If you take an instrument without predefined notes, such as a trombone or a violin, you can produce an infinite amount of notes between Do and Re for example (applies with out of tunes instruments as well). With that logic, you could have an infinite set of 7 notes that are as evenly « spaced » as our current standard. Im sure im missing something obvious.
In: Physics
I disagree with some of the current comments. The real reason is historical and based on various compromises and practicality. I will keep the explanation simple, happy to elaborate.
There are ways to construct scales using the natural patterns of string vibrations or air vibrations in tubes. Under specific conditions, harmonic overtones are produced which is known as the overtone series. Many cultures have experimented with this and the reason it is pleasing has a neuroscience based explanation. In principle, something like the major scale (do, re, mi,…) could be constructed from this but in practice it does not work and does not match the exact notes we use today.
Pythagoras attempted to construct scales using just the ratio of 3:2 (perfect fifth, or do to so) , called Pythagorean tuning but this will fail to produce a scale they fits into an octave for mathematical reasons. As a result, many musicians and mathematicians in the European world produced alternative over the course of 2500 years. Most of these compromises came from altering notes in the scale slightly to force them to fit but came at the expense of sacrificing the “purity” of the notes as they would deviate from the pleasing sound of the overtone series.
For a lot of musical history this did not matter too much if you had a choir, which dominated a lot of church music in Europe. But as soon as you start using many instruments together, which come with various restrictions about the notes you can play, unlike the human voice which is extremely flexible, you run into problems and get clashing notes or need to retune each instrument.
As music theory developed in Europe and larger ensemble of musicians playing became the norm, as well as experimenting with changing keys in music, things became more standardized. Further, European music became dominated by harmony instead of just pure melody which means more notes have to work together and sound good. By the 1800s a musical standard was agreed upon in Europe which was to maintain the intervals of the overtone series as much as possible while also cramming the notes into the octave. The end result is all keys sound the same, unlike alternative tuning systems in which keys can literally sound different because the notes are tuned differently. But we lose the “pure” quality of the overtone series, particularly for intervals of thirds, sixths, etc. However, now musicians can play together easily and you can change keys without retuning your instrument. This is now known as equal temperament and the major scale comes from this tuning, which itself is based on Greek church music traditions. So as you can see, this is historically driven.
Note that many cultures around the world developed alternatives they worked for them that are very different from equal temperament. The reason they had fewer issues is because there was less emphasis on harmony in these cultures so it largely did not matter. However, as Europeans colonized these societies, they brought their music with them. Just as the English language, religion, and other European traditions became the norm around the world, the music systems of other cultures were also replaced with equal temperament and it’s now the world standard. However, if you look closely, there are many cultures still keeping their old music alive.
Tl;dr it’s a historical and practical tradeoff driven by European musical traditions to try to mathematically approximate musical frequencies that occur in nature under specific circumstances.
One final note that although the overtone series is pleasing to many old cultures, this is also largely a question of habituation. The majority of people alive today are used to equal temperament so it sounds good to you. Music from the overtone series is often perceived as “out of tune” because you are adapted to how music should sound. If you listen to music writen in other tuning systems for long enough and go back to equal temperament it will sound strange to you until you adapt to it again. I’ve done this myself with 13-edo (equal divisions of the octave) music.
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