Decrypting Pythagorean Tuning | The Harmony between Math & Physics
HTML-код
- Опубликовано: 23 авг 2024
- I present an alternative approach to Pythagorean Tuning which I believe works better, is easier to learn and apply, and seems likely to be more true to the way it was originally taught by Pythagoras himself.
Big, juicy claims as usual; but at any rate, it works and it’s a curiosity to say the least.
Although I find the tuning of musical instruments interesting in itself; I am researching musical tuning for the purpose of understanding how to tune many things other than instruments.
In future videos on this train of thought, I’ll be exploring how, as it was famously quoted by Nikola Tesla “if you want to understand the world, consider in terms of energy, frequency and vibration”.
We can use our understanding of music and sound to tune coils and antennas, circuits, buildings, our own brain, water - quite a number of things really.
The ideas I present are primarily based on the mathematical foundations built by Marko Rodin (Vortex Based Maths), Malcolm Bendall (Plasmoid Unification Model), Edward G Nightingale (The Template) & Jamie Buturff (Pythagorean Tuning & VBM).
Please forgive any errors that may appear in the video. I’ve tried my best to present the information correctly.
Please like, subscribe and comment!
HELP FUND MY OPEN SOURCE RESEARCH: alchemicalscie...
WEBSITE : alchemicalscie...
RUclips: / @alchemicalscience
RUMBLE: rumble.com/Alc...
TWITTER: / alchemicalsci
LINKS
-The Giza Template with Ed Nightingale (MUFON) • The Giza Template with...
Ep. 829 FADE to BLACK Jimmy Church w/ Ed Nightingale : The Giza Template 2.0 : LIVE
: • Ep. 829 FADE to BLACK ...
Malcolm Bendall’s Lecture Series: www.howtube.co...
- Deciphering the Plasmoid Unification Model: PART 1 | Malcolm Bendall's Alien Maths & Physics: • Deciphering the Plasmo...
- Plasmoid Unification and the Music of the Spheres | PART 2 | The Quest for the Holy Grail: • Plasmoid Unification a...
- Plasmoid Unification P3 | Sacred Geometry, Divisions of Time & the Solar System feat. Cosmic Watch: • Plasmoid Unification P...
- Decoding Vortex Based Maths: The ABHA Cypher (VBM Part 1) - • Decoding Vortex Based ...
Lectures from Marko Rodin at TeslaTech - / @teslatech333
![Tee Grizzley - Detroit (Feat. 42 Dugg) [Official Video]](http://i.ytimg.com/vi/aeKfTtt0x14/mqdefault.jpg)
Fantastic effort! Keep up the good work!
You should try looking at the frequency patterns in an oscilloscope. You can see the mathematical harmonics when you add the frequencies together. If you put the alternate frequencies on separate x,y channels, you can create lissajous patterns depending on the mathematical interval between them.
The main difference between your template and My First Scale attempt is the C. I am very impressed that yours reduced to 1 Hz. I can't fault that one bit. Props!
For a method of finding notes that will seem arbitrary to some...you do end up with lovely notes on a 12-note octave. Most people are used to 12 note octaves, so very impressive to have your own reasons for specific frequencies, can't wait to hear performances!
There are some piano concerts online with the (to me) inexplicable Divine 9 scale. When transposed to A=432, of the 11 other significant notes per 12-halftone octave, THREE are identical to yours and the others are all within 0.5%. Derived in a totally different way. In the concert, it just sounds fine (A=427 there), but SOME small passages sound MAGNIFICENT. Might be due to similar relationships to your scale.
I will never look at my guitar the same way. What a mesmerizing life we have.
Was trying to figure that out for a few years, thanks 🙏
what?? a few years?
Hear me out guys...frequencies follow below. Looking at the various strengths of various logics to compile tone ladders, I wonder whether an advance musical piece even needs a set keyboard like the piano. When we let an acapella choir sing slow harmonies, perhaps sometimes a note borrowed from another scale will make more sense than one from our piano, whatever its tuning.
Sing two notes, say C=256 and G=384 (3:2)...what is the third note that would sound best with those two individually and combined, say to fall in between? Let's not look on our tone ladder but derive it mathematically. The square root of 1.5 (384) give 313.43 Hz in the middel of those two. How'd that sound?
Taking 256*1.25=320 Hz... 5:4 is then the 384. Quite a close resonance.
Or 256*1.2=307 Hz, 306*5/4=384 Hz. Let's listen to those chords and just pick the middle note as we deem best! :-D
i like what you're doing. but i think the point of this video was to lay some foundational work regarding the sacred geometry, harmonies, and ratios. As they say in the other videos that the these are important to understanding how the thunderstorm generator works.
