Domaine 6 — śruti / microtuning theory (Brihaddesi de Mātaṅga, Sharma 1992)
Synthèse 6c.3 du domaine 6 depuis :
- 76 concepts (cluster śrutis = cluster_id 95 : 12 affirmations, 6 règles)
- 60 règles génératives 6b
- 105 affirmations sourcées (Sharma vol. I §III pp.014-020 + vol. II)
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POLITIQUE ANTI-FABRICATION — règle absolue de ce domaine
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Le Brihaddesi NE PROPOSE PAS un système de microtuning canonique.
Mātaṅga *rapporte* plusieurs traditions concurrentes :
• mīmāṃsā-stricte / Bharata : 22 śrutis (aff#2154, aff#2158)
• différentialiste : 66 śrutis (aff#2154, aff#2158)
• infinitiste : śrutis innombrables (aff#2154, aff#2158)
• vamsa / instrument à anche : 9 śrutis (aff#2152, aff#2153, R_4p0_013)
• triple-classification : 3 classes par vaiguṇya (aff#2136)
• Tumburu (fourfold humoral) : 4 classes (aff#2144)
• Kohala : autorité citée (aff#2151)
Conséquence pour la modélisation :
- PAS de table cent-grid canonique (aucun système avec valeurs en cents
n'est sourcé dans le BrD ; tout ratio numérique serait fabriqué).
- Chaque énumération de śrutis = constante attribuée à une AUTORITÉ.
- Les opérations comparent des autorités ; elles ne tranchent pas.
- Les śrutis sont des "points de domination" sur un continuum tonal,
sans pitch fixes (aff#... aishvarya_definition_continuum).
Chaque type / constante / opération / contrainte cite ≥ 1 rule_id 6b ou
affirmation_id du pipeline Brihaddesi. Les zones non sourcées sont listées
dans UNRESOLVED.
Python 3.10+. Importable sans dépendance externe.
Contents
Constants (13)
- SRUTI_COUNT_BY_AUTHORITYdict[Authority, int | None]
- SRUTI_OPERATIONAL_DEFINITIONstr
- BHARATA_22_STRUCTUREdict[str, int|tuple]
- SVARA_SRUTI_COUNT_BHARATA_22dict[(Grāma, Svara), int]
- CASTE_BY_SRUTI_COUNT_BHARATA_22dict[int, str]
- VAMSA_STRUCTUREdict[str, object]
- SVARA_VAMSA_RSIfrozenset[Svara]
- SVARA_SRUTI_THEORIESdict[str, dict]
- PRAMANASdict[str, dict]
- SRUTI_MODIFICATION_OPSdict[str, dict]
- TANA_TECHNIQUESdict[str, dict]
- SRUTI_AISVARYA_PRINCIPLEstr
- COKSA_RAGAStuple[str,...]
Operations (12)
Pure functions derived from the rules: given input types, return outputs. Each cites the rule(s) that justify it.
§get_sruti_countlookup
Sourced by
śruti = mesure d'écart de pañcama par augmentation/diminution; nombre contesté (22, 66, ou infini); vīṇā: 22, veṇu: 9
FUNCTION sruti_count(instrument, school):
IF instrument == 'venu': RETURN 9
# competing theories preserved (NOT canonical):
schools := {
'mimansa_strict': 22,
'differentiated': 66,
'infinitists': INF
}
RETURN schools[school] # NO single canonical value
enThe definition of śruti and its numerationvol_I_p007 enOthers Venu etc. accept ninefold śruti.vol_I_p015 + 3 more verbatim
§get_svara_sruti_count_bharata_22lookup
§caste_of_svara_bharata_22classification
Sourced by
Svaras are classified by śruti count into three classes: 4-śruti (brāhmaņas), 3-śruti (kṣatriyas), 2-śruti (vaiśyas).
class(S) := match śruti_count(S) {4 => brāhmaṇa; 3 => kṣatriya; 2 => vaiśya}
sktचतुःश्रुतिस्वरा विप्रास्त्रिश्रुती क्षत्रियौ मतौ। वैश्यौ द्विश्वतिकौvol_I_p031 entwo (svaras) that are comprised of two śrutis (each) (viz. gandhāra and niṣāda)vol_I_p039 §grama_of_pancama_countclassification
(n_srutis_pancama: int)
→ GrāmaSourced by
The two grāmas (ṣaḍja-grāma, madhyama-grāma) are differentiated on the basis of pañcama alone.
