Pitch and Scale

PITCH
svara \svar\ [Sanskrit/Vedic nm, sur "the sun, heaven"; Hindi nm "voice, sound, note"] musical pitch, note
In South Asian music seven scale steps are identified.
ṣaḍja [Sanskrit sas \ShaSh\ "of six"; sadj "six-born"] the principal note from which the other six are derived, the tonic
niṣāda [Sanskrit v, ni - sad "to sink or go down"] the seventh note of the gamut
dhaivata [Sanskrit] the sixth note of the gamut
pañcama [Sanskrit nm, pañch "the fifth"] the fifth note of the gamut
madhyama [Sanskrit nm "the middle"] the fourth note of the gamut
gandhāra [Sanskrit nm, "the name of a people"] the third note of the gamut
ṛṣabha [Sanskrit nm, "a bull"] the second note of the gamut
 
  Solfeggio Svara Name  
  1 doh ṣaḍja  
  7 ti ni niṣāda  
  6 la dhā dhaivata  
  5 sol pañcama  
  4 fa madhyama  
  3 mi gandhāra  
  2 re ri ṛṣabha  
  1 doh ṣaḍja  

 
SCALE
melā [Sanskrit n, "group"] / mēḷa [Telegu n. "group"] "scale"
melākarta [Sanskrit] / mēḷakarta [Telegu]: "scale matrix"
svarasthāna [Sanskrit] "note placement"

 
RĀGA
sampūrṇa rāga [Sanskrit adj "complete"] a rāga having a heptatonic scale
ṣaḍava rāga [Sanskrit n "sweetmeats"] a rāga having a hexatonic scale
auḍava rāga [the name of a constellation] a rāga having a pentatonic scale
janya rāga [ janya Sanskrit adj "derivative"] a rāga requiring accidentals

 
MELODIC MOVEMENT
ārohaṇa ascending scalar movement
avarohaṇa descending scalar movement
vakra crooked scalar movement
jīva-svara [Sanskrit "life-note"] most important note
piṭippu [Telegu "catch"] or characteristic melodic phrase
rāga-chāyā-sañcāra [Sanskrit "rāga -image-phrase"] characteristic melodic development

SOUTH INDIAN SVARASTHĀNA
ṣaḍja sa sa ṣaḍja
kākalī niṣād ni##
kaiṣiki niṣād ni# dha## satśruti dhaivata
śuddha niṣād ni dha# catusśruti dhaivata uttarāṅga
dha śuddha dhaivata
pañcama pa pa pañcama
prati madhyama ma#

śuddha madhyama ma
ga## antara gandhāra
satśruti ṛiṣabh ri## ga# sadhārana gandhāra purvāṅga
catusśruti ṛiṣabh ri# ga śuddha gandhāra
śuddha ṛiṣabh ri
ṣaḍja sa sa ṣaḍja

Venkatamakhi's Meḷākarta
Building on the work of his predecessors — Rāmamatya and Somanātha — Venkatamakhi arrived at his system for deriving 72 different scales (mēḷkarta) through the following presumptions and operations.
1. Sa and pa, as the most important notes in the harmonic series, are fixed in their positions. That is, the overtones produced by the fundamental sa include first its octave equivalent and the fifth (pa). In melodic contexts, you can omit these notes, but they are inherent in the scale.
2. Ma, as the next most important note in the harmonic series, has two positions: śuddha (pure) ma and prati (raised) ma.
3. The second (ri), third (ga), sixth (dha), and seventh (ni) of the scale have three variations, each beginning with a śuddha (pure or natural) position and two raised positions above. Ri and dha, as the notes immediately above the immovable notes of sa and pa, borrow from ancient terminology with the indication that they are four (catus) and seven (sat) srutis above their respective notes. Thus, ri has a natural position (śuddha risabh) with two raised positions above (catus-śruti risabh and sat-śruti rishabh). The third and the seventh employ a different nomenclature, but their śuddh positions are also the points above which their alternates are placed. In practice, these intervals are roughly equivalent to our modern equal tempered semitones, although Venkatamakhi would have used something closer to Just Intonation.
4. When constructing a scale, the notes must always appear in the order sa, ri, ga, ma, pa, dha, ni, sa, no matter which version appears.
5. Venkatamakhi divides his scale into a lower (purvāṅga) and upper (uttarāṅga) tetrachords (groups of four notes), reflecting the importance of stringed lutes in the definition of these scales. The purvāṅga consists of the notes sa, ri, ga, and ma. The uttarāṅga consists of the notes pa, dha, ni, and sa.
6. The first cakra (cycle) has sa and ma fixed in the purvanga. Ri and ga are in their śuddh or lowest positions. Thus, the first mela (scale) of the first cakra has sa, śuddha ri (one semitone above sa), śuddha ga (one semitone above śuddha ri and a whole tone above sa) and ma (a perfect fourth above sa). The second melā of the first cakra has sa, ri, and ma in the same positions as the first melā, but raises ga one semitone. The third mela follows the same pattern with ga now two semitones above ri. The fourth melā starts with sa and ma in the same position, but raises ri to the catusśruti position, two semitones or one whole tone above sa. This leaves only two positions for ga (sadhārana and antara). Finally, with sa and ma still fixed, ri raises to its highest position (satśruti) leaving only one position for ga (antara) so that the first cakra has six melās.
7. The uttarāṅga (upper tetrachord) functions the same way except that now pa and sa are the fixed notes and dha and ni move. More importantly, the six parallel changes in note position take place once for each cakra. Thus, in the first cakra , dha and ni begin in their śuddh positions (dha one semitone above pa and ni one semitone above dha) and remain in those positions while ri and ga go through their mutations in the lower tetrachord. When the second cakra begins, ni raises one semitone to its first raised position (kaisiki) and remains their until the third cakra , when it rises to its highest position (kākili). Again, the upper tetrachord parallels the lower tetrachord in note changes matching one change for every cakra (or set of changes in the lower tetrachord).
8. Matching the six positions of the lower tetrachord with the six positions of the upper tetrachord yeilds 36 different scales. Venkatamakhi then derives an additional 36 melā s by repeating the process with ma in the prati position.

Karnātak Sangit Outline Rhythm and Meter
 
22-Feb-2018