Music theory is supposed to be hard - it's not. It's actually very simple. I teach you how to build the major and minor scales with very simple algebra.
I’m an engineer. I started learning guitar and eventually found a book on music theory that was tremendously helpful. I ended up with a spreadsheet with the modes, chords, scales, and a basic chord-builder, etc. I still can’t play guitar.
Just sit and play. And I don't mean play a scale or a song etc.... just play. Like Pithagoras did. Experiment. Experiment with a single string, with two, with intervals. Play listening to what you like or not. With strumming, with picking with one finger, two. Sliding with the left, etc.... Once you find you like to sit and "play" with the guitar, you start learning how to play it. Stop forcing it.
For those wondering how any of this could possibly be useful: Forming connections. Looking at topics from weird perspectives is fundamental to efficiently learning-by-doing and making personal breakthroughs, both in that topic and in others. As a kid you probably spent dozend of cumulative hours digging through your Lego bin looking for a specific brick and instead finding half the pieces you were looking for *yesterday*. Same deal with mental connections and especially breakthroughs, they appear most consistently when you're focusing on something else and some set of conditions triggers a sense of familiarity.
Nah , actually you look at the 72 nonrepeating tones of a piano and realize that its a 12 tone abacus with 6 columns. You cant discover that on a guitar because the six strings and at least 90 repeated tones will lull to sleep before you find a similar straight line approach for the 4 octaves on a guitar.
This stuff is vital to alternate tuning systems. What we hear in music is not this scale, but an approximation with 12 notes. Other tuning systems such as 31edo strive for similar things
I've been playing for 40 years and I am confused as to the purpose of this angle, I know what he is talking about but this does not clear up anything or simplify it. A basically unscripted narration does not help either.
I think he overcomplicates it a bit. I mean, he's not wrong, but the length of the string and the specific intervals can be simplified with simple finger placement within the shapes of the scales based on the root.
I think you're right, my mother taught me to read music as a youngster and for whatever reason, I've always thought about my playing music in mathematical terms. Being in electronics as a profession, the correlation between algebra and music makes perfect sense to me. I can also see why it doesn't to other people, my brother who is a professionally trained singer doesn't see the connection. Whatever works I guess.
I don’t think this video is meant for beginners. But if your student asked you “but why?”, then this is the video you show them. Otherwise, just have them memorize the intervals and play/recall them well enough and that’s good to move on to other stuff when it comes to performance.
Yeah, that's the thing. It's not that the math is itself is complicated. But one thing is dividing a chocolate bar in 4 pieces, another is dividing one beat in 4. One thing is adding 3 + 4, another thing is adding a major 3th and a perfect 4th, which are basically sound waves that you have to identify with your ears and memorize where they are located in your instrument. In other words, it's basic mtah applied to abstract material, which makes it complicated.
Not really. All it takes to connect meaning to what you’re hearing is to define the meaning yourself. Create your own musical language of what the things you hear mean to you. And label them. That’s how you develop an ear for music. By associations in your mind.
This video really makes the major scale visually understandable. The circles make it look sonic and they hit all the correct frets. A great bit of history in there too.
Sound waves are rather cyclical, since we measure them in cycles. I can't believe this didn't click for me until this video. So yeah, agreed, the circles are an incredible visual component!
That last complete image is astoundingly beautiful. It would be great wall art... serving as a functional reference also. I've known of the relation of most of the harmonics on the strings, but never ever seen it laid out so visually stunning. I can see why it all makes sense now. Thank you!!
The last math class I received a passing grade was in the 3rd grade. I had to repeat 8th grade algebra 4 times and the only reason I was not held back a grade was that all my other subject I had 100%, but math my grades were never above D-. In college I chose journalism as my major because it only required the most basic math. I still had to take remedial math six time and ended up dating the last teacher, a graduate assistant and she mercifully passed me because I simply never got it. Now in my 50s I never use any form of math beyond basic addition etc and always with a calculator. I've been a musician for 42 years and have never been able to grasp music theory. I had to stop this video halfway through because I was literally gasping for breath, sweating and with tears in my eyes.
I'm decent at math at I'm just laughing at the graph @11:45 . This guy has lost the plot here. If you tell someone it's simple and you show them this visual aid they are going to laugh in your face. There are a dozen ways to simplify music theory and this just ain't one of them.
@@ilovebutterstuff hahahahha. the moral was a strong one too- even guys can fuck their way to success/fuck their way out of trouble/fuck their teacher, etc. hahahahaha
Thank you so much. I have always shied away from learning music theory because so much of it just seems like "memorize this" without explaining why. I can't tell you how many times my teacher just listed off the intervals, calling some major, some minor, some perfect, and just wanting me to know their names like it meant anything to me. So many things in music theory for me have just been "this is what we call it when this happens" and it feels like no matter how many things I memorize I still don't know how they fit together or what their purpose is. Thank you for explaining it like the science that it is, instead of making me learn it like a language.
Innumerable amounts of people have felt like you. "Teachers" have miserably failed at making the connections to application, both theoretical/logical and the musical feel/effect one gets.
Per Lydian chromatic theory, "the" major scale built on perfect fifths would be the Lydian scale. (And therefore, as Miles Davis once said, the center note of the piano keyboard should be "middle F" rather than "middle C"...!)
The geometric visuals are great. It has helped me understand the relationship of the frets to the strings. I always wondered why a guitar seemed so different than a piano. I wondered why it's layed out like it is. Its the way it has to be for western music. This was enlightening.
Pythagoras just adapted his maths to existing musical scales. He did not invented them as widely reported. The picture next my username shows a statue of a man playing a harp. This statue is dated 2800 BC. Do you think a harp can be constructed and played without the use of scales? Now, Pythagoras lived some 2200 years after that statue was made. So little we know about history
consider that intervals in music contain much of the emotional content of the music. Most of the ancient harps only had five or six strings. These were based on the perfect intervals including the octave. So they did not have Major and Minor scales.
@@randyleazenby2351 you talk like you have seen one of these harps. If you look closely on the statue you will see this has room enough for maybe 20 strings. You will find it on the N.Y Met Museum as ''harp player''
The question though is how much did they understand about what they were doing or did they just set things up because they sounded good. It's possibly to get a long way on just natural talent.
Hello, I genuine enjoy the perspective you offer. I think anyone who complains that the video is unnecessarily complicated is unnecessary complicated themselves because, clearly, this video is about exploring music through a mathematical lens. It's meant to offer a different perspective to those who already know music theory not teach beginners the fundamentals. There are thousands of videos that explain music theory in "simple" ways on UA-cam and having the choice to explore it this way offers unique insights for me. The diagram was especially appreciated. However, I did note one error worthy of correction: The etymological roots of the term scale in music are not from weights but late middle English from the Latin word "scala" meaning ladder. I'd also appreciate also appreciate recognition of the equal temperament and how, despite it being the standard, does not apply in this context. Thank you.
exactly. Scala = temperament. I noticed Modal has an old Greek meaning of mood and a newer Latin meaning of Mesurement. that would explain modulation, different Mesurement along a scale to arrive at a different key. the "modal harmony" name , would make more sense, if it were Modular Harmony
Yep. Somewhere there must be a video that goes the other direction but I have yet to find it. Math and music theory are intimately tied together but Ive yet to find anyone that can "do both" fluently.
@@johnmcminn9455 Sadly this guys videos are over 95% music related and what little math I could find was well beyond the basics of algebra . It is these basic "translations" between the two languages of music and math that I cannot find anywhere.
wow, welcome back! I just found your channel about a week ago and it has been a revelation. Just when I thought this had become a legacy channel and then this upload shows up. Please keep it up
The History was interesting, but all the circles on the fret board got confusing. Especially when they went behind the 12th fret Colors might help, a different one for each interval.
Dude the lines is right when IT CLICKED, like those are all the ways notes interact and their intersections of sinewaves when played together, music is playing with air to make your brain experience emotion, its the closest thing we have to magic
@@chrishei3111 I was trying to learn algebra using the Music knowledge I have, I failed the test, got kicked out of my home, my cat got eaten by a raccoon the second night I was out side, (I was saving him for when I ran out of money), but I'm glad things worked out for you Chris, I'm wondering in that 8 minutes could have been better spent watching a algebra video. (Just kidding Creator/Uploader, any angle is productive and worth looking into. I did come here for Music and I don't have a cat (any more), I can't stop...😂 I'll show my self out thanks.
This is absolutely golden. Thank you so much for this. That last picture I actually have done when working with geometry a couple of years back. This makes so much sense. Huge thank you
The idea that you can "weigh" the notes, hence the name "musical scale" probably only works in the English world. In french, it's "gamme" (series of things of the same nature but with nuances, as in "shades" in english. "different shares of blue"), in Spanish it's "escala" as in scale in the context of size (1:2 scale of a map for example) or ladder; in German it's "Tonleiter", literally "tone ladder".
