can check yourself the interval between these two equivalent scales w.r.t. their Tonic,
C to A,
G to E,
D to B, etc. etc…..,
and understand that they are separated by the interval of Minor 3rd.
So, through our understanding of Major scales, we can learn the Harmonic Minor Scales easily.
Similar to the above scales of sharps, we can easily analyse and learn the scales of flats also.
In our next lesson!
A – B – C – D – E – F – G - A ( but G is Sharped separately ) – All White notes equivalent.
E – F# – G - A – B – C – D – E ( but D is sharped separately) – Single sharp equivalent.
As we know, E-Minor was arrived at by going Perfect 5th upward from the starting A-Minor.
In the same way, if we proceed with the balance keys also, as we used to do for Major Scale, ie going upward in terms of Perfect 5th every time from the previous scale tonic,
we get the following complete table of Harmonic minor scales of
B-minor (2-sharps)
F# minor (3-sharps)
C# minor (4-sharps)
G# minor (5-sharps)
D# minor (6-sharps) and finally
A# minor (7-sharps)
in that sequential order.
Also, we know that, the leading note shall be separately sharped.
If the leading note happens to be a sharp note already, then it becomes double sharp !
[Double sharp is usually written using a x-mark (cross mark), before the notes].
This double sharp business is little but confusing in the beginning, but you can understand easily with key board in front of you, and try to locate the exact key and everything looks very logical.
For example,
F-Double sharp is equivalent to G, and
C-Double Sharp is nothing but D, and finally
G-Double Sharp is again nothing but A !
So that’s simple !
So, in case of Minor scales, we are now having the method similar to Major scale; similar in approach as well as the number and sequence of sharps etc.
Making our life a lot easier!
Only additional thing to remember is to Put a sharp before the leading note every time without forgetting!
That’s a relatively smaller simpler additional effort compared to our simplified learning…Isn’t it !
Our same old sentence of “Father Charles Goes Down And Ends Battle” helps us in identifying the sequence of sharp notes getting added each time.
Another important observation is :
If we compare the Major & Minor scales equivalent (in terms of sharps) for each of these scales, we get the confirmation that they are separated by the interval of Minor 3rd !
Refer the following equivalent table :
You can check yourself the interval between these two equivalent scales w.r.t. their Tonic,
C to A,
G to E,
D to B, etc. etc…..,
and understand that they are separated by the interval of Minor 3rd.
So, through our understanding of Major scales, we can learn the Harmonic Minor Scales easily.
Similar to the above scales of sharps, we can easily analyse and learn the scales of flats also.
In our next lesson!
Thursday, July 06, 2006
Lesson-35- Harmonic Minor - Concept of Equating With Major Scale !
Our next endeavour is to get into the details of Scales of Harmonic Minor with sharps ! Before that, one approach we shall undertsand to make the matter simple.
Since we know better about the Major Scale, if we could correlate a Harmonic Minor with a corresponding Major scale, then we can blindly follow the relationships for establishing all the Harmonic Minor scales with Sharps (as well as Flats), through some Major scales whioch we already know!
Let us start from A-Harmonic Minor !
Actually A-Harmonic Minor is A – B – C – D – E – F – G# - A
But we will represent this way :
A – B – C – D – E – F – G - A ( but G is Sharped separately )
So now it can be visualized as equivalent to C-Major (with no sharp).
What does this mean while notes writing on stave ?
Thus, A-Harmonic minor will not have any sharps or flats in the Key Signature (just like C Major), but wherever the note G is written (the leading Note of A-Minor), sharp symbol is put in front of the note G every time, separately.
Then for the Next minor scale, as usual, as in the case of Major scale, Go upward by perfect 5th of Tonic of previous minor scale, which leads us to E-Harmonic Minor.
Actually E-Harmonic Minor is E – F# – G - A – B – C – D# – E
But we will represent this way :
E – F# – G - A – B – C – D – E ( but D is sharped separately) .
So, now this can be equated to G-Major which has only one sharp ie F-sharp.
Now, You will realize the advantage of our method of omitting the sharp of leading note and representing them later separately in the case of a Harmonic Minor scale!
What does this mean while notes writing on stave ?
Thus, E-Harmonic minor will have only ONE sharp in the Key Signature (just like G Major), ie F-Sharp, but wherever the note D is written (the leading Note of E-Minor), a sharp is put in front of the note D every time, separately.
Another matter for you to observe is the relationship between the Major scale selected for comparison in terms of sharps and the equivalent minor scale as explained above.
