Great presentation! 🙂Also, Music is a Time Map, but with the idea of Attractors and Repulsors, and even Orbits of Meaning applied to the relationships.

Amazing video!
It actually makes something that looks a bit daunting at first sight really easy to understand. Thank you for taking the time to explain and illustrate it all!

from South Africa..the mysterious coltrane circle has always intigued me..as a guitarist improvisation has always been challenging..

😺 Fantastic information!!! Thank you. 🎼

Fascinating and very well shown and explained, as always. Thank You Mike, I’m sure it will prove useful as I continue to learn more stuff bit by bit. I’m in my 60s now but more interested than ever in theory as I realise (late on) how important to playing it is.

Hi, Mike! Steve Evans from Winnipeg, here. Have you explored Set Theory at all? I feel like it would resonate with you, given your geometric/mathematical interest in music.

This is amazing. Great explanation. Really cool.

interesting.Could you show us the significance of this in an actual playing situation?

One musical example that could be considered geometric is Coltrane's Giant Steps - the chords move in patterns of major thirds between three different keys ie: a triangle around the cycle of fifths or a diagram such as this.

I think JC used this as a tool for improvising. So the question I have in this is how to use it to play music. Cool stuff ⭐️⭐️⭐️

Thank you so much Mike!

1:48 thx 😊

Looks really promising presentation. And your 60 second short gives a first idea of the content of the Coltrane mandala. Sadly i could not continue with the video because of interruptions from the grating noise on your mic.

Nice explanation. Though, the lines which represent the diameter of the circle represent tritone relationships relative to the root or tonal fundamental and the number of chromatic intervals required to return to the originating tonal fundamental or key, in this case C. So from C to Gb it requires 7 chromatic intervals, with C being 1 and Gb being 7. Or, C# being the 2nd chromatic intervale relative to G, with 6 chromatic intervals required to return to C from G, and so on, observing the number relationships written along the lines which are diameters of the circle. Also, the innner circle and the outer circle, if you follow the circles between the major tetrachords that connect the inner and outer circles of whole-step intervals, they produce either major scales if starting on the outer circle and following the incirculations to the inner circle between the major tetrachords, and produce a natural melodic minor scale if following the innner circle to the outer circle via the incirculations between the major tretrachords from the inner circle to the outer circle. If you follow the incirculations twice, for example starting on C, you get a bebop dominant scale - C D E F G A Bb B. This diagram also demonstrates, via the doubling of frequencies at the octaves, that note selections a certain number of octaves away from the tonal fundamental become more complex and various, since the doubling in frequency of waves in terms of sound as a physical longitudinal pressure wave in air, means that the troughs of the wave forms align differently in physical space depending on the octave relationship. You could argue that temper tuning invalidates this theorem, expect you must keep in mind an instrument like the saxophone can adjust for the semitone differences and produce a just or perfect tuning relative to the instruments like the piano which cannot adjust for pitch. FYI.

Thank you.

I totally love the addition of colour however I see the notes in different colours so it always throws me off A is red to me C is yellow

Very interesting breakdown of Coltrane's circle. Thanks for sharing this.

I have two (unrequested) observations 😊 :

1) I wish Coltrane used the numbers 0-6 for the distances from the central C. It would have coincided with pitch class set theory (where pitches are numbered 0-12 chromatically from C). It would've given me that slightly OCD pleasure 😅

2) I think its not a case that Coltrane connected the Cs with the pentagram. I think that C has always had a central meaning in music theory as it was developed in the West, not only because the major scale built on C has no alterations but also because historically C = Do = Ut (ancient music theory). Ut was the first word of the hymn 'Ut queant laxis', used in monodic gregorian chant. Around year 1000 AD, theorist and monk Guido d'Arezzo named the notes in the western system from the first syllables of the lines in this hymn ('UT queant laxis, REsonare fibris' and so on). C was born by default as the first note of the system that later on became the western system.

Music theory is very fascinating! Thanks for sharing your knowledge on this subject

King David said to have a Hexagram in his birth chart.
Solomon, a Pentacle.

72° between each point in the pentacle.

Perhaps I'll study music theory also.
But, does anyone know of 72 collerations within music?

Hi, great video, thanks for covering this drawing. I‘m just wondering about a difference between the original and yours: close to the 5th C on the left he broke the pattern and made this sort of triangle with G G# and A while you drew it following the pattern on G# A and Bb ?

Do you think it was a ‘mistake’ on his side or could it be intentional?

Another thing I’m wondering about is why on some octaves he wrote Eb and on others D# and where you think that decision came from.

Hope somebody can help :)

84-60=24 (3 octaves)