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 1: First steps into western music theory - For the carnatic aficionado

I am hoping this is the beginning of a series of articles on the rudiments of western music theory. It assumes the reader understands carnatic music. This series starts as a result of a conversation with Harish Ganapathy, who figures on my top 3 list of carnatic singers. (I will post a link into a few of his songs shortly :)

I am not an expert at all on Carnatic music. My knowledge of it barely scratches the surface. But I believe I know the basics enough to take the carnatic expert through the basics of western music, and from there you (the carnatic music expert) are on your own.

The 7 basic notes of music remain intact, of course. Different singers pick Sa's at different pitches convenient to them. Basically they are picking a Sa at a frequency that is comfortable to them given the range of their voice. [For the violin player it makes no difference whatsoever, and so they can tune their Sa to whatever is the singer's comfort].

In western music, the concept of Sa is a bit more nebulous. Western music, as most of you probably know has the 7 notes A, B, C, D, E, F and G. Each of these notes maps to a particular fundamental frequency. So one carnatic singer's Sa could map the the note C. And another singer's Sa could map to the note D. Lets say these singers are singing Sankarabharanam. The first singer would then be singing the scale of C Major, and the second singer would be singing the scale of D Major.

Which brings us right over to the concept of scale. The scale concept should not really be confused with the Raga concept of carnatic music. There are only 2 well known and often used scale modes in western music - the major and the minor. These correspond, (for sake of understanding) to Sankarabharanam and Keeravani. Any piece of music in western music is written in either a minor scale or in a major scale.

The Sa of the scale determines what that scale is called. If the Sa is E, then the scale is E major or E minor. If the Sa is G, then the scale is G major or G minor. Within the same performance, singers and instruments effortlessly move between different scales for differnt songs. Even during a single song, the Sa can change from E to G. That means that a song in E major can quite possibly move to G major. (E and G are examples to illustrate. They are not necessarily good movements!). Even within the same piece of music, you can move from G major to E minor. These are all just movements of notes, and western music is extremely flexible in this respect. There is hardly a major piece of music in western classical music which begins and continues right through till the end on the same scale.

Compare this to Carnatic, where a song starting in Sankarabharanam in a Sa mapping to E, will always stay fixed between the defined 7 notes until the end of the song (unless it is a ragamalika or something, which is comparatively much rarer in carnatic music, anyway).

In the next article, I wll talk about the individual notes in western music and how they map to carnatic. That will give a clearer understanding of how the western music performer plays Keeravani starting from G, or Sankarabharanam starting from A, or extrapolating it further, how they play a Kalyani or a Shanmugapriya. The basics are the same, the fundamentals are the same, but the way of reading, the way of writing, and the way of understanding is a little different.