Nazir Ali Jairazbhoy’s Hindustani 32 Thaat system
in spreadsheet format - sorted by number of alterations
(legend and explanation below)

Legend First column = "# of alts" = number of alterations relative to the C major scale. Second column: C = sa (static) G = pa (static) The "boxed" notes indicate 3-note chromatic clusters (there is no 4-note or greater chromatic cluster in this thaat system). Altered note colors are assigned according to "Modalogy's" Chromatic Cube system: Db / komal re = red Eb / komal ga = yellow F# / tivra ma = green Ab / komal dha = blue Bb / komal ni = purple All unaltered tones are black: D / re E / ga F / ma A / dha B / ni   The numbers in the row below each horizontal pitch collection indicate the number of half steps between the adjacent notes (half-step=1, whole-step=2, augmented second=3). Third column = "thaat #" = designation given to the thaat by Nazir Ali Jairazbhoy. Fourth column = "rs axis" = if the structure is radially symmetrical, its primary central axis is indicated. Fifth column = "description" = western-related designations. Sixth column = "hindustani" = the common Hindustani name for the thaat (if it exists).

In Classical Hindustani musics, the sa and pa (Do and Sol) remain constant.

The notes which may be altered (relative to the western major scale) are:

The 2nd degree (Re / re) which may be lowered by a half step (Db / Ra / komal re).

The 3rd degree (Mi / ga) which may be lowered by a half step (Eb / Me / komal ga).

The 4th degree (Fa / ma) which may be raised by a half step (F# / Fi / tivra ma).

The 6th degree (La / dha) which may be lowered by a half step (Ab / Le / komal dha)

The 7th degree (Ti / ni) which may be lowered by a half step (Bb / Te / komal ni).

 

Out of the 32 theoretically possible permutations, only 10 of them are in common use:

Sorted by number of Alterations No alterations: A2 Bilaval / Ionian (rs axis = Re / re) One alteration: A1 Kalyan / Lydian F# / tivra ma (rs axis = La / dha) A3 Khamaj / Mixolydian Bb / komal ni (rs axis = Sol / pa) Two alterations: A10 marva / lydian b2 Db / komal re, F# / tivra ma (asymmetric) C9 Bhairav / Double Harmonic Ab / komal dha, Db / komal re (rs axis = Do / sa) A4 Kafi / Dorian Bb / komal ni, Eb / komal ga (rs axis = Do / sa) Three alterations: A9 purvi / Db minor blues scale add nat7 Ab / komal dha, Db / komal re, F# / tivra ma (asymmetric) A5 Asavari / Aeolian Bb / komal ni, Eb / komal ga, Ab / komal dha (rs axis = Fa / pa) Four alterations: A8 todi / hungarian minor b2 Eb / komla ga, Ab / komal dha, Db / komal re, F# / tivra ma (asymmetric) A6 Bhairavi / Phrygian Bb / komal ni, Eb / komal ga, Ab / komal dha, Db / komal re (rs axis = Bb / komal ni)

Sorted by Jairazbhoy's System A1 Kalyan / Lydian one alteration F# / tivra ma (rs axis = La / dha) A2 Bilaval / Ionian no alterations (rs axis = Re / re) A3 Khamaj / Mixolydian one alteration Bb / komal ni (rs axis = Sol / pa) A4 Kafi / Dorian two alterations Bb / komal ni, Eb / komal ga (rs axis = Do / sa) A5 Asavari / Aeolian three alterations Bb / komal ni, Eb / komal ga, Ab / komal dha (rs axis = Fa / pa) A6 Bhairavi / Phrygian four alterations Bb / komal ni, Eb / komal ga, Ab / komal dha, Db / komal re (rs axis = Bb / komal ni) A8 todi / hungarian minor b2 four alterations Eb / komal ga, Ab / komal dha, Db / komal re, F# / tivra ma (asymmetric) A9 purvi / Db minor blues scale add nat7 three alterations Ab / komal dha, Db / komal re, F# / tivra ma (asymmetric) A10 marva / lydian b2 two alterations Db / komal re, F# / tivra ma (asymmetric) C9 Bhairav / Double Harmonic two alterations Db / komal re, Ab / komal dha (rs axis = Do / sa)

Observations:

- All the modes of the western Ionian set are represented in the named Hindustani system, except for the Locrian. Which is to say, six of the ten named thaats
  parallel the Ionian set modes. (By definition, the Locrian mode cannot exist in a system with a fixed Sol / pa.)

- In Jairazbhoy's system, 9 of the ten named thaats are on his "A list". The only one missing from his "A list" is A7 - which contains all five possible
  alterations, but is unused/unnamed. The first six thaats on his "A list" are sequenced in exactly the same traditional "bright-to-dark" ordering commonly found
  with the western modes:

Lydian - Ionian - Mixolydian - Dorian - Aeolian - Phyrgian
Kalyan  -  Bilaval  -  Khamaj  -   Kafi  -   Asavari  -  Bhairavi

Beginning at the Ionian, the alterations go up in perfect fourths:

A2 = | 0 | (Ionian / bilaval)

A3 = Bb (Mixolydian / khamaj)

A4 = Bb, Eb (Dorian / kafi)

A5 = Bb, Eb, Ab (Aeolian / asavari)

A6 = Bb, Eb, Ab, Db (Phrygian / bhairav)

This mirrors the western circle of fifths as it goes around the flat side of the circle beginning at C to F to Bb to Eb to Ab.

Here, C Mixolydian (F parent) has one flat (Bb), C Dorian (Bb parent) has two flats (Bb, Eb), C Aeolian (Eb parent) three (Bb, Eb, Ab), and C Phrygian (Ab parent) has four (Bb, Eb, Ab, Db).