DIFFERENTIATE(sadja_grama, madhyama_grama) BY position_of(pancama)
enThe two grāmas are differentiated on the basis of pañcama alonevol_I_p088 §is_srutibhinnaconstraint_check
Sourced by
Śrutibhinna: niṣāda takes 2 śrutis of pañcama (which has 4 śrutis)
DEFINE is_srutibhinna(Ni, Pa):
ASSERT Pa.srutis == 4
RETURN Ni.borrowed_srutis_from(Pa) == 2
sktचतुःश्रुते पञ्चमस्य यदा श्रुतिद्वयं गृह्णाति निषादः तदासौ श्रुतिभिन्नोऽभिधीयतेvol_II_p060 Śruti-bhinna = 4-śruti svara modified by 2-śruti svara, with gāndhāra being 2-śruti
FUNCTION is_sruti_bhinna(svara_a, svara_b):
IF srutis(svara_a) == 4 AND srutis(svara_b) == 2 AND modifies(svara_b, svara_a):
ASSERT srutis(gandhara) == 2
RETURN TRUE
RETURN FALSE
enWhere the svara comprised of four śrutis is modified by the one comprised of two śrutis and gāndhāra is comprised of only two śrutis, that is called śruti-bhinna.vol_II_p059 §sama_srutikatvacomparison
Sourced by
Sama-śrutikatva = equal śruti interval between two svaras
DEFINE sama_srutikatva(s1, s2) := (count_sruti(s1, s2) == count_sruti(s2, s1))
ensama-śrutikatva (equal interval of the two svaras concerned, in terms of number of śrutis).vol_I_p025 §authority_disagreescomparison
anti-tranchage: makes disagreement explicit instead of suppressed
§compare_authoritiesenumeration
Sourced by
vamsa (flute bambou) = 9 śrutis reparties en groupes de 2, 3 et 4 śrutis, produits par ouverture/secouage/demi-ouverture des trous
DEFINE vamsa_śrutis():
total_śrutis = 9
groupings = {2: holes_set_A, 3: holes_set_B, 4: holes_set_C}
production_techniques = {'open_hole', 'shake_finger', 'half_open'}
rationale = 'clear_description_via_hole_manipulation'
RETURN sruti_grouping('vamsa')
enSvaras situated in the vamsa (flute)... groups of two, three and four śrutisvol_I_p015 enuse of svaras occurring in the holes of bamboo (flute)... two srutis, three srutis and four srutisvol_I_p015 + 2 more verbatim
Total of 22 śrutis: composed of 9 + 9 + 4 śrutis (two 9-śruti triadic groups plus a middle 4-śruti group).
total_srutis := 9 + 9 + 4 = 22; basic_group := triad(4_sruti + 3_sruti + 2_sruti) = 9 srutis
enthe nine srutis constituting this triad of svaras of four, three and two śrutis is accepted here as a basic groupvol_I_p088 enNine plus nine of the other triad plus four of the 'middle' one would complete twenty-two śrutisvol_I_p088 §list_svara_sruti_theoriesenumeration
Sourced by
Tādātmya = identity-theory of svara/śruti relation: claims svara≡śruti like jāti≡vyakti; refuted by aśraya/āśrayin distinction; one of several alternatives (vikalpana)
THEORY tādātmya: claim(svara ≡ śruti) JUSTIFIED_BY (no_differentia perceived_by_ear, analogous to jāti↔vyakti); REFUTATION: distinction(aśraya=śruti, āśrayin=svara) blocks identification; STATUS: one alternative among vikalpana set
enThere is identification between svara and śruti...just like jāti and vyaktivol_I_p018 enbecause there is no differentia (viśeṣa) between the two that are (equally) perceptible by the ear.vol_I_p018 + 2 more verbatim
Effect-theory: svaras are kārya (effect) of śruti (clay/potter analogy)
DEFINE kāryatva_theory AS (svara = effect(śruti)) ANALOGY (jar = effect(clay, potter_rod))
enSome say that svaras are the kārya (effect) of śruti, just as the jar is the 'effect' of the lump of clayvol_I_p018 Śrutis are transformed into the form of svaras (pariṇāmitā), as milk transforms into curd.
def parinamita(shruti):
return transform(shruti, 'milk_to_curd_analogy') -> svara
enSrutis undoubtedly get transformed into the form of svaras just as milk gets totally transformed in the form of curd.vol_I_p018 §apply_utkarsatransformation_description
returns symbolic description, NOT cents — no cents sourced
Sourced by
Utkarṣa = augmentation/raising of pitch (notably of pañcama) used to measure śruti intervals and effect grāma transformation.
DEFINE utkarsa(svara) := raise_pitch(svara) -> shifts_sruti_interval; APPLY in grama_transformation WHEN murchana changes WITH utkarsa(gandhara)
enThe difference of that (pañcama) through utkarşa (augmentation) and apakarşa (diminution)vol_I_p016 entransformation of one grāma into another through change of murchana with utkarşa of gandharavol_I_p089 §apply_apakarsatransformation_description
Sourced by
apakarşa = lowering/diminution of pitch, counterpart to utkarşa, used to measure śruti differences on vīṇā
DEFINE apakarşa AS pitch_action(direction=lowering, counterpart_of=utkarşa, measurement_use=śruti_difference)
APPLY apakarşa(svara=pañcama) -> diminished_pitch
NOTE interchangeable_with utkarşa IN [BrD, NS]
enThe difference of that (pañcama) through utkarşa (augmentation) and apakarşa (diminution)vol_I_p016 eneither of the two actions could result in both the changes of pitch... used as inter-changeables in both BrD and NSvol_I_p089 §grāma_transformation_via_pancamatransformation
Sourced by
Utkarṣa = augmentation/raising of pitch (notably of pañcama) used to measure śruti intervals and effect grāma transformation.
