Best music theory education channel, hands down. Every explanation is well motivated and intuitive, which is a rarity in music education. I've seen no one else explain the "why" of music theory so clearly
"It´s not instruction, it´s insight" This is so good. I always looked for the underlying Physics of Music explained like this. You explained it extremly well, on the point, clever and efficent(Also just the right amount of foreseeing possible Confusion of the viewer as well as things he already could know and skip)
I actually wrote a paper for my musicology final, discussing why the perfect fifth is responsible for 12 tone. I've basically touched a lot on the universal nature of the perfect fifth, lol.
this video is what made me realize how special non-equal tempered scales are. Thank you. You've inspired me (along with a math discovery i just made) to make my own! TLDR: I learned about the harmonic mean, and realized how you can use it to construct scales using the 'reflection' concept discussed in the video, along with the arithmetic mean (average). These scales are very very close to 12-TET. So I discovered how if you take 4 different means of an octave interval, you can get very close to the 5-8 chromatic scale degrees. Eg, we have 440 Hz (A5), and 880 Hz (A6). If you take the harmonic mean, you get a perfect 4th. (D5) The geometric mean, you get the 6th chromatic note (Eb5), in perfect 12-TET tuning. The arithmetic mean (aka, the average), yields a perfect 5th (E5). And the Root mean squared seems coincidental, but it actually supports this hypothesis i have. It yields a very close approximation to (F5). (440*sqrt(2.5) = 695.70 Hz). In this case, we did these 4 means for f vs 2f (440 & 880Hz). But if you do this for 4f, 8f, and 16f, you can fill out most of the chromatic scale. Just use the reflection concept like in the video and keep dividing by 2. You will see a shocking number of candidates. Strangely, RMS almost always yeilds a 'hit'. Ie, you always get a ratio very close to the 12-TET scale ratios compared to the root. While this seems obvious for powers of 2, the same thing occurs for most integers. So, most of the chromatic scale can be found with taking these different means using f vs f*2^n. Many yeild very nice rational ratios. Most of the scale can be constructed using only the harmonic and arithmetic means. But seeing the geometric and RMS constantly get soooo close to others is what I'm curious about. I haven't found a satisfying way to get the 'missing spots' (ie, 3rd and 9th chromatic note). The 9th one is close to the harmonic mean of f vs 5f. The 3rd note (harmonic minor) eludes me. For now, i have justified it as a 'quarter octave', which is the same definition in 12-TET. Which feels like cheating, except further 'so close'-ratios are found when doing means of f vs 2^(n+0.5) (where n is an integer). Very interesting. Welp, that's my book report. More exploration is needed. Making scales using that reflection concept is very liberating. Really makes you wanna explore the possibilities. 🤔
Your breakdowns of something that normally isn't easy to explain, is amazing! You've taken a difficult topic and made it clear in a fun, fast and brilliant way. Love the "simplified" animations too. Thank you so much. I'm donating for sure! (Just did a test donation, will send more if it worked)
Finally helped me understand Just Intonation, and there was so much I never even thought to ask. This is easily the best educational channel on youtube, you should be a teacher. Seriously, I wish there was someone like you for every subject.
You're an absolute reference for me, not only on understanding of music theory, but also on how to explain it. I recommend your videos as much as I can. I also watch them often to memorize how you explain the different subjects. I really admire your work and hope it will get as famous as it should.
In band our teacher would always tell us to bend the pitch of the third down because it's so sharp in equal temperament. It makes the I chord ring so purely
Amazing set of explanations. I had wondered about 12 tone system for ages but never really looked into it. Thanks, YT, for actually recommending a useful video.
This might be the best video i've seen of this subject. I've played the guitar since I was a kid and only recently started wondering about the "why's: "why the name octave?", "why 12 notes", how things developed in music, and so on. It's like I could not advance in music theory anymore without understanding all of these stuff. And in fact there are still some gaps in the whole basic history of notes/harmonic series/scale that I haven't figured out yet. For example, after reading and watching some videos, I've figured out the basics of the beginning of music, strings vibrations, Pythagoras, wave lenght, frequency, harmonic series, waves that are consonant and sound good to our years. But to get from this to the next step (understading the construction of scales) I'm not sure I understood properly. Apparently the harmonic series (simple ratios="easy" math=good to our ears) is the root of the rest of the stuff (scales, chords; melody and harmony), but I couldn't get the "logical path" from intervals appearing in the harmonic series (physical relations regarding wave lenght and frequencies) to the origin/construction of scales. Maybe I can understand the pentatonic scale (because the first overtones of the harmonic series have these ratio that are "simple" and produce consonant intervals, so it makes sense that everywhere in the world people use these intervals, because our ears perceive as consonant and pleasant), but the 7-scale or the 12-scale, I still don't get it. Maybe I have to watch that part at 9:58 over and over again, because 9/5 and 15/8 don't seem "simple ratios"...it still seems arbitrary for me. And i find interesting to see how many ways people try to explain this subject. The most fascinating for me is to try to reconstruct how things evolved from Pythagoras observations of strings to scales and then finally talking about "octaves" or "fifths" (i'm saying this because i've seen many videos talking about octaves and fifths as if they were a "given", like obvious names that shouldn't be explained in a context). Anyway, i'm just thinking out loud. It's too much stuff and my brain is exploding. I'm almost getting spiritual thinking that 12 is a mysterious number in nature, because it appears everywere. Thanks a lot for this video.
In this video and others like it by other RUclips creators such as 12tone or David Bennett piano, you excellently explain why we have a chromatic scale as well as the pros and cons. One question I hadn't thought of until recently is somewhat phrased "Why these 12 notes?" For example we know that 440 Hz is "A" and then everything else is a relative frequency from that. But how did "A" become standardized at 440? It's only in relatively recent times that oscilloscopes, frequency analyzers or other such equipment could determine that frequency. Traditionally at the beginning of an orchestra performance, the first violin plays an "A" and everyone else in the orchestra tunes to that pitch. A cappella singers often use a pitch pipe to get them on key at the beginning of a song. But again… How do we know that that first violin or the pitch pipe is actually accurate. When were the standards for notes established so that if you heard a concert in one venue or another or even between performances of the same artists, how did you know that they were on pitch according to some established standard?
