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Everything is in just intonation, not just a 12-note scale tuned to G but using many more pitches so that everything is in tune. (Or nearly everything - 1:47 is purely Pythagorean so that the piece does not modulate down a comma.) And yes, some impurities arising from the inherent imperfection of a piano's strings, which tend to produce a slightly stretched spectrum, causing a little beating pretty much no matter what. I did this using Pianoteq, making a 12-note JI scale, then making another scale once the music no longer fits the original scale. I probably made 3-4 scales for this piece, which is unusually little since the music is so harmonically static

Thank you for the answer ❤​@@JustMusic1685

@@JustMusic1685 I personally find it acceptable to modulate around in commas. It is such a small distance that "practically nobody" hears it.

Temperaments are attempts to tune as many just intervals (simple proportions like 3:2 and 5:4) as possible within a limited set of notes, so as to make performance more practical, as well as to prevent the tonic from drifting. But tempered (i.e. not-perfectly-in-tune) intervals still refer to just intervals. That's why we like perfect fifths, major triads, dominant 7ths, etc., and why we use temperaments that represent these intervals fairly well. The closer you tune to the just version (e.g. 3:2), the more in-tune the interval sounds, generally speaking. My arrangements are experiments of a sort, designed to show the just intonation realization of what these tempered pieces imply. I believe these are the Platonic chords Bach is implying. There is a certain uncanniness, at least at first, in hearing familiar pieces and instruments destabilized, and by how quickly the different chords go by (if it were 5x slower, I suspect very few people would protest) - and it is far from perfect, since Bach often implies multiple just-intonation sonorities/relationships at once, and choosing one does violence to the other. This was the first arrangement of this sort I did - I've since found that other pieces (like the Shostakovich A Major Fugue, or anything by Scriabin, Satie, Debussy, or Pärt) tend to sound more conventionally agreeable.

Thank you, yeah I did

much more than 12, I think I used at least 3-4 scales to get all the different keys do you mean how I arrived at the F minor section? the 7:6 third from the A minor chord becomes the 3:2 fifth of the F minor. Then the F becomes the 7:6 third of the D, bringing us back from the "septimal" plane to the "normal" plane and yeah, the second D (0:38) darkens to 13:8!

the Twin Peaks Archive has a drums + bass version and a drums + clarinets version, which I de-noised to minimize the superfluous drums, then retuned both tracks in Melodyne and added my own vibes, rhodes and organs

@@JustMusic1685 damn, i'd love a tutorial on that. removing drums is something i've tried and given up on plenty of times.

Yeah (sorry I forgot to include that in the accidental key!)

lol, i just read the description

Thanks for the suggestion, I'll definitely consider it for the future!

Yeah - good ear!

13/12, with 7/6 minor thirds

Crunchy

Thanks so much! If you want to see my notes (using Johnston accidentals) drive.google.com/file/d/1BNjFt7STS0nNbOxR88vX2eOmRMHFVu4K/view?usp=drive_link The ostinato goes 1/1, 13/12, 7/6, the rest more or less falls into place

th-cam.com/video/j_DeK3GIV60/w-d-xo.htmlsi=qT_SMG-FZXFWorxL Now you can hear it in Pythagorean, though the triads sound pretty harsh. Werckmeister is probably ideal

@@JustMusic1685 Any harshness you may be hearing in Pythagorean is from the timbre not being good. But if you really key in on the center of each note in your hearing and listen to each line melodically all at once, you can hear how it alone is the perfect intonation in the prelude in C, even with the bad timbre which yields a seeming harshness. You will hear how all the other tuning systems are out of tune. When you listen melodically to each line all at once, your brain will also be able to listen and hear how the harmony is perfectly in tune in each chord, it will break the illusion caused by the poor timbre.

@@RememberGodHolyBible Are you using Pythagorean to mean "just intonation"? In that case you would be right. But Pythagorean as it's generally understood among people who talk about tuning is 3-limit just intonation, with 81:64 major thirds, which are far less consonant than their 5:4 brethren, and produce intense beating. That's why in the Middle Ages thirds were considered dubious consonances at best, and unsuitable to begin or end pieces