I'd love to hear your template scale plugged into a good pianist's or organist's MIDI performance, back to back against equal temperament of the same A=432 Hz. There are probably good MIDI performances out there to be used.
Of course, when a musician plays live, the way the notes dance affects the performance. So you have a recording likely performed on an equal temperament instrument, replayed with your template. Not the same pianist on a piano tuned to the template, that would end up sounding better, I would expect. But the robotic replay may already sound promising.
Why was Pythagorean tuning abandoned in the middle of the 16th century? Well because this one has a big flaw... it makes the transposition of a musical piece very complicated and this is because of the wolf's fifth and certain thirds. and here's why...
let's take 65hz as C1. and proceed like Pythagoras...
one octave = *2
a fifth = *3/2 or *1.5
Let's first fix the octave of C1.
C2 = 65*2 = 130hz
then the fifth of C, G
G1 = 65*1,5 = 97.5Hz
then the fifth of G, D
D2 = 97.5*1.5 = 146.25 Hz this note is beyond C2 (130 Hz) so we must bring it back between C1 and C2 simply by decreasing it by an octave (/2)
therefore
D1 = 146.25/2 =73.125
then the fifth of D
A1 = 73.125*1,5= 109,6875 Hz
E1 = E2/2 = (109,6875*1,5)/2 = 82,265625 Hz
B1 = 82,265625*1,5 = 123,3984375 Hz
F#1 = F#2/2 = ( 123,3984375*1,5)/2 = 92,548828125 Hz
C#1 = C#2/2 = (92,548828125*1,5)/2 = 69,41162109375 Hz
G#1 = 69,41162109375*1,5 = 104,117431640625 Hz
D#1 = D#2/2 = (104,117431640625*1,5)/2 = 78,0880737304688 Hz
A#1 = 78,0880737304688*1,5 = 117,132110595703 Hz
F1 = F2/2 = (117,132110595703*1,5)/2 = 87,8490829467773 Hz
And now let's check the magic of the harmony of numbers and nature...
C2 = F1*1,5= 87,8490829467773*1,5 = 131,773624420166 Hz !!!
What the Hell... .we said that C2 is equal to 2*C1!!!
131,773624420166 > 130 !!!
But we had tuned C2 to 130 HZ!!! So C3 has 260Hz and C4 has 520Hz.
And so we have a fifth which relates
130/87.8490829467773 =1.47981055281772 and not 1.5...
So this is where the devil hides!!! Quickly call a priest!!
This drift, even if it may seem minimal when you look at the numbers, is very audible, it is neither a fifth nor a diminished fifth.
So, For 2000 years composers avoided the E#(F) C fifth in the Pythagorean scale. because it is very dissonant.
So imagine, you have written a musical piece and it involves the interval of fifth D#/A# and you wish to transpose your work up a whole tone, the interval D#/A# become F/C...
All you have to do is re-tune your instruments if possible... or get an instrument built in the right key...And if it's an orchestra, let's not talk about it...
This is why the tempered scale is the invention that liberated music...
Long live irrational numbers....
However, we owe the circle of fifths to Pythagoras, thank you Mr Pythagoras
Can you make a video on the differences between 432hz and the solfeggio 417hz? Is it that one is a base number? Thanks
Why is it that no matter whether you double or triple in either axis, the digital root always remains 9?
Your 12-note scale has a lot of the same frequencies as mine, where I started with 432 Hz rather than 256 Hz, and I ignored the concept (through oblivion) of the unison note. I just was NOT committed to finding 12 notes per octave, I just looked for well sounding (mathemetically) notes with higher frequency. I ended up with 15 notes before an octave was achieved. So naming them as the C via A to C doesn't make sense. I didn't intentionally triple any freqs. I hope the extra and different notes work well.
My scale results in frequencies that all reduce to 9 (as I think do yours, an artifact of 432?), and for the common tone range, one or two and often no digits are needed behind the comma. Yet, I have a few of your notes that are replaced by two others, and some of mine are shifted versus yours. The A4, B4, D4, E4, F#4, A5 and C6 are the same. So indeed, your C5 does not overlap with my scale, your C6 does. Random logic with mine. My notes don't necessarily all have an octave, as the steps come in a repeating set of 9 that result in tight mathematical relationships, and octaves occur (at least for 432 Hz consistently) every 15 steps. Existing music will possibly work less well on my scale, but all new music will be possible with the notes that would otherwise be seen as microtonal while firmly on my scale.
Due to the 9-step repetition, which results in 3:2 relationship, EVERY tone on my scale has a 3:2 relationship with a partner 9 steps up or down. All also have a 9:4/4:9 with a tone a full octave + 3 steps away. For harmonies, this may be more important than having octaves for all notes, the 12-step cycle on a 12-step ladder? The 15-step gives an octave about 2-3 times per octave.