In terms of the choice of 440, it is indeed arbitrary. There is some interesting history behind it; there used to be an amazing video on the subject on youtube but I can't find it anymore. And now youtube is swamped by dumb "440 vs 432" videos making it even harder to find good summaries. For a basic summary you could try "Why is A 440 Hz?" by Walk that Bass: ruclips.net/video/GwWXDwqgWjo/видео.html
When 6, 12, 30, and 60 show up it usually means simple ratios are nearby. Simple ratios are also why we have a 60, 60, 24 system for time. Same thing with binary and the powers of 2.
actually thats not necessarily whats going on here. 12tet being so composite is kind of a coincidence. for example 6tet actually completely misses 3/2. 19tet, 31tet, and 41tet all offer remarkable consonance while not being composite at all! when you divide an octave equally, you're doing it logarithmically, because that is how we perceive pitch. composite-ness and consonance arent necessary related.
Hey, awesome video. Can you do a video explaining different historical 12 tone tuning systems and why they might be better than 12-tet for certain pieces in certain keys? I wonder if there is a better tuning system of om playing in say, C major, where I don't need to worry about key changes? If we are playing only Bach for instance, what's the best tuning system to use? I know there is a lot of debate on which tuning system is best for Bach. I'd love to hear your input, especially in video format with the helpful visualizations.
Thanks for the suggestion! -- it's a little too far out of my area for me to seriously contemplate making, though. Have you searched around a bit for existing videos? I feel like it may be pretty well covered already, but I admit that I haven't looked very hard.
You should be able to get a grant from NEA, or some music teachers group. Very well done, and I would recommend it to anyone who challenges or questions the 12 tone system.
Love the explanation. I just struggled to see some of the tonal graphs on my phone screen. I remember from my astronomy days that photo negatives of Astrophotography were used to spot faint objects because our eyes are more sensitive to subtle changes in light objects than dark ones. I'm sure there are analogous affects in sound.
I like the way you graphically show the simple frequency ratios and their relationship to the root and octave. It’s also interesting that the ‘fifth’ at 3/2 the root is itself a 4/3 interval up to the octave, which in turn is a ‘fourth’ interval. As you point out, the fourth and the fifth are nearly perfect with the choice of 12 notes per octave. It’s fascinating with choice of 12 that each half-step interval mathematically becomes 2^(-12), or the twelfth root of two. Just under 6% higher frequency than the half-step below.
1:14 Octet means eight in Latin language, that is where octave word comes from. Since there are 7 notes + 1 repeatitive (root) note in an octave interval which makes 8 in total.
@@AFRoSHEENT3ARCMICHAEL69 Ik this is like 3 months late, but October used to be the 8th month. (Sept)ember (Oct)ober (Nov)ember (Dec)ember. Then the romans screwed up the calendar by adding January and February, and now those names lost their meaning
@@danielcohen2657 According to wikipedia July and August were originally named Quintilis and Sextilis before being renamed to honor Julius and Augustus en.wikipedia.org/wiki/Roman_calendar
Thanks for this great video - like others who have commented, I have been searching for an explanation as clear as yours for a long time. Donation made. Are you able to provide an explanation for what seems to me to be the natural next question? Viz: why does the "Tone, Tone, Semitone, Tone, Tone, Tone, Semitone" sequence for selecting 8 from the 12 tones on the scale make sense? Is it that this selection picks out the 8 tones that are most consonant?
Thanks Daniel, and thanks for the donation! This is a great question. Broadly speaking, the questions of "how many tones in an average scale chosen from the 12 tones" and "which scale out of the 12 tones is likely to be most common" are very influenced by cultural history, but I think a case could be made that there would be a tendency towards something in the neighborhood of 5-9 notes in a scale, for many of the same reasons that are described in this video as applying to the overall tonal system: more tones in a played scale means greater precision required of instrument construction, higher demands on the musician and listener to discriminate pitches, more opportunities for dissonance, etc. Too few tones in a scale means less opportunities for expression. 5-9 seems to be a rough middle ground that works for our monkey brains. As to which tones to select, I'd guess that consonance/dissonance plays a big role. You start with the octave; the fourth and fifth kind of demand a seat at the table. Past that, you pick notes that aren't too close together, are roughly evenly spaced, and which work well in combination with each other. I'm not sure if anyone has proven that the major scale is the most consonant possible collection of notes, but if you add a constraint that you want the fifth of each note in the scale to also be in the scale (i.e. construct the scale using a circle of fifths) then the major scale is as close as you can get (all the notes but the seventh have their fifth in the scale). From this analysis, the root mode of the major scale (AKA the major scale) doesn't have any special claim over the other modes. AFAIK the preference of this mode as the "major scale" over, say, the mixolydian mode (or any of the others, at least the ones with a natural fourth and fifth interval off the root present in the scale), is just an accident of history.
Love your channel - new subscriber! I just wanted to give you my 2-cents worth for the tuning of a pure fifth from a 12-TET 5th. 😄🎹 Oooh, don't know if this is too esoteric for your channel, but I'd love to see a similar take (your explanations are so very clear!) on tempered scales, like 1/4-comma meantone, 1/5-comma meantone, Valotti, and Werkmeister temperaments - etc. (Who's afraid of the Big Bad Wolf Chord?) 🐺
Thank you. I'm studying music by myself, as a hobby. Your channel helped me immensely. I have one question though. Why the C major scale is so ubiquitous? Why we named all the notes and intervals after it? Is this just history and traditions, or there is something fundamentally "good" about it?
Maxim Salnikov history and tradition. I'm not qualified to give the particulars, bit that's the gist. IIRC there are good googleable answers on the net. Glad you liked the videos!
