So question , why does it start being multiplied by 4 instead of 2 ??? Also if you keep going the next harmonic is 2080 hz 8:7 . Do you divide 2080/6 or by 4 now ???
Thank you for this series. I'd be lying if I said you didn't lose me even once, but I learned a great deal, and on second watch a lot of things fell into place.
If we look a bit close at a few first harmonics (let's start from A == 110), we might notice that within the 4th octave (880...1760) there are 8 tones (not 7!!!); These A) all lie within the same octave; B) represent a non-interrupting sequence of small relatively denominators which C) is located as close as it gets to the base frequency. 110 220 330 440 550 660 770 880 990 1100 1210 1320 1430 1540 1650 1760 ..........................................................======================================= So I think that would be a natural way to divide an octave: into 8 intervals, not 7. The argument that on earlier instruments overtones sounded more loudly only supports this idea. And probably that system was the case sometime in the past but then "historically" or just as an artifact of the way musicians tuned their instruments the 8th note was "lost in translation".
Hi Patrick, I know the answer is more than likely in your excellent video but could you please explain with ‘exclusive’ detail why you can hear the Bb overtone when hitting the lower E note (first) on a piano..? A very good long time retired musician / producer friend of mine is captivated by this phenomenon. 🇦🇺🦘
Please enjoy my 17 tone Just tempered scale (all in a ratio over 128/256) Best in the key of C for the whole numbers and storing the note ratios as a single byte. But it sounds best to the ear tuned about 220 hz. A depending on the weather. 128 Hz. 256 145 Hz. 290 154 Hz. 308 160 Hz. 320 165 Hz. 330 171 Hz. 342 179 Hz. 358 183 Hz. 366 192 Hz. 384 201 Hz. 402 205 Hz. 410 213 Hz. 426 219 Hz. 438 224 Hz. 448 230 Hz. 460 238 Hz. 476 256 Hz. 512 If you really want the second’s Here you go, at 21 tones all over 512 for the ratios: 256 284 291 307 313 320 329 341 358 366 370 384 398 402 410 427 439 448 455 461 475 484 512 Here is the scale in Hexadecimal The first is the octave the second the tone at that ratio. 0100 256 011C 284 0123 291 0133 307 0139 313 0140 320 0149 329 0155 341 0166 358 016E 366 0172 370 0180 384 018E 398 0192 402 019A 410 01AB 427 01B7 439 01C0 448 01C7 455 01CD 461 01DB 475 01E4 484 0200 for the next octave.
Learning music theory-- okay, wait I'm confused. You called the second harmonic scale (3:2) a lydian mode. But, we constantly multiplied frequencies by 3/2, so how do we end up with semi-tones and tones? Is it that the 292.5 and 493.59 are the semitones? How can we be multiplying by a constant ratio but end up with notes differently spaced out from each other? Does anyone get what I mean? (I really struggle with music theory and I honestly think it's because no one was ever able to explain it like this. I've always wanted the /why/ it works, I feel like I'll understand it more if I can see its like, mathematical patterns and proof of why it works.)
I want this to be the only video that survives past humanity, or sent into space. So that whoever watches it has all this knowledge....but argue over what that drawing of 7 white and 5 black boxes could be called!!
Aye subscribing. I would love to know why we settled on the 7/12 tone scale divisions of the octave. I have a theory it's rooted in sacr d geometry as the flower of life depicted in most cultures is a 6 sided shape and the inverse of it creates another 6 points for a total of 12 and it's all rooted in our perception of this chaos. We arbitrarily affix definitions to the misunderstood and thereby give it definition. Love your videos!
The intro is actually my favorite scale. When I first discovered it, I've always wondered when I spread the notes out, they kind of sound like "merging" in the same note. I first looked it up and it's called Lydian Dominant. But I found a name that actually made more sense, the acoustic scale. This video explains alot
Might be interesting for a geek....but AC/DC SOUNDS good and that is in the end ALL that matters. On a gig I have never one time have someone come to me and say...hey...that 2 to the 1200th power note in there ROCKED! or that overtone in there sucked.... For me, none of this correlates with "pleasing to the ear". Music is about making memories and causing you to FEEL something that you like to hear. I guarantee you I will never tune my guitar and say...hey...that's 8 cents too high. Van Halen didn't either. He played what he wanted to hear and made the band to to his guitar for sync. The ONLY time a few cents makes a distinguishable difference to me is when I'm trying to sync something I'm trying to learn with my instrument. If it's a few cents off you're never going to get it right. But if you adjust the program up or down a couple of cents, the rest of the tune will stay true. And never one time have I looked at our bass player and said...dude that G is 14 cents flat
I wish you had more subscribers, you deserve it! I'm a huge math and physics nerd but have also played music most of my life. This connection is super important but so few musicians really understand or appreciate it. True you don't "need" to know it to write music, but the physics of music brings even more beauty to it for me. Love it!
i love your math series about music i had a question in my mind and something just wasnt making any sense but you covered it very well now i know the reason why we devide by 2 for the second time is because its sometimes nesseceray to get the number in wanted range
There's no need for any math, beyond counting to 12, and understanding simple half and whole steps. Anything else is redundant. You use your ears to figure out what scales, chord progression and melodies you want to make, not math. Let's ask Chopin, Beethoven, Mozart, Debussy etc what kind of math they used. We can't, because they're dead.. If they weren't dead, they would say that they used their ears first. You are overcomplicated something which is completely unnecessary. It's like teaching people to read before speaking and understanding a language, makes very little sense.
Wow, I gotta say, your explanations are spot-on and super interesting! Not only do you break things down in a clear and easy-to-understand way, but I can totally see that scientist vibe in you. It's like you've got that natural curiosity and analytical thinking that real scientists have. Your passion for the topic really shines through, and it's awesome to see someone who not only knows their stuff but can also explain it in a fun and engaging manner. Keep up the great work!
Patrick, you are an amazing teacher! The demonstration of oscillation was something I could never visualize or understand before. Thank you so much for your help!
It's "lon." The more powerful slide rules back in the day included "lon" scales, which were based on base 'e' logarithms. The Keuffel & Esser 68-1100 "Deci-Lon" is an example of that. It even has "Lon" in the name. In the large manual for the slide rule, the word's "natural" and "log" were never uttered back to back...not once. Instead, it defined the lon as the "natural or Napierian Logarithm." This is because, in practice, it was quite common for some to just call them lons, for short. So it's not a made up word...merely an alternative way to refer to the log base 'e'.
Integration by u substitution, if u = a^2 - r^2 then du = -2r dr . In the integral we want to solve we have r dr and we want to replace it with du but du = -2r dr. Need to solve for r dr - divide both sides by negative 2 -> r dr = -1/2 du
