1 - Why There are Twelve Notes in Music

[@MYKEDANGER]

"I'm not out of tune, I'm just playing one of the hundreds of notes in an octave you just don't know about."

[@DavidSmith-dn4vj]

The way your smile just beams The way you sing off key , key, key The way you haunt my dreams No they cant take that away from me

[@jasoncorley5703]

THANK YOU!

[@kenjohnson6101]

Have you ever tried tuning a 12-string guitar? If you tune the paired strings the the exact same pitch it just sounds flat. A very slight detuning gives it a rich, concert-hall sound.

[@MYKEDANGER]

@@kenjohnson6101 Amazing!

[@ottolehikoinen6193]

@@kenjohnson6101 the common technique is to tune one string a bit above and the other a bit low. Really vibrating sound.

[@arah8998]

I can't understand why people are complaining that this explanation isn't clear. This explanation is really clear to me

[@marcocosentino7239]

Of all the problems one may have with having 53 notes in an octave, I'd say software is pretty down the list

[@James-nr9gm]

Software doesn't care. It's the one thing that isn't a problem.

[@martinh1277]

That's a good Idea! If you see "Millers magical seven (plus-minus two)", then seven is the number of things we can notice at first sight and we don't have to count. Not more than seven notes in a system makes it easier to understand the music. Therefore we have a system with 7 notes. We read, we have 12. Are there really 12 or what happens here?

[@noahlovotti7722]

You can take a scale of certain notes out of 53edo and create a .scl file out of it.

[@massimookissed1023]

I wouldn't want to try moving the piano that had 53 keys per octave.

[@str2254]

This color interpretation is awesome !!!!!!!!! Like there are almost infinitely many colors but we don't care about and just name the ones that are actually different from each other

[@StevenJacks]

Exactly this. Nice comparison. : )

[@darkmysterytemple]

@@StevenJacks yes, I like the color analogy too. And when different people hear the same music some will hear more differences than others due to biological differences just like with eyesight.

[@angelmendez-rivera351]

Not "almost" infinitely. Actually infinitely.

[@theresa.y5221]

@@StevenJacks What is this site?

[@theresa.y5221]

What is this site

[@marcmagee5975]

tl;dr version: Because of math you get 12 or 53 notes. 12 is an easier number to work with. They also fudged the exact tones later. To make it easier to work with.

[@xuly3129]

19 tones?

[@CheekyFest]

maths*

[@clemalford9768]

In Indian classical music there is a theoretical debate whether there are 22 or 24 srutis (microtones) in the octave. It all depends on factors such as the division of the scale. 12 semi tones are there in the scale but how are they divided up determines the type of scale. Even temperament has become the default scale in western music due to harmonic relationships although there are others. In Indian music there are mathmatically thousands of ragas but only a few, maybe 200, that are actually popular. Some different schools of performance (Gharanas) actually play certain notes slightly sharper or flatter depending on the Raga and its tradition so to the western conditioned ear it may sound slightly out of tune but in that Raga context it is essential.

[@2adamast]

Even temperament sounds slightly out often of tune (by design) so nothing wrong with other out of tune systems. I remember naively taking a calculator to try to understand the mess even temperament chords are.

[@panteraforever9411]

Tnx a bunch for the info !

[@bhaskarmaity2890]

Well Sir, as far I am concerned Indian Classical music is out and out different from Western Classical music.

[@clemalford9768]

@@bhaskarmaity2890 Yes no question about that. Different developments over time. Western art music went for the melody, harmony, polyphony, orchestrated ensemble route while ICM went down the road of melody and rhythm. Raga and Tala, Of course, the melody was and is highly ornamented and the rhythm very mathematically developed and precise. There are two systems in Indian music, Karnatic and Hindustani, southern and northern but both are very similar only exposition and technical aspects differ such as the specific use of Shruti. There are some very good duet recordings that demonstrate that. One, in particular, is Pandit Bhimsen Joshi and Dr. Balamurali Krishna performing Raga Bhairav.

[@bhaskarmaity2890]

@@clemalford9768 You are absolutely right.

[@olddoggeleventy2718]

You lost me when low became high and high became low. With that said, I believe I'll get low.

[@keithgood3419]

LOL!!!!

[@iamsammybe]

I agree. I don't understand why he would do that.

[@jusithor]

@@iamsammybe "For the sake of the video let's invert the whole thing so no-one can follow anymore"

[@robertoriggio117]

If you study modal music of the Middle East and India, you will find that there are many more notes per octave, but they are generally grouped into varying diatonic sets of seven pitches per octave. (Of course there are exceptions to this, but generally speaking it is so.) So, to use western solfège, you may have various modal pitch relationships where, if each mode were reduced to a scale starting on the same do, the interval between do and re (or any/all other scale steps) would be different from one mode to another. It is true of all of the systems (e.g. Turkish, Arabic, Persian, Hindustani, Karnatak, etc.), but in the Turkish system in particular, there are many variations of each solfège syllable relative to the tonic, and it also uses various special accidental symbols to express this in western-style notation. And if you attempt to scientifically analyze the pitch of vocalists from any culture, you will also find quite a variety in intonation which may pass and even be considered good in music performances. So, if you allow for such variation on each pitch, I would say that more universal than the concept of12 notes per octave is the concept of seven diatonic notes per octave of varying intonation. Some pieces may use more than this, yet there is often something in the way they are used which implies that some of the extra pitches may be considered alterations of other pitches. And, then, of course, there are those systems which intentionally aim to flout these rules, of course, very academic ones. It is a topic of endless interest and debate!

[@robertoriggio117]

This analysis is based more on observation of composition and performance practice across cultures than on the inherent properties and mathematical relationships between frequencies, btw, though there is some analysis of those relationships as a matter of course.

[@elbschwartz]

Exactly. It's not like in Europe, they invented a 12 tone system first and then started making music with it. It's a result of taking the diatonic scale and transposing/modulating it. It's even built into Western staff notation; there are only 7 pitch classes, A B C D E F G.

[@andresmondaca6173]

I don't know why there is so much hate in the section comments, i think this video is awsome and really simple to understand. TY Steven, this is a great work!

[@angelmendez-rivera351]

It is not hate, just criticism. The video has genuine flaws and inaccuracies to it. It being otherwise simple to understand does not excuse those flaws.

[@andresmondaca6173]

@@angelmendez-rivera351 no

[@angelmendez-rivera351]

@@andresmondaca6173 Saying no is not a counterargument.

[@andresmondaca6173]

@@angelmendez-rivera351 yes

[@angelmendez-rivera351]

@@andresmondaca6173 Okay, I understand you lack the ability to understand and have a conversation with the intellectual and emotional maturity of an adult. Have yourself a nice day/night.

[@Rcknrll666]

Visualizing sound frequency(cymatics) will be the key that unlocks pyramid building technology. As a stone mason of 13 years & musician of 20, im convinced that they were sonically tuned structures. Sound is the highest art

[@KaiCyreus]

Would've loved a lot more auditory demonstration/examples here

[@bambiknow]

exactly!!!!!

[@noahlovotti7722]

Xenharmonic wiki has audio examples

[@fgonzalez90]

Although the 53-notes-per-octave system is way more complex than the 12-notes one, it has a notable advantage: Harmonically, and wisely used, it's an EXTREMELY flexible and good sounding intonation system, with very sweet 3rds and 6ths (detuned by negligible 2 cents from just intonation), and tolerable septimal intervals, without sacrificing the purity of the 5ths and 4ths (as in meantone temperaments). As it has no "wolf intervals", you can modulate with total confidence from ANY key to another. And it's mathematically wonderful, so you can use the infamous C256/A432 pitch reference. It's the perfect tuning system for OCD-musicians like me, haha...

[@StevenJacks]

Well said. I agree 100% :)

[@jameslouder]

A correction, if I may. You say that Equal Temperament was "big in the 16th century." Although the 16th-century musicians knew about Equal Temperament, they did all they could to avoid it. They usually tuned their keyboards in a system called Meantone. Meantone, is beautifully in tune, but only works in certain keys. There are other keys that can't be used at all. To get around this there were experiments with harpsichords having 14, 19, and even 31 keys to the octave. But for the most part they simply accepted an octave with C, C#, D, Eb, E, F, F#, G#, A, Bb, &B In singing and on instruments without fixed pitches (trombones, violins) performers aimed for something approaching Just Intonation, where there are no enharmonic equivalents (e.g. C# and Db are different notes). The big exception was fretted instruments, i.e. the viol and above all the lute. These were indeed fretted in something close to Equal Temperament, but the operative word is "close." Because the frets were made of gut and tied onto the neck (unlike the fixed frets of modern guitars), their positions could be nudged and tweaked to obtain better intonation. Equal temperament gradually came into general use over the course of the 18th century--from about 1750 onwards, But it was not until the mid-19th century that rigorously exact Equal Temperament became the norm. However, this was not entirely the happy conclusion that it's often cracked up to be. The American musicologist, Ross W. Duffin, has written a short and witty book, addressed to non-specialists, called "How Equal Temperament Ruined Harmony (and Why You Should Care) [Norton, New York, 2007] which will repay the interest of anyone who is really interested in the history of our supposedly 12-note scale. Check it out.

