It's time I learn about Indian music. Hindustani? Carnatic? Shrutis? Let's go.
Here's what I think I know. The basical musical notes are called swaras. Their solfege goes "Sa Ri/Re Ga Ma Pa Dha Ni Sa". They're short for "Shadja, Rishabh, Gandhar, Madhyam, Pancham, Dhaivat, Nishad" in North India, or those words with an additional "-am" in south India. I don't know why "Re" is an option as an abbreviation for "Rishabh", but I'd say it's a more common abbreviation than "Ri".
The scales are called ragas. They're tuned in 5-limit just intonation.
When you sing a raga in solfege, you sing the Ga for the third scale degree whether it's a major third or a minor third. Carnatic music distinguishes textually at least between Ga1, a minor third, and Ga2, a major third. Here are some options for each swara:
(P1 # 1/1) :: Sa
(Grm2 # 256/243) or (m2 # 16/15) :: Re1
(M2 # 10/9) or (AcM2 # 9/8) :: Re2
(Grm3 # 32/27) or (m3 # 6/5) :: Ga1
(M3 # 5/4) or (AcM3 # 81/64) :: Ga2
(P4 # 4/3) or (Ac4 # 27/20) :: Ma1
(AcA4 # 45/32) or (AcAcA4 # 729/512) :: Ma2
(P5 # 3/2) :: Pa
(Grm6 # 128/81) or (m6 # 8/5) :: Dha1
(M6 # 5/3) or (AcM6 # 27/16) :: Dha2
(Grm7 # 16/9) or (m7 # 9/5) :: Ni1
(M7 # 15/8) or (AcM7 # 243/128) :: Ni2
You can see that usually "1" means minor and "2" means major. The only time we break this pattern is with the fourth scale degree, Ma, for which "1" means perfect and "2" means augmented.
With only one option for ^1 (=Sa) and for ^5 (=Pa), we get 22 options all together. I've sometimes seen (Gr5 # 40/27 @ 680c) discussed in texts on indian scale intonation - I think "mentioned in Bharata's "Natya Shastra" but not used in modern Indian music" is probably a concise explanation of that.
I've also seen a notation system which gives three options each for Ri, Ga, Dha, Ni, but then equates one of each set of three options to another interval. I think the system is basically this:
S ~ P1 or perfect unison,
R1 ~ m2 or minor second,
R2 ~ M2 or major second,
R3 ~ A2 or augmented second,
G1 ~ d3 or diminished third,
G2 ~ m3 or minor third,
G3 ~ M3 or major third,
M1 ~ P4 or perfect fourth,
M2 ~ A4 or augmented fourth,
P ~ P5 or perfect fifth
D1 ~ m6 or minor sixth
D2 ~ M6 or major sixth
D3 ~ A6 or augmented sixth
N1 ~ d7 or diminished seventh
N2 ~ m7 or minor seventh
N3 ~ M7 or major seventh
Even though there are 16 lines in this table, it's more like 12 distinct sound levels because they recognize these equivalences:
Ri2 = Ga1 :: m2 ~ d3
Ri3 = Ga2 :: A2 ~ m3
Dha2 = Ni1 :: M6 ~ d7
Dha3 = Ni2 :: A6 ~ m7
The 22 notes from the previous sytem, all the 5-limit options, are called shrutis. There are supposedly some different accounts of the shrutis, but I think the above is the most widely accepted. I have trouble finding differing accounts at least. Sometimes you'll see long names for each individual shruti. I've seen enough disagreement that I decided to just use my own interval names for now, but I think I'll figrue it out and give fairly standard long names for shrutis from both Carnatic and Hindustani music shortly.
...
Some old Indian music theorists talked like the 22 shrutis were equally spaced - 9/8 is a distance of 4 shrutis, 4/3 is a distance of 9 shrutis, 3/2 is a distance of 13 shrutis. This is weird, but actually consistent with a 22-EDO (or 44-EDO or 66-EDO) interpretation. But people don't use any of those EDOs for indian music these days, if they ever did.
I think it's exciting that the Chinese guqin and the indian shrutis are both 5-limit; in addition to some 5-limit just intonation efforts in the west, there are multiple independent well developed 5-limit composition systems in this world. If you were ever not sure what to do with yourself in 5-limit, or if you weren't sure of the importance of 5-limit just intonation to humankind, just look around for inspiration. It's everywhere.
Ragas are sometimes separated into two tetrachords - the purvanga ("first part") from Sa to Ma, and the uttaranga ("second part") from Pa to high Sa.
A raga has an ascending form, "arohana", and a descending form, "avarohana". Often the same. A raga has a primary melodic note, "vadi", and a secondary melodic note, "samvadi", which is usually P4/P5 away from vadi.
Not all ragas have 7 notes. Often a note is skipped. The skipped note is called varjya, ("avoided, excluded, forbidden"). In other cases, a varjya note for a raga isn't in the scale - specifying it is just saying you really shouldn't play that note even in melodic ornaments. But often a varjya note means you skip the entire scale degree, like pentatonic scales skip two swaras.
The raga called Mohanam is pentatonic, and it skips ^4 and ^7, i.e. Ma and Ni, in both ascending and descending forms.
The raga called Hindolam is also pentatonic. It skips ^2 and ^5 i.e. Ri and Pa.
A raga will also often have an associated melodic phrase, a pakad, which helps people to identify it.
The cyclic permuation of a scale to get a new mode is called Graha Bhedam in Carnatic music or murchhana in Hindustani music.