Almost every note has a 4:5/5:4 or 5:9/9:5 or relationship. 4:3/3:4 is more rare. A significant compromise I may seek to fix. With 15 step per ~octave, there is even less need to play adjacent keys IMO so less important what the relationship is, but its often 20:19, 21:20, etc. In Divine Nine, the adjacten note is about once in 3 times a 16:15.
256 mid C.. is there any relation to the digital bytes convention
40:15
That's a 9:8 relationship which if I took correct notes, happens half the times you take two tones skipping one key.
You can try that for the 12 different positions. I'm not sure the other 6 times you skip one, it sounds better or worse.
I'm surprised 9:8 sounds bad, to be honest. On my scale that relationship happens about twice an octave, but oddly sometimes it's 2 keys apart, sometimes 3 due to the repeating pattern of nine steps to achieve 3:2, and 2:1 being rare happening only for 2 out of 9 tones.
This makes me wanna bust out my piano again 🎹 it’s been a couple of years
I've been meaning to, but I need to know for sure I can plot my own frequencies to keys. Not ready to commit a big budget, but super curious what harmonies are possible. I have a suspicion that the "angels singing" that many people have reported from near death experiences and the like, which seems to have irreplicable...might have to do with alternative scales and possibly no-scales. One angle hits a note of given frequency, another joins with a note that sounds lovely together, a third adds a note that sounds good with both others, etc. One note fades out, another comes in. If this is done as a game of math...at the end of the song, there may have been many dozens of notes within an octave's range. Why do we need the note we play to make sense with the notes we are NOT playing? Why pick a new note from a tight selection if it sounds bad with most notes already being played or sung? Hit the sweet spot, ignore the keyboard 😀
AI may come in here to explore how no-scale performances could sound. There is no playing along with that on a fixed tone instrument, but a fretless string instrument, trombone, etc, may well be able to play along and harmonize.
Interesting, perhaps like Rodin's 3,9, 6 pattern, the reason why harmonies sound good to us is some kind of asymmetry going on with the notes? I'm not a music theorist but I'd like to think about this more. Queue the meditation music! @@Cloxxki
Top!❤
Dad plays fiddle. There are no frets, no keys. You can put your finger where you like. Wiggle it till it sounds good.
I play bass, fretted and fretless. There is a big difference between the two.
Interesting video, I am a very strong advocate for using Pythagorean tuning in all music, you can see from my channel.
This video though has some errors though. A, not C is the lowest note on the standard piano. But about the tuning, the presupposition of a 12 note scale has caused some issues with your tuning. You also alluded to you finding a way to get rid of the Pythagorean comma, but you didn't it was there at the end between your 'F' and C. I'll explain more below.
The best way to start with Pythagorean tuning, which I just call True Intonation, is to look at sheet music, specifically but not limited to classical and baroque sheet music. Do we see more than 12 different notes on the pages of that repertoire? Yes. There are upwards of 20 some notes that can be found and even more in obscure pieces. There is a reason there is not 12. It is because music is not based on 12 notes per octave, it is based on a set of 17 notes per octave for the overwhelming vast majority of music. You need 17 notes per key area, 7 natural diatonic pitches, plus 5 sharps and 5 flats for a total of 17 per octave.
You made the mistake in this video by assuming C# and Db are or should be the same pitch. They are completely different pitches that serve a different musical function, most of the time they cannot be swapped at a whim without the music sounding out of tune. There is a reason we spell an A major chord A C# E, and NOT A Db E, it is not arbitrary, C# is in tune, Db is in tune, but A to Db is a diminished fourth and A to C# is a major third. They tell the listener different things. A and C# are connected by an unbroken chain of fifths in A major, A and Db are not in an unbroken chain of fifths in A major. You will see more clearly below.
To understand true intonation one truly must sit down with a pencil and paper and draw a horizontal line across the page and put D in the middle and draw out a chain of fifths going up from D going to the right, and a chain of fifths going down from D to the left. Like this, but go as far as you can on the page in both directions:
... Abb Ebb Bbb Fb Cb Gb Db Ab Eb Bb F C G D A E B F# C# G# D# A# E# B# Fx Cx Gx Dx ... and so on.
Study this chain of fifths, for in it holds many many secrets the world is completely clueless about. All of the pitch classes in this chain of fifths are different pitches and can all fit in one octave. E# is a different pitch than F. In your video you went up from C 11 fifths and got an "F", but what you actually got is E#, an augmented third above your original C and it's octaves. The augmented third is a tense albeit useful and distinct interval apart from a perfect fourth.
