Mathematics is one of the basic needs for human brain to enhance logical and analytical thinking. It provides an efficient way to build mental discipline in understanding various concepts of all other fields. History reveals a strong relation between the theories of Music and Mathematics. The great Mathematician Pythagoras(569475BC), often _{12}= {0,1,2,3,4,5,6,7,8,9,10,11}. Melodies in Indian classical music are being produced by unique combination of pitches, which are called as Ragas. Each raga is a collection of pitches in a specific order using a particular formula defined for it. There are 72 Janaka ragas/Melakartha ragas, also known as parent ragas consisting of all seven swaras including the first swara ‘Sa’ of the next octave, whereas there are many janya ragas by omitting/adding few more swaras to the janaka ragas. The arrangement of all swaras in a Melakartha raga is according to the combinations of “Ri”, "Ga”, “Ma”, “Da” and “Ni”. These 72 are broadly divided into 12 chakras with each 6 ragas, and 2 groups one with 36SuddhaMadhyamam(Ma1) and 36PrathiMadhyamam(Ma2).The 36 of each group are with the combinations of Ri, Ga, Da, Ni with 3 variations in each by avoiding the over laps of Ri3Ga1, Da3Ni1. The “KaTaPaYa” scheme which was used by ancient Indian Mathematicians for different purposes is also used to find the Melakartha number of a Janaka raaga. In this scheme consonants of Sanskrit are allotted with numerals 1 to 9, 0 and a Melakartha raga number is determined by decoding the first two letters from the name of the raga. There is a Mathematical algorithm to determine the swaras from a Melakartha number k. For k<=36, the melakartha raga comes under Sudha madhyama M1 ragaas whereas for k>36 it will be a prathimadhyama raaga. The remaining sets of swaras Ri, Ga (Purvangaswaras) and Da, Ni (Uttarangaswaras) are determined by the quotient and remainder when k1/k361 is divided by 6. Taala is a cyclical metre consisting of beats to measure musical time. The three basic units of a Taala cycle are Laghu, Dhrutha and Anudhrutha. Dhrutha has 2 beat counts; Anudhrutha has 1 beat count whereas number of beat counts for Laghu is not fixed. The Indian Carnatic music system consists of 7 major Taalas: Dhruva, Matya, Rupaka, Jhampa, Triputa, Ata, Eka and each of these Taala has a formula to define the units of Taala that a particular Taala should contain. These 7 Taalas has 2 more classifications: Jaathi and Gathi.Jaathi defines number of beat counts in Laghu. There are 5 Jaathis and 5 Gathis: Tisra (3), Chathurasra (4) Khanda (5), Misra (7) and Sankeerna (9). Gathi defines number of sub beats for each beat count for all 3 units Laghu, Dhrutha and Anudhrutha of one cycle of a Taala. These 7 Taalas with 5 of each Jathi and Gatis define 7X5X5=175 Taalas.
There have been some studies to analyse the impact of learning music in improvising mathematical skills in students. Holmes and Hallam ^{1}, conducted a Quasiexperimental design for children aged 4 to 7 who were made into two groups one with musical training the other as controlled groups. The findings of this study provided evidence to significant
Most of these studies were based on western music to analyse the influence of Music training on learning mathematics during the school education. Some of those are on mathematics involved in Carnatic Music. The Indian Carnatic music has a systematic and methodical process of learning and performing. For many years learning music was an integral part of Indian educational system. There were not many studies to observe the analytical skills that are attained in learning mathematics and Carnatic music together which are common for both. Studying these mathematical characteristics of Carnatic musicians help in understanding the importance of mathematical skills need not only science related subjects but also to excel in fine arts.
This study aims first in identifying the aptitude of the Carnatic musicians towards Mathematics as a part of their academics. Then to identify the impact of learning Mathematics as well Music together on their analytical, logical and reasoning skills in both the fields.
The research hypotheses have been formulated, keeping in view the objectives of the study, which is, finding the association between different demographic factors in identifying the Sruthi, Rhythm and Mathematics related concepts.
The present study is undertaken to study the effect of Mathematical skills in their analytical musical skills. This research highlights at what level of association with Mathematics is increasing the observational and logical skills in Carnatic Musicians. Empirical research method is adopted.
The following research hypotheses have been formulated, keeping in view of the objectives of the study.
H_{11}: There is an association between opting Mathematics as part of academics and learning Carnatic music.
H_{12}: There is an association between demographic factors and identification of Sruthi, Rhythm of Carnatic music.
H_{13}: The attributes, association with Mathematics, identification of Sruthi, Rhythm and logical reasoning.
The research is conducted on a sample of 153 respondents which is collected through a structured questionnaire using Microsoft forms on the basis of random sampling method. The data have been analysed and hypotheses have been tested by using valid statistical tools that is descriptive statistics, chi square test using IBM SPSS version 25. Based on the resulting output, the data and results have been interpreted.
A glance at the information on the demographic factors [
S.No 
Variable 
Category 
Frequency 
Percentage 
1 
Age 
1825 
52 
34 
2635 
31 
20 

