💣 Mind Blown! Brings it all back to the Hendrix Chord. I am early on in my musical pursuit at 50 something and your presentation of Geometry / Math and Music is brilliant and inspiring. Thank you.
Hey Milton I really enjoyed this and I had to subscribe because I've been learning music on my own for almost a decade and no other channel comes close to conveying theory in such a simple way. You also give every lesson a spiritual feeling and beautifully link it the reaction music provoques in all of us. Thank you for your dedication and your idea to share your knowledge ^^ It's a pleasure to watch you talk about music.
Yes! Those are my thoughts as well. Professor Marmikedes have both the knowledge and the skill, and kindness, to pass it forward. This is high level teaching. Also, such a dense content broken in very simple blocks. I'm and old musician learning theory fro the first time and I'm deeply in love with his elegant way to present it.
Thank you, what an awesome video. Sometimes I feel like I'm trying to hide the most interesting dissonances I can in any given phrase of music whilst still making the music sound 'good'. This was enlightening.
@@miltonline I am so depressed you dont have 18m followers its ridiculous but I did find a friend today who LOVES your signification work and is making amazing music out of all kinds of things. I will share a link.
@@IngridHurwitz Don't be depressed but thanks for you support. All best to you and your composer friend! (I've had to add sonification to my digital dictionary for this very reason).
This has so much inspirational potential! I want to write/hear a chord progression defined by a pattern of changing shapes or find the most dissonant chord I can play on my guitar fretboard
this is absolutely incredible, i was thinking a lot lately about three topics: numbers of shapes you can draw in the circle of semitones and their symmetries (i'm still looking for a more group theoric approach to this, but this is also really enlightening), quantifying dissonance, and the hendrix chord, which has been my favourite for forever, and you're combining these in one video, all centered around my fav chord. this could not have come at a better time. have you written any books, or what books would you recommend? i was thinking about alternative ways to space out the notes, like you have the circle of semitones, the circle of fifths, and unfortunately those are the only 2 options up to inversions for circles (or really dodecagons i suppose), but i want it to be such that the space between the notes corresponds to their dissonance. the circle of fifths is better for that than the circle of semitones, but neither really represent thirds as a consonant interval. of course if you attempt a circle of either one of the thirds you end up with just a subset of all notes, but if you combine them they span all notes, and they are in fact the only, or at least in some way the purest combination of 2 generators. if you consider the notes as a mathematical group, you could use a semitone (s) as the generator, such that s^12 = e, and you get the integers modulo 12. But you can also look at the notes as the group with generators m and M where m represents a minor third, and M a major third, such that m^4 = M^3 = e, and mM = Mm. It is an isomorphism of Zmod12, so it is essentially still describing the rotational symmetries of a dodecagon, but if we want a shape with edges connecting all the thirds, such that all these connected vertices are also evenly spaced, i reasoned this would be possible in 4D. I figured out some properties of this shape and looked it up and it is apparently called a 3,4-duoprism. i have seen many mentions of the circle of fifths, but have literally found nothing about the duoprism of thirds. of course this shape doesn't represent that fifths are generally perceived as more consonant than thirds, and it also doesn't provide a very intuitive understanding since it's hard to actually visualise, but i wonder if there is an even higher-dimensional, and if necessary non-euclidean space in which we can really capture this dissonance to distance mapping. i need friends that care about this stuff
Very interesting video. But I am not sure about that chart which maps consonance and dissonance. Because of concepts like those presented in the chart I was a big proponent for 5 limit just intonation music. But after working with it intensely for a decade, I came to realize that while out of context the intervals do not usually beat. Within the context of a piece of music, while listening not just vertically at the harmony, but also horizontally at the melodies and voices, listening in both directions, that it became abundantly clear, that 3 limit or Pythagorean intonation, is the true just intonation, both in chords and scales. I personally hear the Pythagorean major third at 81/64 as in tune and the 5/4 I hear out of tune, especially when in the context of a piece of music. I also now hear the 32/27 Pythagorean minor third as more consonant, more in tune, than the 6/5 ratio. The notes in these dyads at the 3 limit ratios have more distinction from each other, while also expressing a ratio that can be easily understood by the brain, even the untrained one. Because all is just ratios based on powers of 2 and powers of 3. The powers of 3 give you all the notes, and the powers of 2 give you all the octave doublings, and so the brain can very easily track and hear these in a piece of music. With 5 limit and higher limit harmonic notes with added dimensions and alternate versions of every note, the music while listening horizontally and vertically simultaneously (simultaneously is the key) sounds very out of tune. But the chart of dissonance and consonance in the video would have one believe that the Pythagorean thirds both major and minor sound not only more dissonant than 5 limit intervals, but also more dissonant than equal temperament thirds. This is not at all my experience. The equal temperament thirds definitely sound worse than both the 5 limit and 3 limit intervals, for there is neither the vertical in tuneness of 5 limit, nor both vertical and horizontal in tuneness as heard in 3 limit. So considering all this, I think the chart, while interesting in a way, is very over simplified when it comes to how we perceive consonance and dissonance.
