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Babylonian Tonal System

Heptachords and Scales
Hurrian hymn

Hurrian hymn, Ugarit, 13th century BCE, Wikimedia (public domain)

Sexagesimal

Babylonian Sexagesimal Arithmetic and Numbers

Balance

Sumerian Symmetry of Opposites, Balance Beam

babylonian heptachords

(pdf) Babylonian Tonal System: Heptachords and Scales PDF Flag

7 scales

kitmum

The scale of kitmum is unique. The basic heptachord is palindromic. The center note is D. The scale is related to pītum and qablītum and is in a kind of center position.

10 semitones per heptachord.

7 tones per heptachord, 6 unique tones.

7 heptachords are shown, but 6♯ = 6♭. So there are only 6 unique heptachords. This can be compared to the days of a week and the role of the sunday.

1 2 3 4 5 6 7
Mon Tue Wed Thu Fri Sat Sun

In total 60 semitones Anu. Cyclic like a watch.

pitum
qablitum

The scales pītum and qablītum build also a pair. The key signatures of the scales are identical. Center notes are E and C, difference is a major third.

isartum

The ambitus is 5 octaves. 5x1200=6000 Cent, 60 semitones, 200 Cent per whole tone, 100 Cent per semitone, equal temperament (Plato: corresponding to celestial city Callipolis). In Sumerian music only just intonation was known with whole tone 204 Cent and semitone 90 Cent. An alternative just intonation was found in Nippur. The delta of the key signature is 2. The scale has 36 unique notes.

embubum

The scales išartum and embūbum are related. The center of the symmetrical scales are different. Center note (Balance point) of išartum is G, center of embūbum is A. The difference is a heptachord. The center note can be interpreted as the main finalis (f). So the Babylonian Tonal System probably knows already the concept of finalis in constructing a melody.

The preceding 5 scales all have two semitones and 4 whole tones in a heptachord. 6 heptachords build a scale, two scales are possible. The 12 heptachords address the 12 notes of the complete tone circle. 5x12=60: The number 60 plays an important role in the Babylonian sexagesimal arithmetic, and represents god Anu.

nid qablim
nis tuhrim

The last two scales nīd qablim and nīš tuḫrim are very different from the first 5 scales. Center notes are B and F. The basic heptachord contains only one semitone. The delta of the key signature is 5. 3 heptachords exist with 7x3=21-2=19 pitches. In Islam, Maryam, مريم is the 19th sūrah of the Qur'an, which announces Jesus. In Baháʼí Faith, a group of 19 is called a Váhid, which means unity. In total 33 semitones, not cyclic.

Proposal

In Babylonian music, only one scale is perfectly symmetric. This mode represents God: kitmum. The six other modes are not perfect and asymmetric. These represent the incarnations and prophets and messengers. Asymmetry is essential for life. Four (incarnations and prophets) are nearly perfect, the two messengers are less perfect.

Dualisms

Temperaments

Emotions

poetry

Strophe

Lutherstophe is a seven-line strophe with the rhyme scheme ABABCCB or ABABCCX. Following seven-line schemes can be transferred from the heptachordal music to poetry:

  1. ABBACCA
  2. ABBAACC
  3. AABBCCB
  4. AABCCBB
  5. AABBACC
  6. AABBAAA
  7. AAABBAA
  1. ABBACCX
  2. ABBAACX
  3. AABBCCX
  4. AABCCBX
  5. AABBACX
  6. AABBAAX
  7. AAABBAX
Alternating rhymes
  1. ABABCCB Lutherstrophe
  2. ABABBCC Rhyme royal
  3. ABACBCB
  4. ABABCBC
  5. ABABACC
  6. ABABCAC Canopus
  7. ABABCCA
  8. AABBCBC
  9. ABBACAC
  10. AABCBCB
  11. ABBCACA
  12. AAABABA
  13. ABABAAA
  14. AAAABAB
  15. ABABBBB

heptaphony

Analog to dodecaphony (twelve-tone technique), a heptaphony (seven-tone technique) can be developed.

kitmum

12 x 6 = 72 tables x 6 = 432 rows (down) x 2 = 864 rows (up)

