10. The Overtone Series and Dissonance

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Have you ever wondered why we call certain intervals ‘perfect’? What’s so perfect about them? Well, the answer lies in the Overtone Series. The Major triad and the V-I Perfect Cadence were not randomly chosen, they are both derived from the Overtone Series.
While each instrument is different, generally, overtones get progressively weaker the higher up you go. So the 85th overtone is much harder to hear than the 2nd or 3rd overtone. So a rule we have to remember is that: Lower overtones are louder and harmonically stronger.
Each of these harmonics is a particular musical note. And, of course, any two notes, including harmonics, form some kind of interval. So every interval can be expressed as a ratio between the frequencies of two notes or harmonics.
So by playing a single note, you’re actually, in effect, playing the entire Major triad of that note. So as you can see, the Overtone Series is very important to music. It determines how music is structured. The Major triad and the V-I Perfect Cadence are not just things that were created out of thin air. They are inherent in the very structure of nature - music is a reflection of the laws of nature.

[@cpsthrume]

5:36 "Music is a reflection of the laws of nature" I really like this insight

[@MelloCello7]

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

[@FernieCanto]

@@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!

[@MelloCello7]

​@@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

[@FernieCanto]

@@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.

[@ronvonk1118]

Thank you so much. As a physics teacher I am working on a project to cover the links between music, physics and mathematics. This video is an excellent example of that.

[@TotalDec]

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

[@debbypajerowski5690]

Wow. I have been trying to understand this for years without success - until now! Thank you so much for this series! (and your other series as well!)

[@m33pr0r]

Thank you so much. This finally perfectly explained why major chords are so popular. I've seen so many explanations that it "sounds right" or "sounds good". But the insight that a single pluck of a string is actually a chord is critical to understanding what chords work.

[@TheSentientCloud]

Oh I love this! Music theory explained to my math brain :D I mean I get sounds and stuff and I can hear it. But I absolutely hate how other videos are like "I'll spare you the math and put things in terms too basic for you to actually understand anything useful" thank you!!!

[@lonelyrabbit133]

Thank you for this video. The harmonic series finally clicked for me.

[@Zalamandar]

This video, combined with the one before it, were VERY well-put together and extremely educational. Everything has been made clear to me in the last 20 minutes. Only thing I might change is maybe slightly less text on the slides, because it sometimes is a bit *dissonant* on the eyes. :P

[@hendrix5757]

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!

[@user-eu5wo2bt8r]

Best description of the overtone series I've found - and I've been looking man. You went into just the right amount of detail Thank you

[@innocentoctave]

Another excellent presentation. One quibble: perceived dissonance and consonance are also in practise a matter of musical context, and the listener's prior familiarity with the interval or chord in question. Chord voicing can also make a considerable difference to how dissonant a given chord sounds.

[@WalkThatBass]

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 :)

[@aaronmasters1455]

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.

[@innocentoctave]

@@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.

[@wiegraf9009]

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.

[@gnad4709]

Since you didn't mention key-related dissonance here (like the minor ii chord would always be dissonant), I hope it would be talked the next videos. Keep it up!

[@HR-yd5ib]

BRILLIAN! Thank you! First and only to explain these bascis properly!

[@bills48321]

This is a great explanation of consonance and dissonance and how the major scale and triad chords are derived from the overtone series. Thanks for presenting it.

[@WalkThatBass]

No worries. Thanks for the comment.

[@xyzct]

Anything that vibrates -- whether a flag pole on a windy day, the Earth after a massive earthquake, or the economy after a war -- plays a major chord.

[@lokanoda]

Really? Where did you read/hear that?

[@xyzct]

@@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.

[@lokanoda]

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

[@copernicus99]

Great video. Also, the overtone series for a single note will contain the notes of the diatonic scale in Western music, so it explains where the diatonic scale comes from. Another aspect of dissonance is beating and roughness, which were not covered in this video.

[@DavidJohnsonFromSeattle]

Thank you! I couldn't find any videos that explained why triads are a thing. I get it now!

[@gaborharrer]

Correct & perfect! Even in a didactic manner. Congratulation!

[@hilaqin7065]

Thank you so much,I have learned a lot,and you are a very good teacher.

[@bradleydoyle6752]

Thanks! I have been exploring orchestration, And these videos have been informative and inspiring.

