Harmonic Wheel (and synesthesia on a side note)

[OHNE]

Has anyone heard of the harmonic wheel? I wanted to paint a circle of fifths as a “cheat sheet” of sorts, to put on my piano, but then I stumbled upon a fascinating image. This one:

I’m a sucker for charts and symbols especially when it comes to music so I investigated further. Turns out it is a variation on the concept of the circle of fifths, only it contains a massive amount of information and it is intended to be used as a tool for composition. Apparently, this is the invention of a Spanish tutor and he has sold copies of the wheel on Amazon for a while, but they are out of print. Or so I believe. I wrote the guy asking if he had any for sale but didn’t get an answer. So I just went ahead and made my own //

I’m still figuring out how to use it, but it’s such a useful tool. Over the past years I have been scribbling notes and charts and overviews of music theory in little notebooks, scraps of paper, digital notebooks, folders on my pc and so forth, but it looks like all I will ever want to know about music is hidden in patterns on the harmonic wheel It’s pretty cool.

Structurally, it is nothing more than five nesting circles of fifths, with an offset of 90° clockwise from the outside to the inside. The resulting positions gives information about scales, chords, chord functions and all the usual, essential stuff I keep forgetting. You need to remember the patterns but as a visual artist myself, my brain is wired to respond to shapes and colors.

This is the shape of a major scale. Just one position to the left and two positions to the right, and one circle outward contains all the notes you need.

But it also gives you the notes of all the triads and fourth chords in that scale.

These are the shapes for C-7, CMaj7 and C7:

And of course, you can apply these shapes to any note by just rotating the wheel. What I find most gratifying is the way you can easlily see the relation between chords that have overlapping notes. Jumping from a G-7 to a EbMaj for example is just changing one note, but that’s not something I come up with on an ordinary day. On this wheel it very easy to make these jumps and see interesting movements and progressions.

Colors / Synesthesia

Warning: esoterica ahead

It was also a lot of fun drawing this thing but there was one challenge that I spent quite a bit of time on: deciding what colors to use for the notes. This is not at all part of the harmonic wheel, but it was part of my original idea to make the cheat sheet. In order to facilitate learning (both for myself and my four year old son) I’m interested in the concept of synesthesia. My synesthetic experience is not well developed, but I believe it is something we can train, especially starting on an early age. Colors and musical notes are just vibrations and frequencies after all, so it’s easy to see how they can correlate. But since I’m not particular opinionated about the topic, I just had to do some research. Turns out people have been assigning colors to notes (and vice versa) for a long time.

Scriabin is very well known for this, but he was also a little bit of an odd one out, assigning colors based on the positions of the notes in the circle of fifths, rather than ascending or descending pitch. After pondering about the subject for a bit I decided to take my cues from a completely other field of study, namely that of the chakra system. The rationale being that these have been assigned colors for a very long time, on top of their correlation with musical notes. In the basic chakra system there are seven energy centers so it all maps out perfectly to a diatonic scale. I even read one particular book that mapped these notes very specifically to the energy centers of the body in both the diatonic scale and the chromatic 12 twelve note scale. Anyway, that’s just a side note.

I did my best to map these colors to the twelve notes and also went ahead and color coded my keystep. It looks like a toy now but hey, real men let go when it fits to the music.

What do you all think? Are you using a tool like this one, do you have synesthetic experiences? Do the color match your own set? Are there any other diagrams that I want to know about?

By the way
the website of the guy who invented the wheel is down (it went offline just as I started my investigations). There is a spanish version but it doesn’t have all the explanations like it did on the English site. And on YouTube there is a series dedicated to the wheel (also in Spanish). I watched it and it is very instructive, but also very dry indeed.

[chalkwalk]

As a general thought, I consider the circle of fifths to be the fundamental mechanism by which I understand harmonic relations (alongside the harmonic series). In particular, the traditional Western 5 and 7 note scales are notes in contiguous arcs from that circle (the note in the arc you consider the root decides which mode). As the interval extends further anticlockwise from the root you get darker scales (ending in the locrian), as it extends clockwise your get brighter scales (ending in the Lydian). Similarly when constructing chords you can add notes to the root clockwise to make brighter chords (stack of fifths) and anticlockwise to make darker chords stack of fourths).

