Why Does Music Only Use 12 Different Notes?

In typical Western

music

we write all of our

music

using

only

12 single

notes

c c sharp d d sharp e ff sharp g g sharp a a sharp and b of course, on an instrument like the piano we have many more than 12 keys to play, but each of these keys is just a

different

version of one of those 12 unique pitch classes, however, as I explored in my previous video on micro tenanity, there are actually more than 12 unique pitch classes that we can choose from

notes

like middle C sharp or C flat half, in fact, pitch is a spectrum with possibly an infinite number of

different

notes available, so why do we

only

use these 12?

Well, the first thing to note here is that these notes were not selected for their particular frequencies, the frequencies themselves are not really what is important. When it comes to making music, for example, we can tune all of these images and as long as we tune them all by the same amount, the piano will still sound as harmonious as ever. It is not the frequencies of the notes that matter, but the intervals. between those frequencies a melody is not really a sequence of notes but a sequence of intervals twinkle twinkle little star is not defined by being these notes or even these frequencies but being these intervals you can choose any tone for the first note and then Whenever you apply this order of intervals you will get a little twinkling star, that is why if we transpose the song to a different key it will still sound like the same song, so going back to the initial question, why

does

western music only use 12? notes well expressed in a few words, it is because these 12 notes are the most practical and effective way to play all the intervals that we consider useful for making music, so what are these useful intervals and why 12 notes in an octave are the best way to access them?

Although musical intervals are technically subjective, most humans will agree on the same handful of images, since the most consonant are the most pleasant and musical. It is widely accepted that the octave is the most consonant and most important interval in music. Separate notes and octaves sound so good together. so complementary that they are actually perceived as deeper or higher versions of exactly the same note, this is called octave equivalence and is why notes separated by an octave are given exactly the same name as each other, for example a and a, The one octave interval is also the simplest relationship we can have between the two frequencies to go up one octave, all you have to do is double the frequency, so one octave above 220 hertz is 440 hertz, a relationship From two to one, this also means that a string that is half the length of another will sound exactly one octave higher, since it will vibrate twice as fast because notes separated by an octave are perceived as different versions of the same note. .

Most tuning systems around the world, including the Western 12-tone system, prioritize the octave and then find a way. To divide the octave into different notes, the Western way of dividing the octave into 12 different notes

does

a great job of allowing us to access our most important musical intervals, so let's go over those intervals now and add the next two most important ones to this keyboard. The consonant intervals are generally considered the perfect fifth and the perfect fourth. Now, of course, we only chose these intervals because they sound good to our ears, however, interestingly, just like the octave it had a simple relationship between its two frequencies, the perfect one.

Fifth and perfect fourth also have very simple relationships between the two notes to go up an octave we multiply the frequency by two, while for a perfect fifth we multiply it by one and a half or for a perfect fourth we multiply it by one and a half third, of course, As I said before, we do not consciously choose these intervals because of these simple relationships, but it turns out that the more consonant an interval sounds to us, the simpler the relationship between its two notes is and this, as you can imagine, is not a coincidence when two frequencies are related to each other by a simple relationship like two to one, the wavelengths of those frequencies will align perfectly and synchronize perfectly and this perfect alignment of frequencies is generally considered to be the reason these intervals are perceived as consonants. with explains to us why they are perceived as harmonious if we play two notes that are not synchronized together in this way you can hear the dissonance the octave the perfect fifth and the perfect fourth are widely considered the most consonant and pleasant intervals after these three through of the order in which different people can rank, the remaining intervals will begin to vary;

However, they will generally follow an order similar to this: the major third, the minor third, the major sixth, and the minor sixth, and as you may have guessed, these intervals once again have simple relationships to the initial note, so now we have all intervals that are generally considered consonants. The remaining intervals offered in the Western 12-tone system are considered dissonant, but this does not mean that they are not useful to us, although dissonance in music seems like something you would want to avoid, music without any dissonance can sound pleasant but it will lack drama or suspense, it will not have a sense of tension and release, so let's add these traditionally more dissonant intervals, these are the key or major second. the minor seventh, the tritone, the major seventh and the semitone or minor second.

These are the twelve intervals available to us in the Western 12-tone system, but why can't we just add a couple of extra images between some of these, for example one? neutral third which would be between the major and minor third or we could have a note between the major seventh and the octave creating a sort of ultra seventh or ultra leading tone, although we can't really just add these two extra microtonals. intervals and leave it that way because it is very important that the notes between the octave are more or less equally spaced, this allows us to easily play in different keys and generally makes the instrument much easier to play with the standard 12 pictures in the eighth. the notes are naturally spaced at fairly equal distances from each other, but if we add just a couple of tonal micronotes this way, it will destroy that equal spacing.

If we are going to add more notes beyond the standard 12, we will need to find an alternative way to evenly divide the octave that still allows us to play all the most important intervals like the perfect fifth, perfect fourth, etc. Nineteen notes in the octave is a pretty good alternative. Nineteen notes evenly spaced in the octave still allow us to play our most important intervals, such as the perfect fifth, the perfect fourth, etc., and at the same time allow us to access a wide range of other microtonal notes. Another option is to have 24 notes in the octave by adding a new microtonal note between each of our 12 standard images.

