Theory of Primodality

[@Dude8718]

The rabbit hole of learning the vocabulary to describe the vocabulary you need to learn to begin to learn this in general goes so deep.

[@minty9959]

i watched 20 mins of this not knowing any music jargin just cause her voice is so nice lol

[@casscarthy7442]

AAAHHH AS A TRANSFEM MUSIC NERD I LOVE EVERYTHING YOU DO!!!! YOUVE HELPED ME SO MUCH WITH GETTING INTO 31-EDO AND VOICE TRAINING. ❤❤❤

[@FacemeltsWasteland]

Accidently Fell asleep watching this last night and holy crap did your samples influence my dreams. What an experience!

[@TachyBunker]

Thank you for this.

[@posti1990]

This cleared up so much. I watched this a few weeks ago and slowly things are making more and more sense since then

[@mattliable1987]

Thank you for this wonderful video, I am trying my best to understand this boat load of information. Cheers zhea your awesome!

[@jacquesdudon7538]

Great conference ! Primodality seems to be what I experienced myself through the scales I found with the photosonic disks...

[@EllieMcEla]

how can you be so smart yet genuinely kind? like wtf you are goals in every kind of way

[@KateCroft]

Totally agree

[@lina31415]

The smartest people are usually the kindest too.

[@thereiffodyssey2000]

Her: 3 hours of genius level groundbreaking microtonal music theory Me: @35:17 that pen flip was gnarly

[@venasc]

1:59:43 If you had to choose between 1M views on youtube and changing the future of music. Oh, you've made your choice. I'm so speechless you took the time to make this! Thank you 🙏

[@thrivinginamber2642]

The sound of a bell sifts out all non-disonant sounds almost instantly, as simple ratios as well as rational ratios cancel out, since all waves radiate from a single point where the bell is tapped, and the clockwise ones interfere with the counterclockwise ones as quickly as their linear paths form a loop and completely overlap and align, so all the short-path sounds cancel instantly, and considering the speed of sound and the size of the bell, this forms the characteristic of the bell, along with the thickness of the wall.

[@Mica45]

I love your cape so much, it's so cool

[@rogerantonybennett5272]

72:80:81:90:96:108:120:128:135:144 72:80:81:90 = mutation / choice of 80 or 81 between 72-90 (8:10=4:5) 80:81 = comma (switch between minor/major) 72:80 = minor tone (9:10) in just modulation (key change) 72:81 = major tone (8:9) this mutation step (comma) 80:90 = major tone (8:9) is often overlooked ! 81:90 = minor tone (9:10) 72:80:90 = minor/major 72:81:90 = major/minor 72:80:81:90:96:108:120:128:135:144 120:128:135:144 ^this is the semitonal change involving 15:16, 128:135, 15:16 which should be familiar to mathematically-minded musicians ! This is quite difficult stuff to understand & perhaps more difficult to explain....

[@homebakedgoods]

Incredible material. What do I need to do to get to a point to absorb this properly? Can you suggest some resources on how to get myself up to speed on this?

[@cubicinfinity2]

For me, just listening to Now and Xen and things like this so my brain get used to hearing these words and occasionally looking up concepts on the wiki. Basically, language acquisition.

[@cubicinfinity2]

Well, it does help to listen to things that you can still mostly understand. So, start by learning the basic stuff about microtonal tunings and gradually branch out. I still don't understand all of this; I'm not rushing myself at all.

[@Trogramming]

That's amazing! I'd seen your channel before just via the youtube algorithm, and I was oblivious to how central you were to these ideas until coming across "Zheanism" on xen wiki. I've been writing in mode 18 of the harmonic series and didn't really know if anyone else was doing something similar until I discovered a blog post by Ethan Hein who briefly mentioned it and called it "The second octave of nonary primodality". A few days later and I've found my way back to your channel :D I didn't realise that's what I was doing at first, it just happened by chance when I realised why my JI scale was nice and it clicked every note was a natural harmonic of 24.4HZ from 18 to 35. (I was using exclusively all 2 3 6 9 denominators) I'm making some software atm for playing JI with custom tunings on normal computer keyboards at the moment and I hope to try and bring these ideas to more people. Thank you for all your work :D

[@lurkdash]

I’m on a long journey building music software to help me archive what I’ve learned about microtonality and you’ve just totally resolved so many inarticulate nagging questions I had about primes I’m this space thank you so much what a gem this stream is

[@Dude8718]

