Scales derived by the Method of Progressions
THE METHOD OF PROGRESSIONS (MURCHHANAS)
We saw in class last time that starting from the harmonic/acoustical
method one arrives at a scale that is approximately the same as the natural
(i.e. non-tempered) minor scale of present day use. Let us regard this as set up
on a fretted instrument, and number the frets as follows:
Scale 1
1
2 3
4
5
6
7
8
S
R g
M
P
D
n
S^
KAFI THAAT
C D Eb
F
G
A
Bb
C^
W H
W
W
W
H
W
TONES
If one plays the instrument on the frets numbered 1 through 8 in that
order, one would end up playing the notes described above. Now imagine that we
start at fret number 2, and play the frets in the order 2 3 4 5 6 7 8, and
complete the octave by playing the fret that would correspond to the note which
is an octave above the fret 2 (We can call this fret 9),. The sequence of
intervals produced would be H W W W H W W, so that if one now retuned our
instrument starting from C, but with these intervals, (namely the sequence H W W
W H W), we would get the following scale.
Scale 2.
S
r g
M
P
d
n
S^
BHAIRAVI THAAT
C C#
Eb
F
G
Ab
Bb
C^
H W
W
W
H
W
W
TONES
One can repeat this process on the scale #2 obtained just now, and
generate other scales. The process described here arises quite naturally in the
context of a string instrument (fretted or not), and was well known in the
ancient world. Greek musical works certainly refer to this process, and so do
the oldest known Indian works, where this procedure is called Murchhana.
Thus the scale #2 is said to have been obtained from the scale #1 by performing
a Murchhana on scale number #1. In
general the word Murchhana refers to
the process of generating a new scale from a given scale by starting at a
different note of the given scale but maintaining the same intervals as the
scale from which one started. finally transposing the scale so obtained to the
original (standard) tonic, which we have taken as C for our illustration.
Applying this process in turn, to the scale #2, we arrive at the sequence
of scales listed below. All these are admissible thaats except for one, the one
marked with ** (after #5 below), which is not admissible, since, by convention,
a scale must contain the note P (i.e. it must contain the perfect fifth starting
from the tonic).
Scale 3.
S
R G
M#
P
D
N
S^
KALYAN THAAT
C D E
F#
G
A
B
C^
W W
W
H
W
W
H
Scale 4.
S
R G
M
P
D
n
S^
KHAMAJ THAAT
C D E
F
G
A
Bb
C^
W W
H
W
W
H
W
Scale 5.
S
R g
M
P
d
n
S^
ASAVARI THAAT
C D Eb
F
G
Ab
Bb
C^
W H
W
W
H
W
W
Scale **
S
r
g
M
M#
d
n
S^
INADMISSIBLE
C C#
Eb
F
F#
Ab
Bb
C^
H W
W
H
W
W
W
Scale 6.
S
R G
M
P
D
N
S^
BILAWAL THAAT
C D E
F
G
A
B
C^
W W
H
W
W
W
H
Repeating this process yet once more brings us back to the starting
point, namely to the scale #1 (Kafi thaat).
Scale 1.
S
R g
M
P
D
n
S^
KAFI THAAT
C D Eb
F
G
A
Bb
C^
W H
W
W
W
H
W
The procedure described here generates six of the ten principal thaats
prevalent in Hindustani music today. The remaining four thaats in current
use are not obtained this way from the Kafi thaat. In fact (see below), those scales contain intervals
which equal one and a half tones, so that they cannot be obtained by the process
described above by starting from a scale which does not contain such an
interval.
Scale 7.
S
r G
M
P
d
N
S^
BHAIRAV THAAT
C C#
E
F
G
Ab
B
C^
H WH
H
W
H
WH
H
Scale 8.
S
r G
M#
P
d
N
S^
POORVI THAAT
C C#
E
F#
G
Ab
B
C^
H WH
W
H
H
WH
H
Scale 9.
S
r G
M#
P
D
N
S^
MARWA THAAT
C C#
E
F#
G
A
B
C^
H WH
W
H
W
W
H
Scale 10.
S
r
g
M#
P
d
N
S^
TODI THAAT
C C#
Eb
F#
G
Ab
B
C^
H W
WH
H
H
WH
H
The reader who is familiar with Greek musical scales will realize that
the Murchhana process is exactly the same as the process used by Greek
musicians to produce new modes from a given mode. Although it is possible to
identify the thaats we obtained above
with ancient Greek modes, we shall not spend the time to do that just now.