Thank you for the video. Was there any study involving the measuring of perception of consonance and dissonance in the animal world (using dogs, cats, horses, domestic animals, etc)? It would be interesting to see it. Being a part time dog trainer, I noticed something: when using normal or a bit harsher voice (deliberately more dissonant), dogs pay more attention to it, look straight in the eyes. Such voice is good to tell the dog it is time to execute a command. But when using a more falsetto-like "singing voice" when praising the dog, which I believe involves more consonant sounds, the dogs react to that with enthusiasm and expects cuddling and a reward. Dissonant - alert and attention; consonant - award and relaxation.
I'm not sure... I'm purely speculating here, but it seems clear that many animals have perceptual abilities of pitch similar to us (given the similar structure of cochlea and the evolutionary value of hearing pitch, not to mention plenty of research confirming it) and while I've not heard of a study about consonance/dissonance in particular, I'd be surprised if an animal like a dog couldn't tell a difference between a pure tone and a tone with inharmonic overtones (e.g. howl vs growl).
Conclusion: 7 times the simplest interval (the octave) is pretty close to 12 times the next-simplest interval (the perfect fifth), so we just lowball the perfect fifth a little bit and say it’s exact. This system, 12-tone equal temperament, has the nice side effect that the other simple intervals are reasonably close to notes in here.
I wondered about this too. An alien could find the compromises that "are ok" for humans unacceptable. There could be completely different evolutionary pressures for hearing. Not even earthly other animals seem to care much for human music.
A não ser que você vá pedir para uma capivara analisar sua música. Se eu não importo com a música que estamos produzindo eu vou me importar com a música de quem? do pássaro que está cantando lindamente aqui fora?? Isso se chama aprendizado ou você coloca o lá 440Hz que o autotune te deu hoje e Aceita isso aí. Pelo seu comentário digo que sua frequência não é a música.
amazing video. I wonder if a digital instrument could be designed that automatically retunes itself to mathematically perfect ratios (rather than even temperament) as it is played?
Yes! It has been done, though the specific vendor escapes me now. Jacob Collier demonstrates it in some video somewhere... I wish I could dig it up. It might be an instrument for Kontakt, I'm not sure, but the idea is exactly as you suggest: as you play, the software is analyzing and guessing the key and so forth, and automatically adjusting chord tunings to cleaner intervals as you go. I think it's a really interesting idea and I hope it gains some more traction. It's not always obvious what the correct adjustment would be: even in a given chord you could argue one way or the other depending on how the intervals stack up. And in a dynamic piece of music what the next chord coming up will be will influence how you tune the current chord, etc, but that doesn't mean it's not worth trying!
When you played that interval at 3:12 I insantly thought of the song "NF - Remember This", I checked it and indeed it is exactly the same :) And I didnt listen to this song for over a month for sure!
I find it intriguing that in the graph at 6:48, the flat 7th is a harmonic 7th (a ratio of 7/4 or 1.75) instead of one of the "just minor sevenths" which are closer to the minor 7th in 12-TET (16/9 [1.777...], which is two stacked perfect 4ths or the inversion of the major second, 9/8; or 9/5 [1.8], which is a stacked perfect fifth and minor third and is still closer to the ratio we get using 12-TET, ~1.7818 [The actual ratio would be 1:2^(10/12).] ).
Sidenote: at 13:54, do you remember which just interval you used? Seems like it would have to be 9/5 since it was sharper than the 12-TET note, but any particular reason?
Yeah I wonder if the authors of that paper just picked out an even ratio near the peak, or if the resolution of their data is sufficient to distinguish between 7/4 and 9/5 and it clearly pointed to 7/4. Either way, 7/4 seems intuitively like it might be the more "naturally consonant" interval, just based on the smaller denominator (though apparently subjective consonance is not quite as simple as that).
@@zozzy4630 It would have been 9/5, yeah. those intervals came from some version of just intonation I was working from (I don't recall where I got it off-hand). I leaned towards systems with simpler intervals (e.g. 9/5 instead of 16/9) because I wasn't trying to build a just intonation scale that was most compatible with 12-TET and modulation and so on, rather I was trying to be "true" to the J.I. idea of each interval being as consonant as possible. Maybe I should have gone with 7/4, but 9/5 seemed more common, IIRC. In other words, no: there was no particular reason, just some loose impressions. :-)
because the consonant 3/2 is the most important one and assuming the number of notes in an octave is an even value, the minimum number of notes in an octave can be calculated with this formula: log(2)/log((3/2)/sqrt(2))=11.76 (approximately 12) by the way now i think that notes are not required to be at an equal distance from each other and they can be just the following ratios to sound good (not using more than 5 as denominator): 1, 6/5, 5/4, 4/3, 7/5, 3/2, 8/5, 5/3, 7/4 (mising ratio in the video), 9/5.
Consistent overtones appear naturally in analog acoustics (especially humans) and desire to land in these positions because the 12-tone scale comes straight from the amazing designer of music, and of everything: ALMIGHTY GOD.
So sounds in nature are generally not dissonant? That's fascinating. I was under the impression that musical notes were just a specific fine tuning of sound for a purpose. I wasn't aware that natural sounds also have a tendency to avoid dissonance.
Hmmm... what timestamp (if there is one) are you replying to, exactly? I might have phrased something poorly. I would say that "dissonance" is a bit of a loaded term, with ties to human psychoacoustics, but that to exist it requires a certain degree of specificity in the sound. E.g. the sound of wind is not usually considered dissonant even though it has plenty of (uncorrelated) frequencies present in it that 'conflict' with each other, but two unnaturally-pure sine tones at a strange interval to each other would be called dissonant. So I would say that most natural sounds are dissonant, pedantically speaking, just because noise in general doesn't involve particular relationships between frequencies, but it's a bit of a stretch since we don't perceive them that way because they aren't feeding us much specific pitch information. Presumably birds and many other animals making a noise experience evolutionary pressure to create sounds that are unusual or distinct in some fashion, e.g. not just noise like wind, rustling plants, splashing water, simple thuds, etc, and that leads to sounds that have particular pitches or rhythmic components to them. Said another way, sounds with less "acoustic entropy" become markers for intelligence, intention, or just presence of a life form. As far as those sounds being dissonant or not, I'm not sure I would make a claim that they tend not to be dissonant overall, but in at least some cases (e.g. human speech, bird songs) the ratio of overtones tend to fall into consonant patterns. And consonance does show up a lot in physics, e.g. frequencies generating overtones of themselves in vibrating bodies, such as in a plucked string or blown flute, and physics also govern the sound-producing organs in birds and humans, so, perhaps I should have said "animal-produced sounds tend to have some in-built consonance due to the means of production, but not necessarily consonance from moment to moment.)