That "whirling" thing when everything is perfectly harmonic is what I always love. I always tried to instinctively tune my guitar in a way where certain chords in a key would be perfectly harmonically intimated so there was no beating, and just the notes were tuned to the harmonic of the root. But it really limits how much you can play cuz guitar is fixed fret so it's not that useful BUT it got me Into wanting to make music based off the harmonic series. It never made me sense that we just round them. I love your work. You are so equipped to accomplish these challenges

[@febilogi]

16:15 this shift is such a mindblowing feeling for me. I'm rewondering the future of music with this knowledge of music theory 🤯

[@franciscofernandez8183]

Around the 1:00:00 mark the talk about "music is math" discussion was really good. I would like to add that math is found everywhere, because it's studies structures and patterns. That doesn't mean that every subject is JUST math, in the same way that Chemistry isn't just Physics, and Biology isn't just Chemistry and so on. Finding patterns and understanding them obviously helps, especially in a subject full of symmetry, harmony and structure like Music is, but that something "helps" doesn't mean it does everything for you. You still need to now the other aspects, and how to use math in that specific context.

[@Irishpineapple97]

Super well explained, very flexible and beautiful approach. This content is AWESOME, thank you ❤️

[@PetraBrown]

I am learning more of your music creations Zheanna, it’s beautiful and bewitching. ❤ from Petra-B

[@JasonLitmanFilms]

I really want to understand this but feels like a different language that just goes over my head, but I'm super curious with the mathematics of it. It's so intense and I feel like such an idiot but I love the music so much. I'm beyond humbled.

[@sagandalya108]

2nd octave of the overtone series represents the bass in arrangement, 3rd the melody and 4th the embellishments, the various tetrachordal structures can be used to give color to basic diatonic music.

[@michaelgonzalez216]

Ahhhhh! I see!! You achieve with tuning what we do with technology. Excellent! Rational!

[@codawithteeth]

definitely gonna be studying this video a lot. thanks.

[@marcoaraujo2817]

dope shit Miss! A pleased pair of ears from Brazil. I'm mesmerized by your music journey.

[@DSKim-ej5uf]

Your video leaves me with a long lasting impression and happiness. It illuminates my heart with the light of the blue morning star. The passing time comes like magic, and while watching your videos, I try to be happy with the warmth and no regrets of the past. The sad memories that make me cry even when I close my eyes sometimes come, but you just have to suffer just that much. The autumn that comes back will also burn brightly near my heart for a while and then pass slowly... And yet, my heart dreams of the same dream again Nevertheless, I do not want to put off the dream I had... I think the video of you, whom I met by chance, sways and resonates with joy because I love the scent of autumn and even the gently scattering leaves. Before the channel opened, I had a good foreboding at the unknown excitement at the door. How did you have such a wonderful talent that is full of the mysterious charm of your video? The video I'm watching right now is the best and the best. In the future, positive energy will surely rush towards you, so please make more good videos of you in the future. Even if I don't have to rush, watching your videos makes me feel like I'm getting more and more loved, so my heart is really happy. Your video on KZbin that an algorithm guided me to. My heart is sincere through a precious relationship. I will give you my sincere praise and support. .

[@PetraBrown]

You have wonderful hearing instead Amelia, imagination is a great gift too, ❤ and artistry from Petra-Brown 🐯🐱🐥🐑

[@PetraBrown]

Sounds like music for a Sci-Fi film Zheanna, awesome ❤ Petra

[@PetraBrown]

Mathematicians don’t warm our beds at night, your music does Zheanna, music is magical, LOL ❤ from Petra Brown

[@joana8502]

great lecture! i kinda see a parallel with sabine hossenfelder's critique of "mathematical beauty standards" in contemporary foundational physics. i think the whole invertible-equivalent-regular-prime-limit-lattice perspective of traditional ji could be summed up as "pitch space has to have the algebraic structure of a group, more specifically a subgroup of positive rational numbers with multiplication". but why assume something so specific and have the multiplicative group of positive rational numbers as a totem for ji instead of the harmonic series? that's where the mathematical beauty standards come in, as in some sense the rational numbers are deemed "perfect", and this perfection is tacitly assumed in order to consider any distinction among prime limits as real or meaningful. integer limits really make much more sense from a sensorial/computational point of view, and they are pretty much unavoidable in "real life". take single precision floating point numbers for instance, the integer limit is 2^23 (i.e. the size of the mantissa part). thus usually computers don't work with arbitrarily complex ratios, even if their integer limits are way higher than what we can perceive in the harmonic series. even if we go back in time, for instance euler dealt with 5-limit exclusively, but integer limits were essential to his perspective on consonance vs disonance. also, i think the relation between math and music depends heavily on what is understood by math. the contemporary dominant idealistic philosophy of mathematics is historically very recent (set theory, aka cantor's paradise, only began in the late 19th century), although mathematicians like to refer to ancient greece. when we look into the history of mathematics (in the west and in the rest of the world), and into ethnomathematics, we can see math that is much more grounded and down to earth, and i think it actually goes a lot better with science in general and even music. so yeah, decolonize math and maybe it will harmonize better with music theory!