The primary ragas of Carnatic music are called Melakarta, and there are 72 of them. I don't think they're all used - they just form the full combinatoric space of 7 note scales with certain nice properties. Other Carnatic ragas are considered derived fromt he primary ones and are called Janya. Hindustiani music has Thaats, which are like families of Ragas.
Let's look at some scales.
I learned about five Hindustanti ragas from the authors of the ShrutiSense program. Here are their shruti names:
P1: Sa
Grm2: Re1
m2: Re1_
M2: Re2
AcM2: Re2_
Grm3: Ga1
m3: Ga1_
M3: Ga2
AcM3: Ga2_
P4: Ma1
Ac4: Ma1_
AcA4: Ma2
AcAcA4: Ma2_
P5: Pa
Grm6: Dha1
m6: Dha1_
M6: Dha2
AcM6: Dha2_
Grm7: Ni1
m7: Ni1_
M7: Ni2
AcM7: Ni2_
P8: Sa_
Some of the intervals get an underscore if they're a syntonic comma off from a more common interval. Also the octave gets an underscore. The interval with a 3-limit just tuning is the more common / unadorned option when the interval has a minor sonority and the interval with a 5-limit tuning is the more common / unadorned option when the interval has a major sonority.
All five ragas from the ShrutiSense authors have the same ascending and descending forms. We'll first look at the ragas Yaman and Kalyan. They have identical scales:
[Sa, Re2, Ga2, Ma2, Pa, Dha2, Ni2, Sa_]
which is
[P1, AcM2, M3, AcA4, P5, M6, M7, P8] # [1/1, 9/8, 5/4, 45/32, 3/2, 5/3, 15/8, 2/1]
They also have the same vadi or primary melodic note, namely Ga2 ~ M3, and the same samvadi of Ni2 ~ M7. And since
M3 + P5 = M7
that looks fine. The two ragas also have the same avoid-note / forbidden-tone / varjya shruti, namely Ma1 ~ P4. The shruti Ma1 isn't in the scale, but they want you to be sure you don't play it even a little bit in melodic ornaments.
These two ragas, it seems, only differ in their distinguishing melodic motif, their pakad. Here's how the ShrutiSense authors share pakads for ragas:
Yaman pakad: [[Ni2, Re2, Ga2], [Ma2, Pa, Dha2]]
Kalyan pakad: [[Sa, Re2, Ga2, Ma2], [Pa, Ma2, Ga2]]
Those don't quite look like melodies to me - the notes don't have duration, and I don't know why they're bracketed that way. But supposedly those two lines hold the key for disambiguating these two ragas.
Let's look at raga Bilaval next. Its scale is simply a 5-limit major scale:
[Sa, Re2, Ga2, Ma1, Pa, Dha2, Ni2, Sa_]
or
[P1, M2, M3, P4, P5, M6, M7, P8]
Its vadi is Sa ~ P1, its samvadi is Pa ~ P5. It has no varjya to avoid. Its pakad is
[[Sa, Re2, Ga2], [Pa, Dha2, Ni2]]
Nice. At some point I'll listen to all the pakads and find out what structure they possess, if any.
Next let's look at raga Khamaaj. Here is its scale:
[Sa, Re2, Ga2, Ma1, Pa, Dha2, Ni1, Sa_]
or
[P1, M2, M3, P4, P5, M6, Grm7, P8]
The vaid is Pa ~ P5, the samvadi is Sa ~ P1. The varjya to avoid is Ni2 ~ M7. And the pakad is
[[Sa, Ga2, Ma1, Pa], [Pa, Dha2, Ni1]]
.
Finally here is raga Bhairavi. Its scale is
[Sa, Re1, Ga1, Ma1, Pa, Dha1, Ni1, Sa_]
or
[P1, Grm2, Grm3, P4, P5, Grm6, Grm7, P8]
You've heard that before, right? Classic raga Bhairavi pakad.
I've seen other ragas described in other sources, but at the level of 12-TET swaras, not at the level of shrutis. I'm going to keep looking.
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Here's some more data from Dinesh S. Thakur in "The Notion of Twenty-Two Shrutis". He has his own shruti notation:
S: 1/1
R11: 256/243
R12: 16/15
R21: 10/9
R22: 9/8
G11: 32/27
G12: 6/5
G21: 5/4
G22: 81/64
M11: 4/3
M12: 27/20
M21: 45/32
M22: 729/512
P: 3/2
D11: 128/81
D12: 8/5
D21: 5/3
D22: 27/16
N11: 16/9
N12: 9/5
N21: 15/8
N22: 243/128
Using this, he describes two pentatonic ragas, namely raga Bhoop and raga Deskar.
Bhoop: [S, R21, G21, P, D21, S']
Deskar: [S, R22, G22, P, D22, S']
These are
Bhoop: [P1, M2, M3, P5, M6, P8]
Deskar: [P1, AcM2, AcM3, P5, AcM6, P8]
Nice. These are just 5-limit and 3-limit versions of the major pentatonic scale. Easy.
He also decsribes raga Todi in 12-EDO, and then tries to infer the shrutis from knowing that ^2 should be its lower variant, R11, and then assuming that notes of the scale are related by factors of 3/2 and 4/3 as much as possible. This is interesting. I'm not sure that it's right, but here's what he came up with:
[S, R11, G11, M21, D11, N21, S']
That's a six note scale, but he says P is also used sometimes. But keeping with the six note scale, we get these intervals:
[P1, Grm2, Grm3, AcA4, Grm6, M7, P8]
I don't think he's very confident in this, but it's something.
...
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