[@alexnekita]

Amazing explanation! Thanks!

[@whitewalker608]

Nice video! Thanks!

[@mrbrown6421]

6:30 - These ratios are used to calculate the theoretical hole positions for 6 hole flutes. In practice, however, the ratios are slightly modified to account for oddities of a vibrating column of air in the flute.

[@deadshaman3772]

I've spotted a little mistake. 1/1 - 6/5 - 45/32 is not a diminished triad, because 45/32 is not a b5. 45/32 = 5/4 (major third) * 9/8 (major second) 45/32 is #4

[@SOULJAJOE010]

that is incorrect but more importantly, he is not incorrect

[@SaulNewbury]

That (and the preceding video) was great! Thank you.

[@chenhou946]

For harmonics 7 to 14, if the harmonic number is n, the interval n/4 is a type of nth interval. For example, 11/4 is a type of 11th.

[@danielirilarry]

Perfect class! Thank you for sharing your knowledge!

[@WalkThatBass]

Thanks, Daniel.

[@berfeito]

I´d totally give it a like, but I don´t want the change the current 440 likes lest it will be out of tune ;)

[@NoChrReq]

The most important and the only information you need to understand music theory. If you could watch just one video, watch this one and make sure you understand overtones/harmonics/chords

[@Hecatonicosachoron54]

I want to share with you my favorite quote, I believe by Arnold Schoenberg. "Dissonances are the more remote consonances of the overtone series."

[@LemricVillaflorOfficial]

:) Perfect explanation. One thing I dont understand though is how do you translate the "Ratio" of Frequencies into notes/tones. Thank you in advance.

[@sammysofa1511]

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.

[@cadencetennant3303]

Very helpful, Sam. Thanks.

[@deepakmeher25]

Thanks for this knowledge. U are generous 🙏

[@saraafonso4646]

Thank you SOOOOOOOO much :)

[@WalkThatBass]

No worries.

[@mypaldan]

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

[@kylegurtowski5012]

Great video thanks, this is exactly the kind of video I've been looking for! I'm new to music, but in the tritone series A:Eb at 9:00, is it wrong to say that they share an overtone at 7:5? My understanding is that these ratios are all approximate so why do we say that M3 is 5:4, but use a more exact ratio for TT than 7:5? [2^(6/12) = 1.414 ~ 1.4 = 7/5 vs 2^(4/12) = 1.189 ~ 1.2 = 5/4]

[@Fred-gs1ur]

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.

[@poldmalone1084]

I have been researching topic and created an equation, 2/(numerator+denominator) = percentage of all overtones from both notes in harmony For a 2:1 ratio, that’s 66% For 3:2, that’s 40%, but for 3:1 that’s 50% For 5:4 that’s 11%, but for 5:1 that’s 33% The perfect fourth would be 2/7 of all notes The perfect fourth is not as good as a 5:1 ratio, so I consider the major third to be stronger

[@vincentjacobsmm]

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.

[@eufalesio1146]

you’re missing something here... the intervals you’re talking about are 5-limit (that is, the numerator and denominator have prime factorizations with only 2, 3, and 5), but there are intervals in 7-limit such as the septimal minor seventh (7/4), which is almost as consonant as the just major third, and even more consonant than the 9/5 minor seventh also, the septimal tritone (7/5) is quite consonant too!

[@mypaldan]

Hey I know this was made three years ago but the table at 6:08 doesn't match up with what he says outloud? What am I missing? He says "Ab F#" but I don't see that Ab anywhere.

[@MASTERFIED]

Nice

[@denestoth414]

when you demonstrated the diminished chord: How come the 5th and the 3rd of the chord dont share a common overtone? They are also a minor 3rd away from one another as the root and the 3rd, so shouldnt the 5th behave the same way, just conflict with the root super hard?

[@Cr8Tron]

Why such high integers to define the tritone's default ratio? Why not 7:5 as an augmented 4th, and 10:7 as a diminished 5th? Also, why not keep it consistent and invert your maj2nd(9:8) to get your min7th(16:9 instead of 9:5), just like you did for the min2nd/maj7th ratios?

[@WalkThatBass]

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.

[@Cr8Tron]

+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.

[@WalkThatBass]

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.