[@ZheannaErose]

This is such an amazing and insightful comment. I listed to Dr Hossenfelder. She is brilliant and so incredibly articulate. I love the idea of mathematical beauty standards and very much feel just intonation and harmony has been subject to them. This gives me a bit to chew on internally for awhile. I love her emphasis on the measurement problem. I tend to believe there is enormous connection between math and music of course but that many times people try to use math to justify sound as opposed to using sound to justify the math - somewhat like preferring theoretical claims over observational claims whereas I tend to strongly prefer observationally based conclusions in music. I will look more into ethnomathematics! How wonderful. Thank you!!

[@ZheannaErose]

"But why assume something so specific and have the multiplication group of positive rational numbers as a totem for ji instead of the harmonic series?" This articulates the question I have been asking so clearly. Thank you! This implicit assumption is essentially baked into nearly every 20th century JI approach. It's just de facto accepted to the point where it seems people have largely forgotten it is a belief itself rather than some inherent truth. It always has seemed to me a very artificial method which is theoretically beautiful (referring to Dr. Hossenfelder now) and because of that beauty, has just been accepted as truth. It's acceptance is deep in the fabric of conventional JI that it has a sort of hegemony where beginners accidentally fall into it without ever realizing it's a belief.

[@PetraBrown]

Bless You Zheanna on your sneeze, ❤ from Petra Brown 🐱🐣

[@miamonteverdi]

i used to think i was a musical genius, but now i'm not so sure. struggling to understand this stuff. feeling very stupid. but one thing is the same as it ever was - music is awesome, and i worship it.

[@someknave]

Great stuff, as a mathematician who is really into some lattice structures I feel very seen by some of your points. I would say that octave equivalence in scale design isn't necessarily the same thing as the perceptual phenomenon. If you have octave periodicity (repeat your scale at every octave) you have octave equivalence not because a falling minor 6th is the same as a major 3rd, but if you have a falling minor 6th in your scale, you have a major 3rd in the next octave. So with octave periodicity you can always reduce any interval by an octave in scale design because the the unreduced interval will still exist in your tuning. Also I think you would like the results of combination product sets, they tend to get viewed through the same lens as lattices in general but are very good at highlighting whatever set of intervals you want to highlight define a structure where every note has a different combination from the same class of intervals. If you don't want to octave reduce you can choose a set where all of the products will be in the same octave like the 5,6,7,8 choose 2 hexany, the 7, 8, 9, 10 , 11 choose 2 dekany or the 11, 12, 13, 14, 15, 16 choose 3 eikosany, those structures have 6, 10 and 20 notes respectively and the major intervals are the ratios of the generators.

[@user-yv6xw7ns3o]

Great stuff, as a non-specialized type ∆ protoliminal unicyclist I wholeheartedly agree and would furthermore just like to underscore that.

[@michaelgonzalez216]

any literature you would recommend on the subject?

[@RobinPerry.microtonalist]

This is fascinating. Thank you!

[@tdubasdfg]

This is just a little over my head but I'm still grasping some interesting stuff along the way. I hope to continue to learn more if you keep teaching more!

[@PetraBrown]

I Love it Zheanna, ❤ from Petra Brown

[@AdrianSheard]

Coming from 12TET 19:42 is jaw dropping. Sorry if this is a noob question but I've never looked into microtonal stuff - do you think in terms of like a modified functional harmony? Like I'm not sure how I would mentally parse what I just heard cause to my ears it's like Cm11 -> ? AmSus -> ?? Abb9 -> ? DbAdd13 -> Db7

[@cablebee8790]

This is an amazing stream. Do you stream often today? I would love to watch more of this.