Yeah scale comes for sure from the latin scala which meaning ladder. I guess thecreator comes off so nervously because he is making stuff up on the fly.
@@sebastianhelm1718 eh things tend to be confused when someone does their own research and makes assumptions connecting their current knowledge with what they're learning, the rest of the video is intriguing correct and helpful or not
Thank you so much for this content. I really know a lot about music theory and had even studied about these measures before but it was the first time I realized the importance of the perfect intervals and their relation mathematically to compose the major and minor keys. You just helped me so much to organize all the content in my head. Thank you so much!
There is so much deeper things than this. Bach actually used set theory for his last unfinished fugue and the most simple think about the main theme is it's symmetrical. The work is called The Art of Fugue BWV 1080
@@gumbilicious1 it was group theory I just double checked the article about it. But even then I don't know any explanation Bach was definitely a genius and the fact that all of his works are mathematically calculated is undoubted. Maybe it's not Bach who knew about group theory but Zoltan Gömz did an observation on this unfinished fugue I'll send it to you if you want. Either way I think it would be too much to say that Bach's last work was universal and prophetical.
Amazing. The ends of the circles are also the natural harmonics, by touching strings there you set the string into another vibration mode. The visuals are beautiful too nice job!
This is absolutely golden. Thank you so much for this. That last picture I actually have done when working with geometry a couple of years back. This makes so much sense. Huge thank you 🙏
I saw a Luthier do something similar once with a compass and protractor ... he was working out the spacing of the frets so i'd imagine he was just working out step one of this same system. Very interesting video. Seeing it all visually explained like that is mindblowing. Well done.
This is a very nice visual representation and also very nice in terms of the mathematical relationships. I really like having this additional information in my arsenal when explaining things to students. Yet, I do have to agree with many of the comments below. This is only clear, when one already "presupposes" that the student understands what a major and a minor chord is, or an interval of a major or minor, for that matter. As you were frustrated, wanting to know "why these notes", a student of yours, learning this as their first exposure to major scales may ask: "why a major chord, and, where the heck does it come from". It also only makes any sense when one, again, presupposes that the new learner has any clue as to which notes they want to "discover" in the major scale. A huge amount of the steps used in this explanation are built upon the assumption that the aim of the discovery is to "find" the notes of a major scale, and also on multiple (sometimes complex) principles in music. As a teaching technique, this does not clarify much for a new student off the bat. It does absolutely help someone who already knows music theory, to have a nice additional angle to understand relationships of notes from a mathematical stance, and also be aware of how the notes relate to each other. This is not, however, a plausible route for explaining how we came to have the actual 12 notes, or the actual 7 notes of either diatonic music or the major scale. Using the above process, one would not "discover" the notes of the scale unless you set out to "prove where they lie", based on your already existing understanding of all of them. Take as an example the 2nd. From an uniformed perspective, why would you use the 9th, and then lower it to the 2nd? That can only be done post-understanding the scale already. Personally, I am not entirely sure how we actually came to have the 7 steps of the major scale, as I stopped studying formal theory after completing G6 theory exam - I then continued learning as I performed in the industry along with other musicians. BUT, I am inclined to think that it grew out of the pentatonic scale more than it grew out of someone using the above method. The pentatonic scale has been around all over the planet, and for ages longer than the major/minor scales, and it does seem somewhat likely that a next experimental step from there could lead to a major scale. Over-and-above that, the pentatonic scale is something that appears to be very much "inbuilt" into most people, and has an easy execution by most humans, regardless of their musical training. Sure, this may be because of it's use over centuries, I agree, but, the ease with which it "falls on the ear" may play a role. As far as I understand it, also, the very major/minor/augmented/diminished intervals owe their description to how they appear in a major or minor scale (scales which you would need BEFORE you understand or describe the intervals), and then, the 4 main chord groups (major/minor/augmented/diminished) owe their existence and description to the combination of intervals (specifically a third and a fifth above 1). Thus, the explanation above, though insightful, does appear cart-before-horse.
Hey. Agreed about this, I was thinking he's starting his reasoning from the result, knowing what he's looking for... You're probably right about the penta too, the first five notes of the circle of fifths is a major penta, an "easy" way to start discovering things.
This system looks like a Five-limit tuning, where the ratio's are made with numbers constructed with the prime numbers 2,3 and 5. It is used in just intonation. No instructions on how to construct other tones are provided, so I guess we'll have to remain in one and the same key or mode thereoff. And the wolf interval of (40/27) between the second and the sixth note of this scale, is also not mentioned at all. I can assure that the ratio's will get even more messy once you start adding the last 5 notes if you don't use a well thought out system. Also the ratios are written the wrong way; as the reciprocals of the actual ratios. If you go up from the tonic to the P5 for instance you go up a fifth so you would multiply by 3/2 (instead of 2/3)
I have previously only seen this ratio stuff presented in scattershot form, a bit here and a bit there. Nothing systematic like this with someone working out a whole scale from fundamentals. So this was revelatory! Thank you! :)
…and when music students needed him most he vanished… Joking aside this is the type of stuff I needed to see first as a prep before picking up a guitar, someone who will actually show me what these terms mean and have a backstory as to its origins making it easier to remember, not just giving me some pneumonic device and calling it a day. Students already have the desire to learn, but this is a much more fundamental way of teaching it in the system we have. Unless we can all agree upon a new system for creating music that isn’t ancient we will have people who fell through the cracks like me. I’m luckily only in my mid twenties but I’ve been interested in music all my life, taking it the most seriously in High School and now College. Teach this to kids old enough to to understand it.
Everyone learns a bit differently and this video is no more complicated than any other that talks about the "why" of music theory. If it didn't make sense to you, then you simply don't think the same way. I'm very much a neophyte, and I'm more in my element with math than music theory to begin with, but I learned plenty from this video. Take the tidbits you can use and they'll accumulate over time, just don't stop learning. And to anyone who feels they don't have the music theory chops to follow, I recommend doing some reading/watching about the basics of scales, degrees, and intervals. Just the 101 stuff, and you'll be following along in no time.
Almost. This confirms my past statements about graphic animations and teaching. That just because you can synchronize words with graphics does NOT mean that you are communicating or imparting knowledge.
Interesting as can be! I have to say, if modern practical music theory was truly algebra, I would never get it, thankfully, it is intuitive and easily understandable because I can hear it, while math makes my mind go fuzzy and dark. By practical music theory I mean being able to construct scales, spell any chord, understand chord progressions, know what bass notes work best, master the circle of 5ths, be able to transpose on the fly, etc. If music theory was taught like this video, I would be sick to my stomach, but still, this is amazing and probably useful for the right person. I'll watch it a few times, who knows, I might play better or be able to record more professionally if I can grok this. Thanks, this is great.
I figured out the third movement by trying to play Hendrix... I guess people call it the 'whole note scale'. Pretty sure he figured it out from Beethoven. God I love music.
you wont. you are looking for a prescriptive system that will allow you to bypass your ears and write good music. this is not music theory, this is the math behind the physics of vibration. music theory is descriptive, and attempts to explain WHY certain "bass notes sound best", among other things. no one cares about how many vibrations per second an octave has or any such nonsense. it doesnt explain why the dominant wants to resolve to the tonic, or what "bass notes sound best", it is the result of someone with good ears and and an innate sense of what works and doesnt, not a system that dials up what sounds good. music theory is DESCRIPTIVE. you probably wont write better music knowing it well, but you will understand why great music works the way it does.
Music theory is NOT supposed to be hard. It IS actually very simple when explained in a sequence of logical building block concepts from the foundation up. Although this information you have presented here is very interesting and logical from a mathematical standpoint I believe it to be very confusing to entry level musicians. I find that most musicians are trying to find practical information that can be applied directly to the music making process without too much extraneous thinking about abstract concepts. The math involved in music making is much more simple than you have presented here. It really never needs to go beyond addition, subtraction and division. Why would you use algebra to build major and minor scales when simple math will do the trick?
It must be more difficult than you surmise. Why? Because. Listen. If music were so easy, then why are so many using the same basic, childlike progressions? Because the real isn't easy, only the clones. And mostly that is what "we" have become. Clones. It's probably more of a societal thing, because that is what the lemmings want. More clones. No math needed for cloning.
Cadential chord progressions, 6415, Andalusian, 2-5-1, blues… those things have been embedded in our subconscious since the moment we started hearing music for the first time in our lives. Of course we respond positively to those things involuntarily. And those that start creating music by themselves, will quickly get bored and start venturing out to go discover that sooner or later we have to accept that the old masters have been doing what we were trying to achieve all along. Originality expressed through the harmonic and arrangement-like nature of music is inherently limiting to certain degrees, before you start having a style or whatever you wanna call it.
