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Babylonian Tonal System

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Basic tetrachords

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The Babylonian Tonal System is based on tetrachords.

1½1, ½11, 11½


\new Staff \with { \consists Horizontal_bracket_engraver \remove "Time_signature_engraver" \remove "Bar_engraver" }
\relative c' { 
  d1 e -\tweak HorizontalBracketText.text "semitone"  \startGroup f\stopGroup g}

\new Staff \with { \consists Horizontal_bracket_engraver \remove "Time_signature_engraver" \remove "Bar_engraver" }
\relative c' { 
  e1 -\tweak HorizontalBracketText.text "semitone"  \startGroup f\stopGroup g a}

\new Staff \with { \consists Horizontal_bracket_engraver \remove "Time_signature_engraver" \remove "Bar_engraver" }
\relative c' { 
  c1 d e -\tweak HorizontalBracketText.text "semitone"  \startGroup f\stopGroup}

and the tritone
111


\new Staff \with { \consists Horizontal_bracket_engraver \remove "Time_signature_engraver" \remove "Bar_engraver" }
\relative c' { 
  f1 g a b}

Two consecutive tetrachords build a heptachord.

Heptachord linear

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1½11½1

 \new Staff \with { \consists Ambitus_engraver \consists Horizontal_bracket_engraver \remove "Time_signature_engraver" \remove "Bar_engraver" } \relative c' { 
  a1^"kitmum" b -\tweak HorizontalBracketText.text "semitone"  \startGroup c\stopGroup d e-\tweak HorizontalBracketText.text "semitone"\startGroup f\stopGroup g }

Heptachord circle

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Heptachord circle

7 heptachord modes

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The 7 modal patterns for the Babylonian heptachords are:

Babylonian tonal system
Mode Pattern Center note Semitones Tritones
kitmum 1½11½1 D 10 0
pītum ½11½11 E 10 0
qablītum 11½11½ C 10 0
išartum 1½111½ G 10 1
embūbum ½111½1 A 10 1
nīd qablim 111½11 B 11 2
nīš tuḫrim 11½111 F 11 2
 \new Staff \with { \consists Ambitus_engraver \consists Horizontal_bracket_engraver \remove "Time_signature_engraver" \remove "Bar_engraver" } \relative c' { 
  a1^"kitmum" b -\tweak HorizontalBracketText.text "semitone"  \startGroup c\stopGroup d e-\tweak HorizontalBracketText.text "semitone"\startGroup f\stopGroup g }
 \new Staff \with { \consists Ambitus_engraver \consists Horizontal_bracket_engraver \remove "Time_signature_engraver" \remove "Bar_engraver" } 
\relative c' { 
  b1^"pītum" -\tweak HorizontalBracketText.text "semitone"  \startGroup c\stopGroup d e-\tweak HorizontalBracketText.text "semitone"\startGroup f\stopGroup g a}
 \new Staff \with { \consists Ambitus_engraver \consists Horizontal_bracket_engraver \remove "Time_signature_engraver" \remove "Bar_engraver" } \relative c' { 
  g1^"qablītum" a b -\tweak HorizontalBracketText.text "semitone"  \startGroup c\stopGroup d e-\tweak HorizontalBracketText.text "semitone"\startGroup f\stopGroup }
 \new Staff \with { \consists Ambitus_engraver \consists Horizontal_bracket_engraver \remove "Time_signature_engraver" \remove "Bar_engraver" } 
\relative c' { 
  d1^"išartum" e -\tweak HorizontalBracketText.text "semitone"  \startGroup f\stopGroup g a b-\tweak HorizontalBracketText.text "semitone"\startGroup c\stopGroup}
 \new Staff \with { \consists Ambitus_engraver \consists Horizontal_bracket_engraver \remove "Time_signature_engraver" \remove "Bar_engraver" } 
\relative c { 
  e1^"embūbum" -\tweak HorizontalBracketText.text "semitone"  \startGroup f\stopGroup g a b-\tweak HorizontalBracketText.text "semitone"\startGroup c\stopGroup d}
 \new Staff \with { \consists Ambitus_engraver \consists Horizontal_bracket_engraver \remove "Time_signature_engraver" \remove "Bar_engraver" } 
\relative c' { 
  f,1^"nīd qablim" g a b -\tweak HorizontalBracketText.text "semitone"  \startGroup c\stopGroup d e}
 \new Staff \with { \consists Ambitus_engraver \consists Horizontal_bracket_engraver \remove "Time_signature_engraver" \remove "Bar_engraver" } 
\relative c' { 
  c1^"nīš tuḫrim" d e -\tweak HorizontalBracketText.text "semitone"  \startGroup f\stopGroup g a b}

