10. The Overtone Series and Dissonance 

This is what I always believed and I'm starting to find out that it's more and more truee

@@MelloCello7 I've been a musician now for more than 20, and every day, I'm convinced of the opposite: music is the fundamental rebellion AGAINST nature. Music is the creation of an aural universe that completely disregards what's supposedly "natural", because, ultimately, I'm the one who decides what notes I'm going to play. Oh, this interval is "unpleasant"? Let me play it *even louder* then!

​@@FernieCanto true, but even your act of rebellion is in fact ordered by the laws of nature. Those 'unpleasant' tones are unpleasant in part to those complex natural relations, and you chose to play them louder because of that natural order, and I also bet that you chose to resolve those unpleasant intervals to something far more ordered or open or at rest. your entire premise music, including your adherence and defiance thereof, is determined by a premise that is naturally ordained

@@MelloCello7 "Those 'unpleasant' tones are unpleasant in part to those complex natural relations, and you chose to play them louder because of that natural order," If you look at the video again and come back here, you'll notice that there's a deeper problem here, which I *tried* to address and seemingly failed. ... well, in reality, there are TONS of problems here, because the video is just completely wrong in almost all its conclusions. But the essential one is that the video is claiming that *aesthetic preference* is ordained by nature. The video conflates "consonant" sounds with "pleasant" sounds (which is wrong), and clams that this comes directly from the harmonic series (which is also wrong). In that case, just my choice of rejecting traditional consonance would already *not* be "a reflection of the laws of nature", but a NEGATION of it. And then, you claim that my negation is itself a form of reflection, but that goes _against_ what the video claims. Not only that, but that ultimately leads to a tautology: if rejecting nature is to reflect it, then EVERYTHING reflects nature, therefore EVERYTHING is "natural", and the whole argument is dissolved into nothing. "and I also bet that you chose to resolve those unpleasant intervals to something far more ordered or open or at rest." That only goes to show you have no idea of some of the music I've made. I mean, not only I've written music that eschews any kind of traditional harmonic resolution, but I openly reject the idea of "unpleasant intervals". There's no such thing. There's no "unpleasant" intervals, only intervals that do not sound adequate in specific moments due to the internal logic of the music in question--and even then, if something seems "inadequate", it isn't always possible to determine if the music has failed, or if we as listeners have failed to understand the internal logic. To simplify: there are no unpleasant intervals, just very stupid listeners. "your entire premise music, including your adherence and defiance thereof, is determined by a premise that is naturally ordained" In short, no. There's no natural order in my music, just _my_ order. And if I have to accept that my order is itself natural, then we fall back into the tautology: *anything* and *everything* is "natural", so there's no point in defining anything as "natural". But yeah, in short, the video is just completely full of it.

I'd be glad to help. I have 20 years of experience.

Honestly, all the videos that comprise this entire playlist are absolutely IMMACULATE in regards to each of their respective educational content, concise presentation, and exceptional analogies used to convey any of the various subject matter!

No worries. Thanks for the comment.

Thanks, Daniel.

Thanks, Paul. Yep, definitely. But I'm talking about relative dissonances here. What one actually hears as dissonant or consonant is subjective and is based on past experience with that interval. The more you hear a tritone interval, the less dissonant is sounds TO YOU. But it is still relatively MORE dissonant than a P5. All things are relative...including relativity :)

I would contend that the 5th relationship can be perceived as meaningful outside of any cultural context. This is because the human ear perceives the overtone relationship as the 2nd overtone "falling" or "returning" to its associated fundamental. Which really takes place in the background but explains why we hear it the way we do. I would disagree with the idea that cultural context determines tonal significance.

@@aaronmasters1455 I wonder whether anybody does hear a fifth - or any other interval - outside a cultural framework. That would require a listener to have no cultural framework. Is this possible? Another objection might be that a fifth consisting of a given fundamental and its second overtone only is a different thing from a fifth consisting of a fundamental (sine) tone and a separately produced fundamental (sine) tone a fifth above. The relative loudness of a fundamental and any of its overtones must have an effect on how the interval is heard. It would also be necessary to suppress the 'reinforcing' effect on the fundamental of the first overtone. Where does this ever occur? I agree that of all the intervals, the perfect intervals are the most likely to be universal phenomena. Whether they are universally received in the same way by all listeners would have to be tested, and would still have a subjective component.