I just stumbled across this channel and it's just awesome. For us who need to know why things are the way they are, as opposed to just read and rehearse rules or facts, to be able to learn them this is gold. Thank you. Now comes the question. Why did you stop and where did you go? You truly made some really good and useful videos. So if you ever decide to make some more I'm sure a lot of people would be happy.
Thank you for sharing this. As an engineer and guitar player for 20 years I enjoyed it. It's a great way to view the roots of how scales came to be and I love how simple the derivation was.
I taught algebra to year 8. I taught it very well. The idea of teaching music theory to Year 8 is way more challenging I believe than algebra. The problem is partly that children are taught a lot of basic numeracy from year 1. I wish that the case was the same for basic solfège etc, but sadly it is not the case.
As someone who knows music theory and also has struggled with algebra, I have to say in my opinion music theory is much easier. But like I said, that’s just my opinion.
@@robertsmith262 I disagree but it's interesting to me that people feel that way. Kind of like how some people can pick up a guitar and self-teach but I'm just like "what am I even doing?". Which is strange to me because I'm self-taught on a lot of stuff.
@@robertsmith262 I find them about equally hard, but music theory was a bit harder because there was more to memorize. And also because sometimes there's ambiguity and you have to rely on your ear to analyze things. Once you understand the basic idea behind algebra, the whole subject becomes simple.
The intention of the video isn’t to teach music theory. It’s to explain, as the title implies, WHY western scales are formed the way they are. It’s very interesting to see how music has basis in math and nature.
It is like the skeleton in it's composition, but I'd say the 'soul' of it is more improvisation than anything else. That creative spark that is impossible to teach.
This was amazing, thank you. It asnwered so many questions for me. I will likely print the final screen-shot and have it framed; its a wonderful visualization.
What a tangle. Our twelve note scale is taken out of the 15 (16-1) pitches of the sixteenth harmonic and the thirty-second harmonic. Split a string in half, and you have the second harmonic, into four and you get the fourth harmonic. Split it again and.again and.again, and you get 8th, 16th and 32nd harmonics. Between each such halving and the next one, there are more and more harmonics, creating more and more of the scale, and by the time you have Split the string in 16 and up to 32, you have all the true harmonic notes, which now has to be tempered to 12 notes, with close to equal pitch increases, in order that the notes can fit together in a twelve key system and a quint circle. The notes left out from the 15 are between the major third, and the fifth, and between the fifth and the harmonic seventh, which also is adjusted. The fifth is close to true between the 12 and 15 note scales, and so are the pitches outside the third and outside the harmonic seventh. The notes replaced are fewer by 3 and their pitches averaged to suit the pitch distances of the more true pitces, which are also averaged , ie moved minimally in order to make equal all pitch distances. This is the physics of it. However a piano tuner has a slight difference in his tempered tuning for, I think, the key of F to sound cleaner.
This is a great visualization, really appreciate the work you put in to this. I’m going to share this. Students of tuning, JI, and specifically those who have studied with or subscribe to the work of W.A. Mathieu would describe what you’re doing here as beginning to build out a 5 limit ‘lattice of tones’. The ratio tunings you cover in this video are the basic Major solfège tones of the Western Musical tradition and they’re also the most basic ‘Sargam’ tones sung by beginning students of Hindustani Classical music (North Indian). My understanding of Pythagorean tuning is that it is based on 3/1 ratio. Learning to recognize and sing pure Pythagorean tunings is challenging and rewarding, the Pythagorean 3rd which unlike the so-called ‘pure’ or ‘just intoned’ third (your third>5/4) is a ratio of 81/64. It is appreciably sharper than both the just third and the equal tempered third. In my experience when sung or played well those Pythagorean tunings have a quality of antiquity to them, it’s interesting to sing a ‘major third’ that feels like a relative of a pure fifth. If you’re not familiar with W.A. Mathieu’s book ‘Harmonic Experience’ I would highly recommend it. It begins by tuning the major scale as you’ve done here (as triadic overtones of the Root, 5th, and 4th) then goes on to deal comprehensively with tuning as it relates to Equal Temperament and makes the case that 12 Tone ET is a negotiation of on the one hand our innate partiality for pure ratio tunings, and on the other our desire for extended range and perceived motion within harmonic territory. There’s actually a lot of good information regarding tuning and tuning systems on Wiki but as far as I know there is no more comprehensive single work on tuning (in the modern era) than the Harmonic Experience. I studied with WAM but I’m not affiliated with the sale of this book, I just honestly think it’s the best book a person can have on the subject. www.amazon.com/Harmonic-Experience-Harmony-Natural-Expression/dp/0892815604
This is so cool!!!!!! I’m kinda lost, so I’m going to watch it a few more times so it sinks in, but thanks for making this video!!!!! Looking at music theory/structure from the way it was made is really interesting and makes more sense than “these are the notes, because reasons. It just is, don’t try to understand why, just try to memorize it”
Geeze! Tough crowd - I loved your video and look forward to exploring your others - presumably getting into equal temperament and the other tonalities it crowded out.
That final diagram minus the fretboard and numbers would make a great coloring book page. It's comforting to know that we had the scale long before the boring lesson in fractions.
I like this take - I don’t think I’d heard anyone talk about building a major chord on the 1, 4, and 5 before to derive the other diatonic nots of the scale. Cool!
I know music theory and leant about the harmonic series, but this was a very interesting to listen too. I think music theory classes would be much more interesting for people if teachers took more time to explain the mathematical aspect of it.
That would help for some people, but not all. I have always understood science & mathematics well & was taught to always ask 'why'. I have only recently started to learn music theory & my music teacher hates this. (She has been a professional musician since school). was unable to explain to me why a 4th & 5th were called 'perfect' apart from the fact they sound nicer than other intervals. To me, knowing a 4th is 4:3 & a 5th is 3:2 explains a lot, although it doesn't really help my bass playing. Those in her band tell me I am over-analysing!
@@TheRip72 You're totally not overanalysing, I think we're simlar and you'll figure out things that can't be put into words if you keep hungry for knowledge like that
@@TheRip72 overanalysing? In terms of learning things about life - no, for sure. In terms of playing music - yeah, you do. Depends on what you’re aiming for.
I am not sure the word "scale" is because of weight-measuring scales. In Italian the "scala musicale" can be translated as "ladder" because there are intervals like a ladder.
I'm a bit confused actually! Not about the Pythagorean ratios of the notes and notes, but by what happens when you construct scales. "Major" and "minor" are recent inventions (Renaissance) - hold overs from the modes. I wish you had constructed the rest of the "chromatic" notes. I'd like to see how that works.
I've been studying music for about 20 years, and chromatic movements are based on the 'root' or key, in which the song was composed. This moves, sometimes called a 'movement' depending on the tempo and composition of the piece, but the ratios between major and minor doesn't really change, unless there is a fair amount of improvisation thrown in there. Remember where the octaves are, regardless of the root, and you can accomplish a masterpiece once you figure in the fourth, and how it complements the fifth, and just be creative! Speed is extremely important. Arpeggios are another monster I can't even tackle, but they follow the same movements within the key in which you are playing.
Your graphic might also be a clear illustration of how our equal tempered notes differ from the pure ratios that Pythagoras identified, if drawn with a little more precision; as soon as you show the major third on the image, we can see how our major third is sharp in comparison. I think this could further be devoloped as useful information for string players, especially those who play fretless, as well as others whose instruments readily allow them to play notes between the twelve we use in modern music. Slide trombone comes to mind. I hasten to add that those who play instruments that we generally think of as restricted to the twelve could also take some advantage of this, as the context permits. Think of blues guitarists and harpists bending into notes (many of them already adjust the note they're reaching for instnctively), as well as reed and other wind instrument players where their ideal intonation comes not from the instrument but from the player's skill. Even the best saxophones only approximate correct pitch, for example, with the rest left up to the player's skill. Of course, successful application of these on the fly adjustment, and so when it's advisable, depends very much on context. For example, on bass I'll flatten the major third if I know the way is clear, but not where other musicians on the bandstand are playing the unaltered third. Mostly I try it in solos for that reason. Sixths and sevenths (both major and dominant) as well as ninths and minor thirds are candidates for this practice. Many singers also do this instinctively, and those with the lead may enjoy a little more leeway here as a good general practice for accompanists is to avoid doubling important melody notes anyway, as doing so can often weaken the melody. Just my opinion from some things I've picked up over the years. Thanks for all the work you've put into this!
Music notation is a special purpose descriptive language. Mathematical notation is a general purpose descriptive language. Do not confuse one with the other.
You are right if music theory only concerns about proportion, length and frequency . However, because music is much more about aesthetics, that means music theory is always subjective and flawed in some ways. With just-tone intonation, or Pythagoras intonation, you get intervals in proportion to each others, but then the distance between each pitch is uneven. Equal temperament is a compromise between getting pure harmony and even steps between two pitches, so that you can modulate from one key to another easily.