2 consecutive heptachords

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 \new Staff \with { \consists Ambitus_engraver \consists Horizontal_bracket_engraver \remove "Time_signature_engraver" \remove "Bar_engraver" } \relative c' { 
  a1^"kitmum" b -\tweak HorizontalBracketText.text "semitone"  \startGroup c\stopGroup d e-\tweak HorizontalBracketText.text "semitone"\startGroup f\stopGroup g a-\tweak HorizontalBracketText.text "semitone"  \startGroup bes\stopGroup c d-\tweak HorizontalBracketText.text "semitone"  \startGroup es\stopGroup f}

Flatward shift for higher notes.

7 consecutive heptachords

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7 consecutive heptachords build the 7 Babylonian modes:

6 cyclic consecutive heptachords

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Circle of fourths, kitmum, 36 notes, 60 semitones = Anu 𒀭

Tuning

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A tuning procedure ‘loosening’ (TU.LU) in Music of Mesopotamia for a 7-stringed instrument based on a transposition to D/D♭:


\new Staff \with { \consists Horizontal_bracket_engraver \remove "Time_signature_engraver" \remove "Bar_engraver" }
\relative c' { 
  d1^"išartum 2-6 5-2" e -\tweak HorizontalBracketText.text "semitone"  \startGroup f\stopGroup g a b-\tweak HorizontalBracketText.text "semitone"\startGroup c\stopGroup }

\new Staff \with { \consists Horizontal_bracket_engraver \remove "Time_signature_engraver" \remove "Bar_engraver" }
\relative c' { 
  d1^"kitmum 6-3 2-6" e -\tweak HorizontalBracketText.text "semitone"  \startGroup f\stopGroup g a-\tweak HorizontalBracketText.text "semitone"\startGroup bes\stopGroup c }

\new Staff \with { \consists Horizontal_bracket_engraver \remove "Time_signature_engraver" \remove "Bar_engraver" } 
\relative c' { 
  d1^"embūbum 3-7 6-3" -\tweak HorizontalBracketText.text "semitone"  \startGroup es\stopGroup f g a-\tweak HorizontalBracketText.text "semitone"\startGroup bes\stopGroup c }

\new Staff \with { \consists Horizontal_bracket_engraver \remove "Time_signature_engraver" \remove "Bar_engraver" } 
\relative c' { 
  d1^"pītum 7-4 3-7" -\tweak HorizontalBracketText.text "semitone"  \startGroup es\stopGroup f g -\tweak HorizontalBracketText.text "semitone"\startGroup as\stopGroup bes c }

\new Staff \with { \consists Horizontal_bracket_engraver \remove "Time_signature_engraver" \remove "Bar_engraver" } 
\relative c' { 
  des1^"nīd qablim 4-1 7-4" es f g-\tweak HorizontalBracketText.text "semitone"\startGroup as\stopGroup bes c }

\new Staff \with { \consists Horizontal_bracket_engraver \remove "Time_signature_engraver" \remove "Bar_engraver" } 
\relative c' { 
  des1^"nīš tuḫrim 1-5 4-1" es f -\tweak HorizontalBracketText.text "semitone"\startGroup ges\stopGroup as bes c }