I/1

A B C D E F G
C A F D B G E
E G B D F A C
D D D D D D D
B E A D G C F
F C G D A E B
G F E D C B A

I/2

A B C D E F G
C A F D B G E
E G B D F A C
D D D D D D D
F C G D A E B
B E A D G C F
G F E D C B A

I/3

A B C D E F G
C A F D B G E
E G B D F A C
D D D D D D D
G F E D C B A
B E A D G C F
F C G D A E B

I/4

A B C D E F G
C A F D B G E
E G B D F A C
D D D D D D D
G F E D C B A
F C G D A E B
B E A D G C F

I/5

A B C D E F G
C A F D B G E
E G B D F A C
D D D D D D D
F C G D A E B
G F E D C B A
B E A D G C F

I/6

A B C D E F G
C A F D B G E
E G B D F A C
D D D D D D D
B E A D G C F
G F E D C B A
F C G D A E B

II/1

A B C D E F G
E G B D F A C
C A F D B G E
D D D D D D D
B E A D G C F
F C G D A E B
G F E D C B A

II/2

A B C D E F G
E G B D F A C
C A F D B G E
D D D D D D D
F C G D A E B
B E A D G C F
G F E D C B A

II/3

A B C D E F G
E G B D F A C
C A F D B G E
D D D D D D D
G F E D C B A
B E A D G C F
F C G D A E B

II/4

A B C D E F G
E G B D F A C
C A F D B G E
D D D D D D D
G F E D C B A
F C G D A E B
B E A D G C F

II/5

A B C D E F G
E G B D F A C
C A F D B G E
D D D D D D D
F C G D A E B
G F E D C B A
B E A D G C F

II/6

A B C D E F G
E G B D F A C
C A F D B G E
D D D D D D D
B E A D G C F
G F E D C B A
F C G D A E B

III/1

C A F D B G E
A B C D E F G
E G B D F A C
D D D D D D D
B E A D G C F
F C G D A E B
G F E D C B A

III/2

C A F D B G E
A B C D E F G
E G B D F A C
D D D D D D D
F C G D A E B
B E A D G C F
G F E D C B A

III/3

C A F D B G E
A B C D E F G
E G B D F A C
D D D D D D D
G F E D C B A
B E A D G C F
F C G D A E B

III/4

C A F D B G E
A B C D E F G
E G B D F A C
D D D D D D D
G F E D C B A
F C G D A E B
B E A D G C F

III/5

C A F D B G E
A B C D E F G
E G B D F A C
D D D D D D D
F C G D A E B
G F E D C B A
B E A D G C F

III/6

C A F D B G E
A B C D E F G
E G B D F A C
D D D D D D D
B E A D G C F
G F E D C B A
F C G D A E B

IV/1

C A F D B G E
E G B D F A C
A B C D E F G
D D D D D D D
B E A D G C F
F C G D A E B
G F E D C B A

IV/2

C A F D B G E
E G B D F A C
A B C D E F G
D D D D D D D
F C G D A E B
B E A D G C F
G F E D C B A

IV/3

C A F D B G E
E G B D F A C
A B C D E F G
D D D D D D D
G F E D C B A
B E A D G C F
F C G D A E B

IV/4

C A F D B G E
E G B D F A C
A B C D E F G
D D D D D D D
G F E D C B A
F C G D A E B
B E A D G C F

IV/5

C A F D B G E
E G B D F A C
A B C D E F G
D D D D D D D
F C G D A E B
G F E D C B A
B E A D G C F

IV/6

C A F D B G E
E G B D F A C
A B C D E F G
D D D D D D D
B E A D G C F
G F E D C B A
F C G D A E B

V/1

E G B D F A C
A B C D E F G
C A F D B G E
D D D D D D D
B E A D G C F
F C G D A E B
G F E D C B A

V/2

E G B D F A C
A B C D E F G
C A F D B G E
D D D D D D D
F C G D A E B
B E A D G C F
G F E D C B A

V/3

E G B D F A C
A B C D E F G
C A F D B G E
D D D D D D D
G F E D C B A
B E A D G C F
F C G D A E B

V/4

E G B D F A C
A B C D E F G
C A F D B G E
D D D D D D D
G F E D C B A
F C G D A E B
B E A D G C F

V/5

E G B D F A C
A B C D E F G
C A F D B G E
D D D D D D D
F C G D A E B
G F E D C B A
B E A D G C F