I like the way you explained it, but this isn't quite right and the explanation is incomplete and misleading without a discussion on tuning systems. The ratios you presented are not the real ratios we use in western music these days. Just like you said, "the second is the fifth of a fifth" and that's how Pythagoras actually divided up the octave, by fifths. You have the fundamental, you stack a fifth on top of it and you get the fifth, obviously. But then you stack up another fifth and you have a ninth, meaning you're past the octave. So you bring the 9th one octave down and you get a 2nd. You stack a 5th on top of the 2nd and you get the 6th. You stack a 5th on top of the 6th and you get a 10th, past the octave again. So you lower the 10th one octave and you get the 3rd. You stack a 5th on top of the 3rd and you get a 7th. If you keep going until you have 12 notes above the fundamental, you'll be ROUGHLY back to the same note one octave up. Meaning you divided the octave ROUGHLY in 12 notes. But you can't really reach the frequency of the octave this way, mathematically. With all 12 notes you could, theoretically build a major scale using any of the notes as the fundamental, or 1st degree. The problem is that if you use these ratios, you'll get a perfectly tuned intervals for one note, the fundamental, but it will be horribly out of tune starting on other notes. Meaning, you have a perfectly harmonic 5th counting from the fundamental you picked, but other notes will have progressively out of tune fifths in relation to themselves. That's why we do not tune our instruments this way and our major scale doesn't really sound like that. What you described in the video tho isn't exactly this. That way of arriving at different pitches starting from the fundamental is related to the rest of the harmonic series (not just the fifth) and, if I'm not mistaken, describes the Just Intonation system instead, not the Pythagorean nor the ones we use. The major scale you get from this process is only a rough approximation of the actual major scale because it uses pitches (harmonically tuned pitches) that are not part of our tuning system. You'll even notice that the circles you're drawing based on these pure ratios don't always line up perfectly with the frets on the fretboard. (And even then, the way guitar frets work is "wrong" and guitars are inherently out of tune instruments. Look up true temperament fretboards. But I won't go into that or this comment would be even longer). The way you arrived at the different pitches (and if you had continued until you arrived at all 12 notes) would still give you a collection of pitches that has the right intervals relating to the starting note, but horribly out of tune intervals relating to other notes. What we did to fix this issue was to divide the octave in 12 different notes, AT THE SAME FIXED distance from each other. Which is not what you get with the Pythagorean Tuning or Just Intonation. This means that we don't get the same perfect ratios you showed and the intervals relating to the fundamental are not perfectly harmonic, but whatever note you pick will have all the intervals relating to itself perfectly equal to the intervals relating to any other note. A 5th from C to G with sound as harmonious as a 5th from D to A, because the distance between the pitches is exactly the same. It is called Equal Temperament after all. Yes, it is a bit out of tune because it doesn't follow the harmonic relations you described, but considering each one of the 12 notes and the intervals and scales relating to it, it is ON AVERAGE closer to a harmonic tuning than the Pythagorean tuning. I hope this makes sense. If it doesn't look up Pythagorean Tuning, Just Intonation, Equal Temperament and, for those interested in guitars, look up True Temperament fretboards.
Yeah, what he said... that makes sense to me. I've tried figuring these things out on my own for years, using geometry, math etc. and you're dead on. Things just don't work that way on a guitar. It was much easier to read this than to watch that video
Music theory gets a lot more involved than this. The connection between music and math isn't accidental, but the complexity goes all the way up to furthest limits of mathematical theory. That's why you can always analyse music mathematically (which is basically what a recording is) but you can't understand or generate it using only formulas alone (which is why AI music gets stuck in the same place as self-driving or drawing hands).
I could follow up to a while, then it got all confusing. I'll be back for this again and again, thanks for putting it out. Maybe using different colours would help as later on it gets very confusing.
I understood that the major scale of C used all the natural notes but skipped all the sharps/flats, (which is why they were called sharps/flats. I knew where these were & that the notes including sharps & flats were (almost) equally spaced, but I didn't know that this was why a major scale 'worked'.
Knowing the elementary and even advanced musical theory will not make a person a musician. Musicians make rapid brain processing decisions in seconds as they engage with their instruments of choice. That process becomes elaborate and complex. That is why when we hear something in music that is emotionally engaging and for our brains, computationally astounding, it is because it is.
Chromatic scale comes from picking a pitch and ascending in fifths until you arrive back at the same note as the starting pitch. Line those fifths up in scale order and you get the chromatic scale. Chromatic scale is questioned and messed with frequently by modern composers and musicians.
This may not be exactly what you have in mind, but, two good math eye openers are the Bossa Nova and Chopin Fantaisie-Impromptu Op. 66 in C# Minor rhythmic structures.
From a naturalist perspective music can to a degree be explained through the overtone series but that is not all since the choice of notes implies that there are tonal categories which cannot be explained by that perspective alone and implies the existence of a sort of idea realm of movements and tonalities. In that sense to explain music through simple theory is like explaining the realm of discourse in society through linguistics.
This is the first time theory has felt natural instead of arbitrary for me, although I've only dabbled. Appreciate the geometric visualization immensely, as well.
I love how you see the layer of math in music. Math has a hidden layer as well. Did you know that numbers sets of number have images encoded in them? You may have heard or seen "Fractal" images before, put simply, these are the images of numbers. So if we put it all together music is math and math is imagery....music should also have a layer of images that can be visible to humans though math formulas and displayed with computers just like fractals.
It’s all chromatic. Here’s how all 12 notes are useable over a Dominant 7th chord (for example). 1-3-5-b7 are the chord tones; safe to sit on all day. 2-4-6-b3-b5 are from Mixolydian and the Blues scale, also very useable. That’s 9 out of the 12 notes, leaving only b2-b6-7 which can be used as passing tones. - No need to think of scales, just think in terms of how useable each of the 12 notes is and in what way.
I’m an engineer. I started learning guitar and eventually found a book on music theory that was tremendously helpful. I ended up with a spreadsheet with the modes, chords, scales, and a basic chord-builder, etc. I still can’t play guitar.
Just sit and play. And I don't mean play a scale or a song etc.... just play. Like Pithagoras did. Experiment. Experiment with a single string, with two, with intervals. Play listening to what you like or not. With strumming, with picking with one finger, two. Sliding with the left, etc....
Once you find you like to sit and "play" with the guitar, you start learning how to play it. Stop forcing it.
I'm also an engineer. A sound engineer. And a musician. And learning psychology currently. Trust the process doctor.
Find a song you really like and learn it, you'll go from there. And since you learned the theory you'll understand it more when you learn it
The difference between science and art. FEEL THAT GUITAR BRO. CRY MELODIES FROM YOUR SOUL
lol
For those wondering how any of this could possibly be useful: Forming connections. Looking at topics from weird perspectives is fundamental to efficiently learning-by-doing and making personal breakthroughs, both in that topic and in others. As a kid you probably spent dozend of cumulative hours digging through your Lego bin looking for a specific brick and instead finding half the pieces you were looking for *yesterday*. Same deal with mental connections and especially breakthroughs, they appear most consistently when you're focusing on something else and some set of conditions triggers a sense of familiarity.
Nah , actually you look at the 72 nonrepeating tones of a piano and realize that its a 12 tone abacus with 6 columns.
You cant discover that on a guitar because the six strings and at least 90 repeated tones
will lull to sleep before you find a similar straight line approach for the 4 octaves on a guitar.
This stuff is vital to alternate tuning systems. What we hear in music is not this scale, but an approximation with 12 notes. Other tuning systems such as 31edo strive for similar things
@@ruoiealpaeiout2103guitar def showed me piano is just a bunch of groups of the same thing
This only makes sense to those who have studied theory already. If you're a beginner, you're gonna end up a tad miffed by this guy, to put it lightly.
I've been playing for 40 years and I am confused as to the purpose of this angle, I know what he is talking about but this does not clear up anything or simplify it. A basically unscripted narration does not help either.
@@streamofconsciousness5826 I concur
I think he overcomplicates it a bit. I mean, he's not wrong, but the length of the string and the specific intervals can be simplified with simple finger placement within the shapes of the scales based on the root.
I think you're right, my mother taught me to read music as a youngster and for whatever reason, I've always thought about my playing music in mathematical terms. Being in electronics as a profession, the correlation between algebra and music makes perfect sense to me. I can also see why it doesn't to other people, my brother who is a professionally trained singer doesn't see the connection. Whatever works I guess.
I don’t think this video is meant for beginners. But if your student asked you “but why?”, then this is the video you show them. Otherwise, just have them memorize the intervals and play/recall them well enough and that’s good to move on to other stuff when it comes to performance.
Once you try to connect music theory to your ears, it's no long 8th grade math; it's years of work.
Yeah, that's the thing. It's not that the math is itself is complicated.
But one thing is dividing a chocolate bar in 4 pieces, another is dividing one beat in 4.
One thing is adding 3 + 4, another thing is adding a major 3th and a perfect 4th, which are basically sound waves that you have to identify with your ears and memorize where they are located in your instrument.
