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
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.
In total 60 semitones Anu. Cyclic like a watch.
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 scale has 43-1=42 unique notes.
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.
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.
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 avatars and prophets and messengers. Asymmetry is essential for life. Four avatars and prophets are nearly perfect, the two messengers are less perfect.
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.
