The Harmonic Series | Illustrated Theory of Music #8
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- Опубліковано 16 лис 2020
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Welcome to the Orchestra of the Age of Enlightenment's, 'Illustrated Theory of Music'. This series of short, informal videos animate the stories behind music theory and provoke new questions about what we think we know. What does a 'quaver' really mean? Why do we use bars? Why does it have to be so slow? The series is led by the OAE’s dedicated musicians but audiences are invited to ask questions, challenge conventional wisdom and help to build a new understanding of music. Please share your thoughts in the comment box below!
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Didnt expect a barbershop quartet to demonstrate 7th 😂
But it is indeed the perfect example
Perfect indeed. The cherry on that sundae would have been to further show that the 2nd, 3rd, 4th, 5th harmonics he played together are actually the standard barbershop C major chord: C, G, C, E. Barbershop tags usually end with the 3rd on top since the top part (tenor) sings over the melody (lead).
This was great fun and so instructive. Needs to be better known. I only found by chance.
One of the best explanations about harmonics I've ever listened to
Harmonics and humoronics lol
Yeah! I wish someone showed me this when I was younger!
Sliding up and down the harmonic series is a great exercise for accuracy
The 7th and 14th harmonic are noticeably flat (close to 1/3 of a semitone) compared to the 12 note equal temperament scale in use today -- can still sound okay if other instruments either aren't playing at the same time or are able to bend their pitches to match, or if the other instruments are playing parts of a barbershop chord. The 11th (especially) and 13th harmonics are very close to quarter tones, and so are harder to use in 12 note equal temperament, but (especially 11th) could work in 24 note equal temperament.
I found a piano where F5 note is 20c flat, G7 (G3-D4-B4-F5) chord sounds better than the piano in tune.
One of my AP Physics students (also an orchestra player) shared this with me after my lesson on harmonics. It is now part of my materials for my class. Super handy, and explains resonance and harmonics in music so well. Thank you!
The "E" makes the C harmonic series capable of creating the major quality of a chord, but what makes the minor quality sound less stable, more dynamic?
The Eb used in a minor chord creates an interesting hidden dissonance: When playing "C", the 5th harmonic "E" still has a fair amount of energy. Back up a moment:
Above the first harmonic, the fundamental, each subsequent harmonic requires more energy to equal the volume of the previous harmonic. When you play C on the piano, all of the string's harmonics sound simultaneously; it is the fundamental that we hear as the pitch. The relationships of the volumes of the other harmonics is what gives the piano (and every instrument and sound) its characteristic quality (timbre).
So when you play a C on most instruments, you're also playing a quieter 2nd harmonic, an even quieter 3rd harmonic, and so on. (The exceptions require another video, hopefully to be made by OAE, or a link provided if it's already done!) This means that when you play a note, even though the harmonics are present, they're usually impossible to easily hear as distinct pitches, but they're there all the same. When you play an Eb with the C to create a minor quality, you're actually creating a subtle dissonance between your Eb and the C's harmonic E, as if you played an E adjacent to the Eb! While the ear may not consciously hear the E, it does a good job of recognizing the subtle dissonance and identifying it as a minor quality. It is that subtle dissonance that drives the minor sound's dynamic quality.
Kudos to whoever did the editing for this, this was really entertaining and informative.
This video just made a lot "click" for me in terms of music theory. Thank you for this great explanation!
Brilliantly explained. As a self-taught amateur musician I never fully understood this concept until now. Thank you.
I really wish this resource was around when I learned Horn. The harmonic series was vital to my understanding of the instrument as a whole.
Brings back memories of fighting with a not so good quality F French Horn And finally switching to a double horn. Opened up a whole new world of fun. A natural horn has a sound that is hard to replicate exactly. But can be done with a little ingenuity on a keyed horn.
I never actually realized before that the minor seventh shows up in the harmonic series long before anything resembling the major seventh does - which poses the question of why the Ionian mode of the major scale ended up being the primary, basic scale upon which all western music is based, rather than the Mixolydian mode which has a more immediate basis in nature (including as it does all five of the first five unique notes of the harmonic series, including the two that define it - a major third and a minor seventh)
Using the 7th harmonic as the 7th of the scale wouldn't produce what is normally referred to as the Mixolydian mode today.