15 :16 This graph is really great. I tried something interesting in Sonic Pi. I wrote a script to play a minor chord and shift the 3rd tone gradually upward to the major chord, the result changed along with it. With this tech, it allows me to modify the power of the emotion. This might be useful, since when we make music on computer, we don't need to worry about the instrument. It means ,if an octave is separated into more fragments, we might control the music more exquisitely. This might be extremely useful when making piano music on computer. let ms(minor second) = 2 to 1/12 == 1.059463 ms to 3 == 1.1892 ms to 4 == 1.259921 ms to 4 - ms to 3 == 0.0707139 6 / 5 == 1.2 ( 6 / 5 - ms to 3 ) / ( ms to 4 - ms to 3 ) == 0.01079/ 0.0707139 == 0.1526274 == 1/6.55. What if we separate an octave into 12*7or 12*8 fragments?
Why is 3/2 (1.5) slightly past the middle between 1 and 2? Shouldnt it be halfway? I know you have it right, my brain is just running in circles trying to rationalize this
@@bigbirdmusic8199 yes, exactly - that's the implication of 1:46, that linear points on the scale are skewed a little sure to the logarithmic(ish) nature of pitch perception.
@@CaseyConnor When you use more than one oscillator, you can ie. set the 2nd to n octave(s) lower or higher. And/or you can more or less slightly detune them to obtain certain "effects". @Mike Parmer: yes!
Kind of like when a violinist vibrates it's fingers on a string to detune it slightly, or the "chorus effect" on electronic instruments.it makes the note pass through the tempered tuning even if the instrument is stretched tuning.
@caseyconnor have you tried to space the 12 tones by 2^(i/12)? So that we have a logarithmic spacing between the notes. By this spacing the difference is much less then the even spacing. the good with sounding the ratios 2^(i/12) 1,000 1,000 1,067 1,059 1,125 1,122 1,200 1,189 1,250 1,260 1,333 1,335 1,400 1,414 1,500 1,498 1,600 1,587 1,667 1,682 1,800 1,782 1,875 1,888 2,000 2,000
Thanks -- what you describe is in fact the "even spacing" -- remember that the notes shown on screen are shown on a logarithmic scale (this is done because pitch perception is itself logarithmic, or at least roughly so. See around 1:45 for the note on that.) 12TET, the "even spacing" as described in this video, is indeed generated via 2^(i/12) just as you describe. So unless I have misunderstood you, you have invented 12TET on your own! :-)
@@CaseyConnor thanks for your answer! :) indeed I searched for frequencies of musical notes and figured that the ratios are exactly 2^(i/12)... so I just misunderstood even spacing for 1 + i/12 :) haha I guess that I invented it for myself from a misunderstanding... actually from this perspective of logarithmic perception, I interpret the ratios 3/2, 8/5 etc. as accidentally close to the evenly spaced logarithmic ratios, which probably mark the real pleasing ratios for our perception.
![Megan Thee Stallion - Mamushi (Remix) [feat. TWICE] [Official Audio]](http://i.ytimg.com/vi/5c0_u9PsrsQ/mqdefault.jpg)
This is the best explanation of this subject I've ever seen, thank you
hey it's the machine learning guy
agreed
man I didn't expect to see you around here ! it's nice ! :)
Couldn’t have said it better myself
Best music theory education channel, hands down. Every explanation is well motivated and intuitive, which is a rarity in music education. I've seen no one else explain the "why" of music theory so clearly
"It´s not instruction, it´s insight" This is so good. I always looked for the underlying Physics of Music explained like this. You explained it extremly well, on the point, clever and efficent(Also just the right amount of foreseeing possible Confusion of the viewer as well as things he already could know and skip)
I'm writing a math report for my high school IB report that's due tomorrow, and you just saved my ass.
I’ve been looking for this video ever since I started to learn the piano 15 years ago, but never knew it. Thank you!
I actually wrote a paper for my musicology final, discussing why the perfect fifth is responsible for 12 tone. I've basically touched a lot on the universal nature of the perfect fifth, lol.
Look into "Comma of Pythagoras" Fifths bear no connection to octaves or semitones. which is why he keeps "bending" here.
this video is what made me realize how special non-equal tempered scales are. Thank you. You've inspired me (along with a math discovery i just made) to make my own!
TLDR: I learned about the harmonic mean, and realized how you can use it to construct scales using the 'reflection' concept discussed in the video, along with the arithmetic mean (average). These scales are very very close to 12-TET.
So I discovered how if you take 4 different means of an octave interval, you can get very close to the 5-8 chromatic scale degrees. Eg, we have 440 Hz (A5), and 880 Hz (A6).
If you take the harmonic mean, you get a perfect 4th. (D5)
The geometric mean, you get the 6th chromatic note (Eb5), in perfect 12-TET tuning.
The arithmetic mean (aka, the average), yields a perfect 5th (E5).
And the Root mean squared seems coincidental, but it actually supports this hypothesis i have. It yields a very close approximation to (F5). (440*sqrt(2.5) = 695.70 Hz).
In this case, we did these 4 means for f vs 2f (440 & 880Hz). But if you do this for 4f, 8f, and 16f, you can fill out most of the chromatic scale. Just use the reflection concept like in the video and keep dividing by 2. You will see a shocking number of candidates.
Strangely, RMS almost always yeilds a 'hit'. Ie, you always get a ratio very close to the 12-TET scale ratios compared to the root. While this seems obvious for powers of 2, the same thing occurs for most integers.
So, most of the chromatic scale can be found with taking these different means using f vs f*2^n. Many yeild very nice rational ratios. Most of the scale can be constructed using only the harmonic and arithmetic means. But seeing the geometric and RMS constantly get soooo close to others is what I'm curious about.