For example, C-Major has no sharps or flats. Similarly, with our above understanding of omitting the sharp of leading note initially, the equivalent Harmonic Minor scale is A-Harmonic Minor.
The relationship between C and A in terms of its interval is that, A-Minor is a Minor Third below C-Major!
Similarly, in the case of the ONE sharp equivalents G-Major and E-Minor, the relationship between G and E in terms of its interval is that E is a Minor Third below G
So we can conclude that Every Major Scale is having an Equivalent Minor Scale, if we select the note a Minor Third below.
Again remember, when we say equivalent, it is just the number of sharps (or flats) in both the scale (as will be represented in the key signature or otherwise), that also forgetting conveniently the sharp of Leading note…..!
For all other purposes, the pattern of Major and Minor scales and their quality of sound and music coming out are entirely different as you already know !
So let us define this Harmonic Minor Scale representation rule while writing on score sheet like this :
1. In the key signature, represent the sharps (or flats as the case may be) of equivalent Major Scale (which is separated by a minor third interval)
2. Then wherever the leading note of the scale is coming, sharpen (raise) the note by proper accidentals (sharps, double sharps, flats, natural symbol etc.) .
If the above rules understood, all our analytical method of forming and writing scales in terms of sharps and flats for Minor scales will be exactly replicated as in the case of Major scales.
So, as in the case of major Scales, all our understandings on Perfect 5th approach, our standard sentences for sharps & flats (Father Charles Goes Down……) etc etc…, for the sequence of notes sharpened or flattened etc. are absolutely valid and make our life easier….! Is that OK….?
Tell me…Is this a process of Simplification or Confusion…?
Initially it may look both way to you…!....... but you will appreciate this method with some deep thinking and homework…!
We will see all minor scale with sharps and flats one by one in our next discussion which will clarify all the above points.
Till Then, have a deep & thorough self-analysis and validation of above understandings !
Since we know better about the Major Scale, if we could correlate a Harmonic Minor with a corresponding Major scale, then we can blindly follow the relationships for establishing all the Harmonic Minor scales with Sharps (as well as Flats), through some Major scales whioch we already know!
Let us start from A-Harmonic Minor !
Actually A-Harmonic Minor is A – B – C – D – E – F – G# - A
But we will represent this way :
A – B – C – D – E – F – G - A ( but G is Sharped separately )
So now it can be visualized as equivalent to C-Major (with no sharp).
What does this mean while notes writing on stave ?
Thus, A-Harmonic minor will not have any sharps or flats in the Key Signature (just like C Major), but wherever the note G is written (the leading Note of A-Minor), sharp symbol is put in front of the note G every time, separately.
Then for the Next minor scale, as usual, as in the case of Major scale, Go upward by perfect 5th of Tonic of previous minor scale, which leads us to E-Harmonic Minor.
Actually E-Harmonic Minor is E – F# – G - A – B – C – D# – E
But we will represent this way :
E – F# – G - A – B – C – D – E ( but D is sharped separately) .
So, now this can be equated to G-Major which has only one sharp ie F-sharp.
Now, You will realize the advantage of our method of omitting the sharp of leading note and representing them later separately in the case of a Harmonic Minor scale!
What does this mean while notes writing on stave ?
Thus, E-Harmonic minor will have only ONE sharp in the Key Signature (just like G Major), ie F-Sharp, but wherever the note D is written (the leading Note of E-Minor), a sharp is put in front of the note D every time, separately.
Another matter for you to observe is the relationship between the Major scale selected for comparison in terms of sharps and the equivalent minor scale as explained above.
For example, C-Major has no sharps or flats. Similarly, with our above understanding of omitting the sharp of leading note initially, the equivalent Harmonic Minor scale is A-Harmonic Minor.
The relationship between C and A in terms of its interval is that, A-Minor is a Minor Third below C-Major!
Similarly, in the case of the ONE sharp equivalents G-Major and E-Minor, the relationship between G and E in terms of its interval is that E is a Minor Third below G
So we can conclude that Every Major Scale is having an Equivalent Minor Scale, if we select the note a Minor Third below.
Again remember, when we say equivalent, it is just the number of sharps (or flats) in both the scale (as will be represented in the key signature or otherwise), that also forgetting conveniently the sharp of Leading note…..!
For all other purposes, the pattern of Major and Minor scales and their quality of sound and music coming out are entirely different as you already know !
So let us define this Harmonic Minor Scale representation rule while writing on score sheet like this :
1. In the key signature, represent the sharps (or flats as the case may be) of equivalent Major Scale (which is separated by a minor third interval)
2. Then wherever the leading note of the scale is coming, sharpen (raise) the note by proper accidentals (sharps, double sharps, flats, natural symbol etc.) .
