Lesson with luderart

luderart has already knows his intervals, scales and how to build chords from the Major and minor scales but wants to start his lessons with a review on interval inversions.

Lesson:

Since you already know quite a bit, understanding the inversion of an interval will be easy.

Basically, an inversion of an interval occurs when the notes of the original interval are "flipped". For example, starting on the note C to E is a Major 3rd. To invert this interval we would simply "flip" the relationship between the ntoes. So, instead of C to E (Major 3rd) we would have E to C which would become a minor 6th. If you count the number of whole/half steps from E up to C you will see that you come up with 4 whole steps which gives us the quality of a minor 6th interval. Below I have included a list of interval inversions. The list of inversion works off of an easy pattern to learn and memorize. I have also attached an example using Fianle.

INTERVAL INVERSIONS:

1) A minor 2nd when inverted becomes a Major 7th

2) A Major 2nd when inverted becomes a minor 7th

3) A minor 3rd when inverted becomes a Major 6th

4) A Major 3rd when inverted becomes a minor 6th

5) An augmented 4th when inverted becomes a diminished 5th

6) A Perfect 4th when inverted becomes a Perfect 5th

7) A diminished 5th when inverted becomes an Augmented 4th

8) A Perfect 5th when inverted becomes a Perfect 4th

9) A minor 6th when inverted becomes a Major 3rd

10) A Major 6th when inverted becomes a minor 3rd

11) A minor 7th when inverted becomes a Major 7th

12) A Major 7th when inverted becomes a minor 7th

13) And the Perfect octave always remains a Perfect octave.

I'm sure after you reached a little ways down the list you noticed the patterns.

* minor intervals become Major

* Major intervals become minor

* Perfect intervals remain Perfect

* diminished intervals become Augmented

* Augmented become diminished

* 2nds become 7ths, and 7ths become 2nds

* 3rds become 6ths, and 6ths become 3rds

* 4ths becomes 5ths, and 5ths become 4ths

Let me know if there is anything that is unclear.

Interval inversion.MUS

Thanks for the clear explanations.

I have the following questions:

1) Are intervals independent of scales? Are they minor or major regardless of the scales on which they exist?

2) Are intervals designated as major, minor, diminished or augmented strictly according to the total of the whole tones and half tones they contain and not according to any pattern of whole-tone half-tone steps? For example C to F is a perfect fourth and E to A is a perfect fourth?

3) Only the perfect intervals become diminished or augmented? The others are only either major or minor?

3) I couldn't open the Finale attachment. I have the Finale NotePad 2001 version. Do I need to download something else?

Thanks for the clear and insightful explanations.

I have the following questions:

1) Are intervals independent of scales? Are they minor or major regardless of the scales on which they exist?

2) Are intervals designated as major, minor, diminished or augmented strictly according to the total of the whole tones and half tones they contain and not according to any pattern of whole-tone half-tone steps? For example C to F is a perfect fourth and E to A is a perfect fourth?

3) Only the perfect intervals become diminished or augmented? The others are only either major or minor?

3) I couldn't open the Finale attachment. I have the Finale NotePad 2001 version. Do I need to download something else?

Thanks for the clear and insightful explanations.

I have the following questions:

1) Are intervals independent of scales? Are they minor or major regardless of the scales on which they exist?

2) Are intervals designated as major, minor, diminished or augmented strictly according to the total of the whole tones and half tones they contain and not according to any pattern of whole-tone half-tone steps? For example C to F is a perfect fourth and E to A is a perfect fourth?

3) Only the perfect intervals become diminished or augmented? The others are only either major or minor?

3) I couldn't open the Finale attachment. I have the Finale NotePad 2001 version. Do I need to download something else?

1) Using the C Major scale as an example, if you take a look at it you will notice that the scale is comprised of various types of intervals.

C-D-E-F-G-A-B

From C to D is a Major 2nd

From D to E is a Major 2nd

But, From E to F is a half step and therfore a minor 2nd.

Also, From C to E is a Major 3rd

But, from E to G is a minor thrid

An interval is just the distance between any two notes. Therefore, it is the arrangement of intervals that make-up or create the scale and not the other way around.

