Article 4: Understanding Intervals : Stepping into Harmony

Understanding intervals is fundamental to understanding harmony. I have already touched on intervals in Articles 2 and 3 and have spoken about three kinds of intervals

1. Major Second
2. Minor Second
3. Augmented Second

If you notice there are two parts to the naming of the interval 

"Major" and "Second"

"Minor" and "Second"

"Augmented" and "Second"

All intervals will have this kind of a naming convention - the first refers to the quality of the interval, and the second to the quantity. The interval from Sa to Ga for instance, is a third. Depending on whether it is Ga1, Ga2 or Ga3, the quality of the interval changes.

Sa - Ga2 - Minor Third

Sa - Ga3 - Major Third

I missed Sa- Ga1 there for a reason. This introduces the fourth 'quality' called Diminished. Sa - Ga1 is called a diminished third. A question that pops up obviously is "Hey, Sa - Ga1 is the same as Sa - Ri2. Wouldnt that be a major second?". This answer is much easier for a carnatic musician to understand than for a beginner in western music. Just like the same note is referred to as Ga1 or Ri2 depending on the context in the raag, the interval is also referred to as either major second or diminished third depending on context. That said, diminished third is an interval that will rarely come up. (but it serves to illustrate this point nevertheless).

Lets flip over now to western notation and examine this concept of intervals. The common intervals that pop up in study are as below. I have illustrated in the key of C, but as I have mentioned before, there is nothing special about the key of C.

C- Db : Minor Second (1 semitone)  => Sa - Ri1

C - D : Major Second  (2 semitones)  => Sa - Ri2

C - D# Augmented Second (3 semitones) => Sa - Ri3

C - Eb : Minor Third (3 semitones) => Sa - Ga2

C - E : Major Third (4 semitones) => Sa - Ga3

C - Ab : Minor Sixth (8 semitones) => Sa - Dha1

C - A : Major Sixth (9 semitones) => Sa - Dha 2

C - Bb : Minor 7th (10 semitones) => Sa - Ni2

C - B : Major 7th (11 semitones) => Sa - Ni3

You will notice that I have omitted Sa - Ma and Sa - Pa. This is because the naming of these intervals is different. They are referred to as perfect intervals. 

Sa - Ma1 : Perfect Fourth

Sa - Pa : Perfect Fifth.

Corresponding to Ma2, obviously we have an interval which is

Sa - Ma2 : Augmentted Fourth

So the interval between the Sa and the Ma of Kalyani would be called an Augmented Fourth or a Tritone. 

Let us extrapolate this a little bit more. Move to Mayamalavagowla raagam.

Let us analyze the intervals between different pairs of notes to get a firm understanding of the interval concept. The Raag notes are of course

Sa - Ri1 - Ga3 - Ma1 - Pa - Dha1 - Ni3 - Sa

Let me use the note D as Sa, in order to illustrate this (I am assuming you will now be able to figure out the notes of D major based on previous lessons)

Sa - Ri : Minor Second (D - Eb)

Sa - Ga : Major Third (D - F#)

Sa - Ma : Perfect Fourth (D - G)

Sa - Pa : Perfect Fifth (D - A)

Sa - Dha : Minor Sixth (D- Bb)

Sa - Ni : Major Seventh (D - C#)

Sa : Sa : Octave (D - D)

Now let us analyze intervals between random notes (not starting only with Sa as we have done so far)

Ri - Ga : Augmented Second (Eb - F#)

Dha - Ni : Augmented Second (Bb - C#)

Ri - Ma : Major Third (Eb - G)

Ga - Dha : Diminished Fourth (F# - Bb)

Dha - Sa : Major Third. (Bb - D)

I am hoping your are getting my drift here. Intervals, as I have mentioned before is the distance between any two notes, and the above set of examples clearly illustrates the names corresponding to the intervals in various contexts. What does this have to do with harmony? Everything. If you dont understand intervals inside out, you are going to be completely lost when we talk chords and chord progressions and passing notes and suspensions. I am going to spend one more article talking about intervals, so we are not done yet :)

Article 3: The minor scale and a bit more

I dropped the last article off with a plan of talking about Keeravani and how other ragas can be mapped onto the western scale. Here goes.

Keeravani's notes translated into intervals are
Sa - Ri2 - Ga2 - Ma1 - Pa - Dha1 - Ni3 - Sa
    IIM   IIm     IIM     IIM  IIm    IIA    IIm

There is a new interval here that I have called IIA. This refers to what is called an Augmented second interval. This is equal to 3 semitones. As a quick refresher, IIM is also called a tone, and IIm is also called as a semitone.

So the interval-lic pattern for the Keeravani raag is
IIM - IIm - IIM - IIM - IIm - IIA - IIm.
Starting with any note on the scale, if we build using this interval pattern, the Keeravani raag will result.

Starting with C for example, this would be
C - D - Eb - F - G - Ab - B - C

Starting with D, this would look as follows:
D - E - F - G - A - Bb - C# - D

This scale pattern is called the minor scale in western music.
So when a piece of music is written in C Major, it comprises the following notes
C - D - E - F - G - A - B - C

When a piece of music is written in C minor, it comprises the following notes
C - D - Eb - F - G - Ab - B - C

With this background, it becomes obvious that any raag (without the gamakam aspect) can be fitted onto the standard piano. Take the root note (Sa) and build the intervals on top of it.

To illustrate, Kalyani, starting on the C note as Sa, would be as follows:
C - D - E - F# - G - A - B - C
The F# is the equivalent of Ma2. Note that it is 3 tones away from C (Sa). This is referred to as a tritone in western music.

The fundamental way in which western music differs from carnatic is that carnatic music is largely horizontal - melody driven. Western music has two dimensions - horizontal and vertical (melody and harmony).

The basic elements of harmony will be the contents of the next article.