V/6

E G B D F A C
A B C D E F G
C A F D B G E
D D D D D D D
B E A D G C F
G F E D C B A
F C G D A E B

VI/1

E G B D F A C
C A F D B G E
A B C D E F G
D D D D D D D
B E A D G C F
F C G D A E B
G F E D C B A

VI/2

E G B D F A C
C A F D B G E
A B C D E F G
D D D D D D D
F C G D A E B
B E A D G C F
G F E D C B A

VI/3

E G B D F A C
C A F D B G E
A B C D E F G
D D D D D D D
G F E D C B A
B E A D G C F
F C G D A E B

VI/4

E G B D F A C
C A F D B G E
A B C D E F G
D D D D D D D
G F E D C B A
F C G D A E B
B E A D G C F

VI/5

E G B D F A C
C A F D B G E
A B C D E F G
D D D D D D D
F C G D A E B
G F E D C B A
B E A D G C F

VI/6

E G B D F A C
C A F D B G E
A B C D E F G
D D D D D D D
B E A D G C F
G F E D C B A
F C G D A E B

VII/1

A B C D E F G
B E A D G C F
C A F D B G E
D D D D D D D
E G B D F A C
F C G D A E B
G F E D C B A

VII/2

A B C D E F G
B E A D G C F
C A F D B G E
D D D D D D D
F C G D A E B
E G B D F A C
G F E D C B A

VII/3

A B C D E F G
B E A D G C F
C A F D B G E
D D D D D D D
G F E D C B A
E G B D F A C
F C G D A E B

VII/4

A B C D E F G
B E A D G C F
C A F D B G E
D D D D D D D
G F E D C B A
F C G D A E B
E G B D F A C

VII/5

A B C D E F G
B E A D G C F
C A F D B G E
D D D D D D D
F C G D A E B
G F E D C B A
E G B D F A C

VII/6

A B C D E F G
B E A D G C F
C A F D B G E
D D D D D D D
E G B D F A C
G F E D C B A
F C G D A E B

VIII/1

A B C D E F G
C A F D B G E
B E A D G C F
D D D D D D D
E G B D F A C
F C G D A E B
G F E D C B A

VIII/2

A B C D E F G
C A F D B G E
B E A D G C F
D D D D D D D
F C G D A E B
E G B D F A C
G F E D C B A

VIII/3

A B C D E F G
C A F D B G E
B E A D G C F
D D D D D D D
G F E D C B A
E G B D F A C
F C G D A E B

VIII/4

A B C D E F G
C A F D B G E
B E A D G C F
D D D D D D D
G F E D C B A
F C G D A E B
E G B D F A C

VIII/5

A B C D E F G
C A F D B G E
B E A D G C F
D D D D D D D
F C G D A E B
G F E D C B A
E G B D F A C

VIII/6

A B C D E F G
C A F D B G E
B E A D G C F
D D D D D D D
E G B D F A C
G F E D C B A
F C G D A E B

IX/1

B E A D G C F
A B C D E F G
C A F D B G E
D D D D D D D
E G B D F A C
F C G D A E B
G F E D C B A

IX/2

B E A D G C F
A B C D E F G
C A F D B G E
D D D D D D D
F C G D A E B
E G B D F A C
G F E D C B A

IX/3

B E A D G C F
A B C D E F G
C A F D B G E
D D D D D D D
G F E D C B A
E G B D F A C
F C G D A E B

IX/4

B E A D G C F
A B C D E F G
C A F D B G E
D D D D D D D
G F E D C B A
F C G D A E B
E G B D F A C

IX/5

B E A D G C F
A B C D E F G
C A F D B G E
D D D D D D D
F C G D A E B
G F E D C B A
E G B D F A C

IX/6

B E A D G C F
A B C D E F G
C A F D B G E
D D D D D D D
E G B D F A C
G F E D C B A
F C G D A E B

X/1

B E A D G C F
C A F D B G E
A B C D E F G
D D D D D D D
E G B D F A C
F C G D A E B
G F E D C B A

X/2

B E A D G C F
C A F D B G E
A B C D E F G
D D D D D D D
F C G D A E B
E G B D F A C
G F E D C B A

X/3

B E A D G C F
C A F D B G E
A B C D E F G
D D D D D D D
G F E D C B A
E G B D F A C
F C G D A E B

X/4

B E A D G C F
C A F D B G E
A B C D E F G
D D D D D D D
G F E D C B A