[@aleisterjames]

I started reading your comment and was wondering if you had read "How Equal...", and lo and behold! A great book, and a must read for anyone really interested in understanding how music works, I'd say. I have developed a system for tuning my guitars that grew out of what I learned from it... The result is better than with any tuner I've tried.

[@jameslouder]

@@aleisterjames I remember, when I was first trying to learn the guitar, how perplexed I was that F# on the first string sounded so abrasive in a D major chord, although it seemed to be just fine in B minor. It was not until later that I began to realize that there was more to this than meets the eye--literally the eye on the 12-tone page. It was the writing of Casals ("The piano is out of tune!") that first sent me inquiring deeper into temperament. Like you, I found my own ways of sweetening things up, which sometimes included letting octaves beat just a tiny bit. It's easy enough to adjust for the piece at hand. In the end I didn't become a guitarist, but rather an organbuilder, which gave me cause to delve into the whole subject very deeply. Equal temperament sounds just awful on the pipe organ because those beating thirds go on and on, instead of dying away in decency--the only thing that makes them tolerable on instruments with struck and plucked strings.

[@robb3724]

I kept scrolling down to see if someone would offer a comment like this. Thank you much!

[@gregoryreese8491]

I appreciate your having taken the time to compose this-a very, very worthwhile comment.

[@jameslouder]

@@gregoryreese8491 Thanks for your kind words--I'm glad you found it helpful.

[@NM-zq5tf]

Why don't you actually play the notes in the 53 note octave? So frustrating, you talk about it, but we don't hear it

[@EshwenAudanal]

Search for 53 tet, 53 edo or 53 ed2. There's lots of music played with different numbers of notes. 10edo is my favorite.

[@DeepakChauhan-gb3tf]

Agree agree

[@davidaustin6962]

No human ear can tell the difference between two adjacent notes in a 53 note octave so if played in sequence it would just sound like a smoothly increasing frequency.

[@kakurerud7516]

played in sequence it would just sound like a pitch bend

[@Coneman3]

Yeah music has to be heard man!

[@--kanal--]

In my opinion, the video still does not justify the choice of 2:3 ratio. Would be very nice if scales using a few other ratios (1:5, 2:5, ...) were also developed, so we can hear how they actually sound and clarify why they do not sound as good as 2:3. I guess another approach could be to look at the overtone series, flattened into a single octave (dividing each frequency by two as many times as needed). Chances are the pitches will group around those 12 points. The notes that emerge at first actually group around notes found in a major scale (in the example of C major, including both B and Bb). The first note that is not the same as the fundamental is the perfect fifth, implying the naturally close relation of a note and its fifth, leading to the circle of fifths, etc. Adding equal temperament to this then defines the ratio of a semitone.

[@miroslavkaspar2246]

i believe its because 2:3 just sounds nice to our ears. If you draw two sinus wave function with their frequency ratios 2:3, they would nicely overlap. so yea maybe that's the cause for taking 2:3 instead of others

[@exedeath]

I would say its, problably because 3 is the next harmonic after 2, and 3/2 is 3 reduced to octave. What I dont know is why they reduced it to the octave. Anyway, using 3 instead of 3/2, the best result is still 12 for numbers below 53 and the next number after 12 is still 53. I guess the result is the same.

[@foolapprentice3321]

Get a tone generator and try it

[@eldarsadykov]

If you start with pure fifth (3/2), then you have 12 notes that are almost equally distrubuted inside an octave. But with pure third (5/4) you have only 3 different notes, and then everything starts to duplicate. In addition, everything above 5/4 starts to sound too dissonant.

[@michaeltrinastic]

The video does explain the choice of the 2:3 ratio (right around the 14:00 mark). Essentially it's because 2:3 is the next simplest ratio after 1:2 (where "simple" means using the lowest possible whole numbers). 1:2 can't generate an interesting scale because it only generates octave equivalents of the starting pitch. 2:3 is the simplest ratio that can actually generate a scale.

[@rarebeeph1783]

If you use either of the ratios 5:3 or 5:4, which are thirds and sixths (not particularly dissonant), instead of 3:2, you get a 31 note scale.

[@StevenJacks]

Very cool! How does it sound?

[@JohnSmith-iu3jg]

Project Overturn aka RareBeeph among a series of others

[@CephaloBooks]

@@StevenJacks kzbin.info/www/bejne/f4iod5uLipqFeZI

[@aeromodeller1]

@@CephaloBooks And kzbin.info/www/bejne/aGSsnomCmt-JasU The tonal system does not make the music. A composer working with a tonal system makes music. This tonal system includes a very good approximation to a 12 tone scale and standard music may be played in it, sounding just as you would expect. But 31 tones allows the composer to use many more tones. Don't judge the 31 tone system from this one composition.

[@jameslouder]

"Not particularly dissonant..." Make that not dissonant at all. The 5:4 ratio, which yields a 31ET scale, is the very ratio of the pure, beatless major third. People think of microtonal music as avant-garde stuff of the 20th-21st century, but the first experiments with this microtonal temperament were carried out in the mid-16th century (!). In 1555 an Italian Renaissance composer and theoretician named Nicola Vicetino published a book on the subject with a design for a harpsichord that could actually play such music. The 31 notes were distributed over two keyboards. Instruments of this kind were actually built and one from around 1600 still survives in a museum. Below is an example of Vicetino's music played on a modern reconstruction. While the melodic lines wander into microtonal territory, the harmonies always remain beautifully in tune, thanks to all those pure thirds. kzbin.info/www/bejne/mJmqqJ2dj52tf7s

[@UberOcelot]

It's really all about providing harmonic movement, where whatever key you're in can take advantage of just about every interval. The few highly dissonant chords then are easily memorized and used appropriately for effect. With 53+ notes per octave, most of those notes exist just to have a perfect interval for some key that you're not currently in, and otherwise need to be memorized for which intervals you actually are supposed to use. Then you have too many flavors of dissonant intervals which will likely never get used.

[@tonyhill8963]

I don't find this to be a very clear explanation at all. In many ways, it actually creates more confusion than clarity.

[@MST339]

Such approach is inspiring though.

[@Whatamood]

u are just too stupid

[@aaronheaton2606]

Perhaps because he never really says why there are 12 tones. I wanted a deep psychological dive into the human mind and maybe even the spirit of God and the very nature of existence. This 12 thing goes pretty deep an isn't confined to music. I am also very curious how eastern theory ended up with 24 tones and what that could mean spiritually for them.

[@aaronheaton2606]

@@Whatamood if you think this video contains any of the whys of 12 tones then you have no room to insult intellect. The closest this video gets is when it talks about dissonance but even that is a mere snowflake on top of the tip of the ice burge.

[@TheSteveSteele]

Aaron Heaton How about an alternate explanation? Care for one?

[@lymansn]

Interesting demonstration of pythagorean tuning. For western music the greeks were the first to figure it out. It started off by the natural harmonics series generated by wind instrumetns such as Horns and Flutes and then they applied the same mathematical ratios (golden ratio) to strings. Pythagoras invented the pythagorean tuning of (3:2) perfect fifths and Octaves (2:1) to matching naturally occuring harmonic overtones. Later the greeks invented 7 modal scales based on pythagorean tuning. 7 tone Modes with 8 notes in a scale. These scales were Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian and Locrian. We still use Ionian (Major) and Aeolian(Minor). Like you mentioned the flaw with natural harmonics is that the octaves between each mode were slightly off from each other. Aristoxenus in the 4th century BC invented the 12 tones between octaves. In the early 1700's J.S. Bach was a big proponent of the using the (Tempered Scale equalizing the 12 tones by going sharp or flat between each tone to equalizing the natural gaps between each of the 12 semitones within an octave. Brass instruments in the baroque period had a bag of different sized crooks to adjust for each Key that they played in. String Instruments also had to retune for each key change. By using the tempered scale you could switch between all of the different keys without re-tuning.

[@lamsonian]

Awesome 👍 Thank you for truthfully elaborating where he left off.

[@chrisjamesr77]

Well, we still do use the other modes, too, though not as much maybe! Personally, I enjoy trying to write things in Lydian, it has a cool kinda sound to it. Though of course it's a little different because we're not using Pythagorean tuning, I suppose

[@theultimatereductionist7592]

The number theory of seeing how close 2^x can get to 3^y is maddeningly difficult & deep.

[@Zachariah-Abueg]

as a lover of math, i'd love to see resources on this!

[@coolrocknroll]

This seems to be very brilliant. When I have evolved from an alpaca to a vicuna I believe I will be able to understand it. Thank you!