\new Staff \with { \consists Horizontal_bracket_engraver \remove "Time_signature_engraver" \remove "Bar_engraver" } 
\relative c' { 
  des1^"qablītum 5-2 1-5" es f -\tweak HorizontalBracketText.text "semitone"\startGroup ges\stopGroup as bes-\tweak HorizontalBracketText.text "semitone"\startGroup ces\stopGroup }

‘tightening’ (GÍD.I)


\new Staff \with { \consists Horizontal_bracket_engraver \remove "Time_signature_engraver" \remove "Bar_engraver" }
\relative c' { 
  d1^"išartum" e -\tweak HorizontalBracketText.text "semitone"  \startGroup f\stopGroup g a b-\tweak HorizontalBracketText.text "semitone"\startGroup c\stopGroup }

\new Staff \with { \consists Horizontal_bracket_engraver \remove "Time_signature_engraver" \remove "Bar_engraver" } 
\relative c' { 
  d1^"qablītum" e fis -\tweak HorizontalBracketText.text "semitone"\startGroup g\stopGroup a b-\tweak HorizontalBracketText.text "semitone"\startGroup c\stopGroup }

\new Staff \with { \consists Horizontal_bracket_engraver \remove "Time_signature_engraver" \remove "Bar_engraver" } 
\relative c' { 
  d1^"niš tuĥrim" e fis -\tweak HorizontalBracketText.text "semitone"\startGroup g\stopGroup a b cis }

\new Staff \with { \consists Horizontal_bracket_engraver \remove "Time_signature_engraver" \remove "Bar_engraver" } 
\relative c' { 
  d1^"nīd qablim" e fis gis-\tweak HorizontalBracketText.text "semitone"\startGroup a\stopGroup b cis }

\new Staff \with { \consists Horizontal_bracket_engraver \remove "Time_signature_engraver" \remove "Bar_engraver" } 
\relative c' { 
  dis1^"pītum" -\tweak HorizontalBracketText.text "semitone"  \startGroup e\stopGroup fis gis -\tweak HorizontalBracketText.text "semitone"\startGroup a\stopGroup b cis }

\new Staff \with { \consists Horizontal_bracket_engraver \remove "Time_signature_engraver" \remove "Bar_engraver" } 
\relative c' { 
  dis1^"embūbum" -\tweak HorizontalBracketText.text "semitone"  \startGroup e\stopGroup fis gis ais-\tweak HorizontalBracketText.text "semitone"\startGroup b\stopGroup cis }

\new Staff \with { \consists Horizontal_bracket_engraver \remove "Time_signature_engraver" \remove "Bar_engraver" }
\relative c' { 
  dis1^"kitmum" eis -\tweak HorizontalBracketText.text "semitone"  \startGroup fis\stopGroup gis ais-\tweak HorizontalBracketText.text "semitone"\startGroup b\stopGroup cis }

kitmum chords

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\new Staff \with { \consists Horizontal_bracket_engraver \remove "Time_signature_engraver" \remove "Bar_engraver" }
\relative c' { 
   <dis fis ais>1 <eis gis b> <fis ais cis> <gis b dis> <ais cis e> <b dis fis> <cis e gis> \break
   <dis, fis a> <e gis b> <fis a cis> <gis b d> <a cis e> <b d fis> <cis e g> \break
   <d, fis a> <e g b> <fis a c> <g b d> <a c e> <b d f> <c e g> \break
   <d, f a> <e g bes> <f a c> <g bes d> <a c es> <bes d f> <c es g> \break
   <d, f as> <es g bes> <f as c> <g bes des> <as c es> <bes d f> <c es ges> \break
   <des, f as> <es ges bes> <f as ces> <ges bes des>
}

Further reading

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  • Crickmore, Leon (2008). A New Light on the Babylonian Tonal System (PDF). Proceedings of the International Conference of Near Eastern Archaeomusicology (ICONEA 2008), The British Museum, London, December 4–6, 2008, editors: Richard Dumbrill and Irving Finkel. London: Iconea Publications. pp. 11–22.
  • "Babylonian Tonal System". Allan Pettersson Fanpage. Retrieved 19 January 2026.