Hurrian hymn, Ugarit, 13th century BCE, Wikimedia (public domain)
Hurrian hymn, Ugarit, 13th century BCE, Wikimedia (public domain)
Babylonian Sexagesimal Arithmetic and Numbers
Sumerian Symmetry of Opposites, Balance Beam
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.
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 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.
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.
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.
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.