[@TedBoyRomarino]

Alpaca and Vicuña reminds me of the charango

[@angelmendez-rivera351]

1:28 - 1:38 This is known as octave-equivalence, which by the way, is not universal among humans, and is not employed in all musical scales. The Bohlen-Pierce scale is an example of a scale that does not use octave-equivalence. In many areas of South Africa, there exist many scales for semi-percussion instruments which do not employ octave-equivalence as well. These are only a few examples. In Western music theory, though, octave-equivalence is always employed. If two pitches differ by a power of 2 in ratio, then they represent the same pitch class. 1:38 - 1:48 This is an exaggeration, but yes, it is rather common in human civilizations. 1:48 - 1:54 No. Many civilizations did not use instruments with strings. 1:54 - 1:57 Well, *now,* yes, because Western music theory has been exported to the rest of the world, but it is historical negationism to say it was always the case. 1:57 - 2:25 Since the speed of sound is constant, meaning it does not vary from place to place or from time to time (technically, it does vary, but the variations are negligible), we have the velocity equation v = λ·f. Here, v is the velocity, which is always the same, and λ is the wavelength of the sound wave, which is proportional to the length L of the string. What happens here is that if you double the length of the string, then you must half the frequency f in order to keep the same velocity. This is why the relationships are inverted. The perfect octave is defined as the pitch interval corresponding to the pitch ratio 2, which is the inverse of 1/2. The shorter the string, the higher the pitch, all because of v = λ·f. 6:05 - 6:15 "Problem" is in the eye of the beholder. Turkish music, and certain forms of ancient Chinese music, have used and currently still use this system, for example. Even some American composers have used this. Of course, pianos would not be able to accomodate this without a major overhaul in design, but there are many instruments that can accomodate for this. For instance, string instruments can handle this just fine. Also, since we live in a digital era, this hurdle is significantly easier to work with, than it was, say 100 years ago. Your presentation has other problems. You talked about the system using 53 pitches, but not the systems in between that still accomodate this type of tuning system you are demonstrating reasonably well. For instance, 22 pitches, and 31 pitches. Also, there is the issue that historically, the circle of fifths was not how we came about using 12 pitch classes. Originally, the Ancient Greeks only used 7 unequal pitch classes in their scales, and a composite scale of 12 was only considered after studying modal transposition of their scales, and incorporating them into a single scale. Since there were Greeks that did use more complex tuning systems, such as septimal just intonation (as with Greek musician Archytas) or Ptolemic just intonation, simply saying that this all came about via the use of the ratio 3/2 (or 2/3) is inaccurate. 8:54 - 9:12 That is false, and scientifically inaccurate. Studies have shown that humans are capable of detecting pitch differences as small as 3 cents. The average just noticeable difference for pitch is about 6 to 7 cents, and the pitch difference between steps in this 53-pitch system is above 21 cents. These are clearly noticeably different pitches. Now, Westerners may treat such a difference as an out-of-tune note, rather than a different note altogether, but they definitely do not sound the same to us. And again, there are cultures where this system is actually routinely used. 9:12 - 9:22 They are the same color only insofar as color names cover an entire bandwidth of infinitely many light frequencies, rather than only one individual frequency. We tend to split the visible region of the electromagnetic spectrum into 8 regions, but we are all cognizant of the fact that in each region, there are infinitely many colors, varying continuously across pitch. 9:28 - 9:34 "Very hard" is in the eye of the beholder. I am sure a person who is accustomed can tell the difference without putting in much effort. 9:36 - 9:45 Yes, but why 12 and not 22, for example? Why 12 and not 24? Why 12 and not 19? In fact, why 12 and not 6? Keep in mind that this is all predicated on the assumption that we need to evenly divide the octave to make music, which is not actually true, and was not true for most of human history. 9:45 - 9:52 This is an even worse argument, as plenty of dissonances already exist in the 12 pitch system you are describing. For instance, the minor seventh, the minor second, and augmented fourth, are all rather dissonant intervals. In fact, in many contexts, the only consonant intervals are the perfect unison, the perfect fifth, and perfect octave. Consonance and dissonance are not absolute, but context-dependent, and they both exist in all systems. 10:05 - 10:21 Making software that supports 53 notes per octave is literally not an issue. This has been done before, and we have gone far beyond this. Physical instruments are real obstacle, yes, but not software. Rather, this is pretty trivial for software. 11:16 - 11:22 No. This is wildly inaccurate. To start with, this Pythagorean tuning system was not used by anyone in the 1600s or prior to that. They used Ptolemic just intonation, where all notes are generated by perfect fifths tuned to 3/2 and major thirds tuned to 5/4, which is not possible in Pythagorean tuning. Just intonation was indeed abandoned for reasons similar to what you outlined here, but they abandoned it not for equal temperament, but for meantone temperament, which they used up until the 1700s. Then, they abandoned that in favor of well-temperaments. Equal temperament did not come into common use until the mid 1800s, and even then it was still not truly popular until the early 1900s. 13:22 - 13:38 Again, eye of the beholder. Even for septimal ratios, many music theorists would agree that the most important ones among them are consonant.

[@Moabhd2012]

"If you can’t explain it simply, you don’t understand it well enough." - Albert Einstein

[@thehousehack]

@1 Minute Math I am not sure which you understand less, Physics, Quantum Mechanics, or what "TLDR" signifies.

[@extramile734]

One simply cannot prevent fire by preparing for fire. Albert Einstein Idiot.

[@xGOKOPx]

But it's explained simply

[@paulcrawford1108]

yea , he lost me .. was going fine at the start then after the 2/3 bit it just was clear as mud

[@StevenJacks]

​@@DariysChannel I don't think I said the lower pitch is the higher frequency. Higher pitches have higher frequencies, of course. I said the shorter line was a lower frequency. You can think of the lines on the screen as a frequency bar graph. This way, I can go low to high, as on a piano, with the frequencies also going from low to high from left to right. Try watching with this in mind, and not that the short lines represent short strings, but rather low frequencies.

[@Dayanto]

It's important to note that every ratio has a different circle. While multiples of 3 (3/2) are amazing with 12 equal tones, and 5 is decent, there are other harmonics such as 7, 11, and 13 that are basically unusable. They are -31, -49, and +41 cents out of tune respectively. That's a large part of why alternative tuning systems (such as 24, 31 or 53-tone equal temperament) are so interesting. Sure, there are more dissonant notes to avoid, but in return you're unlocking completely new types of harmony that are simply not possible in 12 TET. Every tuning system is a compromise, but the more tones you have, the less you need to compromise on average, and the more valid options you (tend to) have.

[@StevenJacks]

VERY WELL SAID! I like this comment a lot. Great contribution and I agree 100%.

[@rrr00bb1]

665 is where circle of fifths closes almost exactly (and maj/min third circles). there is a rough sequence of better near misses.... 5 7 12 19 53 665, etc.

[@stephenfiore9960]

*..I’m a musician, and I find the older I get, the worse the GUITAR sounds. One older musician wrote in an article one time that it is because your “ear” is getting better at listening to harmonious things. In other words when your a younger musician your “ear” isn’t as developed and you don’t notice the problems with equal tempered tuning as much. I had a band leader once who could hear that when I played higher on the neck of my guitar, that my guitar was out of tune. I couldn’t hear it. Also very accomplished piano players have said equal temperament tuning causes each music “key” to have a different “flavor” or “coloring”. And some songs when you switch keys just don’t sound good anymore. Anyways the only place that I know music will sound perfect is in HEAVEN, we are going to see how GOD gets around the equa-temperament problem. A lot of people who have been through a near death experience say everything vibrates so beautifully in HEAVEN. How do you get to Heaven? Answer: ...”For whosoever shall call upon the name of the Lord shall be saved.”* Romans 10:13 - www.biblegateway.com/passage?search=Romans%2010:13&version=KJV

[@LordFennel]

Really interesting video Steven. I like how you've visualised the notes as colours in a circle. It's a lot more coherent than some of the other videos I've seen on the topic, such as the ones done by people like Vihart and Boyinaband. I enjoy your videos a lot, and I'm glad you've started making them again. I like the longer length as well. It allows you to get much more information into your videos. Perhaps an explanation as to why other cultures use different scales than the tradition western 12 tone one would have been nice, but I accept that this particular subject is huge and it's much better to start with explaining basic concepts than to cover complex topics immediately. Thank you for what is, in fact, a very well put-together video. I'm looking forward to more of your content in the future :).

[@James-nr9gm]

This had very little to do with why there are twelve notes. Where did the 3:2 come from? When did people settle on 12? How many people settled on 12?

[@markenangel1813]

as explained, 3:2 is a very simple ratio. the only ratios simpler than 3:2 are: 1:1 (if it even counts) 1:2 (an octave, which makes equivalent notes to the ones you started with) 1:3 (an octave and a fifth, which is equivalent to a 3:2 ratio) you could also invert these, making 2:1, 3:1, and 2:3, but those result in the same 12-note system.

[@James-nr9gm]

@@markenangel1813 I understand the general concept, but where do the ratios come from, etc? The video send to meander, I walked away going "okay so like because of a ratio here or there, we get 12 or 53, and 53 is inconvenient" ...

