🏠

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
isartum

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. The ambitus is 5 octaves. 5x1200=6000 Cent, 60 semitones, 100 Cent per semitone, equal temperament (Plato: corresponding to celestial city Callipolis). The delta of the key signature is 2.

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.

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.

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.

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.

Each of the preceding scales consist of 36 unique pitches, 24 whole tones and 12 semitones. The 12 semitones are 6 whole tones. In total 24+6=30 whole tones per scale (or 60 semitones). For two possible scales: 30x2=60 Anu.

A heptachord contains converted 10 semitones or 5 whole tones. For 6 heptachords: 10x6=60 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. Only one scale with 12 heptachords is possible. (3 heptachords of the 12 are shown.) The delta of the key signature is 5. 5x12=60 represents again Anu for each scale.

kitmum heptachord

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