2) Right. As I mentioned in the answer to your first question, its all about the distance between any two notes and that distance is measured in half and whole steps. So, from C to F is a Perfect 4th becuase the distance between the two notes adds up to a total of 2 Whole steps and 1 Half step. The same is true about E to A. E to A is also a Perfect fourth because if you count up the number of Half and Whole steps from the note E up to A you will see that it also comes to a total of 2 Whole steps and 1 Half step.

3) When a perfect interval is inverted it will still remain perfect. The only thing that changes is whether or not its a 4th or a 5th. For example, From C to F is a Perfect 4th because it has 2 Whole steps and 1 Half step. If we invert the two notes so that we are now going from F to C you will notice that after counting the number of whole and half steps will give you a perfect 5th. 4ths and 5ths (Octaves and Unisons as well) are the only intervals that can be perfect.

4) You can download a free version of Finale Notepad 2007 here:

NotePad

Thanks!

1) Using the C Major scale as an example, if you take a look at it you will notice that the scale is comprised of various types of intervals.

C-D-E-F-G-A-B

From C to D is a Major 2nd

From D to E is a Major 2nd

But, From E to F is a half step and therfore a minor 2nd.

Also, From C to E is a Major 3rd

But, from E to G is a minor thrid

An interval is just the distance between any two notes. Therefore, it is the arrangement of intervals that make-up or create the scale and not the other way around.

2) Right. As I mentioned in the answer to your first question, its all about the distance between any two notes and that distance is measured in half and whole steps. So, from C to F is a Perfect 4th becuase the distance between the two notes adds up to a total of 2 Whole steps and 1 Half step. The same is true about E to A. E to A is also a Perfect fourth because if you count up the number of Half and Whole steps from the note E up to A you will see that it also comes to a total of 2 Whole steps and 1 Half step.

3) When a perfect interval is inverted it will still remain perfect. The only thing that changes is whether or not its a 4th or a 5th. For example, From C to F is a Perfect 4th because it has 2 Whole steps and 1 Half step. If we invert the two notes so that we are now going from F to C you will notice that after counting the number of whole and half steps will give you a perfect 5th. 4ths and 5ths (Octaves and Unisons as well) are the only intervals that can be perfect.

4) You can download a free version of Finale Notepad 2007 here:

NotePad

Going away and will return on Wednesday. We will resume lessons when I get back. :D

Hello Majesty,

Where do we go from here?

I will be sending you a PM

Luder,

what is your knowledge of extended intervals (ex. 9th's, 10th's, 11'ths and so on)?

Well, I don't know about them. But I can guess that they are like the 2nd, the 3rd and the 4th etc. but including an octave.

Luder

Ok, good. I know that you already understand the construction of Major and minor scales and the construction of chords, correct?

If so then would you be able to construct chords on the various scale degrees of either the Major or minor scales?

I don't know much about the construction of cords. I prefer to hear it from you. I know there are triads, major and minor. Tell me how they are constructed and then I'll do the exercise you suggested.

Ok,

The constructin of a triad is very simple and of course are all based of off the specific arrangement of intervals.

Lets use the C Major triad as our example. The notes from bottom to top are, C-E-G. If you notice, from C to E we have an interval of a Major 3rd, from E to G we have an interval of a minor 3rd and finally the "outside" interval from C to G forms a perfect 5th. This is the construction of a Major triad. You need to had a Major 3rd on the bottom, and a minor 3rd on the top.

The minor triad is not too different. Let us use the A minor triad as our example. Again, if you take a look at it you will notice that there are two types of 3rds that make up the minor triad. The notes are,

A-C-E. From A to C we have a minor 3rd, and from C to E we have a Major 3rd. The pattern of the minor triad is the opposite of what makes a Major triad.

Next we have the diminished triad. Let us use the B diminished triad as our example. The notes are, B-D-F. If you look and analyze the 3rds that make up this triad you will see that we have a minor 3rd on the bottom from B to D and another minor 3rd on the top from D to F creating a diminshed 5th for the "outside" interval B to F.

And now, we have the augmented triad. We will use the C Augmented triad. The notes are, C-E-G#. I'm sure by now you can take a look and figure out the construction of this triad based on everything that was mentioned before about the other triads. In this case the interval from C to E is a Major 3rd, and this time the interval from E to G# is another Major 3rd making the "outside" interval from C to G# an Augmented 5th.

Does this all make sense so far?

Yes.

Ok,

Each note of a scales is called a scale degree (you may know this already). These scale degrees are assigned names as well as roman numerals.