DEFINE utkarsa(svara) := raise_pitch(svara) -> shifts_sruti_interval; APPLY in grama_transformation WHEN murchana changes WITH utkarsa(gandhara)
enThe difference of that (pañcama) through utkarşa (augmentation) and apakarşa (diminution)vol_I_p016 entransformation of one grāma into another through change of murchana with utkarşa of gandharavol_I_p089 Constraints (5)
Validators that raise on configurations forbidden by the rules. Each cites the rule(s) it enforces.
§is_valid_sruti_count_claim
(authority, count) is a sourced pairing in SRUTI_COUNT_BY_AUTHORITY
§is_valid_22_school_structure
parts == (9,9,4) and sum==22
Sourced by
Total of 22 śrutis: composed of 9 + 9 + 4 śrutis (two 9-śruti triadic groups plus a middle 4-śruti group).
total_srutis := 9 + 9 + 4 = 22; basic_group := triad(4_sruti + 3_sruti + 2_sruti) = 9 srutis
enthe nine srutis constituting this triad of svaras of four, three and two śrutis is accepted here as a basic groupvol_I_p088 enNine plus nine of the other triad plus four of the 'middle' one would complete twenty-two śrutisvol_I_p088 §is_valid_register_preservation
śruti count of a svara invariant across the 3 sthānas
Sourced by
A svara should be sounded in all three registers with the same śruti count as originally composed.
for all reg in {mandra, madhya, tara}: sruti_count(S, reg) == sruti_count(S, original)
en(A svara) should be made (sounded) in the three registers with the same number of śrutis as it is composed of (originally).vol_I_p054 §can_perform_shake
svara has 3 śrutis (Bharata 22-school) — rule eroded in some alaṅkāras
Sourced by
The traditional rule limiting shakes (kampita) to 3-śruti svaras appears abandoned in certain alaṅkāras.
rule: shake_allowed_on(S) := sruti_count(S)==3; observed_exception: in certain alankaras the rule is relaxed
enHere the traditional rule of having a shake only on svaras with three śrutis seems to have been abandoned.vol_I_p102 §is_valid_vamsa_grouping
groups are a permutation of (2,3,4), summing to 9
Sourced by
vamsa (flute bambou) = 9 śrutis reparties en groupes de 2, 3 et 4 śrutis, produits par ouverture/secouage/demi-ouverture des trous
DEFINE vamsa_śrutis():
total_śrutis = 9
groupings = {2: holes_set_A, 3: holes_set_B, 4: holes_set_C}
production_techniques = {'open_hole', 'shake_finger', 'half_open'}
rationale = 'clear_description_via_hole_manipulation'
RETURN sruti_grouping('vamsa')
enSvaras situated in the vamsa (flute)... groups of two, three and four śrutisvol_I_p015 enuse of svaras occurring in the holes of bamboo (flute)... two srutis, three srutis and four srutisvol_I_p015 + 2 more verbatim
Types (9)
Enums and structures used by operations and constraints. Members are exhaustively those attested in the source.
§AuthorityEnum[str]
central anti-fabrication device: every śruti claim is authority-tagged
11 members
values : bharata, mimamsa_strict, differentiated_66, infinitist, vamsa_tradition, threefold_vaigunya, tumburu, kohala + 3 more
full module docstring
Authorities cited by Mātaṅga as enumerating / classifying śrutis.
These are NOT alternative renderings of one truth — they are distinct
epistemic claims that the Brihaddesi reports side-by-side.
evidence: aff#2154, aff#2158 (the three competing schools 22/66/∞ named
by Mātaṅga); aff#2144 (Tumburu); aff#2151 (Kohala);
aff#2913, aff#3021, aff#2963 (Abhinavagupta commenting NŚ);
aff#2136 (threefold school per indriya-vaiguṇya);
R_208_abhinava_bharati, R_4p1_12 (Abhi Bhā = commentary)Sourced by
Abhinava Bhāratī is Abhinavagupta's commentary on the Nāṭya-Śāstra (G.O.S., Baroda edition).