Normally, the next perfect fourth in this chain would obviously be a Gb. But in this system, the G cannot be flatted, so, instead, the enharmonic alteration F# is introduced.

That brings us to the unnamed A7, which contains all five alterations.

Now, we begin unaltering notes, starting with turning the Bb into B natural (and so on, the naturals going up in fourths):

A7 = Bb, Eb, Ab, Db, F# (no name)

A8 = Eb, Ab, Db, F# (todi)

A9 = Ab, Db, F# (purvi)

A10 = Db, F# (marva)

Clearly, the next in the sequence contains only the F# alteration. But that is A1 (Lydian / kalyan).

So it's a type of clockwise repeating loop, very reminiscent of the western circle:

- Out of the named thaats, 7 of them are radially symmetrical (the six included modes of the Ionian, plus the Double Harmonic). The three asymmetricals are:
  marva, purvi, and todi (which have no western equivalents).

- The Double Harmonic is a scale that saddles east and west. While some western musics (eg. Classical, Jazz) do use the exotic Double Harmonic (along with
  a couple of its modes), in the western mind it is most commonly associated with Eastern European Gypsy, Arabic, and, obviously, Hindustani musics.

- While the useful scales ascending melodic minor (jazz minor), harmonic minor, and even the Harmonic Major occur in several forms as theoretical
   permutations in this system, they must not be very popular in Hindustani musics, otherwise, they'd have names for them.

harmonic minor C4 = hm4 C5 = hm1 C6 = hm5

jazz minor B1 = jm4 B2 = jm1 B3 = jm5 B4 = jm2

Harmonic Major C1 = HM4 C2 = HM1 C3 = HM5

Note that there is a very close relationship between the jazz minor, harmonic minor, Harmonic Major and Double Harmonic scales:

Flatting the 6th degree of the jazz minor results in harmonic minor mode 1 (C jazz minor b6 = C harmonic minor).

Raising the 4th degree of the jazz minor results in Harmonic Major mode 4 (C jazz minor #4 = G Harmonic Major).

Sharping the 4th degree and flatting the 6th degree of the jazz minor results in Double Harmonic mode 4 (C jazz minor #4 b6 = G Double Harmonic).

 

C jazz minor C D Eb F G A B C	C harmonic minor C D Eb F G Ab B C
G Harmonic Major mode 4 C D Eb F# G A B C	G Double Harmonic mode 4 C D Eb F# G Ab B C

Both the C jazz minor and G Double Harmonic scales are radially symmetrical (primary axis centered at G).

The harmonic minor and Harmonic Major are mirrors of each other. They are asymmetrical, but are subsets of the radially symmetrical octatonic dorian blues scale.

D dorian blues scale D E F G G#/Ab A B C D (primary axis of symmetry = D) A harmonic minor mode 4 D E F    G# A B C D C Harmonic Major mode 2 D E F G Ab    B C D

TODI

The defining notes of E phrygian are

E		F		G		C
R		b2		b3		b6
	m2		M2		P4

(qv. Modalogy pgs 168 & 188)

The B (5 / sol / pa) of the E root / do / sa is a given in the hindustani system.

Todi's primary characteristics consist of these same 5 notes

E	F	G	B	C
R	b2	b3	5	b6

The Phrygian Pentatonic

E Todi's natural 7th (D#) acts as a leading tone into the do / sa.
This D#-E-F chromatic cluster makes for nifty little things like turns: E-F-E-D#-E
or surrounding note figures (encirclement / enclosure): E-F--D#-E

Likewise, the A# is a leading tone into the sol / pa making for the chromatic cluster A#-B-C.
This mimics the chromatic cluster surrounding the root so you can then have things like a succession of turns,

eg. E-F-E-D#-E - B-C-B-A#-B,

and other stuff like some kind of 'sidewinder' based patterns:

E-F--D#-E - B-C--A#-C, etc.

G is the go between.

G (the minor third) provides both a way to move smoothly between the two chromatic clusters,
as well as being a nice resting note by virtue of it being the defining minor third chord component.

So boiling it down to layman's terms:
Todi is the phrygian pentatonic with double leading tones to the do / sa and sol / pa.

Those two base tones (do/ sa and sol / pa) are surrounded on both sides by the note a half step away.
This creates two three-note chromatic clusters separated on one side by an augmented second and connected by G on the other side.

E Todi
^D#-E-F--G---^A#-B-C
^7-R-b2--b3---^#4-5-b6

PURVI

The defining tones of the E Phrygian Dominant are

E		F		G#		B		C
R		b2		3		5		b6
	m2		#2		#2		m2

The Phrygian Major Pentatonic
(note the radial symmetry centered at G#)
qv. Modalogy pgs 178 and 188

The phrygian major pentatonic contains the same characteristic notes as Purvi.

The difference between the phrygian dominant and Purvi,
is that Purvi (like Todi) has two leading tones into the E / do / sa and B / sol / pa:
D# and A#
(instead of the phrygian dominant's natural D and A).

Comparison of Todi and Purvi

There is only one difference between Todi and Purvi and that is the quality of the third (Todi has a b3 and Purvi has a M3).

These thaats can be seen as simply two different versions of the phyrgian pentatonics, with double leading tones into the tonic open fifths' components.

E Todi
^D#-E-F--G---^A#-B-C
^7-R-b2--b3---^#4-5-b6

E Purvi
^D#-E-F---G#--^A#-B-C
^7-R-b2---3--^#4-5-b6


It is also interesting to note that D Todi and G Purvi are overlapping mirrors of each other:

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