Exploring the relationships between thaats in Hindustani Music

(24 Nov 2018) music kala

On thaats: the diff graph

The wikipedia article on Thaats lists the following 10 Hindustani Raags along with the most famous raag associated in the third column.

1	Bilaval	Bilaval	S R G M P D N Ś	Ionian	29th	Dheerashankarabharanam
2	Kafi	Kafi	S R g M P D n Ś	Dorian	22nd	Kharaharapriya
3	Bhairavi	Bhairavi	S r g M P d n Ś	Phrygian	8th	Hanumatodi
4	Kalyan	Yaman	S R G m P D N Ś	Lydian	65th	(Mecha) Kalyani
5	Khamaj	Khamaj	S R G M P D n Ś	Mixolydian	28th	Harikambhoji
6	Asavari	Asavari	S R g M P d n Ś	Aeolian	20th	Natabhairavi
7	Bhairav	Bhairav	S r G M P d N Ś	Double Harmonic	15th	Mayamalavagowla
8	Marva	Marva	S r G m P D N Ś	-	53rd	Gamanashrama
9	Poorvi	Poorvi	S r G m P d N Ś	-	51st	Kamavardhani
10	Todi	Miyan ki Todi	S r g m P d N Ś	-	45th	Shubhapantuvarali

We asked the question, if we only consider the swaras associated with each thaat as a string, can we investigate the graph of thaats constructed with edge-weights as the string diff of the notes.

num	name	notes
1	Bilaval	RGMPDN
2	Kafi	RgMPDn
3	Bhairavi	rgMPdn
4	Kalyan	RGmPDN
5	Khamaj	RGMPDn
6	Asavari	RgMPdn
7	Bhairav	rGMPdN
8	Marva	rGmPDN
9	Poorvi	rGmPdN
10	Todi	rgmPdN

Let us first construct the Graph. I write the edge list to file first.

    import pandas as pd
    from networkx import *
    import matplotlib.pyplot as plt
    
    DF=pd.DataFrame(data)                                                                    
    DF.columns=DF.iloc[0]
    DF = DF.drop(0)                                                                                 
    
    def cmp(A, B):
        count = 0
        for a,b in zip(A,B):
            if a != b:
                count += 1
        return count
    
    with open('thaat_edge_list.txt', 'w') as f:
        for i in range(1,11):
            for j in range(i+1,11):
                E = cmp(str(list(DF['notes'].loc[DF['num'] == i])[0]), str(list(DF['notes'].loc[DF['num'] == j])[0]))
                f.write(str(i) + '\t'+ str(j) + '\t' + str(E) + '\n')
    
    G = read_weighted_edgelist('thaat_edge_list.txt',delimiter='\t',
                      nodetype=int,
                      encoding='utf-8')

We can now visualize the graph by coloring the edges by the edge weight.

    colordict = {1:'g',
                 2:'w',
                 3:'w',#'orange',#'orange',
                 4:'w',#'r',
                 5:'w'}#'k'}
    
    nodes = [i for i in range(1,11)]
    labels = {i:DF['name'][i] for i in range(1,11)}
    draw_circular(G,with_labels=True,nodelist=nodes,
                  edge_color=[colordict[G[i][j]['weight']] for i,j in G.edges()],
                  node_color='w',
                  labels=labels)
    plt.savefig('thaat_diff-1.png',dpi=300)

The green edges show edge weight of 1, i.e. these thaats differ by one note.

    colordict = {1:'g',
                 2:'b',
                 3:'w',#'orange',#'orange',
                 4:'w',#'r',
                 5:'w'}#'k'}
    
    nodes = [i for i in range(1,11)]
    labels = {i:DF['name'][i] for i in range(1,11)}
    draw_circular(G,with_labels=True,nodelist=nodes,
                  #width=[G[i][j]['weight'] for i,j in G.edges()]
                  edge_color=[colordict[G[i][j]['weight']] for i,j in G.edges()],
                  node_color='w',
                  labels=labels)
    plt.savefig('thaat_diff-1,2.png',dpi=300)

These include thaats that differ by one or two notes

    colordict = {1:'g',
                 2:'b',
                 3:'orange',#'orange',
                 4:'w',#'r',
                 5:'w'}#'k'}
    
    nodes = [i for i in range(1,11)]
    labels = {i:DF['name'][i] for i in range(1,11)}
    draw_circular(G,with_labels=True,nodelist=nodes,
                  #width=[G[i][j]['weight'] for i,j in G.edges()]
                  edge_color=[colordict[G[i][j]['weight']] for i,j in G.edges()],
                  node_color='w',
                  labels=labels)
    plt.savefig('thaat_diff-1,2,3.png',dpi=300)

.. and those that differ by three…

    colordict = {1:'g',
                 2:'b',
                 3:'orange',#'orange',
                 4:'r',
                 5:'w'}#'k'}
    
    nodes = [i for i in range(1,11)]
    labels = {i:DF['name'][i] for i in range(1,11)}
    draw_circular(G,with_labels=True,nodelist=nodes,
                  #width=[G[i][j]['weight'] for i,j in G.edges()]
                  edge_color=[colordict[G[i][j]['weight']] for i,j in G.edges()],
                  node_color='w',
                  labels=labels)
    plt.savefig('thaat_diff-1,2,3,4.png',dpi=300)

… and finally up to four notes (in red).

What thaats are similar to all other thaats? Look at number of thaats at most 2 notes different

    degreedict = {}
    for i in range(1,11):
       count =0
       degreedict[i] = {'count':0,'name':labels[i]}
       for j in range(1, 11):
          if  i!=j and G[i][j]['weight'] <= 2.0:
             count += 1
       degreedict[i]['count'] = count
    
    for k in degreedict.keys():
       print(degreedict[k]['name'],degreedict[k]['count'])

('Bilaval', 5)
('Kafi', 4)
('Bhairavi', 4)
('Kalyan', 4)
('Khamaj', 4)
('Asavari', 3)
('Bhairav', 5)
('Marva', 5)
('Poorvi', 4)
('Todi', 4)

What thaats are most different from other thaats? Look at number of thaats that are more than 3 notes different.

    degreedict = {}
    for i in range(1,11):
       count =0
       degreedict[i] = {'count':0,'name':labels[i]}
       for j in range(1, 11):
          if  i!=j and G[i][j]['weight'] > 3.0:
             count += 1
       degreedict[i]['count'] = count
    
    for k in degreedict.keys():
       print(degreedict[k]['name'],degreedict[k]['count'])

('Bilaval', 2)
('Kafi', 4)
('Bhairavi', 3)
('Kalyan', 2)
('Khamaj', 2)
('Asavari', 3)
('Bhairav', 1)
('Marva', 3)
('Poorvi', 3)
('Todi', 3)

Putting it all together as an animation makes it clear that for the most part thaats are equally different from each other. and as an animated gif!

While these are purely abstract relationships between thaats, we will be exploring the significance of these relationships on the raags that constitute each thaat next week!