abhinava_bharati := commentary(author='abhinavagupta', base_text='natya_shastra', edition='GOS_Baroda')
enAbhinava Bhāratī, Abhinavagupta's commentary on Nātya-Śāstra G.O.S., Baroda editionvol_II_p008 Abhi Bhā is a commentator on Nāṭyaśāstra (cited on NŚ XXVIII.64, 65, p.42)
DEFINE Abhi_Bhā AS commentator
TARGET_TEXT = Nāṭyaśāstra
CITATION = NŚ XXVIII.64-65, p.42
§SvaraEnum[str]
redefined here for module autonomy (equiv. to domain 3 Svara)
7 members
Sourced by
grāma = cadre tonal; deux grāmas (ṣaḍjagrāma, madhyamagrāma) chacun avec 7 mūrchanās; les tānas servent à distinguer jātis et rāgas des deux grāmas
FUNCTION enumerate_gramas():
gramas := {
'sadjagrama': {murchanas_start_order: [sa, ni, dha, pa, ma, ga, ri]},
'madhyamagrama': {murchanas_start_order: [ma, ga, ri, sa, ni, dha, pa]}
}
ASSERT pancama IN both_gramas # seated in two gramas
# melodic movement must respect grama (gramavirodhena)
RETURN gramas
enPañcama is known as being seated in the two grāmas.vol_I_p016 + 2 more verbatim
mūrchanā = mouvement mélodique débutant par un svara donné, étymologie mūrch (infatuation) + samucchrāya (croissance); ce par quoi le rāga croît
FUNCTION construct_murchana(start_svara, jati):
# etymology: murch (growth) + samucchraya (increase)
murchana := sequence_of_svaras(start=start_svara, length=7)
# e.g. Gandharodicyava -> begins with dhaivata
# e.g. hexatonic andhri -> begins with madhyama
ASSERT murchana[0] == start_svara
RETURN murchana # vehicle of raga growth
enthe mūrchanā beginning with dhaivata obtains.vol_II_p038 enThe mūrchanā beginning with madhyama obtains.vol_II_p044 + 5 more verbatim
§GrāmaEnum[str]
needed because pañcama śruti-count differs by grāma
2 members
Sourced by
The two grāmas (ṣaḍja-grāma, madhyama-grāma) are differentiated on the basis of pañcama alone.
DIFFERENTIATE(sadja_grama, madhyama_grama) BY position_of(pancama)
enThe two grāmas are differentiated on the basis of pañcama alonevol_I_p088 §SrutiClaimdataclass(frozen=True)
An authority-attributed claim about śruti enumeration / structure.
full module docstring
An authority-attributed claim about śruti enumeration / structure.
The Brihaddesi NEVER asserts a count as canonical truth — every count
is delivered as "X says". This dataclass enforces that provenance.
evidence: aff#2154, aff#2158 (multi-school enumeration reported)
§SrutiBhinnadataclass(frozen=True)
Śruti-bhinna relation: a 4-śruti svara modified by a 2-śruti svara.
full module docstring
Śruti-bhinna relation: a 4-śruti svara modified by a 2-śruti svara.
Canonical example: niṣāda takes 2 śrutis of pañcama (which has 4),
with gāndhāra (2-śruti) involved.
evidence: R_857_srutibhinna_definition, r_brd_317_sruti_bhinna_def,
aff#677, aff#682Sourced by
Śrutibhinna: niṣāda takes 2 śrutis of pañcama (which has 4 śrutis)
DEFINE is_srutibhinna(Ni, Pa):
ASSERT Pa.srutis == 4
RETURN Ni.borrowed_srutis_from(Pa) == 2
sktचतुःश्रुते पञ्चमस्य यदा श्रुतिद्वयं गृह्णाति निषादः तदासौ श्रुतिभिन्नोऽभिधीयतेvol_II_p060 Śruti-bhinna = 4-śruti svara modified by 2-śruti svara, with gāndhāra being 2-śruti
FUNCTION is_sruti_bhinna(svara_a, svara_b):
IF srutis(svara_a) == 4 AND srutis(svara_b) == 2 AND modifies(svara_b, svara_a):
ASSERT srutis(gandhara) == 2
RETURN TRUE
RETURN FALSE
enWhere the svara comprised of four śrutis is modified by the one comprised of two śrutis and gāndhāra is comprised of only two śrutis, that is called śruti-bhinna.vol_II_p059 §SvaraSrutiTheorydataclass(frozen=True)
5 vikalpana theories listed without hierarchy
full module docstring
One of the alternative (vikalpana) theories of how svara relates to
śruti, as enumerated by Mātaṅga without elevating any single one.
evidence: aff#2198 ("alternatives starting with tādātmya have been
spoken of by me")Sourced by
Tādātmya = identity-theory of svara/śruti relation: claims svara≡śruti like jāti≡vyakti; refuted by aśraya/āśrayin distinction; one of several alternatives (vikalpana)
THEORY tādātmya: claim(svara ≡ śruti) JUSTIFIED_BY (no_differentia perceived_by_ear, analogous to jāti↔vyakti); REFUTATION: distinction(aśraya=śruti, āśrayin=svara) blocks identification; STATUS: one alternative among vikalpana set
enThere is identification between svara and śruti...just like jāti and vyaktivol_I_p018 enbecause there is no differentia (viśeṣa) between the two that are (equally) perceptible by the ear.vol_I_p018 + 2 more verbatim
Vivartatva (reflection theory): svara manifests as reflected in śrutis, like a face in a mirror
vivartatva(svara) -> svara.appears_in(shrutis) AS reflection(face, mirror)
enJust as the face of men is reflected in the mirror, similarly, svara manifests or (appears as reflected in the śrutisvol_I_p018 Effect-theory: svaras are kārya (effect) of śruti (clay/potter analogy)
DEFINE kāryatva_theory AS (svara = effect(śruti)) ANALOGY (jar = effect(clay, potter_rod))
enSome say that svaras are the kārya (effect) of śruti, just as the jar is the 'effect' of the lump of clayvol_I_p018 §AuthoritySrutiSystemdataclass(frozen=True)
A complete śruti-enumeration system as attributed to one authority.
full module docstring
A complete śruti-enumeration system as attributed to one authority.