In other words, it's basic mtah applied to abstract material, which makes it complicated.
Not really. All it takes to connect meaning to what you’re hearing is to define the meaning yourself. Create your own musical language of what the things you hear mean to you. And label them. That’s how you develop an ear for music. By associations in your mind.
...decades.
@@Marshall_EL34 only if you practice an hour once a week lol yeah then decades. In other cases it's years bruh
This video really makes the major scale visually understandable. The circles make it look sonic and they hit all the correct frets. A great bit of history in there too.
Sound waves are rather cyclical, since we measure them in cycles. I can't believe this didn't click for me until this video.
So yeah, agreed, the circles are an incredible visual component!
That last complete image is astoundingly beautiful. It would be great wall art... serving as a functional reference also.
I've known of the relation of most of the harmonics on the strings, but never ever seen it laid out so visually stunning. I can see why it all makes sense now. Thank you!!
I want to get that as a tattoo. such perfect sacred symmetry
These visualizations are phenomenal. Hope to see your channel grow more soon!
The last math class I received a passing grade was in the 3rd grade. I had to repeat 8th grade algebra 4 times and the only reason I was not held back a grade was that all my other subject I had 100%, but math my grades were never above D-. In college I chose journalism as my major because it only required the most basic math. I still had to take remedial math six time and ended up dating the last teacher, a graduate assistant and she mercifully passed me because I simply never got it.
Now in my 50s I never use any form of math beyond basic addition etc and always with a calculator. I've been a musician for 42 years and have never been able to grasp music theory. I had to stop this video halfway through because I was literally gasping for breath, sweating and with tears in my eyes.
At least you know you're dim.
he jus like me Fr
I'm decent at math at I'm just laughing at the graph @11:45 . This guy has lost the plot here. If you tell someone it's simple and you show them this visual aid they are going to laugh in your face. There are a dozen ways to simplify music theory and this just ain't one of them.
Fuck math dude, you're a great writer! Story had me rollin! 🤣🤣🤣👍
@@ilovebutterstuff hahahahha. the moral was a strong one too- even guys can fuck their way to success/fuck their way out of trouble/fuck their teacher, etc. hahahahaha
Thank you so much. I have always shied away from learning music theory because so much of it just seems like "memorize this" without explaining why. I can't tell you how many times my teacher just listed off the intervals, calling some major, some minor, some perfect, and just wanting me to know their names like it meant anything to me. So many things in music theory for me have just been "this is what we call it when this happens" and it feels like no matter how many things I memorize I still don't know how they fit together or what their purpose is. Thank you for explaining it like the science that it is, instead of making me learn it like a language.
Innumerable amounts of people have felt like you. "Teachers" have miserably failed at making the connections to application, both theoretical/logical and the musical feel/effect one gets.
The intervals are all that matters though. Once it clicks you'll understand everything your teacher was telling you.
Per Lydian chromatic theory, "the" major scale built on perfect fifths would be the Lydian scale. (And therefore, as Miles Davis once said, the center note of the piano keyboard should be "middle F" rather than "middle C"...!)
The geometric visuals are great. It has helped me understand the relationship of the frets to the strings. I always wondered why a guitar seemed so different than a piano. I wondered why it's layed out like it is. Its the way it has to be for western music. This was enlightening.
Pythagoras just adapted his maths to existing musical scales. He did not invented them as widely reported.
The picture next my username shows a statue of a man playing a harp.
This statue is dated 2800 BC. Do you think a harp can be constructed and played without the use of scales?
Now, Pythagoras lived some 2200 years after that statue was made.
So little we know about history
And to say nothing of Asian , African, Polynesian, Native American, Indigenous music around the world with zero contact with Ancient Greek concepts.
consider that intervals in music contain much of the emotional content of the music. Most of the ancient harps only had five or six strings. These were based on the perfect intervals including the octave. So they did not have Major and Minor scales.
@@randyleazenby2351 you talk like you have seen one of these harps. If you look closely on the statue you will see this has room enough for maybe 20 strings. You will find it on the N.Y Met Museum as ''harp player''
He discovered the ratios of the divided string on a monochord and it's relationship to the proportions we see in nature.
The question though is how much did they understand about what they were doing or did they just set things up because they sounded good. It's possibly to get a long way on just natural talent.
Hello,
I genuine enjoy the perspective you offer. I think anyone who complains that the video is unnecessarily complicated is unnecessary complicated themselves because, clearly, this video is about exploring music through a mathematical lens. It's meant to offer a different perspective to those who already know music theory not teach beginners the fundamentals. There are thousands of videos that explain music theory in "simple" ways on UA-cam and having the choice to explore it this way offers unique insights for me. The diagram was especially appreciated.
However, I did note one error worthy of correction: The etymological roots of the term scale in music are not from weights but late middle English from the Latin word "scala" meaning ladder. I'd also appreciate also appreciate recognition of the equal temperament and how, despite it being the standard, does not apply in this context. Thank you.
exactly. Scala = temperament.
I noticed Modal has an old Greek meaning of mood
and a newer Latin meaning of Mesurement.
that would explain modulation, different Mesurement along a scale to arrive at a different key.
the "modal harmony" name , would make more sense, if it were Modular Harmony
Yep. Somewhere there must be a video that goes the other direction but I have yet to find it. Math and music theory are intimately tied together but Ive yet to find anyone that can "do both" fluently.
@@jasondoe6079 well there's You Tuber Marshall Harrison,author of School of Legato, he plays Fusion jazz and has a career as a mathematician .
@@johnmcminn9455 Cool thanks Ill check him out
@@johnmcminn9455 Sadly this guys videos are over 95% music related and what little math I could find was well beyond the basics of algebra . It is these basic "translations" between the two languages of music and math that I cannot find anywhere.
wow, welcome back!
I just found your channel about a week ago and it has been a revelation. Just when I thought this had become a legacy channel and then this upload shows up. Please keep it up
The History was interesting, but all the circles on the fret board got confusing. Especially when they went behind the 12th fret
Colors might help, a different one for each interval.
Dude the lines is right when IT CLICKED, like those are all the ways notes interact and their intersections of sinewaves when played together, music is playing with air to make your brain experience emotion, its the closest thing we have to magic
@@chrishei3111 I was trying to learn algebra using the Music knowledge I have, I failed the test, got kicked out of my home, my cat got eaten by a raccoon the second night I was out side, (I was saving him for when I ran out of money), but I'm glad things worked out for you Chris, I'm wondering in that 8 minutes could have been better spent watching a algebra video.
(Just kidding Creator/Uploader, any angle is productive and worth looking into. I did come here for Music and I don't have a cat (any more), I can't stop...😂 I'll show my self out thanks.
This is absolutely golden. Thank you so much for this. That last picture I actually have done when working with geometry a couple of years back. This makes so much sense. Huge thank you
The idea that you can "weigh" the notes, hence the name "musical scale" probably only works in the English world. In french, it's "gamme" (series of things of the same nature but with nuances, as in "shades" in english. "different shares of blue"), in Spanish it's "escala" as in scale in the context of size (1:2 scale of a map for example) or ladder; in German it's "Tonleiter", literally "tone ladder".
Yeah scale comes for sure from the latin scala which meaning ladder. I guess thecreator comes off so nervously because he is making stuff up on the fly.
@@sebastianhelm1718 eh things tend to be confused when someone does their own research and makes assumptions connecting their current knowledge with what they're learning, the rest of the video is intriguing correct and helpful or not
Shhhh... don't tell him there's a world outside of the US
Weird comment… You give other examples, Spanish, Latin, that actually reinforce the original general point, just not literally.
Thank you so much for this content. I really know a lot about music theory and had even studied about these measures before but it was the first time I realized the importance of the perfect intervals and their relation mathematically to compose the major and minor keys. You just helped me so much to organize all the content in my head. Thank you so much!
THE LEGEND HAS RETURNED!
I should have used the Rocky music for the intro.
There is so much deeper things than this. Bach actually used set theory for his last unfinished fugue and the most simple think about the main theme is it's symmetrical. The work is called The Art of Fugue BWV 1080
Set theory was formalized starting in the late 1800’s over hundred years after Bach died. I am skeptical of your claim
@@gumbilicious1 it was group theory I just double checked the article about it. But even then I don't know any explanation Bach was definitely a genius and the fact that all of his works are mathematically calculated is undoubted. Maybe it's not Bach who knew about group theory but Zoltan Gömz did an observation on this unfinished fugue I'll send it to you if you want. Either way I think it would be too much to say that Bach's last work was universal and prophetical.
As a music nerd.... This hits the spot 😂
Amazing. The ends of the circles are also the natural harmonics, by touching strings there you set the string into another vibration mode. The visuals are beautiful too nice job!