[@aeromodeller1]

At 2:00, you got them backwards. The shorter string is the higher frequency. You don't need to cut the string in half. If you very lightly touch the center of the violin string and bow it, it will vibrate in two halves and the tone will be twice the frequency of the fundamental. If you touch the string lightly at one third, it will sound a tone three times the frequency of the fundamental. Touching the A string at one third and the E string at one half will produce the same note on both strings. The frequency of the open E string is 3/2 the frequency of the open A string. However, the 3/2 ratio is not the only one available. If you look at all the small integer ratios between 1 and 2 for pairs of integers up to 9, you will find 14 ratios and you will be able to find nine of them which fairly well match uniformly spaced tones. If you add 18/17 and 34/18 you get fairly uniform coverage of all twelve up to the ratio of 2; 18/17, 9/8, 6/5, 5/4, 4/3, 7/5, 3/2, 8/5, 5/3, 9/5, 34/18 and 2/1, completing the twelfth interval in the octave.

[@cactusowo1835]

Casuals: There are so much notes on my octave! Take it to 12 Microtonal: *Git gud*

[@beeplus4777]

I've read that Pythagoras studied stringed instruments and found two note relationships that didn't sound dissonant when compared to another: Half sized strings and two thirds strings.

[@infono9874]

Very subtle, too. People can deal with the dissonance, and it doesn't make sense. 12TET is probably worse than 53

[@StevenJacks]

Quite arguable indeed. :) Both systems are good in their own respects, of course.

[@PraetorDrew]

Well, this explains why 53 EDO is so much better than other systems of microtuning.

[@wizard1370]

Just intonation is the only answer

[@StraightEdgeHippie]

Dude, I recognize your voice from Khan Academy algebra. You are a perfect example of "lead by example". Thank you for your contribution to society.

[@StevenJacks]

Haha I'm (sadly) not Sal. I admire Khan Academy's format and wanted to bring the same to my other vids. Hope you enjoy them. Thanks a lot for this comment. :)

[@eveningsun1208]

There are an infinite number of different pitches in the Harmonic Seies, why limit yourself to 12, where the ONLY in-tune interval is the octave?? There is a Guitar company called FreeNote Music that makes guitars in all different tuning systems, including 31-tone Equal and pure Harmonic Series Just Intonation. If you play standard guitar, you’ve never heard or played a purely tuned chord.

[@StevenJacks]

Well said. 12 is such a crutch. :)

[@czntrm]

"7600 notes per octave... that's a little too much" is the understatement of the century! 😂

[@chrisjamesr77]

I actually already knew this stuff, but that's an excellent way to visually represent the whole idea, with the colors, and how two of them that are close enough together look like the same color but aren't quite the same. Like, if I were a music teacher trying to explain this to a student and they weren't getting it, I'd tell them to watch this video. I never thought of it being demonstrated in that way, but it totally makes sense!

[@brunomocellin]

So good to have you back Seteven! If it has one hour, i would watch , because you kind of videos and explanation are the best man ! =)

[@markenangel1813]

i really want sevish to make 53 tone music now

[@ginnyjollykidd]

You'd have to make instruments to play 53 notes per octave, and software that supports 53 notes per octave - Or play a trombone.

[@StevenJacks]

I adore this. :)

[@dlwatib]

Or a violin. Or a cello. Or sing. Software would actually have no problem with 53 notes. That's probably the easiest way to invent a 53 note system, is to use software to control the instruments. Who wants to play a fife with 53 holes? I'm kinda surprised that nobody ever built a 53 note pipe organ. They did, however, invent detuned celeste voices, which doubles the number of tones from 12 to 24.

[@Mintsoda_15]

+ or slide whistle or wine glass with water(glass harp or wine glass xylophone) Also 'Terpstra Keyboard' can play variable microtonals

[@janAlekantuwa]

I suggest using the C overtone series to get accurate pitches for C, D, E, G, and B, then using 2:3 and 4:5 ratios (perfect fifth and major third) for the remaining notes, then correcting Bb and Eb. If we fix C at 1, this is the frequencies of one octave C: 1 C#/Db: 16/15 D: 9/8 Eb: 239/200 E: 5/4 F: 4/3 F#/Gb: 45/32 G: 3/2 G#/Ab: 8/5 A: 5/3 A#/Bb: 402/225 B: 15/8

[@ACaffeineAddict]

I'm completely lost around 4:16. Why are the yellow bars placed where they are?

[@marvinmartian8746]

Same here. Watched that part countless times and I think it could use some annotation after the fact. I liked the part later where he used the circles, but still I'm somewhat lost.

[@TallinuTV]

@@marvinmartian8746 Yeah, there's no explanation of how he gets from cyan lines halfway between the initial red "do's" with a 2:3 ratio (of frequency? - length? - whatever, he confuses that right at the start) with the red lines, to suddenly adding yellow lines close to the red lines with no apparent reason and a line length that looks nothing like a 2:3 ratio with any of the other lines... Feels like he's skipping a step or two, and then he continues doing whatever unknown thing it was repeatedly, and expects it to make sense.

[@keithgood3419]

@@TallinuTV Were we watching the same video??? Because it made perfect sense to me!! Try watching it again maybe you are the one that missed something? I do that and it helps me, either that or I rewind a lot!

[@prestonage]

Yeah no idea where he got that from.

[@prestonage]

I found this video that shows where he got that and explains the whole concept much better: kzbin.info/www/bejne/mnPbnnaflsSVrK8

[@da4mula885]

Why would 53 be too much? Only thing is that daws currently don't support microscales. But more notes don't really make it harder to work with otherwise.

[@StevenJacks]

Great point, but what would you do to address writing sheet music that has to differentiate between so many notes?

[@jasminavandewyck1536]

Thank you. This is really helping me understand some music theory. I am new to the world of music and this is great😁

[@_modiX]

I thought the answer was obvious, but this, wow. Now I finally realise why some notes on my guitar only feel slightly tiny off pitched when I am in a specific key, while they are fine in another key. So in the bigger picture music is organic, not even and resolving perfectly so to speak, because it is part of the nature and we had to cheat to make it simple. The only way to over come this is to pitch all notes based on my primary key I want to play in. However, on a guitar I cannot pitch every note, only every string. So even when I customise my frets, I will have to decide for a key I want the frets to be aligned for, primary. This is stunning to know of. Thank you for this video.

[@jacobmoss4095]

"Why There are Twelve Notes in Western Music" -There, I fixed it.

[@samsamson591]

western? do other places have more?

[@dhakshan]

@@samsamson591 south indian have the same. I confirm it

[@fgonzalez90]

​@@samsamson591 Turkish music generally uses a (subset of notes based on a) theoretical system with 53 pitches in an octave.

[@sylviaxx3574]

there's a scale called Bohlen-Pierce which is based around the 3:5:7 chord. it replaces the octave (1:2) with the tritave or perfect twelfth (1:3) and divides it into 13 steps. it originated from america.

[@elbschwartz]

@@samsamson591 Depends where you draw the line. Classical Arab music for instance divides the octave into 24 notes. But you only use 7-9 of those notes at any given time. At the other extreme, there's lots of traditional music from around the world that only recognizes 5 notes (pentatonic). But the intervals between those notes may have no parallel in Western music.

[@KisoonaKing]

“Now you have 7600 notes per octave, that’s a little too much” 💀

[@anthonydemitre9392]

I understood this only because I knew this all ready, it did seem drawn-out but he forgot to mention the overtones of the note, which was how the Pythagorean system was created but this limited the keys you could play in So they started using equal temperament

[@angelmendez-rivera351]

This is historically inaccurate. The Pythagorean system was not used in medieval times. The tuning theory of medieval Europe was actually the Ptolemic system, which used a lattice of perfect octaves (ratio 2), perfect fifths (ratio 3/2), and major thirds (ratio 5/4), and this is when tertial harmony began to be preferred over quartal harmony. Also, equal temperament became common in use only about a century and half later after just intonation had been abandoned. Just intonation was abandoned in favor not of equal temperament, but meantone temperament and well-temperament.