Used by `compare_authorities()` to surface disagreement explicitly
rather than picking a winner.
Sourced by
vamsa (flute bambou) = 9 śrutis reparties en groupes de 2, 3 et 4 śrutis, produits par ouverture/secouage/demi-ouverture des trous
DEFINE vamsa_śrutis():
total_śrutis = 9
groupings = {2: holes_set_A, 3: holes_set_B, 4: holes_set_C}
production_techniques = {'open_hole', 'shake_finger', 'half_open'}
rationale = 'clear_description_via_hole_manipulation'
RETURN sruti_grouping('vamsa')
enSvaras situated in the vamsa (flute)... groups of two, three and four śrutisvol_I_p015 enuse of svaras occurring in the holes of bamboo (flute)... two srutis, three srutis and four srutisvol_I_p015 + 2 more verbatim
Total of 22 śrutis: composed of 9 + 9 + 4 śrutis (two 9-śruti triadic groups plus a middle 4-śruti group).
total_srutis := 9 + 9 + 4 = 22; basic_group := triad(4_sruti + 3_sruti + 2_sruti) = 9 srutis
enthe nine srutis constituting this triad of svaras of four, three and two śrutis is accepted here as a basic groupvol_I_p088 enNine plus nine of the other triad plus four of the 'middle' one would complete twenty-two śrutisvol_I_p088 §Matrikadataclass(frozen=True)
Mātṛkā — primary unit of tonal sound, "more subtle than śruti" per
full module docstring
Mātṛkā — primary unit of tonal sound, "more subtle than śruti" per
Mātaṅga. Distinct from śruti; subtle basis with numeric correspondence
to śrutis.
evidence: BD_6_1_R017, R_289_matrkas, R_2148_001, R_1673_01,
aff#3002, aff#2202, aff#3032Sourced by
Mātṛkā has two contexts: mother-goddesses and primary unit of language; Matanga uses it as primary unit of tonal sound (more subtle than śruti)
DEFINE matrika:
contexts = {
religious: 'mother-goddesses',
linguistic: 'primary unit of syllabic sound',
musical_matanga: 'primary unit of tonal sound, more subtle than shruti'
}
enMatanga has referred to mātrkā as the primary unit of syllabic sound... the mātṛkās of śrutis would mean the primary unit of tonal sound, more subtle than śrutivol_I_p091 Mātṛkās = subtle bases related to śrutis through a numeric correspondence.
DEFINE matrkas := subtle_bases_of(srutis); RELATION := numeric_correspondence(matrkas, srutis)
enhow many are they in relation to mātṛkāsvol_I_p020 Mātṛkā formation: iḍā and piṅgalā move vakra (crooked)
ASSERT movement({iḍā, piṅgalā}) == vakra IN formation(mātṛkās)
enthe formation of matrkās ... the movement of ida and pingalā is vakra (crooked)vol_I_p094 §VaigunyaImpairmentdataclass(frozen=True)
Vaiguṇya — faultiness of the human voice (organ of speech).
full module docstring
Vaiguṇya — faultiness of the human voice (organ of speech).
Threefold per Abhinavagupta and the BrD.
evidence: R_2050_indriya_vaigunya_threefold, vaigunya_definition,
R_2051_vagindriya_seat_vaigunyaSourced by
Indriya-vaiguṇya is threefold: inborn, humour-imbalance, accident
ENUMERATE indriya_vaigunya.types = ['inborn', 'humour_imbalance', 'accident']; |types| == 3
enindriya-vaigunya, which itself is threefold viz. inborn, born of some imbalance in the three humours and born of accident.vol_I_p087 Vaigunya est un nom abstrait dérivé de viguna signifiant dépourvu de qualité/défaut; désigne la défectuosité du son restreinte à la voix humaine.
RECORD vaigunya { etymology: abstract_noun_of(viguna); meaning: faultiness_of_sound; scope: human_voice }
enVaigunya is an abstract noun of 'viguna' (lit. devoid of guna or quality, or fault). Faultiness of śruti seems to be restricted to the human voicevol_I_p087 Vāgindriya (organ of speech) = primary seat of vaiguṇya per Abhinavagupta
DEFINE vagindriya AS organ_of_speech; ASSIGN role(primary_seat_of_vaigunya, vagindriya) per Abhinavagupta
enAbhinavagupta includes vāgindriya ( the human organ of speech ) in the primary sensevol_I_p087 Constants (13)
Named values pinned directly to source quotes (numbers, ordered lists, named svaras).