This is absolutely golden. Thank you so much for this. That last picture I actually have done when working with geometry a couple of years back. This makes so much sense. Huge thank you 🙏
I saw a Luthier do something similar once with a compass and protractor ... he was working out the spacing of the frets so i'd imagine he was just working out step one of this same system. Very interesting video. Seeing it all visually explained like that is mindblowing. Well done.
Terrific video. Thank you 🙏 In fact the very BEST that I’ve found, on where the major scale comes from, and why. The circles do really help!
Your series is my favorite music theory on youtube
Excellent. Learning guitar as a pianist and drummer has opened up theory in my mind, took 20 years. Golden ratio has entered the zeitgeist.
Outstanding! I have been wondering about all of this for the last several years. Amature self taught musician. Thanks!
This is a very nice visual representation and also very nice in terms of the mathematical relationships. I really like having this additional information in my arsenal when explaining things to students.
Yet, I do have to agree with many of the comments below. This is only clear, when one already "presupposes" that the student understands what a major and a minor chord is, or an interval of a major or minor, for that matter. As you were frustrated, wanting to know "why these notes", a student of yours, learning this as their first exposure to major scales may ask: "why a major chord, and, where the heck does it come from". It also only makes any sense when one, again, presupposes that the new learner has any clue as to which notes they want to "discover" in the major scale. A huge amount of the steps used in this explanation are built upon the assumption that the aim of the discovery is to "find" the notes of a major scale, and also on multiple (sometimes complex) principles in music.
As a teaching technique, this does not clarify much for a new student off the bat. It does absolutely help someone who already knows music theory, to have a nice additional angle to understand relationships of notes from a mathematical stance, and also be aware of how the notes relate to each other.
This is not, however, a plausible route for explaining how we came to have the actual 12 notes, or the actual 7 notes of either diatonic music or the major scale. Using the above process, one would not "discover" the notes of the scale unless you set out to "prove where they lie", based on your already existing understanding of all of them. Take as an example the 2nd. From an uniformed perspective, why would you use the 9th, and then lower it to the 2nd? That can only be done post-understanding the scale already.
Personally, I am not entirely sure how we actually came to have the 7 steps of the major scale, as I stopped studying formal theory after completing G6 theory exam - I then continued learning as I performed in the industry along with other musicians. BUT, I am inclined to think that it grew out of the pentatonic scale more than it grew out of someone using the above method. The pentatonic scale has been around all over the planet, and for ages longer than the major/minor scales, and it does seem somewhat likely that a next experimental step from there could lead to a major scale. Over-and-above that, the pentatonic scale is something that appears to be very much "inbuilt" into most people, and has an easy execution by most humans, regardless of their musical training. Sure, this may be because of it's use over centuries, I agree, but, the ease with which it "falls on the ear" may play a role.
As far as I understand it, also, the very major/minor/augmented/diminished intervals owe their description to how they appear in a major or minor scale (scales which you would need BEFORE you understand or describe the intervals), and then, the 4 main chord groups (major/minor/augmented/diminished) owe their existence and description to the combination of intervals (specifically a third and a fifth above 1). Thus, the explanation above, though insightful, does appear cart-before-horse.
Hey. Agreed about this, I was thinking he's starting his reasoning from the result, knowing what he's looking for...
You're probably right about the penta too, the first five notes of the circle of fifths is a major penta, an "easy" way to start discovering things.
the 7 notes are supposed to correspond to the 7 classical planets. you have to go deeper into how ancient people thought
This system looks like a Five-limit tuning, where the ratio's are made with numbers constructed with the prime numbers 2,3 and 5. It is used in just intonation.
No instructions on how to construct other tones are provided, so I guess we'll have to remain in one and the same key or mode thereoff. And the wolf interval of (40/27) between the second and the sixth note of this scale, is also not mentioned at all.
I can assure that the ratio's will get even more messy once you start adding the last 5 notes if you don't use a well thought out system.
Also the ratios are written the wrong way; as the reciprocals of the actual ratios.
If you go up from the tonic to the P5 for instance you go up a fifth so you would multiply by 3/2 (instead of 2/3)
I have previously only seen this ratio stuff presented in scattershot form, a bit here and a bit there. Nothing systematic like this with someone working out a whole scale from fundamentals. So this was revelatory! Thank you! :)
…and when music students needed him most he vanished…
Joking aside this is the type of stuff I needed to see first as a prep before picking up a guitar, someone who will actually show me what these terms mean and have a backstory as to its origins making it easier to remember, not just giving me some pneumonic device and calling it a day. Students already have the desire to learn, but this is a much more fundamental way of teaching it in the system we have. Unless we can all agree upon a new system for creating music that isn’t ancient we will have people who fell through the cracks like me. I’m luckily only in my mid twenties but I’ve been interested in music all my life, taking it the most seriously in High School and now College. Teach this to kids old enough to to understand it.
Look up 22 shruti and Sagittal notation. Any questions.... look for Paul Erlich
The best video I’ve seen so far explaining this. Good job!
Everyone learns a bit differently and this video is no more complicated than any other that talks about the "why" of music theory. If it didn't make sense to you, then you simply don't think the same way. I'm very much a neophyte, and I'm more in my element with math than music theory to begin with, but I learned plenty from this video. Take the tidbits you can use and they'll accumulate over time, just don't stop learning.
And to anyone who feels they don't have the music theory chops to follow, I recommend doing some reading/watching about the basics of scales, degrees, and intervals. Just the 101 stuff, and you'll be following along in no time.
Almost.
This confirms my past statements about graphic animations and teaching. That just because you can synchronize words with graphics does NOT mean that you are communicating or imparting knowledge.
Interesting as can be! I have to say, if modern practical music theory was truly algebra, I would never get it, thankfully, it is intuitive and easily understandable because I can hear it, while math makes my mind go fuzzy and dark. By practical music theory I mean being able to construct scales, spell any chord, understand chord progressions, know what bass notes work best, master the circle of 5ths, be able to transpose on the fly, etc. If music theory was taught like this video, I would be sick to my stomach, but still, this is amazing and probably useful for the right person. I'll watch it a few times, who knows, I might play better or be able to record more professionally if I can grok this. Thanks, this is great.
I figured out the third movement by trying to play Hendrix... I guess people call it the 'whole note scale'. Pretty sure he figured it out from Beethoven. God I love music.
you wont. you are looking for a prescriptive system that will allow you to bypass your ears and write good music. this is not music theory, this is the math behind the physics of vibration. music theory is descriptive, and attempts to explain WHY certain "bass notes sound best", among other things. no one cares about how many vibrations per second an octave has or any such nonsense. it doesnt explain why the dominant wants to resolve to the tonic, or what "bass notes sound best", it is the result of someone with good ears and and an innate sense of what works and doesnt, not a system that dials up what sounds good. music theory is DESCRIPTIVE. you probably wont write better music knowing it well, but you will understand why great music works the way it does.
Music theory is NOT supposed to be hard. It IS actually very simple when explained in a sequence of logical building block concepts from the foundation up. Although this information you have presented here is very interesting and logical from a mathematical standpoint I believe it to be very confusing to entry level musicians. I find that most musicians are trying to find practical information that can be applied directly to the music making process without too much extraneous thinking about abstract concepts. The math involved in music making is much more simple than you have presented here. It really never needs to go beyond addition, subtraction and division. Why would you use algebra to build major and minor scales when simple math will do the trick?
Totally right.
Major Scale, Triads, Intervals etc.
Plus, melodic and harmonic playing.
I have been told that addition and subtraction aren't "math".
They are the basics of learning to do Math.
A bit like letters equal words in context
There is no algebra in this video, is there?
It must be more difficult than you surmise. Why? Because. Listen. If music were so easy, then why are so many using the same basic, childlike progressions? Because the real isn't easy, only the clones. And mostly that is what "we" have become. Clones. It's probably more of a societal thing, because that is what the lemmings want. More clones. No math needed for cloning.
Cadential chord progressions, 6415, Andalusian, 2-5-1, blues… those things have been embedded in our subconscious since the moment we started hearing music for the first time in our lives. Of course we respond positively to those things involuntarily. And those that start creating music by themselves, will quickly get bored and start venturing out to go discover that sooner or later we have to accept that the old masters have been doing what we were trying to achieve all along. Originality expressed through the harmonic and arrangement-like nature of music is inherently limiting to certain degrees, before you start having a style or whatever you wanna call it.
I just stumbled across this channel and it's just awesome. For us who need to know why things are the way they are, as opposed to just read and rehearse rules or facts, to be able to learn them this is gold. Thank you. Now comes the question. Why did you stop and where did you go? You truly made some really good and useful videos. So if you ever decide to make some more I'm sure a lot of people would be happy.
Video: Music theory is simple
Video: Pythagoras listening
to E=MC hammer
Thank you for sharing this. As an engineer and guitar player for 20 years I enjoyed it. It's a great way to view the roots of how scales came to be and I love how simple the derivation was.
It is actually more geometry than algebra.