[@mustafaenderoztopcu8554]

Thanks for this video made me feel less noob on music. I learned that Pythagoras theory in my childhood but now i got it completely. My master of oud (fretless) said that G♭ is not equal to F♯. ♯ feels thrill and ♭ feels blues. It depends which mode (makam) do you play. It's not subject of math, but subject of emotion it creates. Extra info: Makam system, used by India to Morocco, especially in Turkey has 24 not equidistant notes. Theoretically one semibreve divided 9 peaces called Koma, the smallest range of sound which is recognizable by human ear. I always put a poem on my comments. Musiqi nəşəsi min sevgili cananə dəyər, Əsəri, naleyi-ney arif üçün cana dəyər, Musiqi əhlinə insaf ile qıymət qoymak, Ləhn-i Davûd ilə min təht-ı Süleyman'a dəyər. (Əlaga Vahid) Joy of music worth a thousand lover, Wail of the nay worth a life for the wise, Appraise of a competent musician proper, Thousand of (King) Solomon's throne worth only (King) David's voice,

[@itsv1p3r]

i just wanna know if you're also the guy who said "burger king foot lettuce"

[@dualia-s74m]

lol

[@StevenJacks]

LOL! I just looked this up. Not me, sorry! :)

[@theharper1]

It's a bit confusing to start with three notes each separated by an octave, then reverse the order of the frequencies, then suddenly talk about one octave when the original visualisation had two full octaves. The circular representation makes a little more sense because it's at least related to generating a sinusoid by mapping rotation around a circle over time. However, I don't feel that the explanation really makes clear why twelve notes makes more sense than any other way of dividing up a circle other than to say that 53 notes is a bit much to handle for the fingers and provides adjacent notes which are hard to distinguish. PS Please fix the typographical errors. ;)

[@davidaustin6962]

Totally agree. Seemed like he was saying "what the hey .. Lets call small big and big small for no reason whatsoever". He should have just used a different graphic to avoid the confusion when he did that.

[@jharsch3453]

ascending chromatically, I always imagined the western system of 12 notes as a coil that dangles, much like the circle but while displaying the concept of octaves

[@StevenJacks]

That's it exactly, the coil. It's hard to display in 2 dimensions though :P

[@Photosounder]

Well time for some shameless self-promotion, that's what my Spiral visualiser does (see my channel I guess). I called it spiral because that's a spiral, as in a coil.

[@anastaziuskaejatidarjan4711]

53 is a good number for theorizing microtones. There's nothing wrong with having instruments capable of microtones. Almost everyone already does it. Oh and also, 12tet only became big in parts of Europe in the late 1700's, not the 1600's.

[@pcuimac]

This is easier to understand, if you already understand what you ae trying to say. It's for tze advanced and not the beginner.

[@jamessymons3808]

Take a note, say, 130 Hz (Hz or Hertz means the string wiggles 130 times per second), and call it "C". Multiply it by 2... you get 260 Hz, also call that C (just higher). Multiply that by a simple ratio, say 3/2, you get 390. Multiply that by 3/2, you get 585 Hz. continuing on you get 878, 1316, 1974, 2961, 4442, 6663, 9995, 14993, 22490 Hz. The problem is that these notes span a greater interval than one octave (it is outside of the range of 130-260). Lets say you want to fit these notes into a scale though... all you need to do is just need to keep dividing by two until you get a number that's between 130 and 260. That's the hidden step that was not explained. So 390/2 = 195 Hz... We call this G 585/2/2 = 146.25 Hz... We call this D 878/2/2 = 219 Hz.... We call this A 1316/2/2/2 = 164.5 We call this E 1974/2/2/2 = 246.75 We call this B 2961/2/2/2/2 = 185 We call this F# 4442/2/2/2/2/2 = 138.8 We call this C# 6663/2/2/2/2/2 = 208 We call this G# 9995/2/2/2/2/2/2 = 156 We call this D# 14993/2/2/2/2/2/2 = 234.2 We call this A# 22490/2/2/2/2/2/2/2 = 175.7 Hz.... We call this E# or more commonly F. And that's how we derive a 12 note scale in a tuning system called Pythagorean tuning... But our tuning system divides the octave into twelve equal ratios... you get each note by multiplying the initial frequency by 1.05946. In some ways it is slightly out of tune, but allows one to switch keys without having to buy a new piano.

[@StevenJacks]

Exactly right. This is awesome.

[@BudTristano]

@11:29 - I see how the perfect fifth in the Pythagorean system practically coincides with the perfect fifth in the equal temperament system - the secret to all rock and metal music! This will lead one to the secret of the universe ... \m/

[@noahlovotti7722]

Pythagoras is kinda limited though. Higher prime gives you cool stuff like neutral intervals.

[@kenjohnson6101]

The tempered scale is based on the lucky coincidence that 2^(5/12) just happens to be very close to a simple integer ratio, 3/2. But there are also other serendipitous relationships. 2^(1/3) is close to 5/4, and 2^(5/6) isn't too far from 7/4. So the equal tempered scale has the harmonics based on 3, 5, and 7 covered pretty well. Not perfect, but with just a slight dissonance the beat frequency will sound like vibrato. :)

[@jameslouder]

You're putting the cart before the horse. 12-Equal Temperament was known and used long before anyone had the mathematical tools to work out those fractional exponents. This is not the place for a treatise on the monochord, but if the math interests you I'd encourage you to look into it. I'm not sure what you mean when you say that equal tempered minor 7th [ Bb ] = 2^(5/6) is "isn't too far" from a just minor seventh [ Bbb ] = 7/4. The latter is flat of the former by 31.17 cents, almost a third of a semitone! The Bb we use is more properly considered as the 4th of the 4th = (4/3)^2 = 16.9 = 1.777etc. Its equal-tempered ratio 2^(5/6) = 1.782.

[@kenjohnson6101]

@@jameslouder I just tried this out on my guitar. If you lightly touch the base E string about 1 or 2 mm to the right of the 3rd fret and pluck the string you get a pure harmonic, which is very close to the open B string. If you touch the E string several mm to the left of the 3rd fret you get the next harmonic, which is somewhat close to D played on the B string, 3rd fret -- which you would use for an E7 chord. But the B note sounds sharp compared to the harmonic. You can detune the B string to match the D note to the harmonic, which makes the E7 chord sound good. But then the E chord with the open B string sounds terrible.

[@datnguyenthe8300]

3:45 What happened there? I didn't understand that part, how did we get the yellow "tone"?

[@datnguyenthe8300]

Oh xD i think i got it... so what we do is divide the frequency by 2^n and then multiply by 3^n to get the next "tone"... so f2 = ( f1/2^n ) * 3^n hence the comment at 3:52 - "shouldn't it be on the other side"... and yes, it's just that we chopped the new frequency in half...

[@StevenJacks]

Exactly right. We just keep the 2/3 ratio going to get a new pitch, then use the NEW pitch to do 2:3 to get ANOTHER one, etc etc etc.

[@leeMartin33]

@@datnguyenthe8300 - By 'tone'. don't u mean Note ??

[@yanyanp]

@@StevenJacks Hi Jack, please explain how to move X-axis? at this moment if the X-axis of short blue line is 1.5, use 3/2 ratio to get next x-axis of line will be 2.25, but looks too far to the right?

[@StevenJacks]

@@yanyanp Yeah it's not a linear scale; it's a logarithmic scale. Hope that helps. Let me know how you get on.

[@TheSteveSteele]

For those questioning, here’s what he’s doing (he just doesn’t say this outright). He’s building the Circle of 5ths by using two ratios (2:1 and 3:2). Then, by stacking the 5ths (starting on C), one ends up with C again, resulting in the Circle of 5ths - C G D A E B F#/Gb Db Ab Eb Bb F (then C). Next, by taking those letters and lining them up chromatically or by frequency into one octave (alphabetically) - C Db D Eb E F F#/Gb G Ab A Bb B, one gets a 12- note octave, equally distanced once tempered.

[@bakedutah8411]

Steve Steele 🤣😂🤣😂🤣

[@TheSteveSteele]

Baked Utah Truth makes you happy, huh?

[@bakedutah8411]

Steve Steele, no, it was just your valiant (seriously) effort to clear up confusion. I’m sure it must sound crystal clear to you, but to most who hadn’t grasped it prior to reading your stuff, they still won’t have grasped it after reading your stuff. I mean, “Circle of 5ths”, “ratios”, “stacking”. 😂🤣😂

[@TheSteveSteele]

Baked Utah understood. That would be funny. Well, I’m giving a lecture on the subject in a few weeks and I’ve got my head buried in medieval books and 18th century science (where the music overtone series and math’s harmonic series meet), and it gets deep. So I’m just talking like I just read the “War and Peace” of music theory books. My goal is a big one though. I propose that any freshman level collage music student can learn and understand genius level music theory within a short period of time. The problem is that music theory at the high school and college level it taught incorrectly. My generation is trying to change this. After my music theory lecture is over in a few weeks I’ll make the video available on. KZbin. Maybe you’ll find it useful. Look for my channel.

[@bakedutah8411]

Steve Steele: head buried in medieval books and 18th century science? Where do you live; heaven? 🙂 Good luck with the lecture. I agree with the proposition-and in more than just music theory-that kids could handle a lot more than is currently thrown at them, and that part of the problem is the way we throw it; i.e. how it’s taught. I still find myself, at age _[cough]well past[cough]college age[cough]_ having epiphanic learning moments, often triggered by a well-constructed KZbin video, and thinking, how t f has it taken me so long to realize that! The thought of time wasted would be depressing were it not for the sheer exhilaration of acquiring yet another piece of understanding about the world.

[@stevesawyer4286]

Wow. Thanks! I've probably seen a half-dozen different explanations of these ideas, but this was the first that made sense instantly! I think your graphics helped a great deal. Nice work.

