page_title: Shruti (music)
section_title: Ratios and frequencies
hierarchical_section_title: Shruti (music) / Relationship to Dhwani, Nada, and Swara / Ratios and frequencies
caption_attribution_description: English: 22 Shruti-Mandal (Organogram)
context_page_description: Shruti or śruti is a Sanskrit word, found in the Vedic texts of Hinduism where it means lyrics and "what is heard" in general. It is also an important concept in Indian music, where it means the smallest interval of pitch that the human ear can detect and a singer or musical instrument can produce. The musical shruti concept is found in ancient and medieval Sanskrit texts such as the Natya Shastra, the Dattilam, the Brihaddeshi, and the Sangita Ratnakara. Chandogya Upanishad speaks of the division of the octave in 22 parts.
  The swara differs from the shruti concept in Indian music. A shruti is the smallest gradation of pitch available, while a swara is the selected pitches from which the musician constructs the scales, melodies and ragas. The Natya Shastra identifies and discusses twenty two shruti and seven swara per octave. Of the twenty two shruti, veena scholars identified the 4th shruti to be sa solfege, 7th to be re, 9th as ga, 13th as ma, 17th as pa, 20th to be dha and 22nd as ni shuddha swara. Theoretically, an infinite number of shruti are possible, and later music scholars of India increased the number of shruti in their studies.
context_section_description: It was shown in this research that 22 Shrutis are essentially related to Shadja (Fundamental frequency), by most natural interval ratios, 100:125 (S:G) or 100:150 (S:P) as shown in the Figure below. This helps us to get their precise positions and frequencies.
  Figure showing 22 Shruti-Mandal (Organogram)
  1 denotes a 'lower' shruti or the 'beginning' of the region of the note on a string.
  2 denotes a 'higher' shruti or the 'end' of the region of the note on a string,
  Small letters denote a komal or flatter version (except m, which is 'tara'),
  Capital letters denote a tara or sharper version (except M, which is 'komal'),
  Vertical arrows indicate an interval ratio of 100:125.
  Horizontal arrows indicate an Interval ratio of 100:150.
  Fig. showing 22 Shruti-Mandal (Organogram) (Carnatic).
  12 Swaras with their 16 names are shown as S, R1, R2/G1, R3, G1, G2/R3, G3, M1, M2, P, D1, D2/N1, D3, N1, N2/D3, N3. Their ‘Lower’ and ‘Higher’ Shruti versions are shown respectively marked as ‘L’ and ‘H’ in Italics. Vertical arrow indicates an Interval ratio of 100:125. Horizontal arrow indicates an Interval ratio of 100:150.
  To calculate the frequency of Shrutis, for every horizontal arrow, 50% is added; and for every vertical arrow, 25% is added. e.g., to calculate the 'frequency' of P, consider the frequency of Shadja as 100 Hz (for convenience of calculation). Thus, P comes at 100 Hz + 50% = 150 Hz. The ratio of P thus becomes 150/100. To calculate the 'position' of  P on the string, we can use the law of Galileo Galilei, called in India as ‘Dviguna’ relationship, which states that the frequency ratio is 'inversely' proportional to the length of the string. Therefore, when the ratio 150/100 is 'inverted' we get the position of P on the string as 100/150 or 2/3 or 66.66% length of the string. We can calculate the frequencies and the positions of all the 22 shrutis accordingly.
  Table showing the Ratios, Frequencies, % length of the string where 22 Shrutis are played (*Frequency of the Fundamental frequency or Shadja taken as 100 Hz, as example)
  Thus, Shrutis can be expressed as 1) 'Interval ratio',  2) Audio frequency, and 3) The playing position as % length of the string.
  There is not a single common note between the European 12-Tone Equal Temperament Scale and the 22-Shruti-Indian scale.
  Table shows % frequency above Shadja (Fundamental Tone) of the 
  12-Tone-Equal Temperament Scale and the 22-Shruti-Indian Scale.
  New musical instruments have been made to demonstrate the accurate sounds, the position, and the practical use of 22 shrutis in music, including a 22-Shruti-Harmonium (Indian Patent No. 250197), 22-Shruti-Veena, 22-Shruti-Metallophone and 22 Shruti-Tanpura. In both the Hindusthani and Carnatic classical music, the places for playing 22 shrutis (as % length of the string) remain exactly the same on instruments such as Veena, Sarod, Sitar, Sarangi, Violin as shown in the table and diagram.
  4 Shrutis each of the notes R, G, M, D and N progress in a symmetrical order  of Poorna, Pramana, Nyuna, Pramana as shown in the diagram.
caption: 22 Shruti Organogram (Hindustani)
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