F C G D A E B
E G B D F A C

X/5

B E A D G C F
C A F D B G E
A B C D E F G
D D D D D D D
F C G D A E B
G F E D C B A
E G B D F A C

X/6

B E A D G C F
C A F D B G E
A B C D E F G
A B C D E F G
D D D D D D D
E G B D F A C
G F E D C B A
F C G D A E B

XI/1

C A F D B G E
A B C D E F G
B E A D G C F
D D D D D D D
E G B D F A C
F C G D A E B
G F E D C B A

XI/2

C A F D B G E
A B C D E F G
B E A D G C F
D D D D D D D
F C G D A E B
E G B D F A C
G F E D C B A

XI/3

C A F D B G E
A B C D E F G
B E A D G C F
D D D D D D D
G F E D C B A
E G B D F A C
F C G D A E B

XI/4

C A F D B G E
A B C D E F G
B E A D G C F
D D D D D D D
G F E D C B A
F C G D A E B
E G B D F A C

XI/5

C A F D B G E
A B C D E F G
B E A D G C F
D D D D D D D
F C G D A E B
G F E D C B A
E G B D F A C

XI/6

C A F D B G E
A B C D E F G
B E A D G C F
D D D D D D D
E G B D F A C
G F E D C B A
F C G D A E B

XII/1

C A F D B G E
B E A D G C F
A B C D E F G
D D D D D D D
E G B D F A C
F C G D A E B
G F E D C B A

XII/2

C A F D B G E
B E A D G C F
A B C D E F G
D D D D D D D
F C G D A E B
E G B D F A C
G F E D C B A

XII/3

C A F D B G E
B E A D G C F
A B C D E F G
D D D D D D D
G F E D C B A
E G B D F A C
F C G D A E B

XII/4

C A F D B G E
B E A D G C F
A B C D E F G
D D D D D D D
G F E D C B A
F C G D A E B
E G B D F A C

XII/5

C A F D B G E
B E A D G C F
A B C D E F G
D D D D D D D
F C G D A E B
G F E D C B A
E G B D F A C

XII/6

C A F D B G E
B E A D G C F
A B C D E F G
D D D D D D D
E G B D F A C
G F E D C B A
F C G D A E B

chords

kitmum triads

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
A# B C# D# E F# G# A B C# D E F# G A B C D E F G A Bb C D Eb F G Ab Bb C Db Eb F Gb Ab Bb Cb Db
F# G# A# B C# D# E F# G# A B C# D E F# G A B C D E F G A Bb C D Eb F G Ab Bb C Db Eb F Gb Ab Bb
D# E# F# G# A# B C# D# E F# G# A B C# D E F# G A B C D E F G A Bb C D Eb F G Ab Bb C Db Eb F Gb

kitmum quartal harmony

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37
C# D# E F# G# A B C# D E F# G A B C D E F G A Bb C D Eb F G Ab Bb C Db Eb F Gb Ab Bb Cb Db
G# A# B C# D# E F# G# A B C# D E F# G A B C D E F G A Bb C D Eb F G Ab Bb C Db Eb F Gb Ab
D# E# F# G# A# B C# D# E F# G# A B C# D E F# G A B C D E F G A Bb C D Eb F G Ab Bb C Db Eb

kitmum quintal harmony

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37
E F# G# A B C# D E F# G A B C D E F G A Bb C D Eb F G Ab Bb C Db Eb F Gb Ab Bb Cb Db Es Fes
A# B C# D# E F# G# A B C# D E F# G A B C D E F G A Bb C D Eb F G Ab Bb C Db Eb F Gb Ab Bb
D# E# F# G# A# B C# D# E F# G# A B C# D E F# G A B C D E F G A Bb C D Eb F G Ab Bb C Db Eb

heptachord

kitmum

Basic Heptachord
kitmum mode - Basic Heptachord

7 notes are shown, but there are only 6 unique notes. This can be compared to the days of a week and the role of the sunday.

Basic Tetrachord
kitmum mode - Basic Tetrachord

Related Glareanian Modes

Hypodorian
kitmum mode - Hypodorian
Hypomixolydian
kitmum mode - Hypomixolydian
Aeolian (minor)
kitmum mode - Aeolian

Plots

kitmum Heptachords
kitmum - Octave
kitmum - Hypomixolydian