I haven't found a satisfying way to get the 'missing spots' (ie, 3rd and 9th chromatic note). The 9th one is close to the harmonic mean of f vs 5f. The 3rd note (harmonic minor) eludes me. For now, i have justified it as a 'quarter octave', which is the same definition in 12-TET. Which feels like cheating, except further 'so close'-ratios are found when doing means of f vs 2^(n+0.5) (where n is an integer). Very interesting.
Welp, that's my book report. More exploration is needed. Making scales using that reflection concept is very liberating. Really makes you wanna explore the possibilities. 🤔
Okay! Now this makes more sense :)
Thank you so much for making these videos buddy!
Very good video. I really like your way of explaining things!
Your breakdowns of something that normally isn't easy to explain, is amazing! You've taken a difficult topic and made it clear in a fun, fast and brilliant way. Love the "simplified" animations too. Thank you so much. I'm donating for sure! (Just did a test donation, will send more if it worked)
Finally helped me understand Just Intonation, and there was so much I never even thought to ask. This is easily the best educational channel on youtube, you should be a teacher. Seriously, I wish there was someone like you for every subject.
You're an absolute reference for me, not only on understanding of music theory, but also on how to explain it. I recommend your videos as much as I can. I also watch them often to memorize how you explain the different subjects.
I really admire your work and hope it will get as famous as it should.
Thanks! So glad you find it valuable. :-)
Amazingly well put together! Thank you for making this!
9:40 The most concise and well layed-out 12-tet (and just int.) explanation I've ever seen!
Sir, this was an excellent explanation of a topic that has rattled my brain since I was a teen. Thank you so much for such great insight!
In band our teacher would always tell us to bend the pitch of the third down because it's so sharp in equal temperament. It makes the I chord ring so purely
Nice! Yeah, it can be tuned down 14 cents. Unless it's a minor third, in which case it goes up 16. :-)
your music theory videos are the best i have seen so far.
Amazing set of explanations. I had wondered about 12 tone system for ages but never really looked into it. Thanks, YT, for actually recommending a useful video.
As a music theory teacher myself, I'll recommend this to my students. Amazing work in this channel!
This video is exactly what I was looking for. Thank you for making the understanding of this topic so much easier!
I'm impressed by how long you managed to hold that G note.
39 seconds
This might be the best video i've seen of this subject. I've played the guitar since I was a kid and only recently started wondering about the "why's: "why the name octave?", "why 12 notes", how things developed in music, and so on. It's like I could not advance in music theory anymore without understanding all of these stuff. And in fact there are still some gaps in the whole basic history of notes/harmonic series/scale that I haven't figured out yet. For example, after reading and watching some videos, I've figured out the basics of the beginning of music, strings vibrations, Pythagoras, wave lenght, frequency, harmonic series, waves that are consonant and sound good to our years. But to get from this to the next step (understading the construction of scales) I'm not sure I understood properly. Apparently the harmonic series (simple ratios="easy" math=good to our ears) is the root of the rest of the stuff (scales, chords; melody and harmony), but I couldn't get the "logical path" from intervals appearing in the harmonic series (physical relations regarding wave lenght and frequencies) to the origin/construction of scales. Maybe I can understand the pentatonic scale (because the first overtones of the harmonic series have these ratio that are "simple" and produce consonant intervals, so it makes sense that everywhere in the world people use these intervals, because our ears perceive as consonant and pleasant), but the 7-scale or the 12-scale, I still don't get it. Maybe I have to watch that part at 9:58 over and over again, because 9/5 and 15/8 don't seem "simple ratios"...it still seems arbitrary for me. And i find interesting to see how many ways people try to explain this subject. The most fascinating for me is to try to reconstruct how things evolved from Pythagoras observations of strings to scales and then finally talking about "octaves" or "fifths" (i'm saying this because i've seen many videos talking about octaves and fifths as if they were a "given", like obvious names that shouldn't be explained in a context). Anyway, i'm just thinking out loud. It's too much stuff and my brain is exploding. I'm almost getting spiritual thinking that 12 is a mysterious number in nature, because it appears everywere. Thanks a lot for this video.
Very clearly explained, with minimal math and maximum visuals.
In this video and others like it by other RUclips creators such as 12tone or David Bennett piano, you excellently explain why we have a chromatic scale as well as the pros and cons.
One question I hadn't thought of until recently is somewhat phrased "Why these 12 notes?" For example we know that 440 Hz is "A" and then everything else is a relative frequency from that. But how did "A" become standardized at 440? It's only in relatively recent times that oscilloscopes, frequency analyzers or other such equipment could determine that frequency.
Traditionally at the beginning of an orchestra performance, the first violin plays an "A" and everyone else in the orchestra tunes to that pitch. A cappella singers often use a pitch pipe to get them on key at the beginning of a song.
But again… How do we know that that first violin or the pitch pipe is actually accurate. When were the standards for notes established so that if you heard a concert in one venue or another or even between performances of the same artists, how did you know that they were on pitch according to some established standard?
In terms of the choice of 440, it is indeed arbitrary. There is some interesting history behind it; there used to be an amazing video on the subject on youtube but I can't find it anymore. And now youtube is swamped by dumb "440 vs 432" videos making it even harder to find good summaries. For a basic summary you could try "Why is A 440 Hz?" by Walk that Bass: ruclips.net/video/GwWXDwqgWjo/видео.html
This is one of the best videos of this topic I have ever seen. Perfectly tempered explanation.
When 6, 12, 30, and 60 show up it usually means simple ratios are nearby. Simple ratios are also why we have a 60, 60, 24 system for time. Same thing with binary and the powers of 2.
actually thats not necessarily whats going on here. 12tet being so composite is kind of a coincidence. for example 6tet actually completely misses 3/2. 19tet, 31tet, and 41tet all offer remarkable consonance while not being composite at all!
when you divide an octave equally, you're doing it logarithmically, because that is how we perceive pitch.
composite-ness and consonance arent necessary related.
Really good explanation!
This is so clear and exact at the same time. Thank you!