I seriously doubt that anyone would find the most elementary geometric ratios to be dissonant, but their enjoyment of the consonance will vary considerably (it may sound boring or pleasing or whatever). I also understand that our auditory perception works on approximations so there is some wiggle room on what is dissonant or consonant there.

Really? Where did you read/hear that?

@@lokanoda, lol. Um ...harmonic analysis _absolutely dominates_ all of physics, chemistry, engineering, electronics, and every other major science. _Anything_ in the universe that vibrates -- from the earth's magnetosphere to quantum fields -- has natural or fundamental resonant frequencies, and these have overtone. A major chord is just a fundamental frequency (tone) and its 2nd and 4th overtones. In other words, the first five harmonics make up a major chord. Therefore, anything that vibrates plays a major chord.

@@xyzct I see now. Thanks. Part of the harmonic overtones.

No worries.

@@WalkThatBass Yeah you really are the man for this video.

The ratio isn't describing single notes, it's describing an interval between notes based on their complete cycles (frequencies). For example, the perfect fifth above A completes 3 cycles for every 2 cycles A completes. In other words, every second, A3 is a sine wave that completes 220 cycles. In that same second, E4 is a sine wave that completes 330 cycles. So every time (every second) A3 completes 220 cycles (hz), E4 completes 330 cycles. 330:220 is the same as 3:2. The interval between them is a perfect 5th, which is the same for all notes that are a perfect 5th from each other. C3 to G3? 3:2. Bb2 to F3? 3:2. I hope this helps.

Very helpful, Sam. Thanks.

Agreed, I would say the tritone is a good approximation for 7/5 so I would place it between the minor third and minor sixth in terms of consonance.

that is incorrect but more importantly, he is not incorrect

Wouldn't you still be looking for the number of shared frequencies?

Hi Matthieu, So the Perfect 4th interval by itself sounds perfectly consonant. However, it sounds a little bit unstable when plays in the context of triadic tonal music. It feels like it wants to resolve down to the Maj3rd. It creates a suspended chord which is...suspended (naturally) and want to fall one semitone to the Maj3. It's not that the interval is 'dissonant', it's more that it is unstable. It is avoided in two-voice counterpoint because it suggests a second inversion chord. This is because the Perfect 5th sounds 'stronger' than the Perfect 4th. For example, if we play: C - G (P5th) This sounds like a C Shell/Power Chord. If we play: C - F (P4th) This sounds like a second inversion F Shell/Power Chord. It just sounds like we inverted the 5th - Playing C - F instead of F - C Or you can think of it in terms of a sus chord. The Csus4 chord feels like it wants to resolve to the C chord. The F pulls to the E. So it's a slightly different idea/concept. The P4 is 'unstable' but 'consonant'. The tritone, on the other hand, is both 'unstable' and 'dissonant'. So it's interesting that (in certain contexts) both consonant and dissonant intervals can be unstable. Also, as a side note, what one actually hears as dissonant or consonant is a little bit subjective and is based on past experience with that interval. The more you hear a tritone interval, the less dissonant is sounds TO YOU. But it is still relatively MORE dissonant than a P5 precisely for the reasons I explained in this vid. :)

Matthieu Sebbah theres also the reason that while the major third 5/4 =1,25 and just like the p5 is is a resolved division, the perfect 4th is 4/3=1,33333333333333333333 and so on...

+Awake The fact, that 4/3 yields a quotient having consecutive digits of 3 (that continuously appear throughout all decimal places infinitesimally), does not have anything to do with the ratio's rationality (or "resolved division"). It simply has to do with the fact that we happen to be using a base-10 number system. If you used a base-3 system (and calculated the same operation on the same two numbers - now expressed as "11/10"), you'd find that it would equal a clearly-rational number expressed as "1.1".

Thank you all for your answer. Indeed, the nature of the sound should be independent of our base-10 system ! Great observation Cr8Tron ! I think the most probable explanation is the one of Walkthatbase, since at the beginning of polyphony there were only two voices, the perfect four could be interpreted as an inversion of the perfect fifth in another tonal center system. Thank you all once again for sharing your thought. Cheers :)

They never really make it clear at all. But, like Walk That Bass said, they're basically talking about the net effect of having a suspended chord due to the partials. There is an ambiguity your brain will find, as for which note to perceive as being the root, since the 4th now competes with the one we consider the actual root. This is unlike triads, in which the root is reinforcingly established, via every possible pair of the three fundamental frequencies. It would be analogous to if you were to ask why an augmented chord is considered "dissonant". Even though every pair of its three fundamentals consonantly implies a certain root (via maj3rd intervals), they never come to a consensus on which one the root actually gets to be. So, as Walk That Bass pointed out, it's not the same use of the word "dissonance".