[@PetraBrown]

I can hear you dear Zheanna, As far as Primodality is concerned, I am away with the Fairies, listening to your wonderful self, musicality, ❤ from Petra Brown

[@PetraBrown]

A bit like Experimental Theology in Phillip Pullman’s books, it takes us to unusual places, Primodality takes us beneath the surface of music Zheanna, do we fully understand it? or not? Your music is what means most to me, I can sing or hum along to your music ❤ Petra

[@normanfreund]

Am at the 30 minute stage through this video, so perhaps my questions will be answered further on in the video. Still, it is inspiring me in all sorts of ways to apply this concept to a grid based note playing medium. So you say the root prime plays the role of giving a certain feel, ok, so you could assign this prime p to each row of the keyboard, and going column wise the numerator, hmm, I will have to try this out. Suspect I will not have enough columns on my keyboard, but hey it’s a start. Would be interesting to see what mapping approaches you have taken on grid based keyboards like the Lumatone.

[@RorxorProductions]

Hey Zhea! You mention Ben Monder's 'Thirty-Seven' but I can't find it. What tune are you referring to? By the way, amazing stuff about primodality I'm having so much fun exploring this! 🤯

[@ZheannaErose]

It’s called 37 by Ben Monder from his album Hydra. :) thanks !!

[@RorxorProductions]

@@ZheannaErose found it - it's 39! Hydra is such an incredible album. He has so many incredible albums 😍

[@RorxorProductions]

@@ZheannaErose something adjacent that I'd highly recommend is Origami by Theo Bleckmann ♥

[@AspartameBoy]

You ever visualize the rotation of the interfering waves as they spin around their individual strings?

[@markusmiekk-oja3717]

[asking this about 20 minutes into the video, so, sorry if you already have answered it in the remaining bit of the video] Have you ever considered working with a huge utonal thing - instead of, say 16:17:18:19:..., go in for 32/32, 32/31, 32/30, 32/29, 32/28, ..., and then using modes of that?

[@ZheannaErose]

Yes, utonal primodality stuff can exist. However, there are quite a few more problems with it than overtone based primodality and it comes off to me as more... arbitrary for lack of a better term. The spacing between how you hear is not the same going up as it is going down. The collapsing nature of the harmonic series lends itself very well to how our ears hear. So if we take that collapsing structure and aim it downwards, it will hit a point where the phasing is so intense you will perceive increasingly less periodicity. It actually becomes a gorgeous type of rumbling sound. I personally love it but only way to hear periodicity out of a subharmonic infinite structure would be to start extremely high. The key with prime segments is they can exist as their own meta series where you can't actually generate a theoretically infinite standalone meta series out of the subharmonic form of a prime unless you start theoretically infinitely higher. This is why the reflective downwards doesn't really work well even though it is cool to explore! You can't start 1:2:3:4 downwards from a prime because a prime is only factorable by 1 and itself. There is no 1/2 below the prime. We could start on 44:33:22:11 - that's ok. But you see it quickly approaches a limit where we either have to start higher or we end up falling into the original true harmonic series inversion as opposed to this meta series thing. Stacking pitches from a subharmonic series always creates muddiness (albeit aesthetic muddiness!!!) unless you arbitrarily start at an extremely high frequency and arbitrarily draw a cut off point for subharmonics. As the subharmonics keep counting down, the spacing becomes closer and the pitch point becomes lower. Lower/mid range notes spaced increasingly closer quickly destabilizes clarity. Imagine you start stacking sine waves upwards, you can basically always nest a ton of them upwards spaced wide at first and getting increasingly small and the texture/chord feels strong. If you do the opposite, the chord becomes muddy and discordant. That said, awareness of this creates some really awesome musical possibilities with subharmonic timbres vs harmonic timbres: When going up in pitch with a harmonic timbre, you progressively lose more of it so sounds become shriller and tinnier as they ascend. With a subharmonic timbre, the higher you go, the lower tighter and cleaner your low end becomes.

[@RobWickline]

in the "impressions of primes" section, you seem to be generating the pitches manually on the computer. how are you doing this? you are able to so quickly switch between these different prime scales. i really want to get to experimenting with this concept of, as you say, 'rendering' familiar musical objects through these prime color scales. really a brilliant synthesis of old and new

[@PetraBrown]

Maths don’t warm our beds like sensory experiences Zhea, you are right, LOL from Petra-Brown ❤ My favourite numbers is Two Becomes One by the Spice Girls, Two halves become a whole, Feminine and Masculine qualities make a person whole or complete, feels right anyway.