This video is music to my eyes and brains
alhamdulillah, one of the bestest videos regarding to my questions.
This is the best explanation on youtube. Even for a complete beginner like me, I understand everything in the video. Very informative.
The way you see music is very different. Love it!
Thank you for your good work.
Thanks for this. This is the most useful video on the subject that I've seen. Keep it up - this really helped.
So much good information. Thank you!
Good stuff, really happy to see you are continuing to make content
"If you watch music theory videos to make yourself a better musician". I resent the accusation!
Another wonderful piece of information, thanks!
Hey, awesome video. Can you do a video explaining different historical 12 tone tuning systems and why they might be better than 12-tet for certain pieces in certain keys? I wonder if there is a better tuning system of om playing in say, C major, where I don't need to worry about key changes? If we are playing only Bach for instance, what's the best tuning system to use? I know there is a lot of debate on which tuning system is best for Bach. I'd love to hear your input, especially in video format with the helpful visualizations.
Thanks for the suggestion! -- it's a little too far out of my area for me to seriously contemplate making, though. Have you searched around a bit for existing videos? I feel like it may be pretty well covered already, but I admit that I haven't looked very hard.
The best explanation of this subject! Thanks!!
You should be able to get a grant from NEA, or some music teachers group. Very well done, and I would recommend it to anyone who challenges or questions the 12 tone system.
Very well done. Congrats!
Love the explanation. I just struggled to see some of the tonal graphs on my phone screen. I remember from my astronomy days that photo negatives of Astrophotography were used to spot faint objects because our eyes are more sensitive to subtle changes in light objects than dark ones. I'm sure there are analogous affects in sound.
I like the way you graphically show the simple frequency ratios and their relationship to the root and octave. It’s also interesting that the ‘fifth’ at 3/2 the root is itself a 4/3 interval up to the octave, which in turn is a ‘fourth’ interval. As you point out, the fourth and the fifth are nearly perfect with the choice of 12 notes per octave. It’s fascinating with choice of 12 that each half-step interval mathematically becomes 2^(-12), or the twelfth root of two. Just under 6% higher frequency than the half-step below.
Excellent. Just excellent explanations.
1:14 Octet means eight in Latin language, that is where octave word comes from. Since there are 7 notes + 1 repeatitive (root) note in an octave interval which makes 8 in total.
Why do we call it October when it's the 10th month?
This is where infinity comes from and why 8 is the symbol of infinity because this 7 note modal scales can technically repeat in octaves forever.
@@AFRoSHEENT3ARCMICHAEL69 Ik this is like 3 months late, but October used to be the 8th month. (Sept)ember (Oct)ober (Nov)ember (Dec)ember. Then the romans screwed up the calendar by adding January and February, and now those names lost their meaning
@@Eidolon2003 I thought it was July and August the Romans added (named after Julius Caesar and Augustus Caesar)?
@@danielcohen2657 According to wikipedia July and August were originally named Quintilis and Sextilis before being renamed to honor Julius and Augustus
en.wikipedia.org/wiki/Roman_calendar
You are doing a great work.
Gooood loord! My mind is about to explode couse its not get used to handle the amount of flawless powerfull revelation in such a tiny amount of time.
This needs to go viral. Can the RUclips algorithm take a hint and promote this way more?
wow, I love this, learned a lot.
Best video I have found, finally understanding things clearly
Thank you so much for this! Your videos are just awesome
many thanks, grazie mille , namaste , your work helps me understand and helps me go through depression
a lot of love for you!
Provides excellent insight
Very good... i learned a lot here. You explain well. I'm a blues guitarist so I bend strings a lot.
Excellent video, well done!
Thanks for this great video - like others who have commented, I have been searching for an explanation as clear as yours for a long time. Donation made. Are you able to provide an explanation for what seems to me to be the natural next question? Viz: why does the "Tone, Tone, Semitone, Tone, Tone, Tone, Semitone" sequence for selecting 8 from the 12 tones on the scale make sense? Is it that this selection picks out the 8 tones that are most consonant?
Thanks Daniel, and thanks for the donation! This is a great question. Broadly speaking, the questions of "how many tones in an average scale chosen from the 12 tones" and "which scale out of the 12 tones is likely to be most common" are very influenced by cultural history, but I think a case could be made that there would be a tendency towards something in the neighborhood of 5-9 notes in a scale, for many of the same reasons that are described in this video as applying to the overall tonal system: more tones in a played scale means greater precision required of instrument construction, higher demands on the musician and listener to discriminate pitches, more opportunities for dissonance, etc. Too few tones in a scale means less opportunities for expression. 5-9 seems to be a rough middle ground that works for our monkey brains. As to which tones to select, I'd guess that consonance/dissonance plays a big role. You start with the octave; the fourth and fifth kind of demand a seat at the table. Past that, you pick notes that aren't too close together, are roughly evenly spaced, and which work well in combination with each other. I'm not sure if anyone has proven that the major scale is the most consonant possible collection of notes, but if you add a constraint that you want the fifth of each note in the scale to also be in the scale (i.e. construct the scale using a circle of fifths) then the major scale is as close as you can get (all the notes but the seventh have their fifth in the scale). From this analysis, the root mode of the major scale (AKA the major scale) doesn't have any special claim over the other modes. AFAIK the preference of this mode as the "major scale" over, say, the mixolydian mode (or any of the others, at least the ones with a natural fourth and fifth interval off the root present in the scale), is just an accident of history.
Extremely interesting. Always wondered about this. My mind is blown!
Really good explanation 👍👍
Fantastic video!
wow, best explanation I have seen on the net
Love your channel - new subscriber! I just wanted to give you my 2-cents worth for the tuning of a pure fifth from a 12-TET 5th. 😄🎹
Oooh, don't know if this is too esoteric for your channel, but I'd love to see a similar take (your explanations are so very clear!) on tempered scales, like 1/4-comma meantone, 1/5-comma meantone, Valotti, and Werkmeister temperaments - etc. (Who's afraid of the Big Bad Wolf Chord?) 🐺
இசை பற்றிய விளக்கம் எளிமையாக புரிந்துகொண்டேன்.good
That explains a feeling I sometimes have while playing guitar, that notes don't always totally blend together even though I'm tuned.