The 4th turns up at the 21st harmonic, the major 6th at the 27th.

I'm ending up with different numbers. I noticed the octave excites one out of every two notes (50%), the perfect fifth one out of every three (33%), the perfect fourth one out of every four (25%), etc.

Replying to a very old post but: Makes sense, compare the first couple overtones of a lead playing/singing C and a bass playing the E below that: ...C-C-G-C E-E-B-E-G# You'll notice that the both very audible C and B (making a minor second, very dissonant) will clash

The notes given are from the 12 tone equal tempered system which sacrifices some perfection for more convenient usage of instruments. The harmonic series will produce notes that sometimes fall in between specific notes on a piano. For example, the 7th harmonic in the chart, Bb, is actually a bit flatter than Bb, but still sharper than an A.

Thank you very much

What you described actually exists and it's the 7-limit tuning. The tuning described in the video is the 5-limit tuning. In 7-limit tuning the tritone is 7:5, minor seventh is 7:4. The problem with it is, while interval are "juster" in general, it makes some notes very far away from its equal temperament version. Could be a good or bad thing.

Hi Roman, What Gnad said is correct. The interval ratios you choose for notes actually depends on what tuning system you are using. I will be discussing tuning systems in future videos (when I find the time to make them). Cheers :)

I would love that

Hey mate, So that all depends on what tuning system you use. Different tuning systems will create different interval ratios for each interval. For example, using pythagorean tuning, a Major 3rd is actually 81/64. Or using Quarter Comma Mean Tone tuning a Perfect 5th is actually closer to 643/430. So the ratio between two notes is quite flexible. In this video I've used Five Limit Tuning, just as a default. en.wikipedia.org/wiki/Just_intonation#Five-limit_tuning I hope to eventually make some videos about different tuning systems.

+Walk That Bass Yeah, I guess I'm already aware of it being used. I just got the impression that this video is aiming to promote the idea of people starting from the ground on up, so to speak. Obviously the higher integers have their practical uses, via the various already-established just-tuning systems you mention about. I'm just trying to do some research, before I theorize and put together some aural perception experiments I want to do. The higher-integer ratios seem a bit too contrived for the lower-level aspects I'm questioning right now. Isn't there some just-intonation system that defaults to how I described? Could've sworn there was.

No sorry, I'm not entirely sure. I'm sure there would be something like that. There are enough tuning systems out there. Have a look at these different just tuning systems and see if any come close: en.wikipedia.org/wiki/Tonality_diamond But nah, sorry, can't be of any more help.

Since a major chord and minor chord both have the 5th it can go both ways. The 3rd and 7th affect whether it is major, minor, dominant, or minor-major. The quality of the 5th is still important in the scale though, because you'll lack a V chord which is pretty useful in music. Locrian has a tritone as its 5th degree and not many songs are written in it.

I'd still say they're very much related. The order of where intervals show up, IE the level of consonance, describes how alike tones are in their overtone structures. The circle of fifths also describes alikeness, as the next key has the most notes in common with the previous one. The more diametrically opposed two keys are in the circle of fifths the more dissonant, which also matches how dissonant overtones get the higher up in the series. They're not precisely the same, as the circle of fifths is a bit of a theoretical extraction of a physical principle, but they describe a similar truth, which is that the steps related to the early intervals in the overtone series are the most consonant. It's not a coincidence that both directions in the circle are a perfect fifth and a perfect fourth; The first two intervals in the series of overtones - The octave in relation to the fifth, and the fifth in relation to the octave above.

Still though, wonderful video.

It never shows up in the harmonic series. It’s almost like you want the perfect fourth to be your tonic but it’s not

@@poldmalone1084 so in that case couldnt you use the 4th as a pivot note to change keys in a melody?

How so?

Learn the rules then break them

In indian classical music an octave has 22 notes called shruti. They are NOT based on the 12 note equitempered intonation. Search for the researcher Dr. Vidyadhar Oke or 22 shruti harmonium and you will find answers to many of your queries, Sir.

Yeah. Most people don’t pay attention past the 16th harmonic anyway.