Pythagoras’s octave of Music
Human beings first experienced ‘Shadaj’ and Pancham’s sounding relationship. Along with this, it was also known to him that the Pancham swar is one and a half times the Shadaj swar. It was then considered that Taar Shadaj is one and half times of which swar (as the combination of Madhya Shadaj and Taar Shadaj is also very dulcet). After the search, it is confirmed that the swar is Madhyam. When this happens, a new interval between Madhyam and Pancham came to the picture, which is 9/8. Now, in between Madhyam and Shadaj, a swar is established which is called Rishav. In doing so, it was cleared that the interval of Rishav and Madhyam is equal to the interval between Shadaj-Rishav or Madhyam-Pancham. And at this interval, a swar can be established. So at that interval, a swar was established further to “Re” and it was called ‘Gandhar’. Now there is no interval between Gandhar and the Madhyam that one other tone can be established on it. Whatever happened after the swar Madhya Shadaj, the same thing happened even after Pancham. That is, in between Pancham and Shadaj of Taar Saptak, Dhaivat and Nishad swar were placed in the same the distance of Madhyam and Pancham, in the same order. Now again, there is a very little gap in the middle of the Nishad and Taar-Shadaj which left as it is. In this way, the octave was formed, the interval in between the swar Shadaj and Rishab, Rishabh and Gandhar, Madhyam and Pancham, Pancham and Dhaivat, Dhaivat and Nishad was the same. The gaps between the Gandhara and Madhyam and the Nishad and Taar Shadaj chords were equal but smaller than the first interval. Thus, there were two intervals in one octave one big and the second one is small. The big difference in mathematical terms is 9/8 and the small is 256/243, in which 9/8 intervals are called “tone” and 256/243 is the “Lima”. But Pythagoras called it “Semitone”. Because the attempt of this octave was made by the famous Greek scholar Pythagoras, it is called Pythagorean Scale.
Creation of Saptak by Shadaj-Pancham-Bhav:
On the basis of above said information, the octave made, its Nishad and Gandhar swar did not look more harmonious, therefore the attempt was made to create Saptak in a different way. In these circumstances, an attempt was made to make a Saptak from Shadaj-Pancham-Bhav. On this basis, it is concluded that Pancham is the 1½ of Shadaj. This Pancham is considered as Shadaj and searched for its 1½ swar which came to Rishav. After careful observation, it is clear that the difference that came up high was actually 85/80 in terms of mathematics. Hence this octave was not too satisfactory.
Creation of Saptak by Shadaj-Madhyam-Bhav:
When the octave was not formed by Shadaj-Pancham- Bhav, then searched for Madhyam towards the fifth lower vowel from Taar Shadaj and got Nishad. Similarly, this action continued till the achievement of the movement in the multiplication of the same movement that went through. On this basis, the saptak made, in that the last Shadaj came below from the Shadaj that should have come. This means that the interval this time has come down to 81/80. The scholars call this difference as “coma” or “Praman shruti”.
Creation of Diatonic scale
As no satisfactory scale has been made so far, so the scholars tried to make the best swar saptak. When considered, it was experienced that in addition to the Shadaj, Madhyam and Pancham, if the vowels played in the ratio of four, five and sixes, then they also look melodious. While doing this, when the swar searched in proportion to Shadaj, swar ‘Sa’ ‘Ga’ and ‘Pa’ is detected. Again, in the ratio of 4, 5 and 6, ‘Ma’ ‘Dha’ and ‘Sa’ received. Similarly in the ratio of 4, 5 and 6, ‘Pa’, ‘Ni’ and ‘Re’ received. Due to the two intervals, i.e. tone and semitone only in this octave grossly found, it was called the ‘Dia’ (which means 2) tone of the scale.
The way to keep vowels/swar is called scale. You can do both the ‘aaroh’ (ascending) or the ‘abroh’ (descending) from this sequence.
There are two types of scale: 1. Diatonic and 2. Chromatic. Both scales are made of two types of semitone. Both the tone and semi-tone are used in the die tonic scale whereas the only semitone is used in Chromatic scale.
The Diatonic scale also has two parts, one is called major and the second is called the minor scale. There must be seven voices/swar in each scale. In these, vowels are written over the lines or in their middle. This sequence continues after the seven vowels. But this sequence does not seem to be complete until the eighth vowel is added in this sequence. Thus, this eighth vowel is only twice as high as the first Shadaj. Similarly, the tenth vowel means double the third vowel of the first octave.
The sequence of tones and semitones in it is certain in a particular way. There is a semitone in between the third and fourth and seventh and eighth vowels and the tones in between the remaining vowels.
As we have said in the previous chapter that when any major vowel is reduced by 1 semitone, then it becomes a minor. As the difference of the third vowel is miner from the keynote (i.e. ‘Sa’) in this scale, so it’s called the minor scale.
In this, all the vowels are kept at a distance of 1 meter. Because there is a total of 12 vowels in one octave, so the process of keeping it in the same sequence is called the chronic scale. There are two tones of the same name, like C and C Sharp or D and D Sharp etc. If this scale has to be taken more than 12 vowels then the next vowel number will be exactly two-fold as the first vowel, such as the 15th swar is exactly twice high of the 3rd swar. For example, in the major scale of ‘C’, the next vowel from ‘C’ is the ‘D’ swar at a distance of one tone. In it the empty vowels are the Major Scale of ‘C’ and the filled swar is have been extended to fill the tone with the filled tone And the filled tone has been increased to maintain the distance of semitone.