[@dariostarace]

Hey man! Great effort in making things plain here, and I guess you succeeded ;) thx

[@franklarge1663]

Great video! Question: It sounded to me that you played the As one octave higher than what was written (eg i heard an A4 when it was supposed to be an A3). Did i get that wrong?

[@carloscruz2218]

The harmonic series occur in every note? For example, the note in the 4th overtone, does the series repeat for this note too? If so, that could explain de V - I in minor cadences, for that a dominant chord resolves fine in a minor chord too?

[@fabiogovernato965]

It must be the accent but this video is very clear :)

[@Teslawaverunner]

Can anyone kindly explain the text at 4:12 which says “The second lowest overtone and therefore harmonically the second strongest interval ...”. It’s the words ‘lowest’ and ‘therefore’ that are throwing me. Does it mean ‘lowest’ frequency in the table ? And what is the logic for the ‘therefore’. Thx

[@vegahimsa3057]

Why are we less interested in (what I believe is called 7-limit) ratios with seven, such as 7:4, 7:5, 7:6, and 8:7, 9:7, 10:7, 11:7, 12:7, 13:7 ? Surely those are more pleasant than M2 and TT.

[@thebachemulationproject3268]

Great video! However, the harmonic series has no direct relation to the circle of fifths. Major and minor modes are organized in fifths because of the number of notes of the scale and all the interval relations between their 7 notes. Other scales would be organized in different intervals in their "circles", and they would have a different number of transpositions ^^

[@vincentjacobsmm]

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.

[@armansrsa]

do overtones really get weaker as you go up? Im pretty sure in my own voice when I look at an analyzer singing, it seems as though the mid range is louder than the fundamental frequency. Do you have any videos regarding this and how amplitude might vary across the harmonic series. Im sure certain instruments also have louder harmonics than the actual frequency.

[@carloscruz2218]

Hey Walk That Bass, how we relate the diatonic scale or the major scale with the overtone series? Can we build a diatonic scale or a major scale from the overtone series? Greetings from the Dominican Republic

[@sebastianvega4576]

the harmonic series is happening with free vibrating strings or air etc, got it. If I generate a sine wave on the computer it is perfect and does not generate overtones (because it is not a physical thing in the real world, it is a mathematical simulation of a wave), BUT do my speaker produce harmonics when they express the sine wave? at this point, we again have an actually vibrating object in the real world, so it should, right? does the air between my ears and my speakers, which does vibrate if the sine wave is playing, also create overtones? this drives me a bit nuts, to be honest :P

[@SOULJAJOE010]

Thank you!

[@nicolaslg1421]

Great presentation! But I wonder how would one measure the consonance of intervals with an odd denominator, like the perfect fourth 4:3, the major sixth 5:3 or the minor sixth 8:5

[@wiegraf9009]

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

[@still451]

Hi, I have a question to ask about the position of overtone series, if the fundamental note start from C4, so the next overtone order (by hearing) is C5 or E4?

[@Jdonovanford]

"The chord will sound C if all the notes share at least one harmonic below the 8th harmonic." In the case of diminished triad, this rule applies. However, it is dissonant.

[@milestailsprower4555]

I will round (NOT truncate) to 4dp hertz Root: 1/1 Augmented 2nd/Minor 3rd: 107/90 Tritone: 181/128 My frequencies are: Overtone in the root: 110 220 330 440 550 660 770 880 990 and 1,100 Overtone in augmented 2nd or minor 3rd: 130.7778 261.5556 392.3333 523.1111 653.8889 784.6667 915.4444 1,046.2222 1,177 and 1,307.7778 Overtone in tritone: 155.5469 311.0938 466.6406 622.1875 777.7344 933.2812 1,088.8281 1,244.375 1,399.9219 and 1,555.4688

[@flavioalheira]

Awesome explanation. But why you say "a flat Bb, a flat F#, a sharp Ab and a flat Bb"? I don't get it. I appreciate if tell me. Thank you very much

[@KyleMart]

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.

[@flavioalheira]

Thank you very much

[@TotalDec]

The average person is using 12-TET, not Just Int. I'm assuming no overtones are the same for any two notes not octaves. Right? Edit: Not including the far up harmonics.

[@SaulNewbury]

In the first twenty overtones starting at 65.4hz, you didn't mention the notes of a Perfect 4 or Major 6 ... would these turn up in further along in the series?