[@chambre466]

piano time so cool

[@michaelgonzalez216]

equating a prime number with one and deriving metatonic modes from the overtone series?

[@RobWickline]

maybe a method to approach switching between different prime scales during performance could be similar to how organ presets work on a B-3 or keyswitching and to trigger these with foot pedals

[@PetraBrown]

There is an unpleasant atmosphere on Tik Tok, I am with you Zheanna. ❤ from Petra a UTube fan

[@MatijaKrunic]

Any suggetions on material to learn befoee watching this. I studied composition at uni but have less familairty with tuning. First 5 minutes and im lost.

[@ZheannaErose]

check out my patreon server! ive written a lot to get people up to speed there. eventually gonna make vids on all this. i am traveling to italy in 2024 for a residency to finish my primodal treatise. a lot of early stuff from that is on my music theory server. :)

[@swapticsounds]

Wow, very interesting! I wonder when microtonal music theories will influence more other genres of music.

[@PetraBrown]

Why not lay back under a tree and feel the music in our bodies, that music is so magical Amelia ❤ Petra-B

[@PetraBrown]

Where I am good at maths is counting in decimal coinage or measuring with a ruler, in metric or imperial, I can not convert between miles and kilometres, I know that 3 feet is roughly a metre, I need a longer ruler for longer measurements Zhea, love from Petra-Brown, bless you.

[@untitled6578]

Which scale is used at 22:14?

[@ContrapuntalComposer]

Regarding supposedly not being a math person: I have two masters degrees in engineering and have taken all of the concomitant so-called "advanced mathematics" courses for those degrees... but I do not usually think of all that d***ned algebra (via which the calculus, etc., are represented) as true math. True math is the study of patterns... and as engineer and musical composer, I see electricity, structures, fluids, and music as patterns in the same virtual visual part of my mind that dreams or can play back visual memories and imaginations even as I drive a car in "the real world". I do the math of engineering not by starting with its academic representation, but rather by starting with a mental image of a pattern from which I then derive the practical numerical calculations on-the-fly. This sounds very much like what you do with your music. I think that you are more of a mathematician (or "mathemusician", as Vi Hart would say) than some people who can regurgitate and even manipulate reams of algebraic hieroglyphics divorced from ontological significance.

[@jamiegrant3258]

Have you scheduled your next live video

[@normanfreund]

Thanks for posting. Some cool ideas. After some clarification on the theory: 1) so when you go beyond the first octave, do you continue to use the harmonics, ie frequency ratio = n/p or do you multiply the first octave scale notes by 2; 2) for the higher p primes, do you pick and choose which n of the n/p to use that are actually mapped to your keyboard? Looking forward to try out your ideas.

[@PetraBrown]

Whoops! Your camera has a temperature, needs a soft stroke to calm it down Zheanna, ❤ from Petra-B

[@jackbeattie3886]

hey Shea, what programmes are you using to play these beautiful tunings? Would love to explore them myself, without having to get and frequently retune a real piano!! Thanks :)

[@knopf1er17]

Do you think there is anything special about diatonic tonality and the key structures created by equal tempered 12 note chromatic scale?

[@PetraBrown]

Like Angels playing with my heart, nice on BBC Radio 2 Amelia ❤ U From Petra-B, the Doty one

[@roeesi-personal]

Is hex already done? I remember looking at your bandcamp several months ago but I don't remember it. Did you release it somewhere else?

[@AspartameBoy]

Truth!

[@Transizio]

What is the software used at around the 18th minute?

[@Transizio]

Thanks in advance

[@ZheannaErose]

scala www.huygens-fokker.org/scala/downloads.html

[@PetraBrown]

Your image has disappeared Zheanna

[@spacevspitch4028]

The only thing I can't comprehend is not "believing" in octave equivalence. It's a pretty well established perceptual phenomenon 🤔

[@ZheannaErose]