@miltonline I have a question on the dissonance curve, why is major 3rd considered more dissonant than major 6th or dominant 7th on this graph? Is it a cultural thing? On what kind of data is dissonance measured on this graph, is it based on an audience's perception, if so what kind of people from which regions of the world? I kind of know the major third is not used as a building block in africa, middle east and the balkans (parts of eastern europe), as opposed to western europe. Is this the reason why major 3rd is depicted as having higher dissonance on this graph, equal to tritone (the "devil's" interval)?
Such dIssonance contours are purely subjective (although can involve indirect measures) and have been tested on a wide cohort of ages and backgrounds (and even species). In short there seems to be a convincing biological basis (to a certain extent) for equating simple ratios with consonance, but this is highly malleable on individual/cultural experience.
Really outstanding video, I learned a lot. So your version of the Hendrix chord is C sus2 sus4 b5 which is a mirror of C b2 b5 and the Hendrix chord is E7#9 voiced as E E G# D E G, just wondering if I got that right.
Shortest answer: Yes, that's right and thanks for the feedback! Short answer: we discard any repeats of notes so the Hendrix chord is just E G# D G. And we also reorganise it according to rules (below) so that all inversions are grouped together. 'C sus2 sus4 b5' is C D F F# - a D Hendrix chord which is the 'same' as the E Hendrix chord. So 'my version' of the Hendrix chord is how pitch-class set theory would automatically build it (0, 2, 5, 6) Yes that's a mirror of C Db E F# (0, 1, 4, 6 ) what I call the 'octatonic tetrachord'. Long answer:Okay so pitch-class set theory 'normalises' all chords so that transpositions and inversions of the same chord are all grouped together - so A minor and D minor etc are in the same group, as are any inversions of these chords. The way P-C set theory does this is by thinking of a musical object as a chain of intervals. Notes are all in the same octave with the smallest gap possible between the outer two. Let's take the Hendrix chord which (since we don't care about octaves) is E G G# D. If we reorganise them as D E G G# (se 10:50) then we create the shortest possible range between first and last. Since we are also conflating all transpositions we can put the D at the top of the circle.
@@miltonline Thank you so much for your detailed answer. I plan to fire up my Mac to run your software as it looks like I can just enter in chords and have it calculate it so I can analyze the intervals. I am studying arabic music so its very important for me to study uncommon scales. About half the maqams (arabic scales) are diatonic, the rest use quarter tones.
@miltonline I have an objection to the use of interval classes, because it omits the root and whether the chord is open or closed shaped, which changes how consonant the interval and the chord is perceived, interval classes theory also doesn't align with the dissonance curve for the same reason, to root and the bass note, is the most important part of a chord, the interval from the root and bass to the chord tones determines the effect of the chord, not the interval classes in the chord. Interval classes is an oversimplification and would only work in close form chords where the notes are so closely stacked together and the bass is not obvious (useful maybe in solo guitar/solo stringed instrument music). But in a band or orchestra or a piano arrangement, pitch class theory is not useful, even the different tetrachords you have shown at the end, that have equal distributed interval classes, have different observed consonance because of their different root to chord tone interval relationships, as opposed to the same interval classes contained in the different tetrachords.
Yes, as stated PC-Set theory is super simplisitic (although remarkably powerful given how simplified it is). In reality harmonic dissonance is tied to octave spread, voicing, timbre of instrument, rhythmic and harmonic context and enculturation. No one viewpoint gives a complete picture, but many different lights can start to illuminate a large room.
Awesome, thank you. Clearly explained with some great visual aids. Cheers 👍
Such a mic drop moment at the end of this video! haha. Amazing stuff.
Thank you! The world's first interval vector analysis mic drop I believe.
Love the content mate, your videos have given me some great insights into things I didn't even know that I did not understand! Keep it up
Thanks so much! I shall continue 🥸
Thank you for your _fascinating_ videos, Mr. Mermikides!
I wished my Conservatory studies would have had a course that taught theory the way you do!
💣 Mind Blown! Brings it all back to the Hendrix Chord. I am early on in my musical pursuit at 50 something and your presentation of Geometry / Math and Music is brilliant and inspiring. Thank you.
Thanks so much - enjoy your journey!