[@adamedmour9704]

No he’s misleading you I promise. This is only how one extremely unrepresentative medieval running system works. Pythagorean is not the standard people are comparing to when they say that our modern tuning system is out of tune.

[@thepianoplayer416]

Working with frequency number in Hz we start with 440Hz for an A. 220Hz would be an A that is 1 octave lower & 880Hz would be an A that is an octave higher.

[@StevenJacks]

thepianoplayer416 yes! And if you go all the way down.... 110, 55, 27.5 and so on. It’s interesting to think about how little distance you can alter a pitch before going to a new octave, and especially before hitting another pitch if there are 12 in an octave. Now, if you take use equal temperament and you only have a distance of 100 cents from one pitch to the next half step, that’s really not much distance of wiggle room before returning where you run into another pitch you’d already have, thus creating the same system, with all the pitches tuned up a half step. I think of it like GMT. There’s no reason for GMT to be based on Britain geographically - you can place it anywhere, and base your time zones after the fact. But that anchor (GMT or 440) ‘should’ be agreed upon by the masses and then used as a basis for the rest of the logical system. So 440 works (cuz is 432 really better?) as is GMT decided. An anchor is needed, and should be agreed upon, so people have a foundation on which to communicate. Thanks for reading my tangent and rambling. :)

[@photelegy]

13:46 Doesn't it sound good because we are used to the system we have? Or would our system also sound better for a person who only ever heared a different system (e.g. 1:5)?

[@preetgiuliani5013]

Lets cut it simple. If we compare 7 notes (c thru b) to vibgyor (7 colors) we must understand that the colors will turn inumerable once we see them in transitions from one to another (each blend wud showup a changing shade) and thus giving a unique name or counting the endless possibilities would be crazy. So its pretty easy and simple to understand the 7 purest form of notes and accept their nature

[@curtisnorris868]

Before mathematics was ever applied to music someone first had to figure out that stretching a string over two points and plucking it would produce a sound. No doubt people also experimented touching the string and plucking it to discover the octave at the middle. Going even further someone would have discovered that touching a string at a point one third of its length also would produce a rather prominent sound and the same thing would happen touching a string and plucking it at a point one fourth of the string's length. Going even a bit further people would have also realized that the distance between the one third point and the one fourth point is one twelfth the length of the string. It was not a mathematical formula that brought us the twelve tones but rather it was the discovery of the natural harmonics on a vibrating string.

[@curtisnorris868]

@Paul V. Montefusco It is not a coincidence that the nodes on a vibrating string at the middle point and at the 2/3 point is a perfect fifth.

[@joesterling4299]

I knew each octave doubles the frequencies of the previous one; but I had no idea the system to populate all the notes in each octave was so involved. My preconception matches the tempered approach. Thanks for the education.

[@seiph80]

excellent explanation, I keep coming back to this video

[@StevenJacks]

Thank you very much! :) Glad you enjoy!

[@seiph80]

***** absolutely! I also enjoy your other videos, too

[@mustafaozylmaz6815]

We are using 53 pieces in one octave in Turkish clasical music. Thans for this information. Now i understand why we use 53.

[@StevenJacks]

Awesome! 53 is quite pure intervals indeed, just a lot to keep track of. Well done, then. :)

[@gsilva220]

There's a keyboard that has these 53 notes, it's very weird

[@JesseOrmandMusic]

Steven, this video is an absolute gem. This was the best explanation of the 12 tone octave I have ever seen, and I have seen a lot of them. You also managed to briefly touch on intonation (a very challenging subject), and visually it made so much sense. Thank you!

[@richarddeese1991]

Um... a shorter string produces a higher note because the frequency is higher, but you kept playing the shorter ones as lower octaves, not higher. You also kept stating that that's because the frequency of the shorter string is higher (which IS right), but you're visual & auditory representations kept doing the opposite. That's exactly backward. And, if you choose to make a video correcting this, you may also wish to let people know that it was actually Pythagoras [that most excellent ancient Greek dude!] who formalized the system you're currently unteaching. Doh! Ray Me?!? !thgir ti teG Rikki Tikki.

[@xGOKOPx]

Well what he meant with the string is that obviously longer string make lower sound but for the sake of simple visualization he'll go with "low collumn = low sound". He could've said it more clearly though

[@SickMetalAddict]

Lmao haters will hate. First of all, he did say he's explaining the pitches in reverse, and it's not too confusing on that. Secondly, you're just trolling, he literally said Pythagorean ratio.

[@scotu7075]

Maybe this video is just for people who already understand basic things about music because I understood this explanation perfectly despite not knowing before exactly why there were 12 notes

[@AMReed8]

What program are you using to generate both sound and image?

[@StevenJacks]

That's javascript canvas captured with quicktime, and then logic pro sounds overlaid, and final cut to splice it all together.

[@AMReed8]

Awesome, thanks!

[@TheBeardedMathMan]

I very much enjoyed this, thanks for sharing. How did you choose your colors for the notes?

[@StevenJacks]

That's all based on the hue of colors. 0% hue for C, and then just go around the circle as you go up the octave. :)

[@vikidprinciples]

Steven Jacks seriously cool

[@adamrspears1981]

Can you explain why standard tuning of a guitar is 440 MHz of pitch?? Why 440?? 440 Million cycles per second....why??....

[@mikefule]

They needed a standard. It is in a sense arbitrary. A speed limit f 51 mph or 49mph would be just as sensible as a speed limit of 50 mph, but they needed to choose a number. Similarly, bicycle wheels would work just as well if they were half an inch bigger or smaller, but they need a standard so that rims, frames and tyres can be compatible. Before 440 Hz became the accepted international standard, musicians from different countries/regions used different standards, which caused problems if they wanted to play together. Even now, a different pitch standard is used in some areas and some forms of music.

[@adamrspears1981]

@@mikefule thanks for the clarification. Yes, that makea sense :)

[@huemanatie4392]

It made more sense to me when the long strings were lower and so forth. Flipping them seemed kind of arbitrary at best. The visual should match the sound.

[@aFoxyFox.]

Awesome video! I enjoyed this angle a lot!

[@RicoCobos]

Nice visual, but you never really answer the question.

[@RAndrewNeal]

Yeah he did. He explained exactly why we use twelve notes. Sometimes I miss something and need to re-watch a video and it helps me a lot. Maybe you missed something in this one, because I understood it fine.

[@GrubKiller436]

Because 53 is too big. Anything between 12 and 53 would not be equally spaced. So it's gonna either be 12 or 53 by our 2:3 system. Correct me if I'm wrong. There are different systems that exist though, and I think we should explore them.

[@rantalbott6963]

@@RAndrewNeal He didn't even come close to explaining why there are 12, rather than 9, or 13, or even 17. Here's a text explanation I just found that does: thinkzone.wlonk.com/Music/12Tone.htm There are certain frequency ratios that sound "good" together to the human ear (called "consonant"). The 12-tone equal-tempered scale gets very close approximations of the consonant ratios, without including too many "dissonant" ones.

[@s.vidhyardhsingh3881]

I don’t think that your question even really matters 😜because with twelve notes, music sounds good and quite challenging to learn

[@alicaramba7680]

R. Cobos You should look for an answer in music history books, rather than on youtube:).

[@alainvoit4862]

I learned this over 15 years ago, and this is the BEST explanation I have come across. Fantastic job Steven!

[@batteryacid1]

Do Ré Mi Fa Sol La _Ti_ Do

[@LOLmaster-tn2sd]

Do ra mi fa so na si do

[@tulw2728]

LOLmaster 2234 Do Ra La Ex Plo Ra Do Ra

[@tulw2728]

GroovyParticles Do Ra La Ex Plo Ra Do Ra

[@theunknown617]

Dora la exploradora? xD

[@TheMadisonHang]

Do re me Fa So la te Do

[@4sh024]

Is this why there is no b sharp and e sharp?

[@charliepotter100]

This guy has a really weird idea of what a good explanation is - I wonder if he works in I.T....

[@megadethmofo2035]

Government employee, no doubt.

[@StevenJacks]

Have you tried turning it off and on again?

[@fakename3344]

@@StevenJacks It's probably a pebkac.

[@StevenJacks]

@@fakename3344 Absolutely worst errors to deal with.

[@MYKEDANGER]

@@StevenJacks I like how handled Charlie Potter's criticism. You made a joke about it and brushed it off. Many KZbinrs would choose to respond in hate speach. But you have good character Steven!

[@humanbeing1429]

Has anyone ever wondered why 7 notes in a scale and 12 notes in an octave? Like 7 colours in a spectrum, 7 days in a week, 12 hours in a clock, 12 months in a year, 12 disciples of Jesus, 12 tribes of Israel, etc? There must be some relation between them right?

