Three basic models to describe the western tone system

This is the first episode of a weekly blog post series on harmony theory. Our blog is different in three ways:

  1. We explain harmony theory using music apps. This allows you to checkout everything whenever and where you want. Simply switch on your iPad.
  2. We try to make sure, that you can read every episode within five to ten minutes. Thus the blog is also for people who don’t have much time at their hands.
  3. We found out that there are many overlooked symmetries in western harmony. Be one of the first who knows and talks about it.

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Symmetry Model

We call the theoretical concept discussed within this series “symmetry model”. It consists of some submodels which have one thing in common: All models are not oriented to the root of a certain key or a chord. Much more they are aligned to the so called symmetry tone. The goal of today’s episode is not to explain that in detail. Much more we want to introduce the first three submodels of the symmetry model.

Submodel 1: The key related circle of fifths

Already Pythagoras derived the diatonic scale by tuning tones in fifths. The key related circle of fifths takes that idea and arranges the white keys of the piano in a fifths order. The circle begins with the f and ends with the b. The tone in the center (d) is called symmetry tone.

The key related circle of fifths

Submodel 2: The key related circle of thirds

The second model is the key related circle of thirds. This system is perfectly suited for understanding chords and cadences. The tones are arranged in alternating major and minor thirds. Thus three neighbored tones result in major or minor triads. Again all tones are arranged symmetrically around the symmetry tone which defines also the start and the end of the circle.

The key related circle of thirds

Submodel 3: The key related melodic circle

The third model is the key related melodic circle. The circle arranges tones in major and minor seconds i.e. whole and half tone steps. Like the other circles this model is also aligned to the symmetry tone d. The strength of the key related melodic circle is the representation of melodic scales.

The key related melodic circle

Sound Demo

The following video demonstrates how the tones within the circle sound. It consists of three tracks. The first plays tones in a fifths order, the second in the third order and the last in the melodic order. At the end all three tracks are played together.

Next episode

In the next blog post we’re going to explain how the sound track of the previous was produced. We’ll talk about the iPad music apps used as well as how three models introduced before were applied.

Summary

  1. Three basic harmony models were introduced named key related circle of fifths, key related circle of thirds and key related melodic circle.
  2. Every of these models consists of the same seven tones. Only the order of the tones is different.
  3. Every model arranges the tones mirror-symmetrically around a so called symmetry tone respectively a symmetry axis.
  4. Together these models grab the most important properties of the western tonal system.

27 thoughts on “Three basic models to describe the western tone system”

  1. Here’s the “Just Intonation” view of where these tones come from.

    A familiar family of intervals presents itself in the lowest three octaves or so of the harmonics of a tone, which are simply integral multiples of the frequency of the original tone. The harmonics of the timbres of related tones match up and reenforce themselves into the scale systems that we know, as well as countless ones we can explore further!
    This true harmony was modified in the 19th century into 12 tone equal temperament, so that transpositions to other keys could be done on fixed pitch instruments, and for orchestras with wildly varying tonal restrictions could be brought into an equivalent tonal space.

    Another way of visualizing these intervals is as a spiral of tones, with each successive whorl representing another octave.
    Take a peek at http://www.jhhl.net/tonespiral.html for an interactive tone spiral display!

    An interactive tone spiral is also built into my app Droneo.

    1. Hi! Thank you for the comment and sharing the links. Yes, the link between western harmony and physics is absolutely amazing. I played a little bit around with your tone spiral. Its great! I never saw such an cool visualization of overtone series. Did you think about auralizing the spiral using web audio?

      1. Sure I’ll be adding sound to it. I had a version of this in Processing, I think, that did that, but Droneo is better because you can carry it around with you. What I really am up to is creating structures relating the notes of the generated scales to each other, and turning it into generated music with a new app.

      1. It’s a kind of continuous project; what’s probably going to happen is you’ll build a melody by clicking on the “dots.”

  2. So from what I can see from the key related cycle of thirds is that the root note is C as I have been looking at something at something similar but far more liniar that was written down for me by a guitarist friend for under standing 1,4,5s & 2,5,1s ect… So if I’m correct in my thinking the remaining Sub model 3 & 1 are also in C or are they more flexible models in D that can simply be rotated around the axis to be transposed… Hope you can help shed a little more light on this symmetry tone d… SP Pro & Orphion have had a lot of use in the last day… But I do want to take these models to real world instruments like my guitar & piano so I am really looking forward to this blog digging deeper into these concepts…
    Thanks for the help
    Brockalicious

    1. Hi. Thank you for your questions. Your are right, also sub model 3 & 1 are in C. To transpose it into another key some of the tones have to be raised or lowered. But this will be part of future episodes.

      You wonder why I align the models to the d? That’s truly a little complicated at the moment. Be sure that we will add many examples which show the sense of this step in future. :-)

      Best,
      Gabriel

  3. I really like these three visualizations, they display every possible interval in the natural major/minor scales. I’ve done this myself a long time ago but I didn’t realize the symmetry on D as shown here.

    Another neat visualization I noticed in C major for example is that it contains 3 pentatonic scales. The C F and G pentatonic scales all fit in the white keys.

    Another interesting thing is looking at the pentatonic scale as a combination of the major chord, its relative minor chord, and that symmetry note like D.

    I like looking at music in these neat little organizations because I don’t feel overwhelmed by possibilities. Its like painting a picture with two or three colors, I like creativity in restrictions.

    1. I’m with you on the Joshua Tree b-sides! Right on! In fact, so many of their b-sides are among my all time favorite U2 trkcas (this also goes for the Belle & Sebastian EPs and b-sides). While The Edge was my first guitar hero, and his tones are among my favorites, I still, to this day find them very hard to capture. However, the more I learn about amp tones and electric guitar playing, the more I appreciate The Edge’s dedication to the various, wonderful tones he has created over the decades. As with all great guitarists, the tone is in his ears and fingers and he makes it come through. It Might Get Loud gave his fans a rare glimpse into the inner working of his craft. Nice podcast.

      1. Contractor Support is very willing to work with us to make sure that we ended up with what we waentd. I can’t even count how many times we changed our minds about one particular part of the project and Dave (The contractor we hired through the service) not only helped us figure out what we waentd, but he was very good about making sure that the changes we waentd got done properly. contractorsupportonline

  4. Hey, thanks. BTW, in the text you use the term “melodic” for the the third model but in the video you use “diatonic” . Interchangeable? Even if you think so, consistency would be better at this stage.
    Interesting to see a novel take on these foundational concepts.

    1. Yea, this is a little inconsistency I should fix. Melodic and diatonic is not interchangeable. Strictly speaking all three models are diatonic because they only consist of standard scale tones. Thank you :-)

  5. So here’s a question regarding the symmetry tone; will it always be the second tonal note in the related key?

    1. Look up “Portal: Indian classical music” on Wikipedia. It’s a broad introduction from which you can link to WP entries the many traditions/styles of India’s deep and complex musical history/culture from which you can link to other online sources.

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