I’ve seen lots of “cheat sheets” with concentric circles, or circles with sliding “windows” to create chords and scales. Another interesting one is the spiral of fifths (like what you are looking at I believe). For me, one of the most compelling aspects of this approach is that a lot of the logic doesn’t only apply to 12-EDO scales, but more generally to any N-EDO. You can construct an equivalent music theory in a many such scales (if the 3rd harmonic lies at an interval not coprime with the tone count the circle may be considered incomplete).

[Gahlord]

I think this might be a good place to put Coltrane’s harmonic wheel as well. You can find a copy of it in Yusef Lateef’s book.

[OHNE]

Ah yeah, I know the drawing but I never considered myself smart enough to try and understand it But it’s probably not that scary. Looks good too, thanks for sharing.

[ElectricaNada]

This kind of wheel diagram goes way back. Dick Grove created a wheel diagram like this that he called “the grid”. He was teaching it already by the late 1970s. You can find the diagram in his book “Advanced Modern Harmony".

[OHNE]

Anything more you can share about it? I don’t know Dick Grove and can’t seem to find the diagram.

[Gahlord]

I haven’t dug into Dick Grove’s work in any depth but it looks to me like a Los Angeles variation of the Schillinger System. He ran a small music school and lessons-by-mail company and was apparently charismatic in a gruff way.

[mzero]

Nit: The colors in that chakra chart are misnamed: indigo and violet are swapped!

But on the whole: There really isn’t any rational physical correspondence between pitch classes (C, D, E, etc…) and colors… nothing really “works”: colors don’t have octaves, harmonics and intervals don’t work in light as they do in sound, C is totally arbitrary as a starting point, but red is true bound in how we see. Further, the division into 7 notes derives from the diatonic scale, 12 from desire to modulate, and both have a basis in how the ear hears simultaneous tones. On the other hand, the division of the color spectrum into 7 colors is a culturally learned division - other cultures have different divisions, and it leads to how those people not only name colors, but also how they perceive them.

In short: Sure, assign colors to pitches as form of mnemonic, but there really isn’t any universal justification for one system over another.

[ElectricaNada]

Grove studied the Schillinger system, but he was a jazz composer and arranger — focused intently on practicality, not theory — and his wheel is not found in Schillinger. I don’t claim the wheel is original to him. I bring him up because his work shows that the wheel concept clearly goes back to the 70s and probably earlier.

[OHNE]

I don’t think I have made claims about a universally “true” correlation between the two perceptions, except that some people do experience it as such, and I believe it can be developed and used for example as a mnemonic tool as you say, or as a way to see structures, make compositions, etc. It is this experience that really interests me, not if the experience is “right” or justified. Also, arbitrary choices can take a life of their own as it is adopted by groups of people and cultures, to an extend that the arbitrary nature of the origin ceases to be of significance.

[ElectricaNada]

I took a class with Lalo Schifrin where he asked us to orchestrate the color orange. He approved of some of my classmates’ work but rejected others, offering criticisms such as “That’s not orange; it’s purple”.

[Gahlord]

Certainly earlier than the 70s because Coltrane’s was given to Yusef Lateef in 1967. But if want to get genuinely old with it we’d have to find versions of it that predate Nicolay Diletsky’s from 1679.

While we’re here, there’s of course the Guidonian Hand but I don’t think that’s quite a circle of fifths thing since it predates tonal functional harmony.

[ElectricaNada]

I haven’t been able to interpret the Coltrane diagram, but I don’t think it and your other examples show all the relationships that OP’s wheel does. Dick Grove’s wheel contains those and more.

[Gahlord]

I would add here that just as other people with different acculturation may have different color anchors, so too people with different acculturation may not hear in diatonic harmony in the way that tonal functional harmony acculturates us to hear. Tonal functional harmony and all that goes along with it (modulation, for example) has only been a given in European-derived societies for maybe 300ish years.