[@boptillyouflop]

That's easy... Since the 3/2 ratio sounds really good, you end up with 58% of the scale from C to G, and 42% of the scale from G to C. Because of this asymmetry, you can't divide the scale into 3, 4, 6 or 8 parts, and 9 parts is very dissonant too (except for Gamelan), and 10 notes makes your intervals too small. The remaining options are 5 and 7 notes, which is why everybody ends up with 5 notes (China, Thailand, Americas, parts of Africa) or 7 notes (Europe, Arabia-Turkey-Persia, India, other parts of Africa).

[@KayBenyarko]

That is a flawed title cause it only pertains to western music

[@egilsandnes9637]

@Multorum Unum That's completely and utterly wrong. Other cultures have all sorts of ineresting tunings that are not subsets of the tempered tuning.

[@gumbilicious1]

Everything is flawed, because language itself relies heavily on implied content. Not only would language be incredibly cumbersome if it were exact and precise in meaning, but there is no meaningful way to ensure language has the ability to capture every detail in order to be completely true and precise. It could be pointed out that your statement is flawed because someone can always find a shortcoming of any statement, and all you are doing is pointing out one particular flaw you take issue with. But such actions don't make for meaningful discourse, rather this just encourages petty interactions for the sake of one-upsmanship that lack content that benefits either the reader of the comment or the person who makes it.

[@gumbilicious1]

@Multorum Unum I hope you find this interesting. I have no idea why people are so salty in this thread en.wikipedia.org/wiki/Arabic_maqam

[@egilsandnes9637]

@Multorum Unum Just as an example: en.m.wikipedia.org/wiki/Shruti_(music) There's all sorts of "weird" tunings and traditions around the world. Adam Neely has a very good video on it. (I just can't find it at the moment. It's really worth a watch)

[@egilsandnes9637]

Also, don't forget that there are western musicians that make music with the just intonation. Also check out Sevish on youtube. They use all sorts of funny tunings.

[@davidjames1684]

A simple answer is 2 ^ (1/12) = 1.059... so each equally spaced note is about 5.9% different in pitch to the adjacent note of it and that # of notes (12) is the lowest possible number of notes in an octave that hits the "critical" ratios of 5:4, 4:3, 3:2, and 2:1 which makes those intervals sound good to our ears. There is very little to be gained by doubling the number of notes in an octave to 24 for example and it actually makes it more complicated. 12 is basically a "magic number" when it comes to "Western" tuning of music. The slight problem with 12 is suppose your scale goes from C to C, you will get very close to those 3 ratios but the octave has to line up as 2:1 pitch ratio so some "correction" has to be made within those 12 notes, however where the correction is made affects other scales like from A to A for example. Luckily our ears are not so picky that being a few "cents" off doesn't sound horrible and may actually make the combination of pitches sound "fuller" (such as when a symphony orchestra has violins that are slightly out of tune with each other).

[@midplanewanderer9507]

There might be something wrong with me. @10:48 the "wolf" note sounded in all it's dissonant glory; and a strange, clutching energy rush below the navel, above the pubic line, and a sense of "Oh yeah..that's heavy. Moar pleeze." Very NIN.

[@michaos1]

Best explanation so far. 4:15 Each next fifth is 3:2 in pitch from the previous (and 2:3 in string length with the same tension), but it's good to see ratios to the root pitch (e.g. ~3:4 for a fourth etc. as per Pythagorus) and note names as we climb up the Circle of Fifth: C G D A E B F# C# G# D# A# F. This part confuses a bit.

[@StevenJacks]

Yeah... note names are derived differently. They're kind of the product of the two systems put together (especially all 5 accidentals): Pythagoras and Diatonic scales. Diantonic has 7: A BC D E F G Pythagora arguably has 12, so they're wedged between the notes, and you get the 5 extra accidentals.

[@michaos1]

Thanks for the answer, yet the next biggest question! How did people come up with diatonic scales that had 7 notes? Modes to be clear, they dated earlier. But still, why does any mode have 2 fixed half steps BC and FG? I think the answer is: Because it sounds cool! :) I'm just surprised how well the modern music theory inherits 600 year old notation conventions and 2500 year old Greek tone systems and modes.

[@alexsunga7091]

Wow I didn’t know Khan Academy started doing music explanation videos 😂

[@StevenJacks]

:D That's exactly what I was going for. You're the best :D

[@allstonian13]

"If we keep going with this relationship..." Which one? The 1:2 or the 2:3? And which "string" is divided in half or into 2 and multiplied by three? Did you just make things worse?

[@channel_B5]

You keep going always 2/3-ing the *latest* string.

[@H3000-v7i]

Yeah, from explaining things super slow, and then just jump further without explaining.

[@ottolehikoinen6193]

Thanks for mentioning 53-EDO system, microintervals rule. Very clear exposition

[@LockRocker]

A lot of what everyone is overlooking is that yes, music stems from nature and (especially) strings vibrate in a physical way (hence the harmonics at fractional points of their length... half being loudest, 2/3rds next most pronounced, etc.) We cannot change this, but we can cut your horns and drill your recorder holes to match how strings are since you seem to want to play along. I'm sticking with my string theory people, and you might reexamine just how things fit into this physical reality. It's just a shame a ding dang locksmith had to be the one to bring it up!

[@stephenm3001]

There is no actual demonstration of how it sounds. FOR GOD'S SAKE, why couldn't you just play all those notes and intervals??? I'm just FUMING

[@encrust1]

Agreed. My guess is that what we do hear was created directly from a standard synth/plugin, and that setting up micro-tuning for 53 was just too much hassle

[@alexrigsbee4677]

Monty yeah you could tell it was coming from a standard synth because when he played the perfect fifth he didn't click the little circles, it just played from some other unseen source. Such a shame though, I wanted to hear the semi-tones harmonize!

[@xtr3m385]

Maybe you should sit your *LARDY ASS* down and make a video where you can show everybody how it is done. Instead, you whine and *_fume_* like a fucking *bitch* in heat. *Goddamn losers!*

[@randairp]

@@xtr3m385 It wasn't Stephen M's job to make this video a good video. Valid criticism is valid.

[@dougr.2398]

This is only a casual overview. Many of the elementary intervals such as 3:4, 4:5, 5:6, 6:7 are neglected here as are how the scales sound for equal temperament, “just” or natural tuning, and the mathematics for “well” tempering, based on the 12th root of 2 are omitted here. How many elementary beginning or even more advanced students can “handle” that level of mathematics? Nor even most teachers can! The color visualizations here are excellent!

[@technowey]

For the equally tempered scale, the pitch (or frequency) of each successive note is the frequency of the previous note times the twelfth root of two, which is approximately 1.059. Every 12 notes, the pitch doubles.

[@ThePoisonedYouth]

Didn't really explain at all why we have 12 notes in western music. You talked about semitones and 12-tone temperament, but didn't even mention that there are other music systems other cultures use with different temperaments (the spacing of the notes), like Thai music which sometimes uses a 5-tone or 7-tone temperament. The reason we use 12 pitches is because western civilization has conditioned itself to only find that tuning scale pleasant, but the reality is there's nothing that makes 12-tone temperaments particularly special.

[@boptillyouflop]

IRL the type of musical tradition has a huge influence on tuning: Lots of xylophone/gongs = Ratios not important, 5/7/9-tone temperament (Thai, Gamelan, some Africa) Singing over rich low drone = Tuning based on the harmonic series (Aboriginal music) String/wind instruments, monophonic = Pure ratios, just intonation and quarter tones (Indian, Arabic, Turkish, Persian) String/wind instruments, lots of chords = Tuning in successive fifths, 12-tone temperaments (Chinese, European)

[@FeaturingMaxAsMax]

A little rushed in places but I thought it was a good and simple explanation, and I was surprised at the negative comments. He didn't use terms like "Pythagorean tuning" and "equal temperament" that might have scared people away. I was particularly interested to learn about the 53-note scale, which I had never heard of before. Wikipedia has more on this (including a sound file) at en.wikipedia.org/wiki/53_equal_temperament. It mIght have been fun to mention Arabic scales or maqam, which use 24 notes. One reason that Arabic music sounds haunting and weird to our Western ears is that they have a richer vocabulary of notes. Check out en.wikipedia.org/wiki/Arabic_maqam (includes sound files).

[@StevenJacks]

Thank you very much for the extra resources, FeaturingMaxAsMax.

[@therealfreeman]

Sometimes it's a little confusing following you from one step to the next. Other than that, good video.

[@Popart-xh2fd]

It's true, the first two steps he gives the rations 1:2 and 2:3, however in the next steps for the remaining 12 notes he doesn't mention the ratios used or explains them! I have the feeling he is oversimplifying his explanation hiding important information in it...