There is research showing various cultures whomst do not perceive octaves as strongly or at all as Western ears do. There is significant research done on the Tsimané, a remote tribe in Bolivia who do not hear pure octaves as we do. And when played a melody above their singing range and asked to sing it lower, they have an equal distribution of error by semitones when they go to sing it whereas Western ears have a massive probability spike between 1, 0, and -1 semitones of the expected lower octave. The Tisamane actually show probability spikes at -5 and +5 semitones off the anticipated octave. This is very substantial information that points to the perceptual value of octaves being more a socialized phenomenon. see: news.mit.edu/2019/perception-musical-pitch-cultures-0919 www.cell.com/current-biology/fulltext/S0960-9822(19)31036-X?_returnURL=https%3A%2F%2Flinkinghub.elsevier.com%2Fretrieve%2Fpii%2FS096098221931036X%3Fshowall%3Dtrue Further, if you pay close attention to the tenant I stated at first, the primary point was on *invertible equivalence*, that is to say a 902c (32/19) sound is not the same as a 297c sound (19/16) sound. These are often treated as de facto equal or functionally equal but in primodality they are not. This is not an example of octave reduction equivalence. This is an example of invertible equivalence. I.e. n/p = p/n. In primodality n/p is its own unique identity and p/n is its own unique identity named in reference to whatever prime n reduces to. Despite theoretical octaves being perfect and of course true, that does not mean perception aligns with that inherently. I only tacked octave equivalence on in a more tongue in cheek way to *invertible equivalence*. I treat octaves as functionally equivalent. I.e. intervals of /11 show up /22 but we can think of them as the same identity. However where I refuse to accept perceptual octave equivalence is: 14/11 is not the same thing as 28/11. These are very different experiences. 2:3 is extremely different than 1:3 despite being convent to consider equivalent. They are not the same sound. I have been trained to recognize octaves and can perceive them as functionally similar sounds but if you stand in a physical space and sing 3/2 acoustically against another voice and then slide to 3/1 -- they aren't even close to similar events. I've only ever had one experience before where I had an equave event aside from the standard octave and it was in the aforementioned set up -- active acoustic space, two voices, and trying to experience 3/2 vs 3/1. Lastly, octaves are COMMONLY mistuned by Western musicians: "The experimental results very convincingly show that, on the average, singers and string players perform the upper notes of the major third and the major sixth with sharp intonation (Ward 1970)...The same experiments revealed that also fifths and fourths and even the almighty octave were played or sung sharp, on the average! (A reciprocal effect exists. Pure octaves are consistently judged by musicians to sound flat!) Rather than revealing a preference for a given scale (the Pythagorean), these experiments point to the existence of a previously unexpected universal tendency to play or sing sharp all musical intervals." - Juan Roederer, "Introduction to The Physics and Psychophysics of Music," 1973, pg. 155. If the pure octave is such a fundamentally established perceptual phenomenon it seems weird that universally musicians would tune it sharp by ear and perceive true octaves as flat. I will continue to use and treat octave reductions and octaves as equivalent for the sake of convenience but I reject their equivalence as perceptual experiences.

[@spacevspitch4028]

@@ZheannaErose I certainly agree that inverted intervals are not equivalent in experience. This is pretty clear with 3/2 vs 4/3 but maybe pure theorists don't have much experience really listening deeply to these things? However, the identification of an octave is based on the sensation that we would term as its sense of "equivalence" in the same way we would identify any other interval by _its_ unique "sound-print." So, maybe we don't have a name for the perceptual sound of 3/2 that allows us to identify it as a unique signature but its "3/2-ness" is a perceptual experience in the same way that "2/1-ness" is also unique and identifiable. We just happen to be able to define the 2 pitches as sounding "equivalent". All other intervals have the same potential to be defined by some term but I guess it's simply more difficult to figure out what that term should be. My point here is that if you can say that octave equivalence is merely a cultural phenomenon and not something "built in" to the auditory mechanism of humans, then you could say the same for literally every other interval. Our perception of it (whatever interval it happens to be) and the aesthetic/emotional qualities it evokes are also culturally dependent.

[@ZheannaErose]

I am less confident that all octave equivalence is cultural but I am leaning more confident octave reduction equivalence is. Most importantly though, that point about octaves wasn't initially in my presentation until someone mentioned it in chat and I was more tongue in cheek about it. I really only have issue with the way traditional approaches see invertible equivalence. Indeed octaves sound like duplicate notes dyadically to me. But intervals displaced by octaves sound very different and their harmonic series / timbres are very different. I can still hear the sound print of the octave happening but they are quite different phenomenon and behave way differently when being voiced. 2/1 *is* special - I'd never doubt that. Even if a culture doesn't perceive it, it's a fundamental relationship. Primodality is heavily based on octaves and is fundamentally an octave closing system unless expanded to tritaves or pentaves, etc.