3645 
36 
24 

above 45 
34 
22 

2 
Education 
High School 
4 
3 
Intermediate 
3 
2 

Under Graduate 
54 
35 

Post Graduate 
76 
50 

Higher than Post Graduate 
16 
10 

3 
Association with Mathematics 
High School 
37 
24 
Intermediate 
24 
16 

Under Graduate 
70 
46 

Post Graduate 
20 
13 

Higher than Post Graduate 
2 
1 

4 
Association with Indian Carnatic Music 
Listener 
27 
18 
Learner and Performer (Vocal) 
58 
38 

Learner and Performer (Instrument) 
18 
12 

Teacher and Performer (Vocal) 
17 
11 

Teacher and Performer (Instrument) 
20 
13 

Performer (Vocal) 
9 
6 

Performer (Instrument) 
4 
3 

5 
No. Of years trained 
04 
26 
17 
5_9 
23 
15 

10_14 
34 
22 

1519 
18 
12 

2024 
26 
17 

2529 
8 
5 

>30 
18 
12 
From [
From [
From [
The hypotheses H_{11}, H_{12}, H_{13} are taken for the study and have been tested using Chisquare test for independence of attributes. From [

Variable 
p  Value 
Interpretation 
Age 
Sruthi 
0.924 
There is no association between age and Sruthi and Rhythm recognition; Age and Math ability 
Rhythm 
0.725 

Analytical 
0.583 

Numerical 
0.117 

Logical 
0.386 

Education 
Audio 1 
0.406 
There is no association between Education and Sruthi and Rhythm recognition; but an association between Education and Math ability 
Audio 2 
0.53 

Analytical 
0.155 

Numerical 
0.003 

Logical 
0.044 

Maths association 
Association with Carnatic music 
0.419 
There is no association between Math association and Carnatic music 
Trained 
0.698 
There is no association between Math association and trained in music 

Sruthi 
0.001 
There is an association between Education and Sruthi recognition 

Rhythm 
0.664 
There is no association between Education and Rhythm recognition; Education and analytical ability 

Analytical 
0.563 

Numerical 
0.048 
There is an association between Education and numerical ability 

Logical 
0.457 
There is no association between Education and logical ability 

Trained 
Sruthi 
0.998 
There is no association between trained and Sruthi and Rhythm recognition; age and Math ability 
Rhythm 
0.931 

Analytical 
0.191 

Numerical 
0.172 

Logical 
0.744 

Audio 1 
Analytical 
0.347 
There is no association between Sruthi recognition and Math ability 
Numerical 
0.191 

Logical 
0.535 

Audio 2 
Analytical 
0.176 
There is no association between Rhythm recognition and Math ability 
Numerical 
0.771 

Logical 
0.834 
Our Ancient Indian educational system of “Gurukula” provided each individual holistic and integrated education which was included with learning of all subjects as “Sastras”. As the generations are passing through, we are arriving to the practice of learning different subjects in disjoint cubical. Acquiring Mathematical skills is an integral part of one’s individual learning. Being good in any one or few of the Art forms enhances overall development. In general Mathematics is considered as a subject that supports Scientific and Technical skills which involve the functioning of the left side of the brain. And Music is taken granted as an art form that is involved with aesthetic sense and emotions which involve the functioning of the right side of the brain. But certain cognitive and reasoning skills are common in learning Mathematics and Music. Studying these Mathematical characteristics of Carnatic Musicians may help in understanding the importance of Mathematical skills needed not only Science related subjects but also to excel in fine arts.
In this study it is observed that a considerable count of the Carnatic Musicians are having Mathematics as one of their subjects up to their Under graduate studies. Learning them both can complement each other’s enhancement. By choice or chance some may not opt to continue Mathematics in their higher education, but their aptitude towards Mathematics will certainly enhance the ability to understand the key concepts in Carnatic music.
This study is conducted for a small sample size with 153 Carnatic Musicians scattered in different places of India and few places outside India. There was difficulty in reaching larger number of Musicians and to convince them to be a part of this study. This type of study can be extended to larger groups, added with more parameters so as to observe more interesting and important outcomes.