§SRUTI_COUNT_BY_AUTHORITYdict[Authority, int | None]
core anti-fabrication constant — None=infinite, NOT zero/unknown
7 values
Sourced by
śruti = mesure d'écart de pañcama par augmentation/diminution; nombre contesté (22, 66, ou infini); vīṇā: 22, veṇu: 9
FUNCTION sruti_count(instrument, school):
IF instrument == 'venu': RETURN 9
# competing theories preserved (NOT canonical):
schools := {
'mimansa_strict': 22,
'differentiated': 66,
'infinitists': INF
}
RETURN schools[school] # NO single canonical value
enThe definition of śruti and its numerationvol_I_p007 enOthers Venu etc. accept ninefold śruti.vol_I_p015 + 3 more verbatim
§SRUTI_OPERATIONAL_DEFINITIONstr
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śruti = mesure d'écart de pañcama par augmentation/diminution; nombre contesté (22, 66, ou infini); vīṇā: 22, veṇu: 9
FUNCTION sruti_count(instrument, school):
IF instrument == 'venu': RETURN 9
# competing theories preserved (NOT canonical):
schools := {
'mimansa_strict': 22,
'differentiated': 66,
'infinitists': INF
}
RETURN schools[school] # NO single canonical value
enThe definition of śruti and its numerationvol_I_p007 enOthers Venu etc. accept ninefold śruti.vol_I_p015 + 3 more verbatim
§BHARATA_22_STRUCTUREdict[str, int|tuple]
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Total of 22 śrutis: composed of 9 + 9 + 4 śrutis (two 9-śruti triadic groups plus a middle 4-śruti group).
total_srutis := 9 + 9 + 4 = 22; basic_group := triad(4_sruti + 3_sruti + 2_sruti) = 9 srutis
enthe nine srutis constituting this triad of svaras of four, three and two śrutis is accepted here as a basic groupvol_I_p088 enNine plus nine of the other triad plus four of the 'middle' one would complete twenty-two śrutisvol_I_p088 §SVARA_SRUTI_COUNT_BHARATA_22dict[(Grāma, Svara), int]
Bharata 22-school per-svara count — REPORTED by Mātaṅga, not canonical
14 values
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Svaras are classified by śruti count into three classes: 4-śruti (brāhmaņas), 3-śruti (kṣatriyas), 2-śruti (vaiśyas).
class(S) := match śruti_count(S) {4 => brāhmaṇa; 3 => kṣatriya; 2 => vaiśya}
sktचतुःश्रुतिस्वरा विप्रास्त्रिश्रुती क्षत्रियौ मतौ। वैश्यौ द्विश्वतिकौvol_I_p031 entwo (svaras) that are comprised of two śrutis (each) (viz. gandhāra and niṣāda)vol_I_p039 vamsa (flute bambou) = 9 śrutis reparties en groupes de 2, 3 et 4 śrutis, produits par ouverture/secouage/demi-ouverture des trous
DEFINE vamsa_śrutis():
total_śrutis = 9
groupings = {2: holes_set_A, 3: holes_set_B, 4: holes_set_C}
production_techniques = {'open_hole', 'shake_finger', 'half_open'}
rationale = 'clear_description_via_hole_manipulation'
RETURN sruti_grouping('vamsa')
enSvaras situated in the vamsa (flute)... groups of two, three and four śrutisvol_I_p015 enuse of svaras occurring in the holes of bamboo (flute)... two srutis, three srutis and four srutisvol_I_p015 + 2 more verbatim
§CASTE_BY_SRUTI_COUNT_BHARATA_22dict[int, str]
Sourced by
Svaras are classified by śruti count into three classes: 4-śruti (brāhmaņas), 3-śruti (kṣatriyas), 2-śruti (vaiśyas).
class(S) := match śruti_count(S) {4 => brāhmaṇa; 3 => kṣatriya; 2 => vaiśya}
sktचतुःश्रुतिस्वरा विप्रास्त्रिश्रुती क्षत्रियौ मतौ। वैश्यौ द्विश्वतिकौvol_I_p031 entwo (svaras) that are comprised of two śrutis (each) (viz. gandhāra and niṣāda)vol_I_p039 §VAMSA_STRUCTUREdict[str, object]
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vamsa (flute bambou) = 9 śrutis reparties en groupes de 2, 3 et 4 śrutis, produits par ouverture/secouage/demi-ouverture des trous
DEFINE vamsa_śrutis():
total_śrutis = 9
groupings = {2: holes_set_A, 3: holes_set_B, 4: holes_set_C}
production_techniques = {'open_hole', 'shake_finger', 'half_open'}
rationale = 'clear_description_via_hole_manipulation'
RETURN sruti_grouping('vamsa')
enSvaras situated in the vamsa (flute)... groups of two, three and four śrutisvol_I_p015 enuse of svaras occurring in the holes of bamboo (flute)... two srutis, three srutis and four srutisvol_I_p015 + 2 more verbatim
§SVARA_VAMSA_RSIfrozenset[Svara]
values : ri, dha
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Ṛṣabha and dhaivata belong to the vaṃśa of ṛṣis
ASSIGN vamsa(ri)=rsi; ASSIGN vamsa(dha)=rsi
enThe two svaras ršabha and dhaivata are born in the lineage of rsis.vol_I_p032 §SVARA_SRUTI_THEORIESdict[str, dict]
5 values
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Tādātmya = identity-theory of svara/śruti relation: claims svara≡śruti like jāti≡vyakti; refuted by aśraya/āśrayin distinction; one of several alternatives (vikalpana)
THEORY tādātmya: claim(svara ≡ śruti) JUSTIFIED_BY (no_differentia perceived_by_ear, analogous to jāti↔vyakti); REFUTATION: distinction(aśraya=śruti, āśrayin=svara) blocks identification; STATUS: one alternative among vikalpana set
enThere is identification between svara and śruti...just like jāti and vyaktivol_I_p018 enbecause there is no differentia (viśeṣa) between the two that are (equally) perceptible by the ear.vol_I_p018 + 2 more verbatim
Effect-theory: svaras are kārya (effect) of śruti (clay/potter analogy)
DEFINE kāryatva_theory AS (svara = effect(śruti)) ANALOGY (jar = effect(clay, potter_rod))
enSome say that svaras are the kārya (effect) of śruti, just as the jar is the 'effect' of the lump of clayvol_I_p018 Śrutis are transformed into the form of svaras (pariṇāmitā), as milk transforms into curd.