Western music evolved from the modal framework of ancient Greek and Roman music, still used to this day across the Eastern Mediterranean region. Within it, the primary consonances were the perfect fourth and the perfect fifth. Usually, the modes are built by stacking two tetrachords, with the difference tone to complete the octave placed either between the two tetrachords (making them disjunct tetrachords), or on top of the second tetrachord (making them conjunct tetrachords which share one note).
Ancient Greek and later medieval Islamic music theorists saw the fifth and the fourth as the smallest consonant intervals, meaning that the most consonant modes had the highest number of perfect fourths between the scale degrees. The modern Mixolydian mode, made of two conjunct major tetrachords and a difference tone (CDEF + FGABb + C) fits the description. But this means that the Bb you get here isn't derived from the 7th harmonic, but rather as the perfect fourth from F (a 16/9 interval from C).
Using the 7th harmonic would undermine the structural integrity of a scale based on the perfect 4th and the perfect 5th as the most consonant intervallic relationships. Now, how about the tonal system, which later developed in the West? Here, the 5th harmonic is used to arithmetically divide the perfect fifth (3/2) into two consonant intervals of differing sizes: a major + a minor third (5/4 x 6/5). But the old modal consonances still formed the skeleton of the scale. There's the tonic C, along with its perfect fourth (F) and fifth (G).
It is from these three individual notes, taken as separate fundamentals, that three separate major chords are played (456) to derive the fundamental scale, thus producing C E G, F A C, and G B D. The middle notes in the chords (E, A, B) will be a syntonic comma lower than in the modal system. There are two different ways to arrive at a minor 7th for Mixolydian now: either as the minor third of G (making it 9/5 from C), or as the perfect fourth of F (like in the modal system), which is a syntonic comma lower. However, if one were to use the 7th harmonic (7/4) from C, this would make the minor third from G to Bb unusually small (7/6 instead of 6/5), even compared to the one in the modal system, while the whole step from Bb to C would be unusually large (8/7 instead of 9/8). Forming new chords with this Bb would now necessitate a number of notes far beyond the standard 12, and the scale structure would be completely obscured.
So, the problem with using the 7th harmonic is that it fits into neither of the two frameworks (modal and tonal) that formed the basis of music in the West for hundreds of years. It detracts from the smallest interval considered a consonance in Western music (the minor third 6/5) and introduces a layer of complexity into the scale structure with two new melodic intervals (a smallish minor third 7/6, and a largeish whole tone 8/7).
I could see those last two crooks inspiring some concertos, perhaps containing some Rondos.
Good demo. Especially going all the way to 16. I did this off of a long piano string on a grand where you can get to enough string length. Then I did the same for a organ pipe flute no holes just harmonics to this upper range above 10. It's easier to play as only a tight lip to tube foot is needed. It's all tonging toots and diagram pumps to sound the whole range. But! I can have the "one and a half" you refer to. Smooth glides from open and closed. At this point this can really wail out the blues. Norwegian -Seljefløyte. I had this in a lecture at Purdue early 70's the prof explained this when he got to the seventh he said "that's a wild card" we'll throw that one out. And he went on to about the 10th.
omfg that instrument is crazy. Loved the video. I'll show it to my kids. It's better than any music class at school
Really excellent outline of the harmonic series. Thanks Martin!
Excellent!!! I will be using this with my students!
This was THE BEST demonstration of the harmonic overtone series I’ve ever seen, and I’m a professional musician! Thank you ever so much for this entertaining and thoroughly informative explanation. I will be using this video in my teaching. Please make more videos like this! They are very much needed by all of us who teach music.
Wie cool ist das denn!
Dankeschön !!!
Best explanation! Thank you!
Wonderful! Found by chance, loved it ❤️
Best explanation ever, thank you.
Excellent presentation, thank you!
Informative, clear, entertaining. Just what I was looking for. Thanks a lot!
Thank you very much for presenting this visually and aurally through video. It really is one of the best explanations out there, and definitely gave me a lot of ideas for better presenting this topic to my students. Love the tube changes at the end, as it hit home why instruments are in different "keys." I never stopped to think about this, but now Horn in Eb or Trumpet in C makes sense. Thanks again!
Really nicely done! Thanks for putting that together :)
So enchanting, very enlightening for an amateur musician. Thank you.