Correct. Standard guitar tuning/frets are only 'near enough' for convenience.
see: ruclips.net/video/D8EjCTb88oA/видео.html
Best Explanation of this topic.
Wow that's so good, donation made.
Thank you. I'm studying music by myself, as a hobby. Your channel helped me immensely.
I have one question though. Why the C major scale is so ubiquitous? Why we named all the notes and intervals after it? Is this just history and traditions, or there is something fundamentally "good" about it?
Maxim Salnikov history and tradition. I'm not qualified to give the particulars, bit that's the gist. IIRC there are good googleable answers on the net. Glad you liked the videos!
What a high-quality video.
Thank you for the video. Was there any study involving the measuring of perception of consonance and dissonance in the animal world (using dogs, cats, horses, domestic animals, etc)? It would be interesting to see it. Being a part time dog trainer, I noticed something: when using normal or a bit harsher voice (deliberately more dissonant), dogs pay more attention to it, look straight in the eyes. Such voice is good to tell the dog it is time to execute a command. But when using a more falsetto-like "singing voice" when praising the dog, which I believe involves more consonant sounds, the dogs react to that with enthusiasm and expects cuddling and a reward. Dissonant - alert and attention; consonant - award and relaxation.
I'm not sure... I'm purely speculating here, but it seems clear that many animals have perceptual abilities of pitch similar to us (given the similar structure of cochlea and the evolutionary value of hearing pitch, not to mention plenty of research confirming it) and while I've not heard of a study about consonance/dissonance in particular, I'd be surprised if an animal like a dog couldn't tell a difference between a pure tone and a tone with inharmonic overtones (e.g. howl vs growl).
Conclusion: 7 times the simplest interval (the octave) is pretty close to 12 times the next-simplest interval (the perfect fifth), so we just lowball the perfect fifth a little bit and say it’s exact. This system, 12-tone equal temperament, has the nice side effect that the other simple intervals are reasonably close to notes in here.
Just enough information. Not so much I get lost, not so little it's dumbed-down. As a lifelong musician with no maths perception, I thank you.
COOL informative video! 😊
I wondered about this too. An alien could find the compromises that "are ok" for humans unacceptable. There could be completely different evolutionary pressures for hearing. Not even earthly other animals seem to care much for human music.
A não ser que você vá pedir para uma capivara analisar sua música.
Se eu não importo com a música que estamos produzindo eu vou me importar com a música de quem? do pássaro que está cantando lindamente aqui fora??
Isso se chama aprendizado ou você coloca o lá 440Hz que o autotune te deu hoje e Aceita isso aí.
Pelo seu comentário digo que sua frequência não é a música.
amazing video. I wonder if a digital instrument could be designed that automatically retunes itself to mathematically perfect ratios (rather than even temperament) as it is played?
Yes! It has been done, though the specific vendor escapes me now. Jacob Collier demonstrates it in some video somewhere... I wish I could dig it up. It might be an instrument for Kontakt, I'm not sure, but the idea is exactly as you suggest: as you play, the software is analyzing and guessing the key and so forth, and automatically adjusting chord tunings to cleaner intervals as you go. I think it's a really interesting idea and I hope it gains some more traction. It's not always obvious what the correct adjustment would be: even in a given chord you could argue one way or the other depending on how the intervals stack up. And in a dynamic piece of music what the next chord coming up will be will influence how you tune the current chord, etc, but that doesn't mean it's not worth trying!
Hey, bro. You videos (podcasts))) are amasing! Could you make one about infrasound?
I'll put that on the suggestion list!
I think it would also be useful to depict the equal spacing on a linear scale to show how the spacing of the frequencies looks in that view.
Yeah. Note that you can at least get a loose feel for this on the graph at 6:45 which uses a linear scale.
Why not ask you from where is comming one second, one millimetre, or one gramm???
13:33 made me finally understand
When you played that interval at 3:12 I insantly thought of the song "NF - Remember This", I checked it and indeed it is exactly the same :) And I didnt listen to this song for over a month for sure!
I mean the interval at the very beginning that the song starts with.
@@krzysztofq7420 Hah, good ear, yeah!
wow that was so good ,thank you so much , i learned a lot
Thank u, that was great :)
best English explanation of 12-TET
Thanks! I'd be curious what the best non-english explanation(s) is/are in your opinion?
I find it intriguing that in the graph at 6:48, the flat 7th is a harmonic 7th (a ratio of 7/4 or 1.75) instead of one of the "just minor sevenths" which are closer to the minor 7th in 12-TET (16/9 [1.777...], which is two stacked perfect 4ths or the inversion of the major second, 9/8; or 9/5 [1.8], which is a stacked perfect fifth and minor third and is still closer to the ratio we get using 12-TET, ~1.7818 [The actual ratio would be 1:2^(10/12).] ).
Sidenote: at 13:54, do you remember which just interval you used? Seems like it would have to be 9/5 since it was sharper than the 12-TET note, but any particular reason?
Yeah I wonder if the authors of that paper just picked out an even ratio near the peak, or if the resolution of their data is sufficient to distinguish between 7/4 and 9/5 and it clearly pointed to 7/4. Either way, 7/4 seems intuitively like it might be the more "naturally consonant" interval, just based on the smaller denominator (though apparently subjective consonance is not quite as simple as that).
@@zozzy4630 It would have been 9/5, yeah. those intervals came from some version of just intonation I was working from (I don't recall where I got it off-hand). I leaned towards systems with simpler intervals (e.g. 9/5 instead of 16/9) because I wasn't trying to build a just intonation scale that was most compatible with 12-TET and modulation and so on, rather I was trying to be "true" to the J.I. idea of each interval being as consonant as possible. Maybe I should have gone with 7/4, but 9/5 seemed more common, IIRC. In other words, no: there was no particular reason, just some loose impressions. :-)
because the consonant 3/2 is the most important one and assuming the number of notes in an octave is an even value, the minimum number of notes in an octave can be calculated with this formula:
log(2)/log((3/2)/sqrt(2))=11.76 (approximately 12)
by the way now i think that notes are not required to be at an equal distance from each other and they can be just the following ratios to sound good (not using more than 5 as denominator):
1, 6/5, 5/4, 4/3, 7/5, 3/2, 8/5, 5/3, 7/4 (mising ratio in the video), 9/5.
