how did the standardized musical notation come about?

Oh my gosh I have got this. Not a historian, but I'm studying music history right now so this isn't technically procrastination. Primarily sourced from Norton's A History of Western Music, which is a standard textbook -- so if they get any info wrong/oversimplified, I hope a more scholarly scholar will step in to correct me! Also, if anyone's got info on Eastern musical history that would be welcome.

Music notation as we know it today tells you many things simultaneously: what pitches to play, in what order, for how long, emphasized in what pattern, at what volume, and even in what expressive manner. Early music notation generally didn't have all of those pieces present at the same time.

The earliest known musical notation is Babylonian (ca 1400-1250 BCE), but it's poorly understood and consisted (so far as we know) of a series of interval names. The Greeks had a complex system of music theory, similar but not at all the same as our current system, and a music notation consisting of the alphabetic names of the notes written out with diacritical marks above them giving each a rhythmic unit. Generally speaking, though, most music was passed through oral tradition for most of human history.

The development of standard notation as we know it today came from the Roman Catholic church, and began as a way to stabilize the liturgical plainchants of the Mass. The first definitive references to notation date to 850.

The first step to notation was "neumes," signs placed above the words of the chant that gave the general shape of the melody for each syllable: that is, whether the line ascended, descended, and repeated pitch. They may have also indicated ideas about performance style, which my book glosses over in a way that makes me think there's a long academic argument happening behind the scenes. They did not specify exact pitch or interval, so they only served as reminders of a melody still learned by oral tradition.

Next were "heighted neumes," where neumes' vertical position above the text began to indicate the relative size of intervals, making the melody line clearer but still not giving exact pitches. This was not widely adopted until some clever, anonymous monk scratched a single line around which the neumes could be oriented. In this way, the notation still didn't specify exact pitch, but intervals were clarified.

The monk Guido of Arezzo (ca 991-1033) suggested a refinement to this system, where a line of red ink meant the letter "F," yellow ink meant "C," and two other lines for "A" and "E" were scratched into the parchment around them. These four lines eventually became the four spaces on our modern five-line treble staff. However, scribes could just as easily make the lines stand for other notes, and simply indicate a sign for "C" or "F" next to the appropriate line. This is what our clefs do today: the dots of the bass clef surround the F, the treble clef circles the G, the alto clef embraces the C, etc.

This notation was revolutionary but still lacked a rhythmic component, and was limited to use in the church, primarily as a memory aide rather than a means of initially learning music. When multi-voice pieces began to be written down on the same staff, scribes didn't even feel the need to coordinate the voices. (That is, notes that would be sung at the same time are not written in the same vertical space.)

Rhythmic notation didn't appear until the 1100s-1200s, from a group of musicians associated with the University of Paris and the new Notre Dame cathedral. They were responsible both for a more florid style of chant and the means for writing it down, using "ligatures," or combinations of notegroups, to indicate different rhythmic patterns. which were always based in triple times (3/8 or 6/8). This system was fairly rigid, and the more composers ornamented their melodies, the more they needed a new system of notation.

The Art of Measurable Music (Ars cantus mensurabilis), written around 1280 by Franco of Cologne, codified a new rhythmic notation now called "Franconian." Now, for the first time, relative note durations were signified by note shapes. This has remained the case in Western music ever since. In Franconian notation, the basic unit of time, which we can imagine as a quarter note for the sake of simplicity, was called the tempus; three of them together made a perfection, or measure of three beats. A "long," or a rectangular notehead with a tail, could last for two or three tempora depending on the need to fill a perfection; a "breve," or rectangular notehead, could last for one or two tempora, again depending on the need to fill a perfection, and a "semibreve," or diamond notehead, could be one-half or one-third of a tempus. Thus, the system was exact but still required some mental math and assumed a triple pattern in the rhythm.

A new French musical style (literally called Ars Nova, or the New Art, covering approximately 1310-1380) emerged out of two innovations in rhythmic notation. One: duple or "imperfect" divisions of note values were allowed alongside triple or "perfect" division. Two: the semibreve could be divided into minims (diamond-shaped noteheads with a vertical line attached to their tops), reducing the smallest possible note value. Around 1340, another new innovation, "mensuration signs," or the ancestors of modern time signatures, appeared. These mensuration signs would tell you, essentially, whether you were in 9/8, 3/4, 6/8, or 2/4 time. For the first time, now, the shape of noteheads could indicate durations that remained unchanged by the notes around them -- meaning composers could for the first time write down syncopation.

Our modern rhythmic notation is a direct descendant of Ars Nova notation. Around 1425, scribes began to write all the notes with open noteheads (sometimes called "white" notation), presumably corresponding with the switch from writing on parchment to paper and the corresponding not to ruin the page by scratching through it. Renaissance composers added shorter and shorter note values, filling in the head of the minim and adding one or two flags to its staff, while gradually the long fell out of use and the breve became more infrequent. Around the end of the sixteenth century, diamond-shaped notes fell out of use in favor of round noteheads. Bar lines appeared in the seventeenth century, and our modern rhythmic notation was more or less complete.

As a side note, tabulature (writing down what strings to pluck on an instrument rather than the note those strings sound) has been around since at least the Renaissance era. It has the advantage of being easy to learn for performers and of easy transposition into other keys, but also lacks rhythmic notation.

Let's see here. Other things I left out. Accidentals can trace their origins back to Guido of Arezzo, whose solmization system (ut, re, mi, fa, sol, la) allowed sight-singing of hexachords, the basic unit of music theory at the time, based on the intervallic relationship whole-whole-half-whole-whole. The hexachord could be found in three positions: on C, G, and F. The hexachord on G (g-a-b-c-d-e) used B-natural, and wrote it as a "square b"; the hexachord on F (f-g-a-bflat-c-d) used B-flat, and wrote it as a "round b." The "square b" and "round b" over time evolved into our natural, sharp, and flat signs, but their original purpose was to indicate whether B should be sung in solmization as mi (for the G hexachord) or fa (for the F hexachord).

Dynamic markings were first used by Giovani Gabrieli (1557-1612), to indicated contrasts between two choirs singing simultaneously. They were used sparingly until pretty much the eighteenth century, until instruments became capable of greater dynamic shade and variety; especially, the piano, whose hammer motion was capable of touch-sensitive dynamics, replaced the harpsichord, whose plucked-strings motion was not.

Dynamics and expressivity like phrasing or stacatto have always been present in music, but before at least about 1800 their use was primarily determined by traditional performance practice, passed from teacher to student and from performer to listener. Even music from the Baroque period has a lot left off the page, from expected ornamentation to shades of dynamics and phrasing. As composers became more and more artists in their own right (where performers had always been the stars before), and art after the Enlightenment got more interested in interacting with quicksilver shades of human emotion, more and more expressive markings were written down.