Just brilliantly explained and fun to watch.
THis is awesome!
Amazing! Thank you for your video ...blessings !
Absolutely fantastic video. Going straight to my trumpet students!
The 7th harmonic is actually the barbershop 7th. The 11th is used, for example, in Hungarian and Romanian folk music, especially in Transylvania. Folk musicians can play and/or sing it. They just live with it when playing the overtone flute, although its pitch and be adjusted to some extent by partially closing the end hole of the flute. The 11th harmonic can also be a blue note in blues and jazz, along with neutral 3rd and 7th, both being used in various types of folk music.
Fascinating! 🖖🏻
Exceptionally well explained! And also entertaining. This video really improved my understanding of the harmonic series. Many thanks!
What a wonderfully simple and logical explanation! Thanks!
Great video and fantastic editing. The use of examples from all over the place was really fun and helpful.
Que buena explicación!!! Felicitaciones!!
Amazing! Wonderful video.
This was really interesting. Thanks!
Amazingly clear and fun!
I have been studying this on guitar and lap guitar, this was very insightful , I love learning about other instruments, they seem so weird I also like getting tunes out any I come across, I lot carries across, knowing theory helps too, it's just the techniques are different, harmonica sax and vocals strike me as a lot of effort after playing guitar for years lol
11:30
And if you get a horn with, say, three keys.... then you can play a harmonic series starting on any note you like!
Brilliant thank you !
So well explained. Thanks a mil.
Wow thank you so much! This video was really helpful!
I found that quite Enlightening to be sure!
This is lovely!
This is an amazing demonstration! Thanks for making the theory of harmonics easy to understand. If I was a band teacher I'd definitely show this video to my students!
Great explanations.
Fascinating!
Wonderful explanation ! Thanks a lot ! :D
Wow, excellent explanation!!
Amazing lesson. Thank you!
perfect video
Wonderful and fun presentation.
LOVED IT!
Hey,I liked it !
This IS great! He also looks a little like Lady Elaine from Mr. Roger's Neighborhood.
I'd never heard of her, but yes I do!
this was so fun!!!! and helpful actually ahhaa thanks!
Thank you very much, that was very instructive!
oh look I'm still subscribed! excellent!
I can only imagine what it is like to play in the OotAoE...you've got a real collection of wags
and individuals, all of them, consummate players.
Thank you, this was such a informative video!
Music is not in my nature; I used to think it wasn't, but now I'm beginning to think it might be . Thank you fo enlightenment.
thank you so much.
Around 11:10, I hit the 'like' button so hard that it sounded atonal. Thanks for this very informative video!
I'm triggered as a fan of microtonal theory, the 11th and 13th are terrific as they are! It's just most common practice music doesn't operate beyond 5-limit harmony so they don't really fit it. Sticking an 11th harmonic on top of a major third in either of its harmonic forms (4:5:6 or 6:8:10 or 3:4:5) has this almost electrifying sound in my opinion. Not that you'd use it all the time but it adds a real "zap" that tingles my ears in a good way.
excellent
Good Class! thank you!
8:59 is where he plays an excerpt from Music for the Royal Fireworks :D
I wish I could give this video a double thumbs-up :D
Duuuuuddddeeeee….. yes. Thank you.
Brilliant
It would be helpful to mention the math behind this. Each overtone has a frequency that is a small whole number ratio of that of the fundamental. That is both why the series exists and why notes in our 12 tone scale sound good together.
Also, it is not obvious to the target audience that notes that are not in the harmonic series of a natural horn cannot be played.
Thanks Lee, but I do say that you can’t play fractions of wavelengths. And wavelengths and frequencies are highly related as you know! The whole number ratio of frequencies is exactly equivalent to the whole number of waves.
To my knowledge, early use of thirds was only "vulgar" on keyboard instruments that used Pythagorean temperaments.
That's interesting, thanks.
Well, not really. They weren't used much in vocal music either. Just look at medieval songs, and you will notice that the harmonies (on strong beats) are mainly based on 4ths, 5ths and octaves. 3rds and 6ths only became consonant during the renaissance.