Interestingly in Ancient Greece, geometry was closely connected to algebra. The Greeks used geometry to solve problems that we would use algebra for.
I taught algebra to year 8. I taught it very well. The idea of teaching music theory to Year 8 is way more challenging I believe than algebra. The problem is partly that children are taught a lot of basic numeracy from year 1. I wish that the case was the same for basic solfège etc, but sadly it is not the case.
As someone who knows music theory and also has struggled with algebra, I have to say in my opinion music theory is much easier. But like I said, that’s just my opinion.
@@robertsmith262 I disagree but it's interesting to me that people feel that way. Kind of like how some people can pick up a guitar and self-teach but I'm just like "what am I even doing?". Which is strange to me because I'm self-taught on a lot of stuff.
@@robertsmith262 I find them about equally hard, but music theory was a bit harder because there was more to memorize. And also because sometimes there's ambiguity and you have to rely on your ear to analyze things. Once you understand the basic idea behind algebra, the whole subject becomes simple.
I finally realized why my parents gave me that silly spirograph game for Christmas.
The intention of the video isn’t to teach music theory. It’s to explain, as the title implies, WHY western scales are formed the way they are. It’s very interesting to see how music has basis in math and nature.
Mathematics in music is like the skeleton of our physical body. It's the soul of it that makes it beautiful.
It is like the skeleton in it's composition, but I'd say the 'soul' of it is more improvisation than anything else. That creative spark that is impossible to teach.
@@ilovebutterstuff What you said makes no sense as a reply to what they said
Straightforward algebra does indeed capture harmonics. It's only fractions, and you can algebraically solve for the rest.
This was amazing, thank you. It asnwered so many questions for me. I will likely print the final screen-shot and have it framed; its a wonderful visualization.
Gonna need some time for this to marinate. I’m not a guitar or string player, so I had to draw on my understanding of waves in physics to grok this.
(2) in "Slicex" you could create New Drum Loops and softs in any order from different slices. And keep the loop slices playing in and
What a tangle. Our twelve note scale is taken out of the 15 (16-1) pitches of the sixteenth harmonic and the thirty-second harmonic. Split a string in half, and you have the second harmonic, into four and you get the fourth harmonic. Split it again and.again and.again, and you get 8th, 16th and 32nd harmonics. Between each such halving and the next one, there are more and more harmonics, creating more and more of the scale, and by the time you have Split the string in 16 and up to 32, you have all the true harmonic notes, which now has to be tempered to 12 notes, with close to equal pitch increases, in order that the notes can fit together in a twelve key system and a quint circle. The notes left out from the 15 are between the major third, and the fifth, and between the fifth and the harmonic seventh, which also is adjusted. The fifth is close to true between the 12 and 15 note scales, and so are the pitches outside the third and outside the harmonic seventh. The notes replaced are fewer by 3 and their pitches averaged to suit the pitch distances of the more true pitces, which are also averaged , ie moved minimally in order to make equal all pitch distances. This is the physics of it. However a piano tuner has a slight difference in his tempered tuning for, I think, the key of F to sound cleaner.
Now that's pretty cool. From time to time I wondered how what we know now came to be and how in hell it is what it is..... amazing.... thank you
This is a great visualization, really appreciate the work you put in to this. I’m going to share this.
Students of tuning, JI, and specifically those who have studied with or subscribe to the work of W.A. Mathieu would describe what you’re doing here as beginning to build out a 5 limit ‘lattice of tones’. The ratio tunings you cover in this video are the basic Major solfège tones of the Western Musical tradition and they’re also the most basic ‘Sargam’ tones sung by beginning students of Hindustani Classical music (North Indian).
My understanding of Pythagorean tuning is that it is based on 3/1 ratio. Learning to recognize and sing pure Pythagorean tunings is challenging and rewarding, the Pythagorean 3rd which unlike the so-called ‘pure’ or ‘just intoned’ third (your third>5/4) is a ratio of 81/64. It is appreciably sharper than both the just third and the equal tempered third. In my experience when sung or played well those Pythagorean tunings have a quality of antiquity to them, it’s interesting to sing a ‘major third’ that feels like a relative of a pure fifth.
If you’re not familiar with W.A. Mathieu’s book ‘Harmonic Experience’ I would highly recommend it. It begins by tuning the major scale as you’ve done here (as triadic overtones of the Root, 5th, and 4th) then goes on to deal comprehensively with tuning as it relates to Equal Temperament and makes the case that 12 Tone ET is a negotiation of on the one hand our innate partiality for pure ratio tunings, and on the other our desire for extended range and perceived motion within harmonic territory.
There’s actually a lot of good information regarding tuning and tuning systems on Wiki but as far as I know there is no more comprehensive single work on tuning (in the modern era) than the Harmonic Experience. I studied with WAM but I’m not affiliated with the sale of this book, I just honestly think it’s the best book a person can have on the subject.
www.amazon.com/Harmonic-Experience-Harmony-Natural-Expression/dp/0892815604
Thank! Just put it in my cart
Seem really interesting
This is so cool!!!!!! I’m kinda lost, so I’m going to watch it a few more times so it sinks in, but thanks for making this video!!!!! Looking at music theory/structure from the way it was made is really interesting and makes more sense than “these are the notes, because reasons. It just is, don’t try to understand why, just try to memorize it”
Geeze! Tough crowd - I loved your video and look forward to exploring your others - presumably getting into equal temperament and the other tonalities it crowded out.
That final diagram minus the fretboard and numbers would make a great coloring book page. It's comforting to know that we had the scale long before the boring lesson in fractions.
I like this take - I don’t think I’d heard anyone talk about building a major chord on the 1, 4, and 5 before to derive the other diatonic nots of the scale. Cool!
I know music theory and leant about the harmonic series, but this was a very interesting to listen too. I think music theory classes would be much more interesting for people if teachers took more time to explain the mathematical aspect of it.
That would help for some people, but not all. I have always understood science & mathematics well & was taught to always ask 'why'. I have only recently started to learn music theory & my music teacher hates this. (She has been a professional musician since school). was unable to explain to me why a 4th & 5th were called 'perfect' apart from the fact they sound nicer than other intervals.
To me, knowing a 4th is 4:3 & a 5th is 3:2 explains a lot, although it doesn't really help my bass playing. Those in her band tell me I am over-analysing!
@@TheRip72 You're totally not overanalysing, I think we're simlar and you'll figure out things that can't be put into words if you keep hungry for knowledge like that
@@TheRip72 I'm the same way. The seeming arbitrariness of everything makes it hard to integrate.
@@TheRip72 except that it’s not really true, because western music adapted equal temperament about 400 years ago, The ratio of a fifth is 1:1.498
@@TheRip72 overanalysing? In terms of learning things about life - no, for sure. In terms of playing music - yeah, you do. Depends on what you’re aiming for.
Thanks for providing visuals so I can have more excuse to annoy my friends about this
In a lot of towns, villages and countries around the world are things called schools, with things called books in them.
Glad you're back!
I am not sure the word "scale" is because of weight-measuring scales. In Italian the "scala musicale" can be translated as "ladder" because there are intervals like a ladder.
Glad to see you back
glad you're back!
Our Sensei has returned!
So wonderfully explained. I hope to see more!
Subscribed! Cheers,
Johnny English
I'm a bit confused actually! Not about the Pythagorean ratios of the notes and notes, but by what happens when you construct scales. "Major" and "minor" are recent inventions (Renaissance) - hold overs from the modes. I wish you had constructed the rest of the "chromatic" notes. I'd like to see how that works.
Take the Circle Of 5ths and note where the minors fall in relation to the majors.
@@BGDonH no
I've been studying music for about 20 years, and chromatic movements are based on the 'root' or key, in which the song was composed. This moves, sometimes called a 'movement' depending on the tempo and composition of the piece, but the ratios between major and minor doesn't really change, unless there is a fair amount of improvisation thrown in there. Remember where the octaves are, regardless of the root, and you can accomplish a masterpiece once you figure in the fourth, and how it complements the fifth, and just be creative! Speed is extremely important. Arpeggios are another monster I can't even tackle, but they follow the same movements within the key in which you are playing.
@@ilovebutterstuff when you say fourth and fifth, do you mean tonicisation?
Major and Minor are probably equivalent to Ionic and Aeolian.
I loved 8th grade algebra. I've now helped my own kids through 8th grade algebra. Now, maybe I can understand music
Great vid! Going back and watching the old ones now. Subbed
You just put off an entire generation from the wonderful world of music. I want to eat a plate of beans tonight.
But at the same time, fascinated many who are scientifically minded. I was interested in this, my music teacher feels it is irrelevant.
You just put off an entire generation from the wonderful world of math...
Whoa. That was excellent. Thank you for making this.
Your graphic might also be a clear illustration of how our equal tempered notes differ from the pure ratios that Pythagoras identified, if drawn with a little more precision; as soon as you show the major third on the image, we can see how our major third is sharp in comparison.