If the above rules understood, all our analytical method of forming and writing scales in terms of sharps and flats for Minor scales will be exactly replicated as in the case of Major scales.
So, as in the case of major Scales, all our understandings on Perfect 5th approach, our standard sentences for sharps & flats (Father Charles Goes Down……) etc etc…, for the sequence of notes sharpened or flattened etc. are absolutely valid and make our life easier….! Is that OK….?
Tell me…Is this a process of Simplification or Confusion…?
Initially it may look both way to you…!....... but you will appreciate this method with some deep thinking and homework…!
We will see all minor scale with sharps and flats one by one in our next discussion which will clarify all the above points.
Till Then, have a deep & thorough self-analysis and validation of above understandings !
Lesson-34 - Harmonic Minor - Some Minor Complications & Resolving !
Hi All,
Warning ! Take a deep breath (and time !) for this lengthy discussion…! This demands your absolute concentration !
To start with, let me repeat the pattern of Harmonic Minor once again :
( Whole + Semi + Whole ) + Whole + ( Semi + One & Half + Semi)
Using the above pattern, Can we get a Harmonic Minor scale with all Pure White Notes (as in the case of C-Major) ?
The answer is NO !
One case nearest to this level is the Harmonic Minor Scale starting with the note "A", which will be like this :
A – B – C – D – E – F – G# - A
Here also, it has one note as sharp.
Let us see one another case of case of D-Harmonic Minor,
Here it is getting complicated !
We are getting the one flat note as well as the sharp in the same scale, (based on the strict rule of selecting “One note only once” for the scale formation ) !
D – E – F – G – A - B(b) – C# -D
Which is peculiar, because so far, in case of Major scale, it is either sharp everywhere or flats everywhere. At no instance, we used both !
So what will happen ?
In case of Harmonic Minor, could we not get , (as we used to get in Major scale), any equivalent easy method to get step-by-step increase of either Sharps or Flats?
Also How to avoid the complicated flats and sharp combination of representation within the same scale?
Don’t get dis-heartened ! There is a way !
A slight compromise is required for the sake of simplicity !
Let us make some small adjustment of representation of note ! Then everything will fall in line automatically !............How ?
Let us get back to the A-Harmonic Scale which we just saw!
The actual notes of A-Harmonic minor to preserve the pattern of minor scale, are like this :
A – B – C – D – E – F – G# - A
So if we take A– Harmonic Minor and temporarily forget about the sharp of G, which is its leading note, and write this as follows:
A – B – C – D – E – F – G - A ( G is to be sharped later )
Now, we can say, this is like the pure white keys equivalent of C-Major…..?
Do you agree ?
So there lies the solution…!
We exactly follow that pattern, but only representing in different way..!
Warning ! Take a deep breath (and time !) for this lengthy discussion…! This demands your absolute concentration !
To start with, let me repeat the pattern of Harmonic Minor once again :
( Whole + Semi + Whole ) + Whole + ( Semi + One & Half + Semi)
Using the above pattern, Can we get a Harmonic Minor scale with all Pure White Notes (as in the case of C-Major) ?
The answer is NO !
One case nearest to this level is the Harmonic Minor Scale starting with the note "A", which will be like this :
A – B – C – D – E – F – G# - A
Here also, it has one note as sharp.
Let us see one another case of case of D-Harmonic Minor,
Here it is getting complicated !
We are getting the one flat note as well as the sharp in the same scale, (based on the strict rule of selecting “One note only once” for the scale formation ) !
D – E – F – G – A - B(b) – C# -D
Which is peculiar, because so far, in case of Major scale, it is either sharp everywhere or flats everywhere. At no instance, we used both !
So what will happen ?
In case of Harmonic Minor, could we not get , (as we used to get in Major scale), any equivalent easy method to get step-by-step increase of either Sharps or Flats?
Also How to avoid the complicated flats and sharp combination of representation within the same scale?
Don’t get dis-heartened ! There is a way !
A slight compromise is required for the sake of simplicity !
Let us make some small adjustment of representation of note ! Then everything will fall in line automatically !............How ?
Let us get back to the A-Harmonic Scale which we just saw!
The actual notes of A-Harmonic minor to preserve the pattern of minor scale, are like this :
A – B – C – D – E – F – G# - A
So if we take A– Harmonic Minor and temporarily forget about the sharp of G, which is its leading note, and write this as follows:
A – B – C – D – E – F – G - A ( G is to be sharped later )
Now, we can say, this is like the pure white keys equivalent of C-Major…..?