@@JustMusic1685 Check out the music on my channel, you will see. When I say Pythagorean, I mean 3 limit intonation where the notes are spelled correctly and subsequently tuned according to their spelling, on a chain of 3/2 fifths, what I simply call True Intonation. Yes, with 81/64 major thirds. No, 5 limit rational intonation is not right for music, it is woefully out of tune and incoherent as an overal intoantion system. In the middle ages 7ths were seen exclusively as dissonances too, as were 2nds, but now, they can be used as consonances of sorts. In the middle ages you could not have two notes a tritone apart on subsequent beats because the tritone was too close in memory to be heard. So using the preferences of music theorists in the middle ages concerning consoncen and dissonance is not persciptive when it comes to intonation. The whole concept of 5 limit and meantone in the west comes from Ptolemy, a very wicked philosopher, and Zarlino, a Roman Catholic and member of the order of the fraciscans, not people to follow. Music from the beginning was most entirely in Pythagorean as the standard for thousands of years. Thinking of music from a primarily harmonic perpective is new and comes from farily evil people. I am not saying to not consider harmony, it can certainly be useful and important, but one must acknowledge that music is primarily melody first, and all harmony comes from melodic lines moving together. When assessing intonation, one must consider the whole system of the intonation, and not one particular interval in a vacuum outside of musical context to see whether it beats or not. One must listen both melodically , that is, each note in each chord moving from one note to another over time (in real music), as well as the sounding harmony in every given instant of time. Both need to be in ones awareness at the same time while listening, that is what I call holisitc listening. The true intonationi that meets all of these fields in a perfect manner, leaving nothing lacking, is what the world calls Pythagorean just intonation, (3 limit rational tuning that is correctly spelled). We have been lied to, and not only lied to but brainwashed, literally, into thinking that 5 limit tuning is ideal intonation in music. The system of 5 limit rational tuning (what most people mean when they say just intonation) is very incoherent. You have multiple sizes of every interval. You have infinite notes in the diatonic scale, yes, infinte. There is no consistency of melodic intervals. You have 3 dimentsions of movement for notes in music tuned this way, and 2 dimensions for pitchclass (excluding the octaves). This means that the ear must track frequencies and ratios of those frequencies not only in one moment but over time and to varying degrees, both up and down, in 2 dimensions at once, plus then also that of the ocatves. There is also a comma inside the diatonic scale. You might be able to trick yourself into thinking it is just, by listening to music that is relatively simple, and arrangeed in a way to hide the incoherent flaws of the system as best as possible, but it is only every hiding, a trick. Sure the buzzing sound of the 5/4 can sound pleasing and restful in a moment, but it creates a huge waterfall of problems for the system of intonation at large. Music is NOT an interval in an instant. It is sound ordered coherently over time, the over time part is essential to grasp. And apart from all this, 5 limit tuning is impractical for acoustic instruments, especially keyboards, whereas True Intonation is totally practical WITH indefinite modulation possible, on acoustic keyboard instruments, albeit with a differnt keyboard layout from that which is standard today, but one that has better ergonomics for the hands and much further reach for the hands as well. The whole reason we have 12 tone equal temperament as standard in the world is because people think the 5/4 is the just major third. The whole reason all music is out of tune is because of this ONE misconception and then particularly wicked people capitalizing on the ignorance of man. How? Because the whole reason Pythagorean just intonation was abanddoned was because people were sold on the idea that the just major third was the 5/4 interval and that the 81/64 could not be sung in tune, both of which are total lies. So people tried to create keyboards for this 5 limit system, but found they could only play in a very select few keys while adhering to the principles of 5 limit tuning. So some started added more keys, but the layouts became more and more complex, and had terrible