Now, singers were probably trained to sing in Pythagorean tuning (and Pythagorean tuning is probably one of the contributing factors to why thirds weren't used much), but still, they could have adjusted the notes by ear. It's probably just that the "beauty" of the third wasn't yet "discovered" because people didn't know exactly how to deal with thirds. You need to put a concept into use before people can get familiar with it. And if 3rds had really never been used "as consonances", then people simply weren't used to the sound of it.
It's hard to imagine how people before us perceived music. It's easy to think that of course what sounds great to our ears has always sounded great to people's ears. But that's simply not the case. Music has evolved to become more and more dissonant over time, and there's a reason to it - when the previous generation comes up with a new thing, they can teach that to the next generation, and this way new knowledge builds on top of older knowledge. Now we have the tools to make more dissonant things sound good, and those tools are common knowledge.
@@MaggaraMarineIt's worth noting that this aversion to thirds wasn't universal, either: Vertical harmony in vocal music seems to have developed independently of the European organum tradition in Subsaharan Africa and throughout Melanesia and Polynesia, although precisely when is difficult to say given the lack of written records, and those traditional musics frequently feature thirds as consonances. Likewise, even if we are speaking solely of Europe, the consonance of simple mathematical ratios with higher prime limits than 3 were at least understood through Greek treatises om music theory, although the actual musical practices were implemented far more in the Byzantine tradition, and going by early settings of English folksongs such as "Sumer is icumen in" from the early 1400s, one may surmise that what harmony there was in non-academic traditional music in Western Europe was likely closer to just intonation than the Pythagorean standard of liturgical performance. (One thing which is also often glossed over is the clear and heavy influence of Jewish, Arabic and Persian music on mediaeval polyphonic composition, particularly in the complex, dissonant overlapping vocal lines and intricate ornamentation of certain melodic gestures, but that's its own topic; as an aside, it's also worth noting that which traditional Middle Eastern theory was, like Gregorian chant, generally monophonic or heterophonic, taking after the ancient Greek theorists, these theorists observed that 5/4 is actually much closer to the product of eight stacked fourths reduced by several octaves than that of four stacked fifths, although this poses some other issues…)
so close to 100k
Hears wear me head starts two Hurt, Al!
Nice
4:39 somehw this reminds me of that buzzlightyear sound
11:40 et cetera... hahahaahaha!
Excellent. Interesting that horns in F aren't dealt with - but it's brilliant anyway!
2:40 BRRRRAAAAAAAP
how to get right length of any note is there any formula
Very cool video I just have one gripe. I would list the tones in the harmonic series as scale degrees (11511357b1etc...) rather than the pitches based in a C major scale. I understand this explanation is correct for the length of tubing you are using in the video (which fundamental frequency is C), however not all instruments are tuned to a fundamental C.
Bernstein talks about this in his discussion on the development of harmony in the western world he did for (I think it’s the BBC???) and how western art music is built upon the discovery of the harmonic series in nature and harnessing it with instruments and singing.
*edit* Admittedly, I made this comment before I watched the entire video. He does clarify this at the end, albeit briefly. However a scale degree explanation might have also been useful.
You are right, and that is why I go on to other length tubes at the end. And the notes are written in the staff in the background...
When you played the horn it sounded like the same sound we hear when we watch an animated movie or tv show with an elephant. That last note you ended on in relation to the fundamental is the characteristic elephant sound we hear. What interval is that?
It is 3 octaves above the lowest possible note.
@@martinlawrence1148 interesting. So that sound is just made up of harmonics. I wonder if I can play that on the guitar somehow.
@@elementsofphysicalreality yes, an elephant's trunk is acoustically the same as my natural horn. And the harmonics on a guitar string are in the same place too. You can hear them if you place your finger lightly on the string in the right place, as I expect you know. Might be difficult to get as much sustain as a horn, unless it's an electric...
Paul Gascogne😮
Nothing goes wrong for embouchure warm up as well as for embouchure muscle memory to assist with pitch name accuracy and tuning. All the partials should be performed by horn players while waking up embouchure
What is the name of that horn?
That is a natural horn, made by Andreas Jungwirth of Vienna, a copy of a Bohemian horn from 1790, when Mozart was still alive!
You look like Bruckner!
This video about harmonic series is even great as Martin’s, and even more detailed, lovingly complementing what we just watched:
ua-cam.com/video/Wx_kugSemfY/v-deo.html
4:38 Thus spoke Martin Lawrence.... 😉
There are 2 ways to think of the wave lengths: 2 strings with the same length, but different numbers of waves, the same wavelength, but 2 different string lengths.
I didn’t hear a tanpura, or a shruti box, or harmonium, or anything accompanying the sitar in that Indian example. And the sympathetic strings on the sitar play many notes, not a drone…
I thought the other examples were good.
8:39 5.03968 waves
11:09 5.2748m long
I still dont get why are pianos out of tune. When the problem is 11th and 13th harmonics. What does it have to do with anything. What happens when i tune every single string on the piano to the exact pitch they are supposed to vibrate in. (Frequency ratio 12th root of 2)
I know there are problems with the higher and lower strings being tuned flatter/sharper because of inharmonicity but what about the middle range. Why 5.0-something instead of 5.
Ah, that’s because of the Pythagorean comma! If you tune all the fifths to exactly the ratio 3:2 as they should be, after 13 octaves you should get back to the initial note, but you don’t, it’s sharp by a small fraction. Do the maths! So you have to squash each fifth equally so they fit.
The 11th and the 13th harmonics are not the problem, because Western European music neither uses them, nor does it even attempt to approximate them. Western music uses intervals mathematically derived from the relations between the first three prime numbers, their powers and multiples: 2, 3 and 5. These relations produce the most sonically pure consonances.
To get octaves, one need only use 2 (doubling), while for perfect fifths and fourths the prime 3 is also needed: the perfect fifth is a 3/2 ratio, and the perfect fourth its inverse at 4/3. Finally, pure thirds and sixths need all the three primes (major third: 5/4; minor sixth: 8/5; minor third: 6/5; major sixth: 5/3).
Tuning a scale using simple ratios produces sonically pure consonances, but it has problems. One is that it features discrepancies between similar tones derived in different ways, which are called commas. The two commas of relevance here are the syntonic comma and the Pythagorean comma.
The syntonic comma is the discrepancy between intervals derived from the first two primes (octaves and perfect fifths/fourths), and those which also use the third prime (thirds). For example, an E derived as a pure major third from C, a 5/4 interval, and an E arrived at after four consecutive perfect fifths (3/2) from C, which amounts to 81/64 from C after octave reduction, are separated by a syntonic comma, which is about 21.5% of a semitone.
The Pythagorean comma, on the other hand, is the discrepancy between the first and the second prime. Multiplying by 3/2 (a perfect fifth) twelve times doesn't in fact equal multiplying by 2 (an octave) seven times, because twelve fifths are slightly larger than seven octaves. The amount by which the resulting interval after 12 consecutive fifths is larger than seven octaves is called the Pythagorean comma, and it's about 23.46% of a semitone. The circle of fifths never closes in just intonation for this reason.
Different systems of temperament attack different problems of just intonation. The system used for the piano and all modern fixed temperament instruments is called 12-tone equal temperament. It narrows (tempers) all the fifths very slightly, by exactly the twelfth of a Pythagorean comma, so that after 12 of them the circle of fifths closes. This is in practice the same as logarithmically dividing 2 (an octave) into 12 equal parts (semitones). This makes all the fifths/fourths very slightly out of tune for the sake of making all 12 keys sound the same, but the approximation of thirds/sixths isn't good at all. The latter are quite poor from a harmonic perspective (the major third is 14% of a semitone sharp, the minor third 16% flat). This can be mathematically verified: the 12-tone equal temperament major third is 2^(4/12)=1,2599210..., while the pure major third is 5/4=1.25.
Double it and give it to the next person
Well, yes, but this sort of confuses the chronological development of Western harmony. The diatonic scale (C D E F G A B etc.) and its permutations precede triadic harmony by many centuries, dating back to the ancient Greeks and even further back to the Akkadians/Sumerians. Basically, harmony is an emergent property of the diatonic scale (reinforced by use of brass/woodwind instruments), not the basis of it.
You may be right. I don’t know about Akkadian or Sumerian music (I would love to hear some!). But Pythagoras certainly talks about dividing the string up into whole number intervals to get the harmonic series, and knew what we call a fifth was the ratio 3:2 etc. The Greek modes, as I understand it, used scales derived from the harmonic series, and didn’t use what we would call triadic harmony, a much later invention I agree. But you could say that triadic harmony was derived from Pythagorean scales.