[@danielmeixner7125]

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

[@cameronvadnais4388]

This is good.

[@banchyy09]

I don’t understand why the quality of a chord is determined by the 3rd and the 7th if the 5th is lower on the overtone series. So when picking chord scales, as long as the guide tones match, we can use any scale really, regardless of the quality of 5th. Shouldn’t the 5th be driving this decision? My ear tells that it shouldn’t be. I agree the variety of 5th doesn’t change the overall sound too much, but I’m wondering what the harmonic justification is

[@KyleMart]

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.

[@romanlankin]

Thanks for the brilliant lesson. As far as I can see from what you said - the natural scale at a certain point (right after 6:5 minor third, actually) refuses to follow "more consonant" rule. Otherwise there would be ratios 7:6, 7:5, 7:4 et cetera. Well, I can understand that 7:6 is too close to 6:5 and might be ignored because of that, but why 7:5 wasn't preferred to 45:32? Or 7:4 - to 9:5? Why does this happen? Hope to understand that in your reply or a next video.

[@gnad4709]

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.

[@WalkThatBass]

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 :)

[@WadWizard]

I would love that

[@fakename8850]

I’m gonna have to be that guy. 8:50 Wouldn’t it be best to label 16:15 as A and Bb, not A and A#?

[@fakename8850]

Still though, wonderful video.

[@wyattwahlgren8883]

I think this is a really good video, but there's one thing to clear up: I heard that if you use a third in the bass, its overtones clash with the overtones of the other voices. Is there a way to show this?

[@vincentjacobsmm]

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

[@enudenud]

hey walkthatbass, as always thank you for this great vid. I have a question though. During the Renaissance period, for instance in the music of orland de lassus or giovanni palestrina, the perfect four was considered as a dissonance while the major 3rd as a consonant interval. But following your video it seems that the perfect four is 'more consonant' than the major 3rd. Do you have any explanation why historically the perfect 4th was considered as a dissonance?

[@WalkThatBass]

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. :)

[@Doctorcanniball]

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...

[@Cr8Tron]

+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".

[@enudenud]

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 :)

[@Cr8Tron]

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".

[@Plebsk]

7:27

[@armansrsa]

so why was the perfect 4th considered a dissonant interval?

[@poldmalone1084]

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

[@armansrsa]

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

[@blackholesun4942]

Confused after table 😵😵

[@henrikljungstrand2036]

You are doing a mistake not considering the septimal subminor seventh, third and tritone: 7:4, 7:6 and 7:5, and likewise the septimal supermajor second, third and tritone: 8:7, 9:7, and 10:7. 45:32 is an awful tritone compared to the beautiful tritone 7:5. And 7:6 is as beautiful as 6:5. And 7:4 is even better than 9:5. And 8:7 is slightly better than 9:8 Also you are missing out on the consonant intervals larger than an octave: the twelfth 3:1, the major tenth 5:2, the subminor tenth 7:3, the subminor fourteenth 7:2, the eleventh 8:3, the major ninth 9:4 etc as well as the semiconsonant neutral ninth, fourteenth and half sharp eleventh 11:5, 11:3, 11:4, and the subneutral ninth, thirteenth and third flat eleventh: 13:6, 13:4, 13:5. Even though the completely octave reduced harmonics after the 8th are mostly inaudible, their octave transpositions to the next octave are clearly audible.

[@fidrewe99]

Nice explanation, but... Octave, fifth and forth are called consonant, but slightly more dissonant intervals sound much more pleasant to me. If you're restricting yourself to only twelve tones you're missing out some very intersting intervals. Music is not designed to fit an equal step twelve tone scheme. It's only convenient for playing instruments.

[@kernalfleak]

Learn the rules then break them

[@shriramparanjape5817]

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.

[@shupesmerga4694]

nayabag na

[@7REDDRACO7]

your frequencies are all screwed.

[@bradleydoyle6752]

How so?

[@mf6921]

Was I the only one who couldn't hear the first three notes?

[@josejimenez8991]

Yup... this is where my nightmare started

[@winterheat]

wow so complicated... I wonder how Beethoven or Chopin did it when probably at that time they didn't know anything about overtone and dissonance

[@peterwood-jenkins3634]

Overtones to the human ear is one thing, but some can not be heard by the human ear

[@jacobruiz97]

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