In C major/A minor (and their other modes) the 17 note scale is from Gb through the chain of fifths to A#, if you modulate to D major for example, the scale will move from Ab through the chain to B#, so the 17 notes that can be used in a key center with a given tonic chord without implying modulation is 17. The 12 of the modern day only exists because when you flatten the fifths that are perfect by 1.96 cents it creates a closed loop, and gets rid of the comma distinction between notes like C# and Db, but pure harmony is destroyed.
The reason for the seven letter note names is because there is special coherence with a seven note scale derived from an unbroken chain of six perfect fifths. The brain can hear special coherence there and there are phenomena that occur in those scales which happen with no other number of notes.
Just to articulate again in your video you went up by fifths to get a minor 7th, but that is impossible. You can't get a minor 7th by going up by fifths, only by going down by fifths. From C up to A# is an augmented 6th, but down 2 fifths from C is Bb (the actual minor 7th) which is lower by a Pythagorean comma from A#. To put it simply A# tends to act a leading tone pulling to B, Whereas Bb tends to pull down to A, And more times than not, it most definitely matters which you use and which you write down. C E G Bb is C7 chord with dominant function to F, whereas C E G A# is a German augmented 6th chord that tends to resolve to G or Em. The augmented 6ths because it is a larger interval tends to want to resolve outwardly by a limma (aka a diatonic half step), whereas the minor 7th, C and Bb want to collapse inward towards each other, with the Bb going to A and the C going to to F or staying put on C.
See how in the chain of fifths to the left, going down by fifths it is undertonal and flat, and going up by fifths is overtonal and sharp. This is very important to understand.
Pure harmony for music that is in tune both melodically and harmonically at once is Pythagorean tuning, true intonation. Like I said, check out some of the examples on my channel to see what I mean. The world is lying about intonation 12 tone equal temperament and what is called just intonation, is not what is truly in tune for music. God made music accessible, man has greatly confounded it, thinking himself wise. Also, stay away from alchemy it is very very bad. It you want true spirituality it is in the Lord Jesus Christ and in the words in the King James Bible. I say this from experience both in alchemy in the past and now in salvation in Jesus.
does this work for other music systems like the eastern systems?
Yes, but not by deriving the scale by only going up by fifths, which is an error even for western music. You must also go down by fifths to get notes like F and all the flats, going up you get the natural diatonic notes apart from F and all the sharps.
The "perfect fifth" seems exceedingly arbitrary. 7 half notes, 4 white and 3 black keys. And we don't know about the tuning, but let's call it a perfect fifth. I just don't get it. Maybe I will after this video.
So in your case you take a 3/2 of another note and call it a G because that's what we are used to calling that key and you started with a 256 Hz placing it in the C4. 3+2=5? 5th note down, doubled? Makes no sence :) The 3:2 relationship sounding well, that does make sense :)
It’s the Pythagorean triangle applied to wave function. The, long side of the triangle, is the 2:3 ratio wave form total, that creates the 5th harmonic peak. Thats also why it’s fractal. Imagine a triangle rotation and translation on its 2 and 3 side, alternating, and overlapping to create the numbers we wright as a “5th”. If that’s too wierd just go on wiki it’s pretty clear.
@@TheIgnoramus Thanks for attempting. My brain often finds simple things very complicated 😀
My very basic knowledge of A²=B²*C² totally saved me in highschool exams, by the way. It's ALL I recollected when stepping across the threshold of the exam hall. Utter blackout. I have to calculate surface area of a sloped plane with a sphere, that sort of thing. I have NO idea how to. I started crafting formulas "I" came up with (I no longer believe the ego did that), tested them, proved them, and got me some points. Not using any of the formulas I was taught for this. I didn't score well, but enough to never having to redo highschool, despite my dreams to the contrary (still, 3 decades on). It was the life's work of some mathematician, just work I've never never found, done a few times just to get some points for exam. I used to think I was so clever, but now I think it was spiritual guidance. When we "let go" (I was clueless I thought "whatever"), creative juices may start flowing. It took a lot of paper and weird scribbles but with a total blackout and hefty math, I got out of school. Thanks to pythagoras, most or all I was scribbling down was derived from te above, the ONE THING I sort of understood. This was an exam kids get at 17 or 18 years old, highest level available in The Netherlands. I bet 99% of adults can't do that. 10-20% or so do that exam, and more then forget. I already forgot when stepping into the exam hall. :-D
@@Cloxxkiwatch the video again, and look at the LAMBDA chart till your eyes bleed. Math will liberate us all.
Use digital root math. You’ll save yourself the headache.
The large numbers used in these western models are pointless
123rd like 😎