[@santibeis]

There are many stretchable equivalences.

[@charles4050]

@@ZheannaErose shoot I've been working on a universal theory to analyze all music regardless of tuning system or lack thereof, and I was confident that I found a way to do it. That is, until I realized that it is true that octave equivalence truly is not an objective concept. Either I have to make the way I analyze quality of harmonic root movements much more complex (to include more interval types) or just come up with a whole new system. Damn lol Or I can just reject that notion entirely and stick with my theory lol

[@PetraBrown]

No time for a lovely quality on Tik Tok, I prefer your work Zheanna, LOL from Petra-B xxx

[@eddy_sonik]

👍i LoVe ! 💙⚪❤

[@PetraBrown]

Sounds like theme music for a film Amelia, it’s dramatic and oriental, a Japanese Sci-Fi film about a poor sighted alien with very good hearing, the alien can use the direction of sound to fly through spaced, The alien stands outside different houses, hearing different styles, one was sad, making the alien cry, another was happy cheering up the alien, then a cop saw saw the alien standing outside the Albert Hall in London, it was August, the person watched the alien moving the hands about in time to the music, the alien’s long finger was conducting an invisible orchestra. ‘Who are you, where are you from stranger?’ ‘From the floor of the universe, some other aliens have been stealing your brass etc and letting go of them in space, expecting them to play, they fell through space and we tried playing with them, they made funny sounds, quite tuneful but messy Amelia. ❤ from Petra-B imagine it?.

[@jacksonelmore6227]

I listen to this asleep on my hour long shuttle ride to the construction site as asmr

[@PetraBrown]

I can see you now Zheanna, it’s night time where I live, so many hours ahead, I am watching your video about Primodality, it’s awesome ❤ from Petra-B xxx

[@Dude8718]

This is the type of music that should be played from a Tesla coil through plasma.

[@ivanbrown304]

35:57 i disagree with your comment on the mediant pillars being reinforced with each other on the topic of using modal logic because mediant shouldn't be a term used in this essay considering its a term coined from a theroem of hugo Rieman. the term is not to be confused with a left over comeplemtation fo the 5th. complemtation of the 5th being the major 3rd and within the octave the 4th. Please don't confuse terms.

[@ivanbrown304]

to extend that comment mediant is to be used for secudal scalar horizontal approach not to used for sonorties that erect interval relations.

[@ZheannaErose]

"Mediant" was absolutely not created by Hugo Riemann, you are about 200 years too late. First evidence shows Antoine Parran in 1639. It likely even predates this time because of how arithmetic and geometric mean works. In this case, we are in pure JI not derived by generator stacking and thus not a closed regular system. This means compliments aren't consistent. There is no structural regularity. It is not homogenous. You do not need to derive notes through generators. The auditory and structural effect of mediant zones still remains. I don't think you understand what was said. 35:57 says that overtones have key relationships with each other which are necessary to open up intra-primodal color. I.e. the 13th harmonic is the min3 of 11. Therefore, we can now generalize and say auditorily, the 13th harmonic is the bIII region of 11. Thus, a primodal /11 Dorian is part of the same set of notes as /13 Lydian. Or a /11 ionian is /13 phyrgian. These are intra-modal relationships via mediant root movement. Functional mediants aren't just dependent on 5ths. You are just used to thinking of them that way because the regular diatonic scale is derived by fifths and thus most steps have their mediant compliment. Mediants can operate and do form an entirely different root axis in music even in the absence of fifths. In 12-equal this axis ultimately refolds back. In JI, it doesn't close. Riemann theory couldn't be less useful in this discussion because it's dependent upon translation across the tempered, folded space which implies all pitches are derived the same way (therefore consistent compliment potential). JI is infinite pitch space and primodality deals with curating that infinity into core colors which are the building blocks of all other harmonic scales and ultimately all overtone relationships. Mediant is accurate to say here for multiple reasons: 1) on the most literal level they are mediants, i.e. division of the middle of a 2p:3p space (1639) what Riemann called a compliment 200 years later. The great irony being a real linear middle division would actually yield a neutral third. The Major mediant isn't even the middle of 2:3 unless you are thinking arithmetic mean. 2) In this case, 11 to 13 is absolutely a mediant movement. /11 Dorian has the same notes as /13 Lydian. This is a mediant relationship. It's not derived by fifths though. Please don't ever tell me I am confusing terms when you are just fundamentally wrong in your first sentence. Pick a different tone next time.