I think this could further be devoloped as useful information for string players, especially those who play fretless, as well as others whose instruments readily allow them to play notes between the twelve we use in modern music. Slide trombone comes to mind.
I hasten to add that those who play instruments that we generally think of as restricted to the twelve could also take some advantage of this, as the context permits. Think of blues guitarists and harpists bending into notes (many of them already adjust the note they're reaching for instnctively), as well as reed and other wind instrument players where their ideal intonation comes not from the instrument but from the player's skill. Even the best saxophones only approximate correct pitch, for example, with the rest left up to the player's skill.
Of course, successful application of these on the fly adjustment, and so when it's advisable, depends very much on context. For example, on bass I'll flatten the major third if I know the way is clear, but not where other musicians on the bandstand are playing the unaltered third. Mostly I try it in solos for that reason.
Sixths and sevenths (both major and dominant) as well as ninths and minor thirds are candidates for this practice.
Many singers also do this instinctively, and those with the lead may enjoy a little more leeway here as a good general practice for accompanists is to avoid doubling important melody notes anyway, as doing so can often weaken the melody.
Just my opinion from some things I've picked up over the years. Thanks for all the work you've put into this!
Music notation is a special purpose descriptive language. Mathematical notation is a general purpose descriptive language. Do not confuse one with the other.
What were the historical music theory books you read? I'd like to dig them up if I can. Thanks for the content!
Boy, am I glad that they use 12 notes instead of just the 7 major scale notes.
So this is why I can't comprehend music theory, it's just 8th grade algebra! Puts things in perspective for sure
The artistic application of that "8th grade algebra* is far beyond the average 8th grader.
You are right if music theory only concerns about proportion, length and frequency . However, because music is much more about aesthetics, that means music theory is always subjective and flawed in some ways. With just-tone intonation, or Pythagoras intonation, you get intervals in proportion to each others, but then the distance between each pitch is uneven. Equal temperament is a compromise between getting pure harmony and even steps between two pitches, so that you can modulate from one key to another easily.
If you divide an octave in half- you get a try-tone! It's the same as splitting the Atom. ...BOOM!
Now I know why I failed 8th grade algebra
I like the way you explained it, but this isn't quite right and the explanation is incomplete and misleading without a discussion on tuning systems. The ratios you presented are not the real ratios we use in western music these days. Just like you said, "the second is the fifth of a fifth" and that's how Pythagoras actually divided up the octave, by fifths. You have the fundamental, you stack a fifth on top of it and you get the fifth, obviously. But then you stack up another fifth and you have a ninth, meaning you're past the octave. So you bring the 9th one octave down and you get a 2nd. You stack a 5th on top of the 2nd and you get the 6th. You stack a 5th on top of the 6th and you get a 10th, past the octave again. So you lower the 10th one octave and you get the 3rd. You stack a 5th on top of the 3rd and you get a 7th. If you keep going until you have 12 notes above the fundamental, you'll be ROUGHLY back to the same note one octave up. Meaning you divided the octave ROUGHLY in 12 notes. But you can't really reach the frequency of the octave this way, mathematically. With all 12 notes you could, theoretically build a major scale using any of the notes as the fundamental, or 1st degree. The problem is that if you use these ratios, you'll get a perfectly tuned intervals for one note, the fundamental, but it will be horribly out of tune starting on other notes. Meaning, you have a perfectly harmonic 5th counting from the fundamental you picked, but other notes will have progressively out of tune fifths in relation to themselves. That's why we do not tune our instruments this way and our major scale doesn't really sound like that.
What you described in the video tho isn't exactly this. That way of arriving at different pitches starting from the fundamental is related to the rest of the harmonic series (not just the fifth) and, if I'm not mistaken, describes the Just Intonation system instead, not the Pythagorean nor the ones we use. The major scale you get from this process is only a rough approximation of the actual major scale because it uses pitches (harmonically tuned pitches) that are not part of our tuning system. You'll even notice that the circles you're drawing based on these pure ratios don't always line up perfectly with the frets on the fretboard. (And even then, the way guitar frets work is "wrong" and guitars are inherently out of tune instruments. Look up true temperament fretboards. But I won't go into that or this comment would be even longer). The way you arrived at the different pitches (and if you had continued until you arrived at all 12 notes) would still give you a collection of pitches that has the right intervals relating to the starting note, but horribly out of tune intervals relating to other notes. What we did to fix this issue was to divide the octave in 12 different notes, AT THE SAME FIXED distance from each other. Which is not what you get with the Pythagorean Tuning or Just Intonation. This means that we don't get the same perfect ratios you showed and the intervals relating to the fundamental are not perfectly harmonic, but whatever note you pick will have all the intervals relating to itself perfectly equal to the intervals relating to any other note. A 5th from C to G with sound as harmonious as a 5th from D to A, because the distance between the pitches is exactly the same. It is called Equal Temperament after all. Yes, it is a bit out of tune because it doesn't follow the harmonic relations you described, but considering each one of the 12 notes and the intervals and scales relating to it, it is ON AVERAGE closer to a harmonic tuning than the Pythagorean tuning. I hope this makes sense. If it doesn't look up Pythagorean Tuning, Just Intonation, Equal Temperament and, for those interested in guitars, look up True Temperament fretboards.
Yeah, what he said... that makes sense to me. I've tried figuring these things out on my own for years, using geometry, math etc. and you're dead on. Things just don't work that way on a guitar. It was much easier to read this than to watch that video
I think the coolest part of music is that you don’t need any theory or lessons to play. Theory is cool but music is a language. Cheers
Music theory gets a lot more involved than this. The connection between music and math isn't accidental, but the complexity goes all the way up to furthest limits of mathematical theory. That's why you can always analyse music mathematically (which is basically what a recording is) but you can't understand or generate it using only formulas alone (which is why AI music gets stuck in the same place as self-driving or drawing hands).
finally! Welcome back
I could follow up to a while, then it got all confusing. I'll be back for this again and again, thanks for putting it out. Maybe using different colours would help as later on it gets very confusing.
Great video I can get over the pronunciation of 5th, “start from the fift” is so endearing somehow.
This is trippy to watch, very cool
Had to put the playback speed to .75 to let the info really hit right, but this is a cool visualization. Getting into that musical alchemy.
Well done, I have been pondering that question for some time...
I understood that the major scale of C used all the natural notes but skipped all the sharps/flats, (which is why they were called sharps/flats. I knew where these were & that the notes including sharps & flats were (almost) equally spaced, but I didn't know that this was why a major scale 'worked'.
Knowing the elementary and even advanced musical theory will not make a person a musician. Musicians make rapid brain processing decisions in seconds as they engage with their instruments of choice. That process becomes elaborate and complex. That is why when we hear something in music that is emotionally engaging and for our brains, computationally astounding, it is because it is.
This is sooooooo helpful and informative. Really great stuff here
Chromatic scale comes from picking a pitch and ascending in fifths until you arrive back at the same note as the starting pitch. Line those fifths up in scale order and you get the chromatic scale. Chromatic scale is questioned and messed with frequently by modern composers and musicians.
This may not be exactly what you have in mind, but, two good math eye openers are the Bossa Nova and Chopin Fantaisie-Impromptu Op. 66 in C# Minor rhythmic structures.
"Music is the pleasure the human mind experiences from counting without being aware that it is counting." Wilhelm Leibniz
From a naturalist perspective music can to a degree be explained through the overtone series but that is not all since the choice of notes implies that there are tonal categories which cannot be explained by that perspective alone and implies the existence of a sort of idea realm of movements and tonalities. In that sense to explain music through simple theory is like explaining the realm of discourse in society through linguistics.
Loved the video! Great job 🎉
This is the first time theory has felt natural instead of arbitrary for me, although I've only dabbled. Appreciate the geometric visualization immensely, as well.
The blacksmith tale is a mythology, involving the forge and fire, by which one transmutes lead into gold.
Its so similar to a chaos fractal. Every division holds the entire system in itself smaller and smaller or bigger and bigger.
I love how you see the layer of math in music. Math has a hidden layer as well. Did you know that numbers sets of number have images encoded in them? You may have heard or seen "Fractal" images before, put simply, these are the images of numbers. So if we put it all together music is math and math is imagery....music should also have a layer of images that can be visible to humans though math formulas and displayed with computers just like fractals.
It’s all chromatic.
Here’s how all 12 notes are useable over a Dominant 7th chord (for example).
1-3-5-b7 are the chord tones; safe to sit on all day.
2-4-6-b3-b5 are from Mixolydian and the Blues scale, also very useable. That’s 9 out of the 12 notes, leaving only b2-b6-7 which can be used as passing tones. - No need to think of scales, just think in terms of how useable each of the 12 notes is and in what way.
If your goal was to frustrate beginners so that they will believe that they'll never understand theory, you have succeeded.