Of course, it maintains all of our standard intervals while adding a wide range of new microtonal notes. Some musicians have written music using systems like these. Evan Wistenkratsky, for example, developed a quarter-tone piano that features 24 notes per octave, but as you can see, having access to these extra notes makes the instrument much more confusing to play, although 19 notes per octave or 24 notes per octave allow us to play a wide range of additional microtone intervals. I think most musicians would agree that these additional microtonal notes are not useful enough. To justify reducing the playability of our instruments, of course some instruments like the violin or trombone do not have to be modified to access notes between the standard 12, but instruments like these are still built to optimize 12 notes in an octave in the design of the instrument.

The size and shape depend on making sure the instrument can comfortably access 12 notes in the octave. The design of a musical instrument must strike a balance between being comfortable and practical to play and having access to as many notes as possible, and it works. That over the centuries we have come to the conclusion that 12 notes in an octave repeating up and down on the keyboard is the best solution for this compromise. 12 notes in an octave is the best way to access the most consonant and useful musical intervals while optimizing the playability of our instruments, that's right, we've found our 12 notes, so now we can simply double each one of those frequencies to get another set an octave up and we could halve them to get another set an octave down and if we do that a couple more times we'll end up with the full duration of a modern piano.

The jobs are okay, well, not quite. There remains one more topic to discuss temperament. Look, right now we have tuned our instrument to what is called just intonation. Our intervals are. tuned in perfect proportions, which is ultimately the purest way to tune an interval, but although this is the purest way to tune our intervals, it presents a problem. Remember when I mentioned before that our notes need to be evenly spaced if we are going to be able to play well in different keys, even though the 12 just intonation notes are quite far apart, they are not perfectly evenly spaced, this is because each interval was tuned using a different ratio away from the root, for example the fifth between a and e are a perfect ratio of three to two and this means that if we play some music in the key of major it will sound really pure and perfect, However, if I try to play in a key other than E-flat major, for example, things aren't going to sound as harmonious.

The problem here is that even though this perfect fifth between A and E was a perfect relationship of three to two, the perfect fifth between E flat and B flat is not, when you change the key you are effectively changing the path , so unless you retune your instrument relative to that new path, every time you change keys other keys will simply sound out of tune, this is really limiting as we want our instrument to be able to sound good in any key not to mention the possibility of playing chromatically outside the key, so how can we fix this well with something called temperament if we want to be able to play multiple keys on one instrument and play chromatic music that goes outside the key that we?

We will have to adjust or moderate some of these intervals. The way these intervals are adjusted to make the tuning more versatile is called temperament and throughout history various temperaments have been used, each finding its own way of achieving a compromise between preserving how these intervals should sound and being able to play in different pitches and keys, the system we use today and which has been almost universally adopted is called twelve-tone equal temperament. Twelve-tone equal temperament ensures that each note is exactly the same distance from all other notes. so, in equal temperament, a perfect fifth between a and e will sound as in tune as a perfect fifth between b flat and f or d and a or e and b.

The way this is accomplished is, instead of tuning each interval as a perfect ratio, we simply tune the octave as a pure ideal ratio and then divide the space between each octave into 12 equally spaced notes. This division does a pretty amazing job of approximating these intervals, but of course, aside from the octave, the intervals in 12-tone music with the same temperament are no longer exactly perfect proportions and are therefore slightly out of tune. Some equal tempered intervals are only slightly different from their pure intonation counterparts, for example the perfect fifth and perfect fourth are only 1.96 away from their ideal pitch, however some of these intervals are significantly higher. or flatter, a major third of equal temperament, for example, is more than 13 sharper than it would be in pure intonation.

You can hear this difference more clearly in the chords if I play a C major chord in our usual twelfth equal temperament key, you'll hear a wah wah sound. Because the three chord images are not perfectly in tune with each other, this wah-wah sound is called a knock, however, if I tune the C major chord with intonation alone, this knock sound disappears, although as I mentioned almost all the musical pieces. that you've ever heard has a 12-tone equal temperament, so even though these intervals are slightly out of tune, they're in tune enough that we don't really notice any kind of difference when we listen to our music, so I hope this video has at least partly answered the question of why Western music generally uses only 12 notes for such a simple-sounding question.

The answer can actually be quite confusing, sincewhich is a tangle of history, physics and human preference and of course need not be limited to just 12-note microtonality, for example, is music that uses notes beyond and among the standard 12 images and many non-Western cultures around around the world use completely different tuning systems. In fact, I'm planning a future video on how different cultures around the world approach tuning and tone, so if you're trained in a non-Western style of music, I'd love to hear from you. I'm also very grateful to mod art, who gave me a copy of their piano tech software to help me make this video. a super versatile piano plugin that allows you to tune your keyboard to any possible tuning, so I thought it would be appropriate to conclude this video with this piano piece that I composed with just intonation and, as always, a huge thank you to everyone who supports me . on patreon including adam granger andrei scientiagia andrew andrew brown andy deacon austin barrett austin russell bob mckinstry britney parker bruce mount cameron all available chris Cabell christopher ryan kieran bennen darren harvey d david lee fish david defunder dr darren wicks elena scorchenko espen hansen eugene leroy eyes fd hodor gillamo latona james kao j.a cookensberger joe watson jonas sodastrom justin vigger lavender monroe meg fellows squared tune composers michael vivian nancy gillard paul miller paul hazelpeter dunphy roger clay sam lin steve daly thomas armstrong tim beaker tim payne toot vidad flores and vladimir kodakov you