def parinamita(shruti):
return transform(shruti, 'milk_to_curd_analogy') -> svara
enSrutis undoubtedly get transformed into the form of svaras just as milk gets totally transformed in the form of curd.vol_I_p018 §PRAMANASdict[str, dict]
3 values
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Anumāna (inference) is accepted as a pramāṇa by all Indian philosophical systems except Cārvāka; requires preceding pratyakṣa (perception of concomitance); elaborated by Nyāya.
anumana := pramana WHERE accepted_by = ALL_indian_systems EXCEPT {carvaka}; prerequisite = pratyaksha(vyapti); elaborate_treatment_by = 'nyaya'
enAll the systems of Indian philosophy except the Carvaka system, accept anumāna as a pramāṇa... It has to be preceded by perception (pratyakṣa).vol_I_p091 Arthāpatti (negative inference / postulation) is a pramāṇa propounded by Mīmāṃsā and accepted by Advaita Vedānta; Nyāya subsumes it under anumāna; invoked in svara-śruti relation debates.
IF means_of_knowledge == 'arthapatti': school in {mimamsa, advaita_vedanta} => independent_pramana; school == nyaya => subsumed_under('anumana'); usage_in_music: establish(svara <-> shruti) via negative_inference
enIf by arthāpatti (negative inference) or by the pramāņa presuming vyāpti-grahaṇavol_I_p019 enArthāpatti is one of the pramāṇas... propounded specially by the mīmāṃsā system and accepted by Advaita Vedānta. Nyāya includes it under anumāna.vol_I_p091 vyāpti-graha = apprehension of universal concomitance, presupposition of anumāna (e.g. smoke→fire)
DEFINE vyapti_graha AS presupposition(anumana) WITH example='wherever smoke, there fire'
envyāpti-graha (apprehension of universal concomitance)vol_I_p091 §SRUTI_MODIFICATION_OPSdict[str, dict]
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Utkarṣa = augmentation/raising of pitch (notably of pañcama) used to measure śruti intervals and effect grāma transformation.
DEFINE utkarsa(svara) := raise_pitch(svara) -> shifts_sruti_interval; APPLY in grama_transformation WHEN murchana changes WITH utkarsa(gandhara)
enThe difference of that (pañcama) through utkarşa (augmentation) and apakarşa (diminution)vol_I_p016 entransformation of one grāma into another through change of murchana with utkarşa of gandharavol_I_p089 apakarşa = lowering/diminution of pitch, counterpart to utkarşa, used to measure śruti differences on vīṇā
DEFINE apakarşa AS pitch_action(direction=lowering, counterpart_of=utkarşa, measurement_use=śruti_difference)
APPLY apakarşa(svara=pañcama) -> diminished_pitch
NOTE interchangeable_with utkarşa IN [BrD, NS]
enThe difference of that (pañcama) through utkarşa (augmentation) and apakarşa (diminution)vol_I_p016 eneither of the two actions could result in both the changes of pitch... used as inter-changeables in both BrD and NSvol_I_p089 mārdava = adoucissement/abaissement; assigné à une śruti quand un svara est suivi d'un svara plus haut; sert avec āyatatva à mesurer la śruti de pañcama
FUNCTION assign_mardava(svara_i, svara_next):
IF pitch(svara_next) > pitch(svara_i):
svara_i.quality := 'mardava' # softness/lowering
# used as measure for sruti differentiation of pancama
RETURN svara_i.quality
enthrough mārdava (lit. softness) and āyatatva... is the measure of śrutivol_I_p016 enșadja which is higher than nișāda (is subjected to) mārdava or looseningvol_I_p046 + 1 more verbatim
§TANA_TECHNIQUESdict[str, dict]
3 values
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Praveśa is the act of a lower (or higher) svara being made to enter/merge into the higher (or lower) svara; it is the augmentation (viprakarṣa) of the lower ṣaḍja that must be omitted.