Consistent overtones appear naturally in analog acoustics (especially humans) and desire to land in these positions because the 12-tone scale comes straight from the amazing designer of music, and of everything: ALMIGHTY GOD.
Seek therapy, not 'god'.
Beautiful stuff
Darn that Tritone be real sharp in Equal Temperament in comparison to Just Intonation...
7/5 is a very consonant interval
So sounds in nature are generally not dissonant? That's fascinating. I was under the impression that musical notes were just a specific fine tuning of sound for a purpose. I wasn't aware that natural sounds also have a tendency to avoid dissonance.
Hmmm... what timestamp (if there is one) are you replying to, exactly? I might have phrased something poorly. I would say that "dissonance" is a bit of a loaded term, with ties to human psychoacoustics, but that to exist it requires a certain degree of specificity in the sound. E.g. the sound of wind is not usually considered dissonant even though it has plenty of (uncorrelated) frequencies present in it that 'conflict' with each other, but two unnaturally-pure sine tones at a strange interval to each other would be called dissonant. So I would say that most natural sounds are dissonant, pedantically speaking, just because noise in general doesn't involve particular relationships between frequencies, but it's a bit of a stretch since we don't perceive them that way because they aren't feeding us much specific pitch information. Presumably birds and many other animals making a noise experience evolutionary pressure to create sounds that are unusual or distinct in some fashion, e.g. not just noise like wind, rustling plants, splashing water, simple thuds, etc, and that leads to sounds that have particular pitches or rhythmic components to them. Said another way, sounds with less "acoustic entropy" become markers for intelligence, intention, or just presence of a life form. As far as those sounds being dissonant or not, I'm not sure I would make a claim that they tend not to be dissonant overall, but in at least some cases (e.g. human speech, bird songs) the ratio of overtones tend to fall into consonant patterns. And consonance does show up a lot in physics, e.g. frequencies generating overtones of themselves in vibrating bodies, such as in a plucked string or blown flute, and physics also govern the sound-producing organs in birds and humans, so, perhaps I should have said "animal-produced sounds tend to have some in-built consonance due to the means of production, but not necessarily consonance from moment to moment.)
Fascinating
Really cool vid
13:31 was very educational
15 :16 This graph is really great. I tried something interesting in Sonic Pi. I wrote a script to play a minor chord and shift the 3rd tone gradually upward to the major chord, the result changed along with it. With this tech, it allows me to modify the power of the emotion. This might be useful, since when we make music on computer, we don't need to worry about the instrument. It means ,if an octave is separated into more fragments, we might control the music more exquisitely. This might be extremely useful when making piano music on computer.
let ms(minor second) = 2 to 1/12 == 1.059463
ms to 3 == 1.1892
ms to 4 == 1.259921
ms to 4 - ms to 3 == 0.0707139
6 / 5 == 1.2
( 6 / 5 - ms to 3 ) / ( ms to 4 - ms to 3 ) == 0.01079/ 0.0707139 == 0.1526274 == 1/6.55.
What if we separate an octave into 12*7or 12*8 fragments?
Also, electronic instruments could "retune" themselves on the fly to make each chord sound more consonant.
@@Vandalfoe Oh, so in math, this is not a chord any more, this is a new hue?
Why is 3/2 (1.5) slightly past the middle between 1 and 2? Shouldnt it be halfway? I know you have it right, my brain is just running in circles trying to rationalize this
Is it because its logarithmic?
@@bigbirdmusic8199 yes, exactly - that's the implication of 1:46, that linear points on the scale are skewed a little sure to the logarithmic(ish) nature of pitch perception.
@@CaseyConnor ahh yes that was driving me crazy. thanks for responding so fast! Great video as well!
So this is why detuning function in synth sounds nice sometimes. Right?
Hmmm, I'm not familiar with what you describe, but it sounds plausible.
@@CaseyConnor When you use more than one oscillator, you can ie. set the 2nd to n octave(s) lower or higher. And/or you can more or less slightly detune them to obtain certain "effects". @Mike Parmer: yes!
Kind of like when a violinist vibrates it's fingers on a string to detune it slightly, or the "chorus effect" on electronic instruments.it makes the note pass through the tempered tuning even if the instrument is stretched tuning.
@caseyconnor have you tried to space the 12 tones by 2^(i/12)? So that we have a logarithmic spacing between the notes.
By this spacing the difference is much less then the even spacing.
the good with
sounding the
ratios 2^(i/12)
1,000 1,000
1,067 1,059
1,125 1,122
1,200 1,189
1,250 1,260
1,333 1,335
1,400 1,414
1,500 1,498
1,600 1,587
1,667 1,682
1,800 1,782
1,875 1,888
2,000 2,000
Thanks -- what you describe is in fact the "even spacing" -- remember that the notes shown on screen are shown on a logarithmic scale (this is done because pitch perception is itself logarithmic, or at least roughly so. See around 1:45 for the note on that.) 12TET, the "even spacing" as described in this video, is indeed generated via 2^(i/12) just as you describe. So unless I have misunderstood you, you have invented 12TET on your own! :-)
@@CaseyConnor thanks for your answer! :) indeed I searched for frequencies of musical notes and figured that the ratios are exactly 2^(i/12)... so I just misunderstood even spacing for 1 + i/12 :) haha I guess that I invented it for myself from a misunderstanding... actually from this perspective of logarithmic perception, I interpret the ratios 3/2, 8/5 etc. as accidentally close to the evenly spaced logarithmic ratios, which probably mark the real pleasing ratios for our perception.
Great video
Others: "I studied music for years!"
RUclips: *shows recommended videos*
Me: "learned in a few minutes more than in any music lesson"
10/10 video
musicians: close enough
Pay attention to 10:35. This is why xenharmonics work so well.