ergonomics for the hands of man. Then they tried encorporating temperaments (compromises) to get some intervals as close to the 5/4 as they could, but this created wolf intervals and other problems epnding on the particualr compromise, and even then there were still places you could not modulate to. And even in more Pythagorean-esque temperaments some keys were a bit harsh to the ears, and it was never quite right in every place musically. So when the wicked Jesuit Order found record of 12 tone equal temperament in China in their dealings over there, they brought it back to the west, and began to promote it. Note that in China where 12 tet was invented, it was rejected, for its impurity, and the Chinese people's lack of desire to endlessly modulate. But in the west people took the bait, allured by the notion of endless modulation possibilities. But they had the answer all along: Pythagorean just intonation. You can endlessly modulate a 17 note chromatic scale within a larger system of 53 notes (or more). 17 notes per octave per tonic chord, the 7 naturals plus the first 5 sharps in the chain of fifths and the first five flats. In the chain, in a major key, it is the b5 through to the #6. So in C major and all its relative modes the notes available in that key that are totally functional are: C Db C# D Eb D# E F Gb F# G Ab G# A Bb A# B This 17 note scale can be modulated up and down the chain of fifths endlessly, and there are several keyboard layouts that accomate it very well, much better than the standard 12 note layout, but from my research no one yet has discovered these layout apart from myself. I have not published them because of the sheer amount of work that would be needed to make a video showing all the deisgns laid out, and plus there is a genuine lack of interest. I can count the muscians on one hand that would be excited for such a thing. Most people believe as you do about intonaiton for the same reasos which you do, which I also did, until I saw the situation more celarely and my ears and eyes were opened. One other very interesting thing to note, is that standard msuic notation, what it displays, IS Pythagorean just intonation, it does not display equal temperament and it does not display 5 limit rational tuning. You find more than 12 notes present in standard sheet music, you have Cb and B natural, Fb and E, Db and C#, G and Abb, etc. These notes, the very concept of a "key" comes from Pythagorean just intonation. A key is defined as SEVEN notes derived from an UNBROKEN chain of six fifths. In 5 limit tuning, like I said above, there are INFINTE notes which can appear in the diatonic scale alone, let alone the chromatic scale. Even if the tonal canter is made not to drift, it is very very rare to have music which only has 7 notes in the diatonic scale. You need AT LEAST 8, but more often than that, 9, and then there are myriad examples where you need much more than that, and that is WITHOUT the tonic drifting a comma. If the tonic drifts a comma it is all the more notes needed. You may be able to get by in major or minor setting, in simple music. But try composing in dorian in 5 limit intonation, you have TWO different tonic notes for the same scale. The diatonic scale has NO DEFINITION at all in 5 limit. And this is not all intellectual and conceptual contensions that I have, the ear hears these in the music, the incoherence. But poor timbre, and misinformation, and people repeating the lies, and conditioning their ears and brains to only listen and check intonation in an instant of time rather than OVER time, that is, melodically also, has brought the music of man to where it is today, completely out of tune. And because 5 limit tuning in music is based on a lie which is neither satisfying completely nor practical, it has set muscians and theorists to seek deeper and deeper perversions in order to try and arrive at tunings which will scratch their itch, but they never arrive. Higher and higher limits, more and more computers, less and less acoustic real music, more and more higher number ETs, less and less awarness of melody, skipping from one incomplete incoherent tuning to another, without end. Or just reverting to 12 tet for its simplicity and versatility (something which btw, is in truth, just an approximation of Pythagorean Just intonation). 5 limit tuning is a new thing, a distorting of true intonation. True Intonation is the foundational ideal of all tonal music, but remains foolishly ignored all because of one fundamental misconception about one interval. The imperfect consonance, the major third.