I will use C Major as an example...

C D E F G A B

I ii iii IV V vi vii*

Notice how the roman numerals are sometimes upper and lower case. When a chord is build on a scale degree with an upper case roman numeral the triad is understood as Major. When a triad is build on a scale degree with a lower case roman numeral the triad is understood to be minor. If you notice scale degree vii has the symbol * next to it. In printed music it would look like a degree circle which denotes a diminished chord.

Here are the names of the scale degree...

I - Tonic

ii - Supertonic

iii - Mediant

IV - Subdominant

V - Dominant

vi - Submediant

vii* - Leading Tone

let mw know if this is something you already know.

The uppercase and lowercase Major Minor was something new to me. I knew about the names Tonic Supertonic etc. but haven't memorized it. Should I?

Yes, you should memorize the names.

O.K. I'll make sure I memorize it. Meanwhile you may proceed.

Ok,

The issue with the upper and lower case Roman Numerals is slightly different with the minor scale (harmonic minor). And I would like for you to tell me why.

Using the C Harmonic Minor scale, I want you to build triads on the seven scale degrees and tell the properties of each triad. Tell whether the triad on the given scale degree is Major, minor, etc...

Because the arrangemet of the major and the minor chords differs with the different whole-tone half-tone sequence in the minor scale, one being on the vertical (chords) and the other on the horizontal (scales).

A question: Does this uppes & lower case Roman numeral scheme of denoting major & minor not also apply to intervals in scales? If so, how is it written?

I didn't know the differences between the different types of minor scales by heart, so I checked Walter Piston's book on harmony (by the way, is that one of the best reference books on harmony) to remember the characteristic of the Harmonic minor scale. (Why is it called the Harmonic?)

Here are the chords I built on the degrees of C Harmonic minor:

i: C-Eb-G (Minor triad)

ii*: D-F-Ab (Diminished triad)

III: Eb-G-B (Augmented triad) Upper case or what?

iv: F-Ab-C (Minor triad)

V: G-B-D (Major triad)

VI: Ab-C-Eb (Major triad)

vii*:B-D-F (Diminished triad)

Did you want me to send it in notes with Finale? If so, please tell me.

Ok good.

This time for a little more practice I want you to do the same for the Natural and Melodic minor scales. Remember, the Melodic minor is different when ascending and descending

Yes, this time you can use Finale.

C Minor Natural Scale Triads:

C-Eb-G (Minor)

D-F-Ab (Diminished)

Eb-G-Bb (Major)

F-Ab-C (Minor)

G-Bb-D (Minor)

Ab-C-Eb (Major)

Bb-D-F (Major)

C Minor Melodic Ascending:

C-Eb-G (Minor)

D-F-A (Minor)

Eb-G-B (Augmented)

F-A-C (Major)

G-B-D (Major)

A-C-Eb (Diminished)

B-D-F (Diminished)

C Minor Melodic Descending:

Same as C Natural Minor

PS. I am still new to Finale. I tried using it but did not know how. I couldn't figure out how to change a note once I enter it.

having modem troubles. Should be able to get back on track by next week.

Ok, here is the next exercise. I will give you a chord and I want for you to tell me know it functions in other keys (using roman numerals).

For example:

C Major chord -

I in C Major

IV in G Major

VI in E minor

Here are your chords...

1) E minor

2) D Augmented

3) F Major

4) G diminished

5) C# Major

6) Ab minor

7) C Augmented

Well, this was quite difficult and that was part of the reason why I took so much time. It was difficult in part because my knowledge of scales or rather my mental facility with scales and by heart knowledge of them is not adequate. Therefore I had to take time figuring out my scales:

Here are my answers. I hope I haven't missed any!

1) E minor: i in E Minor, iii in C Major, iv in G Major, v in A Minor

2) D Augmented: III in B Melodic Minor Ascending (only one)

3) F Major: IV in C Major, III in D Minor (Natural), IV in A Minor, I in F Major

4) G Diminished: vii in Ab Major, ii in F Minor

5) C# Major: V in F# Major, I in C# Major, IV in G# Major, VI in D# Minor, III in A# Minor, E# Minor

6) Ab Minor: vi in Gb Major, vi in Cb Major, i in Ab Minor, iv in Eb Major

7) C Augmented: III in A minor Melodic ascending (only one)