Griha Bedham: View points to a raga
One of the many mathematical aspects of Carnatic music is in 'Griha Bedhams'. Bedham refers to "seeing the difference". Griha means 'home'.
A raga is a set of 'rules' that specify what 'notes' of the octave must be used for that given rule and how to move from one note to the other.
If one can imagine the 12 notes as points in space with each note present in that given scale as a highlighted point, Shankarabharanam (the major scale equivalent) will look like:
.
Now, instead of playing sa ri ga ma pa da ni sa, if one 'shifts' the key to the next immediate note, 'ri', it would look like:
The resulting notes that will get played will be ri ga ma pa da ni sa ri. This suddenly sounds like the minor scale karaharapriya. Bedham is hence treating one of the notes of a given raga as 'sa' and rendering a new one from there in such a way that the new raga has the same 'note positions' as the notes in the unshifted raga.
But carnatic music is not just about 'notes'. Carnatic music treats each note in a given raga as a wave function. The 'ri' in two different ragas might occupy the same space but how it 'varies' with time might be different. This makes for an interesting and intellectually challenging mathematical play that requires not just the ability to imagine spatially but also immense knowledge of the vast number of ragas.
The rough equivalent of 'bedham' is called a 'mode' in the western music system however, since there is usually not any 'rule' associated with how you 'shake' a note, it turns out to be challenging in the plane of harmony (composers typically use one of the 'modes' of a given scale in one of the many lines in a symphony).
I've made some example renditions:
A raga is a set of 'rules' that specify what 'notes' of the octave must be used for that given rule and how to move from one note to the other.
If one can imagine the 12 notes as points in space with each note present in that given scale as a highlighted point, Shankarabharanam (the major scale equivalent) will look like:
.
Now, instead of playing sa ri ga ma pa da ni sa, if one 'shifts' the key to the next immediate note, 'ri', it would look like:
The resulting notes that will get played will be ri ga ma pa da ni sa ri. This suddenly sounds like the minor scale karaharapriya. Bedham is hence treating one of the notes of a given raga as 'sa' and rendering a new one from there in such a way that the new raga has the same 'note positions' as the notes in the unshifted raga.
But carnatic music is not just about 'notes'. Carnatic music treats each note in a given raga as a wave function. The 'ri' in two different ragas might occupy the same space but how it 'varies' with time might be different. This makes for an interesting and intellectually challenging mathematical play that requires not just the ability to imagine spatially but also immense knowledge of the vast number of ragas.
The rough equivalent of 'bedham' is called a 'mode' in the western music system however, since there is usually not any 'rule' associated with how you 'shake' a note, it turns out to be challenging in the plane of harmony (composers typically use one of the 'modes' of a given scale in one of the many lines in a symphony).
I've made some example renditions:
- Hamsanandhi and Mohanam (2.0MB). Its surprising how something as happy as a mohanam can be 'seen' from a very pathos-oriented raga like Hamsanandhi
- Simhendra Madhyamam and Suddha Dhanyasi (2.5MB)
- Sarasangi and Dharmavati (2.0MB)
- Keeravani and Vakulabharanam (1.1MB), as I had mentioned in one of my previous posts how these two ragas are obtainable from each other using griha bedham