@@JustMusic1685 Check out the music on my channel, you will see. When I say Pythagorean, I mean 3 limit intonation where the notes are spelled correctly and subsequently tuned according to their spelling, on a chain of 3/2 fifths, what I simply call True Intonation. Yes, with 81/64 major thirds. No, 5 limit rational intonation is not right for music, it is woefully out of tune and incoherent as an overal intoantion system. In the middle ages 7ths were seen exclusively as dissonances too, as were 2nds, but now, they can be used as consonances of sorts. In the middle ages you could not have two notes a tritone apart on subsequent beats because the tritone was too close in memory to be heard. So using the preferences of music theorists in the middle ages concerning consoncen and dissonance is not persciptive when it comes to intonation. The whole concept of 5 limit and meantone in the west comes from Ptolemy, a very wicked philosopher, and Zarlino, a Roman Catholic and member of the order of the fraciscans, not people to follow. Music from the beginning was most entirely in Pythagorean as the standard for thousands of years. Thinking of music from a primarily harmonic perpective is new and comes from farily evil people. I am not saying to not consider harmony, it can certainly be useful and important, but one must acknowledge that music is primarily melody first, and all harmony comes from melodic lines moving together. When assessing intonation, one must consider the whole system of the intonation, and not one particular interval in a vacuum outside of musical context to see whether it beats or not. One must listen both melodically , that is, each note in each chord moving from one note to another over time (in real music), as well as the sounding harmony in every given instant of time. Both need to be in ones awareness at the same time while listening, that is what I call holisitc listening. The true intonationi that meets all of these fields in a perfect manner, leaving nothing lacking, is what the world calls Pythagorean just intonation, (3 limit rational tuning that is correctly spelled). We have been lied to, and not only lied to but brainwashed, literally, into thinking that 5 limit tuning is ideal intonation in music. The system of 5 limit rational tuning (what most people mean when they say just intonation) is very incoherent. You have multiple sizes of every interval. You have infinite notes in the diatonic scale, yes, infinte. There is no consistency of melodic intervals. You have 3 dimentsions of movement for notes in music tuned this way, and 2 dimensions for pitchclass (excluding the octaves). This means that the ear must track frequencies and ratios of those frequencies not only in one moment but over time and to varying degrees, both up and down, in 2 dimensions at once, plus then also that of the ocatves. There is also a comma inside the diatonic scale. You might be able to trick yourself into thinking it is just, by listening to music that is relatively simple, and arrangeed in a way to hide the incoherent flaws of the system as best as possible, but it is only every hiding, a trick. Sure the buzzing sound of the 5/4 can sound pleasing and restful in a moment, but it creates a huge waterfall of problems for the system of intonation at large. Music is NOT an interval in an instant. It is sound ordered coherently over time, the over time part is essential to grasp. And apart from all this, 5 limit tuning is impractical for acoustic instruments, especially keyboards, whereas True Intonation is totally practical WITH indefinite modulation possible, on acoustic keyboard instruments, albeit with a differnt keyboard layout from that which is standard today, but one that has better ergonomics for the hands and much further reach for the hands as well. The whole reason we have 12 tone equal temperament as standard in the world is because people think the 5/4 is the just major third. The whole reason all music is out of tune is because of this ONE misconception and then particularly wicked people capitalizing on the ignorance of man. How? Because the whole reason Pythagorean just intonation was abanddoned was because people were sold on the idea that the just major third was the 5/4 interval and that the 81/64 could not be sung in tune, both of which are total lies. So people tried to create keyboards for this 5 limit system, but found they could only play in a very select few keys while adhering to the principles of 5 limit tuning. So some started added more keys, but the layouts became more and more complex, and had terrible ergonomics for the hands of man. Then they tried encorporating temperaments (compromises) to get some intervals as close to the 5/4 as they could, but this created wolf intervals and other problems epnding on the particualr compromise, and even then there were still places you could not modulate to. And even in more Pythagorean-esque temperaments some keys were a bit harsh to the ears, and it was never quite right in every place musically. So when the wicked Jesuit Order found record of 12 tone equal temperament in China in their dealings over there, they brought it back to the west, and began to promote it. Note that in China where 12 tet was invented, it was rejected, for its impurity, and the Chinese people's lack of desire to endlessly modulate. But in the west people took the bait, allured by the notion of endless modulation possibilities. But they had the answer all along: Pythagorean just intonation. You can endlessly modulate a 17 note chromatic scale within a larger system of 53 notes (or more). 17 notes per octave per tonic chord, the 7 naturals plus the first 5 sharps in the chain of fifths and the first five flats. In the chain, in a major key, it is the b5 through to the #6. So in C major and all its relative modes the notes available in that key that are totally functional are: C Db C# D Eb D# E F Gb F# G Ab G# A Bb A# B This 17 note scale can be modulated up and down the chain of fifths endlessly, and there are several keyboard layouts that accomate it very well, much better than the standard 12 note layout, but from my research no one yet has discovered these layout apart from myself. I have not published them because of the sheer amount of work that would be needed to make a video showing all the deisgns laid out, and plus there is a genuine lack of interest. I can count the muscians on one hand that would be excited for such a thing. Most people believe as you do about intonaiton for the same reasos which you do, which I also did, until I saw the situation more celarely and my ears and eyes were opened. One other very interesting thing to note, is that standard msuic notation, what it displays, IS Pythagorean just intonation, it does not display equal temperament and it does not display 5 limit rational tuning. You find more than 12 notes present in standard sheet music, you have Cb and B natural, Fb and E, Db and C#, G and Abb, etc. These notes, the very concept of a "key" comes from Pythagorean just intonation. A key is defined as SEVEN notes derived from an UNBROKEN chain of six fifths. In 5 limit tuning, like I said above, there are INFINTE notes which can appear in the diatonic scale alone, let alone the chromatic scale. Even if the tonal canter is made not to drift, it is very very rare to have music which only has 7 notes in the diatonic scale. You need AT LEAST 8, but more often than that, 9, and then there are myriad examples where you need much more than that, and that is WITHOUT the tonic drifting a comma. If the tonic drifts a comma it is all the more notes needed. You may be able to get by in major or minor setting, in simple music. But try composing in dorian in 5 limit intonation, you have TWO different tonic notes for the same scale. The diatonic scale has NO DEFINITION at all in 5 limit. And this is not all intellectual and conceptual contensions that I have, the ear hears these in the music, the incoherence. But poor timbre, and misinformation, and people repeating the lies, and conditioning their ears and brains to only listen and check intonation in an instant of time rather than OVER time, that is, melodically also, has brought the music of man to where it is today, completely out of tune. And because 5 limit tuning in music is based on a lie which is neither satisfying completely nor practical, it has set muscians and theorists to seek deeper and deeper perversions in order to try and arrive at tunings which will scratch their itch, but they never arrive. Higher and higher limits, more and more computers, less and less acoustic real music, more and more higher number ETs, less and less awarness of melody, skipping from one incomplete incoherent tuning to another, without end. Or just reverting to 12 tet for its simplicity and versatility (something which btw, is in truth, just an approximation of Pythagorean Just intonation). 5 limit tuning is a new thing, a distorting of true intonation. True Intonation is the foundational ideal of all tonal music, but remains foolishly ignored all because of one fundamental misconception about one interval. The imperfect consonance, the major third.