[@PetraBrown]

I wear prescription glasses my self, if the copyright sign is clear then it’s copyrighted Concerned fan Petra-B ❤

[@PetraBrown]

Some of us with longer attention spans find shorts too brief, and it repeats itself, very little substance, even with your longer videos Amelia, I save them, pause them and return to them and watch more. LOL from Petra-Brown xxx

[@weareone1575]

What software do you use to experiment with this stuff? I saw you using something with a simple UI that let you choose tunings?

[@lambertronix]

1:03:39 BEN MONDER

[@PetraBrown]

It’s too short to enjoy, twenty five minutes and enough to keep me going, shorts are too don’t give time to absorb it Amelia, with longer videos of say 2 hours, I can pause it after 15 minutes and then come back and resume where I left of, ❤ from Petra-Brown

[@simonlarsen7025]

Of all beautiful lies platonism is by far the most riveting, as if being submerged in crystalline fluid.

[@ZheannaErose]

I would not say I am a platonist. To me the "object" isn't the numbers. The value isn't in the numbers. The value is in the sensory experience of sound. That sensory gestalt is impossible to express or capture outside of just the sound. The numbers are simply a way to discretely share the ingredients required to generate the sensory experience.

[@simonlarsen7025]

@@ZheannaErose Would wholly agree with that, especially with the notion of normativity or value tout court being phenomenologically grounded, though I would not consent to the fact that the value experienced is exclusively sensory in nature, though it is hard to imagien it without a sensory foundation. As a side note I don't consider platonism reducible to pythagoreanesque matthematical ontotheology or late 19th early 20th century logicist ponderings. The thought of platonism being the most beautiful of lies lay in the fact that if one is adequately familiar with modes of pattern and deviation, one can remain in the abstract with no reference to sensory experiennce in the creative phase, and have sensory experience obey to some extent when said pattern is instantiated. But I'm not an artist in anyway. Nur ein verrückter spekulant. But that discussion runs infinite anyway. Been watching a lot of your stuff today. Reached out to someone today for the first time. You're quite inspirational.

[@leifsearle1546]

Hey Zhea you should put more of your songs on Spotify

[@PetraBrown]

I wonder if he ever put a proper copyright on his stuff, or he is just out to trip people up so as to make money Amelia, you are a genuine composer ❤ from Petra-Brown

[@22tfortnitevevo]

how do y’all even begin to understand this 😭 help

[@PetraBrown]

Imagination helps us make beautiful music and art, I am in agreement, I can count well, kilometres is like, invisible to me, learning tunes and music by the Spice Girls or ABBA, Classical music by Grieg and Johanne Strauss Zheanna, ❤ from Petra Brown, alas, I am not related to Melanie-B.

[@AspartameBoy]

This could be generated in virtual reality

[@PetraBrown]

Gossamer may have a face like Beethoven, who does he think he is, you are better looking with inner beauty too Zheanna ❤xxx from Petra-Brown 🏳️‍⚧️🏳️‍🌈

[@leotard2536]

Get this girl an unregistered firearm right away

[@PetraBrown]

Are you a tortured genius Amelia aka Zheanna? these things are meant to test us. LOL from Petra-B

[@sonatab2646]

what

[@PetraBrown]

How does Apple Card payments convert from Sterling to Dollars Amelia when I buy singles of your music as I am British? LOL from Petra-Brown 🐇

[@KateCroft]

UwU

[@Kaiveran]

OwO

[@ZheannaErose]

U_U

[@KateCroft]

O_0

[@PetraBrown]

You are right Zheanna, who needs them Amelia ❤ U from Petra-B, they don’t love us .

[@markcbeaumont4670]

Musical homeopathy maybe?

[@PetraBrown]

My Mum taught me to play the piano, her teaching excluded modern pop music, It demotivated me, not like your Trans Voice Lessons, I feel more Feminized now Zhea❤ Petra-B

[@PetraBrown]

Talking of primodality, how would a maths expert describe us humans in numbers form, even to each other Zheanna, we would look and sound unrecognisable, LOL from Petra-B

[@PetraBrown]

Perhaps Willy Wonka has affected the camera, lick the camera lens and it tastes like Chocolate Zhea, chocolate love from Petra-B ❤xxx

[@PetraBrown]

Your Hot Zhea, ❤Petra

[@PetraBrown]

Tim Tok is not that nice, they bully people like us, ❤ Petra