pravesa(low, high) := merge(low, high) via augmentation(low) OR mardava(high); viprakarsa(lower_sadja) -> omitted
enPravesa is the viprakarşa (augmentation) of şadja that is lower and has to be omittedvol_I_p045 enthe act of the lower or higher svara being made to 'enter' or merge into the higher or lower svara respectively.vol_I_p046 Praveśa happens through augmentation (prakarṣa) of the lower svara or by lowering (mārdava) of the higher svara.
trigger(pravesa(L,H)) := prakarsa(L) OR mardava(H)
enpravesa (takes place) on account of the prakarşa (augmentation) of the lower svara or by the mārdava (lowering) of the higher svara.vol_I_p046 Nigraha is the omission or non-touching of the immediate svara; one of two tāna-performance methods (with praveśa)
DEFINE nigraha = omit(immediate_svara); CONTRAST pravesa = identity_of_sound; tana_methods = {pravesa, nigraha}
enperformance of tana is twofold viz. with pravesa (lit. entering) and nigrahavol_I_p045 enNigraha is, on the other hand, the omission or 'non-touching' of the immediate svara.vol_I_p046 + 1 more verbatim
§SRUTI_AISVARYA_PRINCIPLEstr
explicitly states NO fixed pitch points — anti-cents-grid
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Aiśvarya (supremacy/power) of śrutis refers to their domination as cognizable points on a continuum of tones (no fixed pitch points).
AISHVARYA = {'meaning':'supremacy_of_shrutis_on_tone_continuum','no_fixed_pitch_points':True}
enAiśvarya lit. means supremacy, power, sway, sovereignty etc. The power or supremacy of śrutis could be that in Indian music the 'tones' are not used as notes on definite pitch-pointsvol_I_p087 §COKSA_RAGAStuple[str,...]
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Five cokṣa (pure) rāgas: śāḍava, pañcama, kaiśikamadhyama, cokṣasādhārita, cokṣakaiśika; distinguished from bhinna and other categories
ENUM coksa_ragas = [sadava, pancama, kaisikamadhyama, coksasadharita, coksakaisika]
sktषाडवः पञ्चमश्चैव तथा कैशिकमध्यमः। चोक्षसाधारितश्चैव चोक्षकैशिक इत्यपिvol_II_p052 enFive cokṣa (śuddha, pure rāgas) have been spoken of, the bhinna ones are of the same number.vol_II_p051 Śuddhā gīti (alias cokṣa) is complete (pūrṇā) with mandra, amandra, tāra ranges, straight, attractive, and equal svaras/śrutis.
SHUDDHA_GITI = {
'alias':'coksha',
'completeness':'purna',
'ranges':['mandra','amandra','tara'],
'qualities':['straight','attractive','equal_svaras_shrutis']
}
enThe cokṣa (suddhā) gīti is spoken of as being complete (pūrṇa) with mandra (low), amandra (not low, medium), tāra (high)straight, attractive, equal svaras and śrutis.vol_II_p049 Unresolved (9)
Concepts present in the domain but no rule pins their values — listed honestly, never invented.
cents-grid / numerical ratio for any śruti systemAucun ratio (Pythagorean, just-intonation, log2, Daniélou) sourcé dans le BrD. Le BrD donne uniquement comptes entiers per-svara + définition opératoire (utkarṣa/apakarṣa). Imposer une grille de cents serait fabrication. ABSOLUTE NO-GO per user feedback memory.
jāti-classes of śrutis (dīptā/āyatā/mṛdu/madhyā/karuṇā)5 jāti-de-śruti attendues du NŚ mais aucune règle 6b ni affirmation du BrD-Mātaṅga ne les énumère individuellement avec assignation par śruti. Traces partielles: aff#1849 (mṛdu = synonyme de mandra), cluster 500 'dipta' vide. NON modélisé.
66-school internal structureaff#2154 / aff#2158 nomment l'école 66-différencialiste, aucune règle ne donne la sous-division. Compte total seulement.
infinitist school internal descriptionaff#2154 mentionne ananta-śruti ; aucun mécanisme (densité, distribution) précisé.
fourfold Tumburu classification (humoral) — contentaff#2144 cite Tumburu comme autorité du fourfold humoral, mais contenu des 4 classes non extrait.
Kohala's specific śruti doctrineaff#2151 cite Kohala mais ne donne pas le contenu de sa position.
alaṅkāras exempting 3-śruti shake-ruleaff#3148 mentionne 'certains alaṅkāras' sans les nommer.
shuddhakaisikamadhyama grāma assignmentDisputé en source (référencé en domaine 3) ; non modélisé ici.
abstract concepts without operational śruti tiesvalakṣaṇa, viśeṣa, viśeṣa-bhinna, vikalpana, pratyaya, anumāna, arthāpatti définis dans la grammaire générative 6b mais sans opération exécutable sur śrutis. Conservés comme PRAMANAS et théories vikalpana, non comme opérations.