Hey Milton I really enjoyed this and I had to subscribe because I've been learning music on my own for almost a decade and no other channel comes close to conveying theory in such a simple way. You also give every lesson a spiritual feeling and beautifully link it the reaction music provoques in all of us. Thank you for your dedication and your idea to share your knowledge ^^ It's a pleasure to watch you talk about music.
Thanks for the very kind and supportive comment. It inspires me to make more :)
Yes! Those are my thoughts as well.
Professor Marmikedes have both the knowledge and the skill, and kindness, to pass it forward. This is high level teaching.
Also, such a dense content broken in very simple blocks.
I'm and old musician learning theory fro the first time and I'm deeply in love with his elegant way to present it.
Thank you, what an awesome video. Sometimes I feel like I'm trying to hide the most interesting dissonances I can in any given phrase of music whilst still making the music sound 'good'. This was enlightening.
That Max patch is amazing! Would you share it?
Mind-blowing as always!
Thank you so much for watching.
Beautiful and fascinating! Thank you.
Thank you for watching!
Thank you for these wonderful videos, Milton!
Great content! More please!
Your videos are so beautifully narrated. You remind me of Dan worrel from the fab filter tutorials who everyone loves for the way he speaks 😂
Very kind! *frantically google Dan Worrel*
❤ absolutely love your channel
Thank you so much - I really appreciate it.
@@miltonline I am so depressed you dont have 18m followers its ridiculous but I did find a friend today who LOVES your signification work and is making amazing music out of all kinds of things. I will share a link.
sonification autocorrect
@@IngridHurwitz Don't be depressed but thanks for you support. All best to you and your composer friend! (I've had to add sonification to my digital dictionary for this very reason).
I found the link.
ua-cam.com/video/UOlLsNV_K78/v-deo.html
Brilliant video
This has so much inspirational potential! I want to write/hear a chord progression defined by a pattern of changing shapes or find the most dissonant chord I can play on my guitar fretboard
I support this.
this is absolutely incredible, i was thinking a lot lately about three topics: numbers of shapes you can draw in the circle of semitones and their symmetries (i'm still looking for a more group theoric approach to this, but this is also really enlightening), quantifying dissonance, and the hendrix chord, which has been my favourite for forever, and you're combining these in one video, all centered around my fav chord. this could not have come at a better time. have you written any books, or what books would you recommend?
i was thinking about alternative ways to space out the notes, like you have the circle of semitones, the circle of fifths, and unfortunately those are the only 2 options up to inversions for circles (or really dodecagons i suppose), but i want it to be such that the space between the notes corresponds to their dissonance. the circle of fifths is better for that than the circle of semitones, but neither really represent thirds as a consonant interval. of course if you attempt a circle of either one of the thirds you end up with just a subset of all notes, but if you combine them they span all notes, and they are in fact the only, or at least in some way the purest combination of 2 generators. if you consider the notes as a mathematical group, you could use a semitone (s) as the generator, such that s^12 = e, and you get the integers modulo 12. But you can also look at the notes as the group with generators m and M where m represents a minor third, and M a major third, such that m^4 = M^3 = e, and mM = Mm. It is an isomorphism of Zmod12, so it is essentially still describing the rotational symmetries of a dodecagon, but if we want a shape with edges connecting all the thirds, such that all these connected vertices are also evenly spaced, i reasoned this would be possible in 4D. I figured out some properties of this shape and looked it up and it is apparently called a 3,4-duoprism. i have seen many mentions of the circle of fifths, but have literally found nothing about the duoprism of thirds. of course this shape doesn't represent that fifths are generally perceived as more consonant than thirds, and it also doesn't provide a very intuitive understanding since it's hard to actually visualise, but i wonder if there is an even higher-dimensional, and if necessary non-euclidean space in which we can really capture this dissonance to distance mapping. i need friends that care about this stuff
Does anyone know the name of that tool that Professor Mermikedes uses to display the interval vector? At 6m52s
Very interesting video. But I am not sure about that chart which maps consonance and dissonance. Because of concepts like those presented in the chart I was a big proponent for 5 limit just intonation music. But after working with it intensely for a decade, I came to realize that while out of context the intervals do not usually beat. Within the context of a piece of music, while listening not just vertically at the harmony, but also horizontally at the melodies and voices, listening in both directions, that it became abundantly clear, that 3 limit or Pythagorean intonation, is the true just intonation, both in chords and scales.
I personally hear the Pythagorean major third at 81/64 as in tune and the 5/4 I hear out of tune, especially when in the context of a piece of music. I also now hear the 32/27 Pythagorean minor third as more consonant, more in tune, than the 6/5 ratio. The notes in these dyads at the 3 limit ratios have more distinction from each other, while also expressing a ratio that can be easily understood by the brain, even the untrained one. Because all is just ratios based on powers of 2 and powers of 3. The powers of 3 give you all the notes, and the powers of 2 give you all the octave doublings, and so the brain can very easily track and hear these in a piece of music.