Do you agree ?
So there lies the solution…!
Step-1 :
Represent the harmonic Minor scale omitting the sharp of Leading note (so that it can be equated mentally to particular Major scale in terms of number of sharps or flats )
Step-2 :
and then add back the sharp on the leading note separately, later.
You wont believe….! This also incidentally solves our problem of complex representation of using both sharp and flats in the same scale !
Otherwise please be assured that we are not changing the pattern of Harmonic Minor scale at all in the final outcome !
We exactly follow that pattern, but only representing in different way..!
Lesson-33 :Harmonic Minor Scale - Part-2 : Establishing the INTERVALS !
Just now, we have established the Pattern of the Harmonic Minor Scale.
Coming to our next stage analysis we are going to establish the Intervals w.r.t. Tonic.
Let me re-emphasize our earlier learning that , irrespective of any scale, the name of the each note from 1 to 7, it is called, Tonic, Super tonic, Mediant, Sub-Dominant, Dominant, Sub-Mediant & Leading note !
( and of course Octave, the repeated tonic note… to complete the scale..)
Also you remember that the intervals w.r.t. Tonic to other notes of a Major scale are
“ Everything is Major interval except the 4th and 5th which are Perfect interval"
Again recall, while converting Major to Minor, we effected changes in 3rd and 6th note by way of reduction of semitone….!
So the changes in case of intervals also shall be for the 3rd and 6th only which now changes from Major to Minor intervals ….thats all…..!
All other remain the same….!
By consolidating in our usual way, we get the following :
The above also clearly indicates our earlier understanding that, Major Scale can have minor intervals and a Minor scale can have Major intervals….!
For all other intervals between any note to any note in a Harmonic Minor scale, I am leaving that exercise to you to check for yourself, using our Standard Intervals Table given earlier….!
These Minor 3rd and Minor 6th intervals are the crucial one which makes the difference between the Major Scale and Minor Scale…!
So try that on key board repeatedly and feel it and register that in the mind strongly…!
So second part of analysis is also over for the Harmonic Minor Scale..
What next…? Listing of Harmonic Minor scales with Sharps and Flats…..!
Before jumping into that analysis, one question I want to pose to all of you…!
In case of Major scale, we started with a all pure white keys major scale viz.. C-Major…!
And then started traveling Perfect 5th upward for sharp and Perfect 5th downward for flats…!
To repeat that, in case of Minor scale also, “Can we get any Pure All White Minor scale to start with ?
Try and answer ! (I need not remind you that we should preserve the Pattern of Minor scale discussed above, when you try from each white key…! )
We will see the answer in next Lesson!
Coming to our next stage analysis we are going to establish the Intervals w.r.t. Tonic.
Let me re-emphasize our earlier learning that , irrespective of any scale, the name of the each note from 1 to 7, it is called, Tonic, Super tonic, Mediant, Sub-Dominant, Dominant, Sub-Mediant & Leading note !
( and of course Octave, the repeated tonic note… to complete the scale..)
Also you remember that the intervals w.r.t. Tonic to other notes of a Major scale are
“ Everything is Major interval except the 4th and 5th which are Perfect interval"
Again recall, while converting Major to Minor, we effected changes in 3rd and 6th note by way of reduction of semitone….!
So the changes in case of intervals also shall be for the 3rd and 6th only which now changes from Major to Minor intervals ….thats all…..!
All other remain the same….!
By consolidating in our usual way, we get the following :
The above also clearly indicates our earlier understanding that, Major Scale can have minor intervals and a Minor scale can have Major intervals….!
For all other intervals between any note to any note in a Harmonic Minor scale, I am leaving that exercise to you to check for yourself, using our Standard Intervals Table given earlier….!
These Minor 3rd and Minor 6th intervals are the crucial one which makes the difference between the Major Scale and Minor Scale…!
So try that on key board repeatedly and feel it and register that in the mind strongly…!
So second part of analysis is also over for the Harmonic Minor Scale..
What next…? Listing of Harmonic Minor scales with Sharps and Flats…..!
Before jumping into that analysis, one question I want to pose to all of you…!
In case of Major scale, we started with a all pure white keys major scale viz.. C-Major…!
And then started traveling Perfect 5th upward for sharp and Perfect 5th downward for flats…!
To repeat that, in case of Minor scale also, “Can we get any Pure All White Minor scale to start with ?
Try and answer ! (I need not remind you that we should preserve the Pattern of Minor scale discussed above, when you try from each white key…! )
We will see the answer in next Lesson!
