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This is the Sumerian cuneiform tablet known as MS 2340, and is the EARLIEST known Musical Text.
... Dating from around the 26th Century BC ...
..."this tablet contains the EARLIEST known record of music and musical instruments in history. It lists 9 types of musical strings and 23 types of musical instruments and music.
The name of one of the stringed instruments is a Semitic word, ki-na-ru, the later kinnaru known from the Mari letters and Ras Shamra texts (13th century BC) and still later the Biblical Hebrew kinnor."...
"""The system of phonetic notation in Sumer and Babylonia is based on a music terminology that gives individual names to 9 musical strings or "notes", and to 14 basic terms describing intervals of the 4th and 5th that were used in tuning string instruments (according to 7 heptatonic diatonic scales), and terms for 3rds and 6ths that appear to have been used to fine tune (or temper in some way) the 7 notes generated for each scale. The combination of string names and interval terms is used to describe the tuning procedure and the generation of the 7 scales and form a skeletal phonetic notation. """
Sumerian Cuneiform tablet known as MS 5105, 4 stringed lute tuned in ascending perfect fifths.
This is the EARLIEST known Musical Notation.
with headings, "intonation" and "incantation", respectively.
the lute was fitted with four strings,
the strings were tuned in ascending fifths: C-G-D-A,
frets were used, and their values, tonal and semitonal, were purposely calculated
"""Most significantly, the discovery of this text attests of a music syllabus in educational institutions about 4000 years ago. """
Sumerian Cuneiform Tablet known as UET VII 126, is known as the 'String Naming Text'.
This tablet was inscribed in about 626–539 BC, however, it is a copy of the 32nd tablet of the series nabnītu, based on the discovery to a duplicate fragment from Nippur, N 4782, dated to 1800–1500 BC.
The information this tablet contains is the EARLIEST information that we have regarding the names of strings and pitches. The tablet is bilingual with the left column in Sumerian and a translation into Akkadian in the right column.
This is a critical text, because it provides the names of nine strings of a musical instrument (presumed to be the lyre) and is a key for understanding the other musical texts.
Sumerian Tablet known as CBS 10996, the 'Interval Text'.
The tablet names intervals in terms of the string names from UET VII 126.
The Ancient Sumerian Cuneiform Tablet discovered by Leonard Woolley in the 1920's, dating to ~2000 BC, known as UET VII 74, the 'Tuning Text'.
This text is known as “the tuning text” because it provided the decisive clue to the understanding of the Babylonian musical system and its terminology.
The tablet describes the tuning of the sammû instrument, using a set of instructions for tightening or loosening various strings.
If the sammû is (tuned as) X and the (interval) Y is not clear, you tighten/loosen the string N and then Y will be clear.
A complete translation of this tablet is provided in [Dumbrill 2005], pages 49–50. It provided a breakthrough in understanding of Babylonian musical scales:
The tuning system uses only intervals from the odd-numbered lines of CBS 10996, so the only intervals that needed to be tuned by ear were musical fourths and fifths.
UET VII 74 provides for the tuning of seven complete, related tunings, each with the name corresponding to the first interval tuned. These seven tunings appear in UET VII 74 and in other documents in a standard order: išartum, kitmum, embūbum, pītum, nīd qablim, nīš tuḫri, and qablītum.
The tuning system, based on perfect fourths and fifths, is analogous to and substantially predates the Pythagorean tuning system of ancient Greece.
Each of the seven tunings names an “impure” interval, which corresponds to the tritone interval in the tuning and produced a dissonant chord. The tuning instructions are also designed to re-tune that impure interval using a perfect fourth or fifth to obtain another interval in the series of seven tunings.
Perhaps most significantly, each of the seven tunings has a pattern of tones and semitones (whole steps and half steps) that closely matches the seven modes of the present-day diatonic scale. One significant difference is that the Babylonian tuning procedure uses intervals of fourths and fifth that produce a Pythagorean-type tuning, where the Western music tradition has, for the last two centuries, has “tempered” that scale so as to distribute the dissonance of the tritone throughout the tuning (i.e. “equal temperament”).
"""The absence of strings 8 and 9 in CBS 10996 is also cleared up in UET VII 74: Whenever string 1 is tuned, string 8 tuned to an octave away. Likewise, string 9 is tuned an octave away from string 2, etc. """
The ancient musicians and mathematicians KNEW about and were fluent with the √2.
They proved that to us with the ancient Babylonian cuneiform tablet known as YBC 7289 from ~1800 BC.
Giving the result of √2 in sexagesimal (1, 24, 51, 10), proving they had the modern TRITONE.
Or from the ancient Indian Vedic perspective ~1000 BC - In the Baudhayana sutra it appears as: The measure is to be increased by its third and this [third] again by its own fourth less the thirty-fourth part [of that fourth]; this is [the value of] the diagonal of a square [whose side is the measure].
Either way you look at, the ancient folks had √2 down pat. So they knew the octave, and how to equally subdivide it. The mathematical formula for this musical TRITONE interval would be the geometric mean of √(AB), where A=1, and the next octave B=2, thus 1.414 = √2.
look what happens when you cut pythagoras' epogdoon in half = √2
Ancient Homework Assignments
HEBE-ERIDU THE SON OF ADAD-LAMASI SAT WITH IL-SIRI IN ORDER TO LEARN MUSIC. AT THAT TIME, IN ORDER TO STUDY SINGING, THE TIGIDLU-INSTRUMENT, THE ASILA, TIGI INSTRUMENT, AND THE ADAB INSTRUMENT SEVEN TIMES, ADAD-LAMASI PAID IL-SIRI 5 SHEKELS OF SILVER. ILI-IPPALSANI, THE SCHOOLMASTER
HEBE-ERIDU THE SON OF ADAD-LAMASI SAT WITH IL-SIRI IN ORDER TO LEARN MUSIC. AT THAT TIME, IN ORDER TO STUDY SINGING, THE TIGIDLU-INSTRUMENT, THE ASILA, TIGI INSTRUMENT, AND THE ADAB INSTRUMENT SEVEN TIMES, ADAD-LAMASI PAID IL-SIRI 5 SHEKELS OF SILVER. ILI-IPPALSANI, THE SCHOOLMASTER
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