3 Ways to appreciate modern intonation will also increase your understanding of music theory and music history.
The answer is complex, tangled in history, physics, and human performance. A related question is why are there only 12 notes in the chromatic scale? Mathematical ratios, human ingenuity, and cultural norms provide the answer.
Where did our modern intonation come from?
How did we get our 12-tone scale?
Mathematics from the Pythagorean theorem starts us out with the octave and perfect 5th. Octaves and 5ths worked well because they were consistent, but not 3rds. The most popular interval in this approach is the octave. To help you appreciate modern notation the chart below shows the consonant progression from the octave to the tritone (augmented 4th).
Just intonation, referred to as pure intonation, consists of tuning musical intervals in whole number ratios of frequencies. An interval tuned this way is pure.
Just intervals (and chords created by combining them) consist of tones from a single harmonic series of an implied fundamental. An implied fundamental could be an octave.
Western musical rarely uses pure intervals. The need for different keys using the same intervals makes using just intonation impractical. The benefit of just intonation is that the intervals sound very consonant, and pure to the ear – at least until there is a need to change keys.
Changing keys is common in singing. Songs are representations of intervals and can be transposed. But changing keys in just intonation makes the intervals start to fall apart and sound more out of tune. Adjusting this can help one appreciate modern notation.
Interested in more information about Music Theory? Here’s a book I recommend.
12-Tone Equal Temperament
And the solution is… 12-Tone Equal Temperament (12-TET)
A better solution for Western music is called 12-Tone Equal Temperament (12-TET). Rather than forcing frequency ratios to pure-sounding whole number ratios, it makes a compromise to divide each octave into twelve equally-sized intervals and adds them together to get larger intervals. The resulting 12-tone equal temperament derives from an octave split into a series of equal steps. Has this content helped you appreciate modern notation?
Below are some resources for further information: