Why Does Music Only Use 12 Different Notes?
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- เผยแพร่เมื่อ 26 ก.ค. 2020
- Why does Western music divide the octave into 12 different notes? Why not 13, or 19 or 24 notes? For such a simple sounding question, the answer is actually a tangle of history, physics and human preference. Get ready for some serious music theory!
Thank you to Modartt for gifting me a copy of their amazing Pianoteq software. Find out more here: www.modartt.com/pianoteq
Thank you to Fred Scalliet for adding French subtitles to this video!
Sources:
Gamelan Music: • Sound Tracker - Gamela...
12Tone talking 12TET: • TET for Tat: Why Do We...
Where does the 12-tone scale come from: • Where does the 12-tone...
Audio Spectrum (AdminOfThisSite): • 20Hz to 20kHz (Human A...
Perception of Octaves: www.quantamagazine.org/percep...
Playable Harmonic Series: alexanderchen.github.io/harmo...
Octave circularity in the auditory brain: www.neuroscience-of-music.se/e...
An extra special thanks goes to Vidad Flowers, Austin Russell, Christopher Ryan, Bruce Mount, Toot & Paul Peijzel, the channel’s Patreon saints! 😇
SUPPORT ME ON PATREON: / davidbennettpiano
❗ CORRECTION: At 5:41, it should read "For Major Sixth multiply by 1.666, and Minor Sixth multiply by 1.6" but I got them the wrong way around 😅 Thanks to Hans Bakker for spotting this 👍
Most people actually haven't come to any conclusion that 12 is the best. They simply adopt it unconsciously. In my opinion, 12 is the best option for 5-limit harmony, but once you go beyond that, you're better off upgrading to a system like 22 or 31. Most musicians don't even know what extended Just Intonation (7-limit harmony, 11-limit harmony, 13-limit harmony, etc.) is, and couldn't begin to understand the usefulness of alternative tuning systems like 22 or 31EDO.
AcTuAlLy iTs 1.6666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666
@@Frahamen Why stop there?
How dare you
That piece at the end of video; did you upload a separate video for it?
What is its title?
Im not "playing the violin badly", I'm just experimenting with microtonality
no, my finger isn't too far back. im playing an e half flat.
Its simialr to UK comedian Eric Morecombe "Im not playing the wrong notes...Im playing all the right notes but in the wrong order"
haha!
You've picked the best instrument for it! I say have fun
And I sing perfectly in micro-tonality!!
Maybe more will be added in the next update.
Musical DLC
only OGs remember the early access when there was no Si/Ti, and Do was called Ut
Lo!KA I also cannot wait to see the C flat flat flat sharp semi sharp dim aug dominant 3 5 7 9 11 13 15 major minor sus4 Tritone Lydian blues Locrian Phrygian Dorian Mixolydian Minor scale!
They never should have let EA get control of music.
Eastern tonality expansion pack lmao
I'm a non-musician trying to understand what music is. I had to look at maybe 6 or 7 videos on "basic music theory" before I found one that explained the plain fundamental facts about music, musical notes and intervals so clearly explained in this video. Well done. Thank you.
best way to understand is to grab an instrument while you watch these and take your time fiddling around
I totally agree with you. The same happened to me too. Undoubtedly one of the best videos(if not THE best...) on the matter on the whole TH-cam stuff!
I should write the exact same comment!
Am I to infer, that some key signatures sound more "in tune" than others, in "true intonation"? Depending of course whether the music piece contains alpt of those oddball pitch intervals.
My late wife was the musician in my family. She played multiple instruments. She knew all about temperament and tonality. I, on the other hand, was only trained in vocal music, so the intervals are the important thing. It’s great to see both points of view in one video. Also, being a retired engineer, I appreciate the mathematics.
Your wife seems like a wonderful person, I hope she rests in peace
@@Fernsaur what if she doesn’t want to?
@@alysdexia She has no choice.
@@Picasso_Picante92 that’s what you think.
As a human being, I appreciate your comment
music in school: hella boring
music when you voluntarily are interested in it and research music theory on your own: cool and interesting
Marvin Bennett ok
Everything basically...
Marvin Bennett thanks for telling us how old u are😅
Jacques Shellacques Im not laughing at his age but how it was really unnecessary to say how it was back in his age (like how does that have to do with anything). Lol, why would I laugh at someones age, Im gonna become old too. Btw u have horrible logical sense. How is age something given at birth? Thanks for driving this conversation into politics for no reason whatsoever.
Marvin is David's long lost brother
“There are usually only 12 notes”
Trombones and fretless string instruments:
*they will never understand our power*
Muahaha unlimited power
He explains later even those are designed to most easily reach those 12 notes.
Beware the horror of monotony!
@@magnusm4 And he's wrong.
but people with perfect pitch can still detect what notes the fretless instruments are hitting.
@@jeromem.evardome10_kr15 who says you have to play in 12 TET? The violin is intended to be tuned to perfect 5ths (or equal temperament depending on your preference) but nothing prevents you from playing notes outside the scale except not knowing where to set your finger. With false harmonics, there are an infinite amount of harmonics we can play as well.
Same for trombone and other non-chromatic instruments in the family. I'm less versed in how they work but the principle is the same. Harmonics ring freely on certain intervals (1/2, 1/3, 1/4, so on) but the slide gives you the potential to play notes anywhere on the scale.
60 years ago I worked for a company that pioneered electonically produced tones. The organs were tuned on 12 PCBs using an oscilloscope to equal temperament. When done, I was charged with 'tweaking' the potentiometers on each PCB to make them sound 'right'. We never discovered the science behind this phenomenen. This video explains this perfectly. Thank You.
What company was that? Very interesting story! Thanks
What's cool is that you don't need to know the mathematics. We can play by ear 👂, which means we have all this frequency analysis tech built into our brain already. How awesome is that!
Not my ass reading ‘PCB’ as ‘Perfect Cherry Blossom’. 😂
@@cockysonuvaBSounds like Allen Organ Company
Printed Circuit Board
I have a Master's degree in Music Theory, and you just explained this subject so much better than I could have!
Maybe he has a doctorate.
Nice
I’ve been playing music professionally for over 50 years, and this is the first time I’ve completely understood this.
You need to subscribe to Adam McNeely's TH-cam channel. He makes the most insightful videos on such topics.
@@amjan yeah, Adam's great too. Completely different styles. Not sure which is better or best but a combination of the two is better than either.
Well, I’ve understood music theory since I was about 10 (so, 1977) and have been tuning pianos for 36 years (at concert level for at least 30) and his explanation completely confuses the matter.
His explanations might be useful for programming a digital keyboard but I don’t find it much use for practical application.
The 12 note scale exists because much of it exists in a single vibrating string under tension. In a single string, it is easy to identify the fundamental, octave, 12th, double octave, M17, M19, m21, triple octave, M23, M24 and so on.
If you start tuning a stringed instrument in a cycle of Perfect 5ths, which exist in the physical vibration of each string, you will arrive with the 12 tone scale. It will produce a wide octave, so you have to narrow the 5ths (or widen the complimentary 4ths as appropriate) slightly to achieve a perfect octave and a useful scale, but that is how we got to a 12 note scale.
@@AlDunbar David seems to be very limited in terms of the variety of genres he is familiar with. He is very pop music oriented. This I find somewhat disappointing and even frustrating.
@@tannertuner Thanks for the great insight, Tanner!
"Um you're a little pitchy"
" actually im exploring microtonal notes"
😂😂😂 gonna use that from now on
Thanks for explaining this. Your explanation about tempering helped me to understand something my 7th grade music teacher said 50 years ago. He told us that in Bach's time the harpsichord would need to be retuned every time the performer wanted to play a piece in a different key, and that if we were to hear a piece played back then, it would sound strange to our ears. Now, I understand why.
Gives another meaning to "The Well tempered Clavier"
@@nano9285 The well tempered clavier is a collection of preludes and fugues in every key. The intention is to demonstrate tempering of keyboard instruments as a means of being able to play in any key without retuning.
Weird but as a mathematician and an average guitarist, this has made a lot of music make a lot more sense to me! Thank you
It's always beautiful to see mathematics show up in other fields :)
It's an excellent video but I'm stunned that you weren't taught this long ago. As musical intervals ARE mathematical...
I got all this stuff decades ago age 7 and strangely it made great sense and it "wore off." After my twenties it got harder to remember and apply it to music.
Well, you're getting it now - better late....
I saw a great video on harmonic series and music. Light bulb came on. Dimly, but on.
I'm really bad with music and been trying for DECADES to get it explained and most music people can't explain it well, this was a massive help.
DECADES is how I tune my 7 string
@@TonyHavenMusic Dammit I didnt even think of that. Good point.
“It’s not the frequency, but the intervals”
This makes so much sense!
😃😃
When played on the same instrument, yes. When an ensemble plays together, they have to tune to a common standard, e.g. 440 Hz (=A). Otherwise, they'll sound terrible.
This is why(?) traditional Indian Classical music has a movable Sa (Do). It doesn't matter where you agree the tonic is, the interval math remains the same.
interesting! Anyone else finds equal temperament more in tune than just temperament.
Must be related to listening habits.
@@thesoundsmith Do you think this is why certain guitar tunings sound similar to that droning Indian sound? A guitar tuning really experiments with intervals.
There is another reason why you only have 12 notes, if you follow a pattern by taking any starting note (A for example at 440) and multiply it by 3/2 you get the 5th above it. If you then take that note and do the same thing and if the resulting note is more than an octave above your original starting note divide the frequency by 2 to bring it into the same octave you get a pattern like this 440 (A), 660 (E), 495 (B), 742.5 (F#), 556.875 (C#), 835.3125 (G#), 626.4844 (D#), 469.8633 (A#), 704.7949 (F), 528.5962 (C), 792.8943 (G), 594.6707 (D), 446.003 (A) You can see that when you come back around to the original note it is only a few cents different from the starting note (440 vs 446.003) it doesn't fall half way between A and A# so you can't really just keep following the pattern because you wouldn't end up with 24 notes, so there is a reason to stop the cycle of 5ths at this point where you have covered the 1st 12 notes. I don't think a 24 note scale makes any sense from this because it doesn't naturally flow from the maths.
What you're describing is Pythagorean tuning, which is a known system discovered by Pythagoras millennia ago. But 3/2 and 2/1 are ratios that don't ever meet up in the real world. I would suggest the difference between your two A's, six cents, is very noticeable, which is why Pythagorean tuning is not ideal for most Western music. Agreed about the 24 tone octave.
Pathagorean tuning is all about pure tones, but equal temperment only has pure octaves and everything else is out of tune slightly from a pathagorean pure tone. In a perfect world we would tune to pure tones (pathagorean) and have pure octaves as well, but that's not mathmatically possible.
12 EDO is only convenient since 12 fifths is approximately seven octaves and we close the circle of fifths off at that point.
Pythagorean tuning, on the other hand, does not stop at 12 fifths, but at 53, at which point you're just slightly sharp of 31 octaves. Nowadays, you'd narrow each fifth by about one-fourteenth of a cent to get 53 fifths equal to 31 octaves. This is why 53 EDO can be considered a standardisation of Pythagorean tuning.
Agreed. Also, the 5th is the first non-octave harmonic on a vibrating string, this suggests that from a physics/math perspective the fifth is the most consonant (i.e. literally "harmonious") non-octave tone. Then, the fact that repeating fifths derives 12 notes in an octave as you said, no more than 12, no less than 12, this indicates why 12 divisions of an octave is optimal. And the perfect octave is necessary because that is the tone we relate all the intervals to and thus make sense of the melodies and harmonies from, so it wouldn't make sense for the octave to "drift" as it does slightly when deriving the twelve tones from repeating fifths. I feel this perspective is not as widely held as it should be, so I'm glad to see you saying it, and I wish this video did too.
Ever since I opened myself up to quartertones, I've discovered harmonies and intervals that are some of the most beautiful things I've ever heard.
Be interested to hear/see examples of these alleged beauties!
This should be taught in schools as a linked maths-music lesson to show students how maths is embedded in many aspects of life. Excellent explanation of the 12-tone octave - thanks!
You should read Dirk Gently's Holistic Detective Agency.
Er ... I did learn this in school.
@@AndrewBlucher Good!
@@Pagliacci_Rex SciFi?
@@AndrewBlucher i didn't. And i WAS in a music school. Turns out that unless kids played piano or wanted to get a certificate as piano technicians in the future, the school didn't care two shits about actually teaching us anything but the history of european music and endless lists of compositors
As a musician who also makes videos, I know how hard it is to try to organize complex information in a clear manner. You´ve absolutely nailed this, great job!
Thank you! This one really was a challenge so I’m really glad it came across ok! Thanks
Great explanation! I've been an amateur musician for 40 years and nobody has ever explained intervals to me this way.
i just found your channel and really appreciate how you break down normally complicated topics so simply. this topic especially. i’ve always wondered about this. your explanation is so simple and crystal clear. thank you very much!
Well, some questions are better left unans-- wait, it's David Bennett?
**Click**
Always has been
@@christianrobiso9373 underrated comment
Just learned more music theory in 18 minutes then I have my whole 55 years…bravo.
75 years. Bravo for sure.
@@Steve_K292 years. Amazing.
@@josephkim3223 108 years, brilliant
@@virgilvandoge3599 116 years. Stunning.
@@epicormic_bud791 years. Breathtaking. Any other vampires watching this video?
This is fantastic. I've had years of musical training and many more years of teaching myself and these kinds of basic concepts always eluded me. I love videos like this that can really get to the core of the concepts at hand and explain them thoroughly and so clearly.
This is my favourite music theory channel. Many of the others are just "Look at this mad chord progression Tool used" but this one is made for people who really want to learn music theory and the topics are ones which can quickly be applied practically to compositional or harmonic ideas. It's designed to be something you can use rather than something to make you go "wow". It's very well organised and presented too, again to be followed and understood, rather than to make you go "wow".
I’m 58 and started playing piano at age 2. I make my living from music. I studied my entire life and though I knew the basics of this I have never understood it as I do now. Your videos are superb and I always learn something from them. Thank you.
Well said.
I'm 53 and just taking up the ukulele, violin and harp. Guess I'm an extra late bloomer.
@@tia283 Try the trombone. It's the funnest.
@@tia283 Are you 53 years old or 53 tone equal temperament?
@@ValkyRiver Ha, ha
Hardly anyone explains music topics as good as you. And young you are. Should have 10Msubs!
Cheers! That means a lot!
I came to the comment section to say exactly that. I learnt music theory at a too young age and have forgotten lots of things. David is refreshing my memory and filling in the gaps, in such a clear, pleasant way. And has excellent music taste 👌🏼 Thanks so much!
Yeah Even an Old man didn't Explain this Music theory. But this Young Man he do lots and lots of Effort the explain this Extraordinary Theory. That's why I Subscribe. 😄
Ditto !
Divedown25, no one corrected your grammar so neither shall I, except to say, ditto!
this is great :) thank you! I was wandering about this a long time and no one has explained this to me in such a clear and demonstrative way :) the tuning software helped a lot !
Thank you David for making this video. I had struggled to understand the why behind the chosen notes along with making the connections to the tuning and the various note names that are thrown around. This info was just what I needed to tie it all together. Well done and only 17 minutes long :)
Cheers.
I don’t play music or know why I was recommended this but I was fascinated and watched to the end. This was so well explained. Great production!
Thanks!
Really informative production here; most interesting
Thank you! 😀😀
I wrote a piece in 19-TET recently. I’m considering doing a video of all 53-TET intervals.
Absolutely LOVE the song you created at the end. Haunting, yet mesmerizing. A real foot tapper, as you were yourself doing.😎👍💜
Hey Dave, awesome job. This is pretty advanced stuff to me but it's totally fascinating considering that the frequency was first discovered about 120 years ago. I guess the intervals were not measured initially but were set by ear. Awesome! Thanks for such an interesting video.
It should be mentioned that before Bach instruments were tuned to the key the piece was written. Bach was a bit of a scientist. He was the first to prove an instrument can play in all twelve keys without continually tuning the instrument. The Well Tempered Clavier was written to prove it could be done.
Wrong.
Equal temperament was already fairly common with string instruments in Bach's time, he certainly didn't invent it.
The Well tempered clavier books weren't composed with 12TET in mind, in fact, well temperaments are another class of temperaments altogether.
@@delibirdempire4792 I didn't mean to suggest he invented it. He promoted and advanced the form. He didn't show tunings but had diagrams. There were numerous ideas of tunings. Bach did advance the idea of a way to tune an instrument that did not require continual tuning. I believe with his own music he used various tunings. Bach does deserve credit for making a case for solving the tuning problem.
@@penultimatename6677 I agree. Bach (and most composers of that era) experimented with tunings for musical effects. The temperaments Bach used for the WTK books (well temperaments) gave each key a different musical feel. Each prelude had a distinct "sound". Playing in all twelve keys was already very possible though (with equal temperament)
"Tuned to the key..." is a nonsense as it is not possible to tune any key to just intonation. The musical system for key instrument was almost "Meantone". Well-tempered systems have been (re-) invented by Werckmeister. Well educated musicians with string or wind instruments as well as singers against this didn't and don:t follow until today a fixed tuning system. They perform/ed their music according or near to just intonation. Even when making music in common with key instruments. Besides there exists already a real pipe organ with 12 keys per octave but about 60 frequencies per key (+/- 30 Cent) and an internal program controös every performed music in real time to just intonation. Either with 3-5 limit or 3-5-7 limit if desired. More information you will find at
www.hermode.com
and the nistory of western tuning from pythagorean over meantone, well tempered to equal tempered is also described on one of its pages.
@@hermodetuning3208 of course it's possible to tune to the key. As you wrote, on wind or string instruments it's simply a matter of choice. Even fretted instruments often had movable gut frets to adjust the temperament. Only keyed instruments had an issue with changing temperament.
Ah, a 24 TET scale - the beautiful sound of tuning a guitar after a restring
-Superb- explanation of the physics behind our music. I've wondered about this for years and looked for but never found a thorough explanation until yours. Thanks...
Thankyou so much for this video. I've been asking people this question for literally 20 years and the replies I've had from musicians and physicists never tallied with each other. This is the first time I've heard someone explain it to me (a non-musician) in a way that I understand. Great video and I will be sure to check out your others.
Modern pop-music: may I introduce you to the first three notes of the major scale.
they are wel aware of those thanks
And then there are guitarists, where perfect tuning is just an opinion.
Yeah if I could find my tuner, i guess now it’s just gonna slowly get worse and worse
And blues wouldn't be blues without 1/4 bends.
Same with all string instruments, minus the harp
@@rainyday6430 and minus also the piano and harpsichord. Not sure about the Hurdy Gurdy.
If you tune by harmonics, you can easily tune the open strings to a just intonation. But then any fretted notes will be off. E.g. tune the B string harmonic at the 5th fret to the G string harmonic at the 4th fret. Voila, you have a just intoned major third (B) of G. But now all of the fretted notes on the B string will be flat, unless maybe its a crap guitar and the action was too high anyway, or if you bend every note slightly on the B string :-)
This answered many questions I had but could barely form into words. It also showed me how much more there is to music than I thought there was, and how incredibly complex and magical it is. Thank you.
What brilliantly clear, and beautifully structured and presented, teaching. Well done! And thank you for giving me such an insightful view of something I've never before been able to get my head around.
Excellent Video! You really nailed this!
Thanks!
He did! By far the best video on that topic I have seen. I was already struggling with this in school. It seems pretty nonsense to learn letters and where there are on the piano without having the physical background of the frequencies and why this is so established. Now, this becomes so clear and easy. I really ask myself why nobody in school has ever taught me this in a way that David does.
Using numeric examples (frequencies here) will nail it for students struggling with the usual teaching methods.
12 tone equal temperament! Wow
The genius of Hendrix: he claimed to
see music notes and tones.. as hues, or grades of varying colors inside his
mind. And incorporated these into an
idea he had, similar as an artist uses
a colorwheel. But it came naturally to
him, as he was an open channel that
delivered our earth - some incredibly
unique ballads and compositions.
A spiritual conduit to the ear attuned.
This summary is the best I've seen on yt. And I was searching for information about this physics-music related area for some time now. Awesome video!
Thank you Jakub! That means a lot!
Check out Howard Goodall's musical big bang the episode on equal temperament that is also rather good.
Great video. You clearly show and explain the foundations of music theory.
This was a very helpful and educational broadcast. It had a, “University Professor like feel to the music lecture.” It explained it all in quite a good detail of the how and why, in dealing with the basic understanding of the mystery of music playing and arrangements. Thank you, well done. 👏🏆
I remember taking piano lessons when I was a kid and realizing this point myself (@ 1:35). So just as an experiment I transposed the song "Minuet" by Mozart into different scales/chords just for fun but of course keeping the same interval. I found it fascinating that it was still the same song even if I started on a different note and just retained the intervals.
My son did the same thing with a song when he was young. Played the same short song in every key till the octave. He figured it out.
Bach did one called A Well Tempered Clavier.
@@mikegacek9182 This is easy when you know the scales, but a lot of people do not realise that the notes in every scale are the same intervals apart.
I only discovered this when I had not done my homework, forgot a few of my scales and had to work them out during an exam, where I did not have an instrument.
Surprisingly, many professional musicians do not realise the mathematical relationship. They simply obey the scale.
You have explained in 17 minutes what I have been trying to understand for 40 years! BRAVO!
When I was first learning music theory I struggled so much because I'd have these types of questions like, "but WHY these 12 notes" and it would only leave me confused and hard to wrap my head around what I needed to learn. This video though, does such a good job explaining it that I wish I saw it sooner. Really wrapped up all the things I wondered about while emphasizing what is most important for us to take away from intervals. Thank you
This was fascinating. It answered so many questions I've had for decades. It makes sense now. Thank you!
Thank you, David. I really needed this video.
Long ago I got frustrated with piano and trumpet because nobody could tell me why some key had 3 flats and another had 2 sharps, or why it mattered. Without the Why, it all seemed like rote memorization of arbitrary rules - something I still find painful. Many years later, you are the first one to successfully show me how those rules can be derived from physics and biology. Now, everything I learn has some foundation I can return to when I need help understanding or remembering.
Two months later, I've made more progress than I did in all of my high school years. I like practicing now; even scales are interesting. The music I love makes more sense to me and I am learning to reproduce some of those sounds.
With your help I am little bit happier. Thank you.
I know you made this comment 5 months ago but I thought I'd take a crack at the "why" behind your original question: Do-Re-Mi-Fa-So-La-Ti-Do.
Tradition in music theory/composition is that when writing out the notes in a key, you must use each letter once - and only once. Starting with the key of "C major" and listing out the notes in the major scale gives you:
C - D - E - F - G - A - B (1 - 2 - 3 - 4 - 5 - 6 - 7)
There are no sharps/flats in this key (simply because history decided to start with C.) If you were sitting at a piano and you knew the musicians around you were jamming in C major - and you knew the above - you would know that you will only be playing the white keys on the piano (because the black keys are sharps/flats.) The distance between each note in the above scale in terms of steps is Root-Whole-Whole-Half-Whole-Whole-Whole.
So now let's repeat what we just did for C major with G major:
Repeating the "Root-Whole-Whole-Half-Whole-Whole-Whole" pattern with the key of G major, we work out the below:
G - A - B - C - D - E - F# (1-2-3-4-5-6-7)
This is where we run into our first "sharp" and the "why" is because the pattern we are applying (Whole-Whole-Half-Whole-Whole-Whole") is what you may have learned as Do Re Mi Fa So La Ti Do. Subjectively, we enjoy what we have come to call the major scale and above intervals are enjoyable to our ear.
OKAY SO WHAT?
If those two things make sense, the real beauty here is that you can very quickly deduce how many sharps/flats are in a key [or identify a key if you know how many sharps/flats are in it] by learning the Circle of Fifths.
The Circle of Fifths is a 360 degree relationship between each key, similar to a clock, with 1 sharp being added every "hour." In our example, C major was 12 o'clock with no sharps. To find 1 o'clock, move up a fifth from C. The "fifth" of C is G - so "G" is our 1 o'clock, 1 o'clock means 1 sharp. To find our 2 o'clock, move up a fifth from G - arriving at D. If D is our 2 o'clock that means D major should have 2 sharps, does it?
D - E - F# - G - A - B - C#
Yep - it has 2. The first one is the one we already identified (the F# from G, note how it has moved into the 3rd position.) And now, our new C# occupies the spot (7) previously held by F#.
C = 12 PM/No Sharps, G = 1PM/Sharps, D = 2 PM/Sharps.
So now to really tie this all together - this means if you ever need to quickly know the sharps and flats of any key, just apply the rules we learned. For example I'll show how to quickly list the key of A major.
First, we know that ALL letters must be used, so let's do that. Starting with A:
A - B - C - D - E - F - G
To figure out where to put the sharps - we need to know where A is on the Circle of Fifths. It would be our 3 PM spot (A is a fifth up from D). This means that A has 3 sharps. Where do we put them?
Every "hour" on the clock includes the sharps from the hours before it. So 3 PM would contain the sharps found in 1PM and 2PM.
If A is 3, we know we need to include the sharps we already identified at 1 PM and 2 PM. Those sharps are F# and C#, so A major must include those sharps - plus one more.
A - B - C# - D - E - F# - G
Where is the 3rd sharp? When a sharp is introduced into the key, it first occupies the 7th spot (the F# in G) then the 3rd spot (in the key of D major, the F# moved from the 7th of the previous key to the 3rd in D major- and a new sharp was introduced into the 7th). After 7th, then 3rd, the sharp will arrive at the 6th.
1) List them all
2) Know the circle of fifths
3) find where your key lies on the circle, it needs that many sharps.
So A:
A - B - C# - D - E - F# - G#
I doubt anyone will ever read this, but it was fun. Learning the logic behind the CoF makes it incredibly intuitive and really unlocks the mystery of sharps/flats.
@@donaldbryant5587 @Donald Bryant Wow thank you so much for this. This comment probably gave me more insights than some of the videos i've watched on the circle of fifths. Just wanted to thank you for it. Found it by luck but im very happy that i did.
I know exactly where you're coming from, Ron. This video has greatly clarified things for me too. Donald's Circle of Fifths explanation is excellent as well, so having the two of these is a huge help. Best wishes with your musical journey. (Ron Shaw, Australia)
@@donaldbryant5587 Awesome.
Thank you !
@@IsaacAsimov1992 Huge compliment, thank you Ron. Be well.
If you're wondering what "evenly spaced" means, it means the frequency ratios between notes that are next to each other are all the same. That ratio multiplied by itself 12 times has to equal 2, so the ratio must be the 12th root of 2, i.e. R =1.059. The other intervals are the powers of that number from 1 to 12, for instance a whole tone is R squared and a minor third is R cubed.
But the 12th root of two even spacing can sound slightly "off" in some keys, although for instruments like pianos it has to be accepted as a quick retuning is usually not possible. Take a look at the pure ratios and how close they are to the even temperament ratios. www.earmaster.com/images/book/m11639/m11639.id104934.png
@@karhukivi 12th roots of two = even temperament. They sound equally "off" in all keys.
@@RagingGeekazoid If you are a very discerning listener, yes! I often retune my guitar when I play in a different key, that's easy, but what do you do with a piano - only tune it exactly for one key?
@@karhukivi Sorry about the wording. I should have written "equally" instead of "evenly". Anyway, I was just explaining what "equally spaced" means in the video at 7:10 and 13:10. What you do with a piano is called "equal temperament", which is tuned exactly the same for all keys, which is exactly what the video describes starting at 12:35, and which is exactly what I've been explaining. Is that clear enough now? 🙄
@@RagingGeekazoid They are not "equally" off key in equal temperament. With A at 440 Hz, perfect C should be 264 Hz but with ET will be 261.6, a difference of 2.4 Hz. However perfect E should be 330 Hz but with ET is 329.6, only 0.4 Hz off. is that clear?!!
OH MY GOD!!!! This is simply the best explanation I've ever heard! 🤩. I've been playing music for 20 years and this was just so satisfying to watch. Really sensational job cover all the bits in your explanation. just wow!
scales, tuning and temperament are my thing, I’ve studied them quite extensively. Also as a Balinese gamelan specialist who also studied gamelan tuning, I was very pleased to see that excerpt at the end of Wayan Tembres’ piece. On the subject of the origin of our 12tet system, most academics today agree that the explanation that 12-TET Music interval are chosen because they are the most consonant and pleasing to the ear is very eurocentrist explanation... in fact new research propose that most tuning system simply find their origins in the types of instruments that were instrumental (see what I did there) in that musical culture’s development. While the physics explanation of waveform you gave is correct, these fraction relationship (octave, third and fifth) only exist in wind and string instruments. That is, when you make a sustained musical sound on a string the spectral analysis of the sound will reveal that almost all the intervals of the 12tet system are present in just that single note. That is what we call partials of a sound. The first is of course the fundamental, 2 is the octave, 3 is the fifth, 4 is another octave, 5 is third, 6 is the fifth again, 7 is actually the minor 7th, 8 is octave again, 9 is a neutral 2nd, etc. as you keep goings up the more inharmonic the partial becomes in the case of a string, but the main "loudest" (if I can use that term) partials, the first 5-6, are strongly harmonic. These partials at their resptective amplitudes are what creates the distinctive sound of a string (which is how additive sythesis manages to emulate string sound by adding the partials to the fundemental at correct amplitude). The same is true for wind instruments but the exact order and amplitude of the partial are different, in fact with a wind instrument the partials are all completely harmonic. Since most of European musical culture evolved from those two instruments the 12 note system does indeed make the most sense and is likely the reason we developed it over the century into what it is today. Arguably some of the most diametrically opposed but equally sophisticated scale system found elsewhere in the world often derive their scale from pitched percussion instruments instead of strings and wind instruments. In Indonesia for example, the pelog system divides the scale in seven non equally distant tone, one theory for the origin is to look at the sound spectrum of a tuned metal bar, it is quite different from a string, after the fundamental, the next audible and strongest partial is not even an octave but somewhere closer to the triton, the next one is closer to the fourth, and the one after that is basically a 2nd, and so on. tuned metal bar are thus considered inharmonic, at the complete opposite from a tubular wind instrument. These specific partial are very close to how the pelog system is divided, not exact but close enough to suggest a strong correlation in the evolution of the scale and the instruments it evolved from, metal xylophone type instruments. Alright I’ve said enough about all this... I’ll finish with this little annecdote: Bach of all people was vehemently against equal temperament, arguing it made music boring, which temperament he preferred however is still subject of much debate in the musicology world ;)
Do you have a source for the harmonics of a tuned metal bar? I would not have expected another harmonic sequence to exist.
@Balmung Barbossa there aren't many places in Asia that weren't colonized... also the chinese traditional system is also derived from the hamonics series of a string like our, and while it is not equal tempered, it is very close to a twelve tone system, and so easy to make the switch, and many east asian musical culture are heavily influenced by China in their history. I would also point to globalisation more then colonisation, but regardless, my point is not that equal temperament isn't pleasing to some or to many, I grew up with it and I find it very pleasing, I am a classically trained musician, I studied western style composition, etc. I am not saying it's not a great system.and I would expect people in ohter culture to find it pleasing as well, but I also find indian music's sliding temperament very pleasing, and chinese music's non equal tone system more pleasing, Balinese note and timbre relationship also very pleasing with their beating sound (instruments are tuned 6hz appart to have a beating relationship that creates a global vibrato). The point I was making is simply that historically speaking there are other factor that explain it's development then simply 12 tet = the most pleasing way to organise sounds.
@@ThomasdenHollander The primary sources I would point you to are unfortunatly not online, but two very interesting book on the subject, Tuning Timbre Spectrum Scale by William Sethares his very interesting and is research in general is very interesting (more recently working on what a 10-tet and 7-tet system would sound like), and the second one is Musical Mathematics: On the Art and Science of Acoustic Instruments. For the harmonics of a free standing bar, you can check out hyperphysic hyperphysics.phy-astr.gsu.edu/hbase/Music/barres.html#c3 if you use the formulas there and apply them to a fundemental (say A 440 ;) you will get the intervals I mentioned. you can also navigate around, you will find similar graph for string, open pipe and close pipe. it's a very cool music science website. I can also point you to this articles on the harmonics of a tuned metal gong also very interesting and unexpected, asa.scitation.org/doi/full/10.1121/1.3425742
@@PierrePblais Thanks, looks very interesting!
@@PierrePblais Woud you put in a Audiosample, of a Instrument played in a nice tuning. I gooled this awhile, and it was hard to find a Song where i was shure i was hearing something special. Just place some Examples, all i hear is pretty formal Pianosongs, the one in the Video was nearly the best of them.
When singing in a chorus I have met a few people who enjoy exploring all those "in-between" notes. It is hard to resist being drawn into their madness!
Haha🐵🐵🐵
I prolly laughed more than I should.
This reminds me of a choir master who, after a particularly dissonant practice, stopped us to exclaim... "That's brilliant, you've got all the right notes - now shall we try singing them at the same time?"
Dude you Rock. I haven't seen anyone else on here who explains these things so clearly, completely and accessibly, with great relevant visual and audio examples. Thank you, I'm spreading the word. :)
THANK YOU! I've been trying to wrap my head around this for so long. You delivered the key insights in the perfectly logical order to make it instantly click for me. Ten thumbs up! :D
3:15 - provided the strings are the same mechanically and under the same tension. On a guitar, all of the strings are almost exactly the same length, but have very different frequencies; this is accomplished by making the "higher" strings thinner and stretching them more tightly (in some appropriate combination).
That was literally the first formal training that I can remember getting on music. Thank you so much I learned a ton.
Brilliant video! Thank you for the upload.
I literally only clicked on this video to see whether you'd specify Western. Actually, it was to see whether others would call you out for not saying in the title, but in that fraction of a second I decided to see which one happened.
I was just watching Rob Scallon’s video on the history of guitar. In the video, they showed earlier versions of the guitar with adjustable frets. They went on to discuss how this helped with varying keys and intonation. Additionally, they discussed how current guitars are designed with equal temperament in mind and are always slightly out of tune. I was pretty lost during this part of the conversation. Your video has helped me understand what they were talking about. Thank you!
Great! It can be a confusing topic so I'm glad my video helped!
And as the man says, it's that major third thing - the interval between the g and the b - I guess that's why tuning those two strings can be such a pain!
And the major third is why, for the longest time, pipe organs were tuned in quarter-comma meantone tuning instead of equal temperament, because some limitation in the usable keys was considered preferable to having the major third wrong.
Don't forget that the guitar is not in equal temperament like the piano (piano isn't truly in equal temperament as well thought, the notes are stretched) because physics. If you want to see a real equally tempered guitar check out True Temperament frets. But being out of tune is a big part of the iconic guitar sound so it sounds less like a guitar after them, more like piano or midi, so most of the professional guitarists don't like them. I personally really like the 22edo, 19edo and 31edo guitar sound with the straight frets (in this order) so the guitar sounds unique but doesn't lose it's signature sound
When I was younger, and had much more acute hearing, that "slightly out of tune" thing used to drive me up the wall. I'd spend an hour trying to tune my guitar because of it, and I couldn't understand why it was happening.
I'm still lost, even with a band director son and all 5 children, and wife, musicians in and of themselves. So grateful that I play the radio...
Yes but can you tune your radio?
@@natedunn51 No but you can tune into it.
@@amandaslough125 But can you tuna fish?
@@kenkinnally6144 REO good question!
Yes I was scratching my head as well. My guitar playing sounds like an 87 note octave.
Wow! This answered so many questions I'd had about music. Thanks for posting!
Thank you Mr. Bennett, your examples make it easy to hear the result of different tuning choices.
Where were you ten years ago, when I was figuring all of this stuff out for myself with great frustration and confusion?
Kidding aside, this is a really good, comprehensive, yet concise rundown. Most of what I've found on this topic has been either stupidly simplistic, or unbelievably complex, going into minute detail about every rabbit trail possible. This is a good rundown that just about anyone can grasp, without resorting to the "because we're western, and therefore colonialist and evil" non-explanation given by those who I suspect don't actually understand the material they're trying to teach. Thanks for being a good teacher!
Thank you! I'm so glad that this video was accessible and straightforward! I was so worried about this video being too dense!
Tell me about it. i once spent three days (daze) trying to tune a grand piano WITH A DIGITAL TUNNER -yeah, don't do that.
Most of the theory at this level that I learned came from a book I ran across in the library, "On The Sensations of Tone" by Hermann von Helmholtz. At the time, there was no internet yet.
I have been reading blogs and watching videos about this for months, and this is by FAR the BEST explanation I have found SO FAR. It is clear, concise, intuitive, and with visual representations that make this whole thing easy to track. It is also not overly jargony.
basically we have 12 note because of Pythagoras. When he applied the system of using only 3/2 and 2/1 ratios he completed the circle of fifths. After 12 fifth you have almost the same note . that means that (3/2)^12 is almost an even number.
If we used the Chinese system at the time we would have a completely different music. Of course we might have develope the tonal system any way. But Pythagoras and his system of fifths made the breakthrough. And when we started using well tempered tuning than you could use any Key and octave and it would sound good.
Fantastic information, very well arranged and delivered! Thank you!!
This is to my knowledge the best video on this topic. Thank you for sharing!
That was really well done. As a non-musician I don't always understand the theory and mechanics behind the notes and their arrangement. You made this very understandable.
This is so well presented. I would love to see this aforementioned video on non western tuning systems.
so helpful as always! thanks David!
Dear David, thank you, this exactly what I have been trying to understand since I started learning how to play an instrument - why notes are like this. Thank you, it’s a very informative material, easy to grasp, at least for my STEM mind. Thank you.
not gonna lie, the "ultra 7th" note sounded interesting for some vocal tricks as in a "quite not reaching the octave" kind of thing
I agree!
David Bennett Piano the neutral third, ultra seventh, the quarter tone below the flat seventh and the quarter tone above the P4 all sound like the blues to me. That slightly bent away sounds.
He kept saying "you can't just stick extra notes in there." I completely disagree, _yes, you can,_ unless you're stuck playing a traditional keyboard. Woodwinds can hit some but not all quarter-tones without lip bending (or rolling in/out for flute) -- except for quarter tone flutes, which do exist but are rare, and slide whistles and slide saxophones and such which of course can hit any arbitrary pitch in their range. As a composer, you have to know what quarter tones are readily available and which ones are more difficult to access, so you don't write something that's such a twister as to be unplayable. This means that composition is _not freely transposable_ any longer, but that is not the same thing as saying "you can't just add in arbitrary notes". If you want a note that's 30 cents flat, and you can confirm that this is physically playable, then go for it. How you notate it is a different matter entirely, and there are several systems in common use.
Even writing for trombone, you have to worry about the possibility that a microtonal shift will take the player beyond the end of the slide, either upward or downward, so that is not 100% freely transposable either. Strings you can mostly get away with calling for any altered pitch you require, any time you need it, the exceptions being if you're on an open string. (But string players tend to bend their pitches toward Just Intonation for whatever key they're in at the moment anyhow.)
@@mal2ksc I been playing the guitar since I was 8 yrs old.
somewhere along the line I knew how to BEND or vibrato the strings.lol
to vari degree..there's FRETLESS instruments such as the violin.
Actually none of my guitar are truely in tune.
I seldom use an electronic tuner..becuase when I press down
on the strings..it's slighty out of tune ( the higher the action...the more out
of tune
@@oneeyemonster3262 A proper setup can deal with a whole lot of the intonation issues of a deliberately high action. There are players that keep the action high because even when you can't hear a buzz, low action can limit the maximum vibration of a string. They manage to play in tune because their instruments are set up for their particular needs. But yes, of course pressing harder makes strings go sharp. It's a crucial performance technique on the sitar.
To add to the chorus of praise. I actually know this material *really* well, having dived into continued fractions as an approach to numbers "close to" simple ratios, and also the writings of William Sethares on dissonance curves. I still found this video enjoyable to watch.
Thanks Raph! That means a lot! I was nervous making the video as it’s such a big topic! But I’m glad people are happy with the result.
Thank you for this. Just started learning music/ piano this world just continues to unfold, looking forward to watching more of you perspective and knowledge
A dirt simple explanation to a very complicated subject. Kudos for a job very well done David.
David, I've been appreciating and enjoying your videos, they are all so thoughtful and absorbing as well as being well-researched and produced. But in this one, you have surely exceeded even your high standards. This is simply one of the best music educational videos that I have ever seen - a complex subject clearly explained and articulated, placed in a carefully thought-out structure, all enhanced by first-rate graphics. And the whole work is presented with enthusiasm and an obvious love for your subject. Keep up the fine work!
Back in the days of landline telephones, I used to tune my guitar to the dial tone...
I still tune to the 60Hz hum.