[@oliverfiedler8502]

it is allway up the same ratio 2:3 C:G:D:A:E:B:F#:C#:G#:D#:A#:E#:B# but B# is not the same as C !!! thats why the 13th tone is near but not the same as the first (it is 23,46ct higher) and so on with the 54th tone etc (no simplification and no hidden information) our whole 12tonsystem is based on pythagoras idea of combining tones with the 2:3 ratio and after doing so 12 times he skipped the pythagorean comma - (23,46ct) the difference between the first and the 13th tone what you can see here very clear in the linear or in the circle picture i agree there are some didactical "problems" in this video (changing from stringlength to frequency etc) but i guess the system with the 12 tones is best and most beautiful explained

[@StevenJacks]

This is correct. It's always 2:3. The ratios between the other notes (for example, 1st note to a 3rd note (skipping the second) is based around 2^whatever : 3 ^2. You can composite all the 2:3s to find these ratios if you want. Further, there are plenty of resources (wikipedia) that can tell you the ratios between any pitches you wish, and they're not relevant to the approach this video takes. :) We're simply finding pitches based on the last pitch, rather than comparing them all to one another. Thanks for watching and keep the questions / comments coming. These are great topics for discussion.

[@johngarzoli4547]

Since many tuning concepts and practices outside of Europe don't use 12 tone-equal-temperament and some such and Thai and Lao use something closer to 7 note equidistant, (at least in tuned percussion), the very idea that something slightly off from equal temperament might "not sound very good" needs qualification. I suppose what is meant is, that such sounds may not sound good to a listener unaccustomed to music that uses tuning systems other than 12 tone-equal-temperament. But even then, there is good evidence demonstrating that familiarity can help a listener become accustomed to any pitch relation (interval) so whether something 'sounds good' is entirely dependent on subjective interpretation

[@thehonestman26]

I come from a family of professional musicians and have played music my entire life. I stopped on this video just for fun. I'm sorry, but his has to be one of the most confusing explanations I've ever heard. What troubles me the most is how many people may have given up after watching this and just figured that learning music is too complicated.

[@dnwy7466]

It's confusing because of all of the false premises used. If he's wise he'll delete and start again with the facts and leave out the misinformation and naive assumptions, and perhaps discuss many of the excellent modern microtonal and traditional music styles around the world which DON'T use 12 notes instead of giving the impression most of the world doesn't exist if it doesn't fit his misunderstanding of music.

[@StevenJacks]

@@dnwy7466 Just most mainstream American music industries, K-pop, C-pop, J-pop, major music softwares, a standard piano, guitar, orchestra, most musical apps on your phone, most music coming out of europe back in the day, etc etc etc. use 12 notes per octave. I'm sure Suzuki and Yamaha products are much more common in 12 tones (or subsets there of). Outside of Indian Ragas and Middle Eastern scales that are indeed tuned differently, virtually all non-12 note music is experimental, and quite modern. And again, they're not in the mainstream of music heard around the world; especially on the average top 40 list. Besides, when you start off with a music student trying to pick up a guitar to play some riffs, I'm sure the first thing you do NOT say is "Dude, let's try some microtonality." Another way to think about this is English is not the most widely spoken language in the world. It's #3 based on number of speakers, behind both Mandarin and Spanish. Yet schools around the world are enforcing English in schools as a mandatory secondary language. English is becoming quite the standard, as 12 notes per octave has been for centuries. Other languages exist, and shouldn't be forgotten, but we have to start somewhere and have a basis, right?

[@dnwy7466]

@@StevenJacks If all your vid and it's title implied was "most American kids listen to mass-produced *mainstream* music, then I understand your reply here. Unfortunately it goes far further selling to the uninformed a very naive view of music. If the vid title and content instead implied more accurately that it was referring to mainstream westernised tastes as opposed to "outright music" then it would be somewhat less misinformative, although not without notable logical 'leaps of faith' to attempt in vain to prove a less than accurate point. I'm not saying the vid has no value, for example at best it benefits beginner music history fans by reiterating the basics of a naive and out dated over simplified version of the ratio system in terms of some common western habits; if the vid stayed within that remit it would have value to inspiring beginner historians without being loaded with misleading western-pop-biased pseudo-scientific (etc) assumptions about music as a whole. Although I'm grateful to educators like yourself, I believe in educators minimising cultural bias and associated misinformation - which has a tendency to spread. Thanks for your reply, I understand where you're coming from, unfortunately that wasn't presented as the scope of the vid in title or content. I wish you continued success. And.. btw.. you claim beginners are not interested in playing with microtones when they start out. Well, firstly, you'll be surprised what creative beginners play with, non-semitones, synths, vocals and bends being obviously examples, but secondly, perhaps beginners and singers playing with enjoying deviating from the childsplay semitone would be more prevalent if their educators were more inspiring and didn't simply undersell the reality and potential of music and improv by regurgitating naively oversimplified popular academic tropes.

[@StevenJacks]

@@dnwy7466 Quite true, Dn Wy. I agree with everything you said. As to your point, this is a quite biased video (though I would argue justifiably so, and you would not. :) Agree to disagree there, yeah?) Your examples of microtonal approaches for beginners are cop-outs though, you know as well as I do that a pitch bend is rooted in a standard note. Those exist easily in most 12et music anyway, as many of the great guitarists pitch bend all day long, but they still come back home to 12et that their guitar is tuned to. Also, I've traveled the world a bit, and talked to many people around the world, and found that we can all relate with the backstreet boys, and that American (and British and what have you) top 40 are trending not just in LA, not just in the US, but all over the world, as are K-Pop especially, but also Despacito and Gangnam style. Many more people (perhaps a majority, at least of youtube users) the world over know about these guys and their music, way more than know about microtonality...

[@ivangushkov3651]

Robert Donaldson maybe the problem is that you come from a family of musicians. There are no musicians in my family, and I have always seen music theory as this impenetrable confusing mess, where everyone teaching it assumes you already have understanding of it. Like, they teach you a scale but never explain why the scale is the way it is. Or what a scale is. Or why there is a scale. Or why the notes are ordered the way they are. Or wtf notes are. As a dumb engineering student, I found this to be a very simple, elegant way to justify the 12 note system with a bit of cool math.

[@davidjohns4745]

I liked your method of illustrating the concepts Thanks for clarifying something that has confused me for a long while. Somebody has to build the 53 note instrument soon.

[@forrcaho]

Sorry, this is a really bad explanation. You go through Pythagorean tuning (without calling it that (?)) which only requires talking about octaves and fifths. However, you only mention the possibility of other ratios as an aside at the end, brushing them off with the strange comment "the problem with using more and more complex ratios like this is that your initial interval doesn't sound very good". That's not true, at least for ratios of 5; the just major third (5:4) and just minor third (6:5) sound far more consonant than their Pythagorean counterparts (81:64 and 32:27 respectively). The major and minor thirds in the equal-tempered scale are approximations of these ratios built on 5, although not particularly good ones.

[@StevenJacks]

I agree completely. This is Pythagorean tuning for sure. What I meant by "not sounding very good" was in comparison to the octave and the fifth. The more complex you get, the more dissonant they get. Even though both a pythagorean major third and minor third sound fine to our ears, they're arguably not as pure as the octave and fifth. Great comment, and thanks for the critique.

[@forrcaho]

@@StevenJacks I think "sounding good" may not be exactly what you mean -- or at least, if I understand what you're getting at, that's not what I'd call it. Music theorists use the word "consonant" to describe a relationship between pitches that seem to go along together, and the octave and the fifth are definitely the most consonant. But the octave is so consonant that the pitches making it up are even called "the same note"; it doesn't seem to have much substance. The fifth seems to have "something there", but it's very sparse -- it's often described as being "strong" (giving us metal's "power chords"). It seems to me that it's only when we consider thirds that we get anything like conveying an emotion -- something like happiness with major thirds and sadness with minor thirds. To me, it is when we start dealing with thirds that harmonies begin to "sound good", in the sense of conveying some sort of nuance.

[@StevenJacks]

@@forrcaho Right. Go with consonance. :P Other systems may work, but the one that we have developed and widely use is the octave:fifth, because of their consonance. :)

[@boptillyouflop]

In European music, you HAVE to tune in consecutive fifths, because chords sound REALLY bad if the fifths in them are off tune. In C major, your C major chord C-E-G forces you to tune G one fifth over C, and other chords G (G-B-D), Dmin (D-F-A), Amin (A-C-E), Emin (E-G-B), F (F-A-C), Bb (Bb-D-F), Eb (Eb-G-Bb), Ab (Ab-C-Eb), and Db (Db-F-Ab), and B7 (B-D#-F#-A) lock up all the notes in a circle of fifths: Db-Ab-Eb-Bb-F-C-G-D-A-E-B-F#. Indian and Turkish music don't have chords, so they do use 5:4 and 6:5 thirds.

[@forrcaho]

​@@boptillyouflop You can have exact thirds and fifths in one key only, or close thirds and fifths in some but not all keys, or settle for noticibly out-of-tune fifths in order to be able to play in all keys in an equally acceptable (but by no means great) tuning. Western music was loath to abandon consonant thirds, which is why keyboard tunings went through a series of compromises that kept more-in-tune thirds at the cost of not being able to play in all keys -- first meantone, and then the Werckmeister tunings -- before finally settling for equal temperament. It took hundreds of years for equal-tempered thirds to sound acceptably consonant to Western ears.

[@cosmicsprings8690]

Hello sailor...good insight