@@martinlawrence1148 That's not quite right. Pythagoras (who is a semi-mythological figure, none of whose writings survive) is credited with being the first to mathematically describe the intervals 3:2, 4:3, and 2:1. But he did not describe the harmonic series. That mathematical development didn't happen until the 14th century in Western Europe.
"But you could say that triadic harmony was derived from Pythagorean scales." Pythagorean-ism describes a system of tuning where all intervals can be produced by adding or subtracting 3:2 and 2:1. If you stack seven 3:2's and rearrange it so it fits within one octave, you get the scale 1:1 9:8 81:64 4:3 3:2 27:16 243:128. We would hear this as the major scale. The problem is that the triadic harmony derived from this scale is really bad. The major third 81:64 is around 408 cents. That's 8 cents sharper than the equal tempered major third of 400 cents, and 22(!) cents sharper than the "pure" or "harmonic" major third of 5:4 (386 cents).
What happened in Europe is that around the 15th century, musicians and composers because increasingly attracted to the sound of "good" thirds and sixths -- the simple intervals 6:5, 5:4, 8:5, and 5:3. But none of these are obtainable in a Pythagorean system. So what started as fudging intervals here and there eventually developed into meantone temperament, where the purity of 3:2 is sacrificed to improve the thirds and sixths. At this point it can no longer be considered Pythagorean. The general contours of the scales being used (i.e. the diatonic modes, the major/minor scale, dorian, phrygian etc. etc.) stayed the same, but the tuning actually moved away from Pythagorean as triadic harmony was being developed.
@@karawethan I stand corrected on Pythagoras. But the pure 3rds and 6ths you refer to ARE derived from the harmonic series, which is the point I am making.
I'd be interested to know why Greek scales ended up with 7 notes in them rather than 5 (as is common in many cultures) or indeed any other number. Can you shed any light on that?
@@martinlawrence1148 I personally don't like the language of musical scales/intervals "deriving" from the harmonic series. It makes it sound like people were aware of the harmonic series in some abstract/mathematical sense and then consciously applied it to music. The real reason has to do with what is called phase locking, basically the auditory perception of how the overtones of 2+ sounds line up with one another (or don't). An interval like 27/16 (major 6th) will sound more dissonant than nearby 5/3 because the overtones of that interval do not sync-up quite as well. BUT...27/16 is simply the 27th partial of the harmonic series brought down into a usable octave. Conversely, there is no 5/3 partial. It is instead the relationship between the 5th and 3rd partial. We recognize 5/3, 6/5 (difference between 6th and 5th partial) and 8/5 (octave inversion of 5/4) as highly consonant, even though they don't appear "naturally" in the harmonic series. That, and we favor those over actual low-level partials like 7/4 or 11/8, which have no close approximation in our musical system (but actually sound pretty consonant once you get used to them). The real kicker is that so far, we have only been considering harmonic timbres. There are all sorts of musical sounds with *in*harmonic timbres (mostly idiophones), meaning that their overtone profile looks nothing like the harmonic series. Consequently, intervals like 5/4, 6/5 etc. may sound more dissonant than nearby irrational intervals.
Sorry for the overly long explanation. Regarding ancient Greek scales having 7 notes, I am not from ancient Greece so I couldn't really tell you. But there does appear to be a strong preference not only cross-culturally but really throughout time for 5 and 7 tone scales. Some have hypothesized that this relates to the idea of a scale being "well-formed" or "maximally-even." You want a scale where the tones are distributed more or less evenly across the octave (not bunched up at either end or at the middle). Symmetry can be a desirable feature, but totally perfect symmetry is not (that may have something to do with the relatively rare occurrence of 6 and 8 tone scale systems). And, you don't want so many tones that it becomes hard to tell them apart and remember melodies. There may be other reasons, but 5 and 7 seems to be a natural sweet spot.
The equal tempered notes are not that complicated.
It's just about lowering each fifth of the same micro interval, 1/12 of the pythagorean comma.
Roughly 2 cents.
All the other intervals obtained by superposing lowered fifths
Dude looks like Flea
actually, the B flat is also untuned but it's less noticible