With 5 limit and higher limit harmonic notes with added dimensions and alternate versions of every note, the music while listening horizontally and vertically simultaneously (simultaneously is the key) sounds very out of tune.
But the chart of dissonance and consonance in the video would have one believe that the Pythagorean thirds both major and minor sound not only more dissonant than 5 limit intervals, but also more dissonant than equal temperament thirds. This is not at all my experience. The equal temperament thirds definitely sound worse than both the 5 limit and 3 limit intervals, for there is neither the vertical in tuneness of 5 limit, nor both vertical and horizontal in tuneness as heard in 3 limit. So considering all this, I think the chart, while interesting in a way, is very over simplified when it comes to how we perceive consonance and dissonance.
@miltonline I have a question on the dissonance curve, why is major 3rd considered more dissonant than major 6th or dominant 7th on this graph? Is it a cultural thing? On what kind of data is dissonance measured on this graph, is it based on an audience's perception, if so what kind of people from which regions of the world? I kind of know the major third is not used as a building block in africa, middle east and the balkans (parts of eastern europe), as opposed to western europe. Is this the reason why major 3rd is depicted as having higher dissonance on this graph, equal to tritone (the "devil's" interval)?
Such dIssonance contours are purely subjective (although can involve indirect measures) and have been tested on a wide cohort of ages and backgrounds (and even species). In short there seems to be a convincing biological basis (to a certain extent) for equating simple ratios with consonance, but this is highly malleable on individual/cultural experience.
Really outstanding video, I learned a lot. So your version of the Hendrix chord is C sus2 sus4 b5 which is a mirror of C b2 b5 and the Hendrix chord is E7#9 voiced as E E G# D E G, just wondering if I got that right.
Shortest answer: Yes, that's right and thanks for the feedback!
Short answer: we discard any repeats of notes so the Hendrix chord is just E G# D G. And we also reorganise it according to rules (below) so that all inversions are grouped together. 'C sus2 sus4 b5' is C D F F# - a D Hendrix chord which is the 'same' as the E Hendrix chord. So 'my version' of the Hendrix chord is how pitch-class set theory would automatically build it (0, 2, 5, 6) Yes that's a mirror of C Db E F# (0, 1, 4, 6 ) what I call the 'octatonic tetrachord'.
Long answer:Okay so pitch-class set theory 'normalises' all chords so that transpositions and inversions of the same chord are all grouped together - so A minor and D minor etc are in the same group, as are any inversions of these chords. The way P-C set theory does this is by thinking of a musical object as a chain of intervals. Notes are all in the same octave with the smallest gap possible between the outer two. Let's take the Hendrix chord which (since we don't care about octaves) is E G G# D. If we reorganise them as D E G G# (se 10:50) then we create the shortest possible range between first and last. Since we are also conflating all transpositions we can put the D at the top of the circle.
@@miltonline Thank you so much for your detailed answer. I plan to fire up my Mac to run your software as it looks like I can just enter in chords and have it calculate it so I can analyze the intervals. I am studying arabic music so its very important for me to study uncommon scales. About half the maqams (arabic scales) are diatonic, the rest use quarter tones.
Is there a source for 1:50? Thank you kindly for sharing knowledge btw
Sources like this should do the trick! en.xen.wiki/w/Gallery_of_just_intervals
@miltonline I have an objection to the use of interval classes, because it omits the root and whether the chord is open or closed shaped, which changes how consonant the interval and the chord is perceived, interval classes theory also doesn't align with the dissonance curve for the same reason, to root and the bass note, is the most important part of a chord, the interval from the root and bass to the chord tones determines the effect of the chord, not the interval classes in the chord. Interval classes is an oversimplification and would only work in close form chords where the notes are so closely stacked together and the bass is not obvious (useful maybe in solo guitar/solo stringed instrument music). But in a band or orchestra or a piano arrangement, pitch class theory is not useful, even the different tetrachords you have shown at the end, that have equal distributed interval classes, have different observed consonance because of their different root to chord tone interval relationships, as opposed to the same interval classes contained in the different tetrachords.
Yes, as stated PC-Set theory is super simplisitic (although remarkably powerful given how simplified it is). In reality harmonic dissonance is tied to octave spread, voicing, timbre of instrument, rhythmic and harmonic context and enculturation. No one viewpoint gives a complete picture, but many different lights can start to illuminate a large room.
❤️❤️🎵❤️❤️