I think you have explained this complicated topic really well. Thank you :)
Thanks Dave, that's very interesting. Your just-intonation composition is beautiful. Good on you, mate.
I'm a violin player and teacher, and pianos always sound out of tune to me. Thanks for this video so I can show my students why this is!
It is worth noting that pianos are always out of tune. They are supposed to be. :P
Well I play the piano and they do sound out of tune for an array of reasons. One of them being that the overtones don't line up, how much depending on design, materials and string length/tension. Add to that the compromises of the equal tempered scale, which makes for example thirds and sixths sound a bit off to say the least. It's always a compromise. There are digital pianos that sound more in tune and it also sounds wrong. So tuning a piano is basically damage control.
Maybe its tuning to 440hz that gets to u. Some people with perfect pitch say 440 sounds off and 432 sounds much better to them. They sound the same to me so I couldn’t tell u.
@@crazyjhey8050 good point. Well I know that many violinists actually prefer a higher tuning, say, 442Hz or even higher. And of course a violinist has a much higher sensibility regarding pitch. I think the trouble already starts with the fifth, which is slightly off in the equal tempered scale. Try to listen to a Hammond organ with the Leslie speaker on stop. I find it in unbearable, but wonderful as soon as it starts spinning.
Usually the other way around. Violin type or any wind instrument players have to tune their ears to when a piano or electric keyboard because they are better in Tune. I had my piano teacher who also plays bassoon professionally played along with my electric keyboard and she said the tuning of her playing was somewhat off compared to the keyboard. So you just have to get used to playing with what is in the room. My keyboard could of been too perfect, not sure at the time.
Viewing songs as intervals instead of notes opened my mind a whole new way AND THEN you added the part about octaves sounding so good together they’re perceived as the same note - I’d never once in my life realized octaves aren’t actually the same note. They have the same letter names, but these are completely different frequencies. I see music a whole new way.
You might like this too- the energy of your cell phone (radio), your microwave oven, and light from eg the sun, are only different because they’re of different frequencies…
Really loved your piece at the end of this one!
Thank you! This is the best video explaining the subject!
It's funny how my ears are so accustomed to equal temperament that just intonation actually somehow sounds "weird"
That's true. You can also say that perfect intervals are more dry or shallow, while those small differences in the frequencies can make the sound richer or interesting. Like with singing and auto-tuning: when perfectly in pitch, it sounds unnatural or boring.
@@alobpreis I disagree, I find the major third in just intonation really steady and pure. I sing in a choir and often we are told to sing a little higher (or lower) to attain these just intervals. We sing medieval and renaissance music... But I agree that equal temperament may bring some charm too !
advanced musicians (choir, strings, brass, barbershop, woodwinds) will adjust to fix the minor/major thirds. advanced pianists will avoid being a third away from the melody. when they do so our ears will pick this out and tell us that the music is "better".
What is interesting to me, is that after listening to just intonation music for a while, it starts sounding good, but then going back to equal temperament, everything sounds awful...for a little while until my ears get used to it again.
@@alanedwards9578 it's mostly the thirds that sound awful
These are the dissonant intervals less commonly used
Jazz: let me introduce myself
+ Film Scoring, raga, EDN (Electronic Dance Noise...)
Have you tried using a neutral third before?
@@ValkyRiver I prefer a flat unison
Gaint Steps Anyone?
The best explanation I have ever heard regarding this ----- articulate and well presented.
This gives me an idea - when composing 8-bit chiptunes, the tuning with perfect ratios will probably sound miles better than 1/12 tuning. I was wondering why Game Boy has so many frequencies between notes and I think now I know how to use them.
If I was a Music teacher, I would definitely show this to my students. I love it how you make even complex music theory understandable for everyone! Keep up the good work!
I've developed a genuine interest in music theory and the analysis of music in general.
I'd love to hear about non-western tuning systems from you!
Thank you!
David, the combination of consideration and preparation put into your educational videos is unmatched on the internet. In fact, as a collection, your videos are the compelling example of how and why education is transformative when done right. The scores of admiring comments are well deserved. Thank you for sharing your practical insight and infectious enthusiasm.
Wow! Thanks Brian, that really means a lot 😃😃😃
I just stumbled onto this site, courtesy of the TH-cam algorithmic spirits, and already I'm wondering if this is the music equivalent of 3brown1blue's superb math videos.
I picked up some details, nice job! might have to watch the middle part a few times.
Excellent video. Explained so many simple things about the nature of music that I´ve found nowhere else. For me, the simplest one, and most beautiful, being the thing about the string vibrating in different frequencies, when you presented them graphically.
Thank you so much for this. I've always needed to understand why we've ended up with the particular notes that we have. It always seemed so arbitrary and answers like "it's just the most pleasing to the ear" were never satisfactory. The visual of the frequencies being in sync with each other made it all clear now :)
I have been dying for a channel like this! Thank you for your eloquent teaching.
Thank you! 🙂😃😃
Brilliantly explained; thank you so much, David. This was _Eureka!_ levels of mind-expanding for me.
Really lovely overview. Thank you, sir
My dad was a piano technician and he once mentioned something about "spreading" the octaves out a little so the interval between notes was just a tad longer, he said this was a good compromise and tends to sound better than straight equal temperament. But my memory is a little fuzzy.
This is actually related to the physics of strings under great tension, and not because of an attempt to create pure intervals. Piano strings tuned to the integer ratios described in this video will still beat, necessitating that the piano be tuned "slightly out of tune."
Your dad was absolutely right. Especially if you play music from the romantic period an equal tunig it is tantalising to (especially my) ears. The spreading makes the piano sound more brilliant and richer.
I'm assuming Elton John uses that technique.
Aaah, once again, brilliant video! So well broken down and easy to follow, without being over simplified. Thank you :)
Thanks! I'm really glad you found this video was easy to follow! I was worried that it was too dense and nerdy 😅
Thankyou! You clarified several mysteries for me.
So much information presented cleary and easily understandable. Your videos are awesome, I am a big fan. Thank you very much for teaching us.