Graphical Chord and Scale Calculator,

by Michael Horvath



Use alternate polygon type.
Mark each step using arrows.



This is a musical chord and scale calculator. It allows you to select an interval, chord or scale and find the chord(s) or scale(s) possessing coincident notes or intervals. For instance, the Major seventh chord (maj7 or M7) is based on the Major triad, with an additional Major seventh interval added on to it. Therefore, it will be displayed when finding the matching or fitting objects for the Major triad. Further, the interval between the second and third steps of this chord is a minor third; therefore, the minor third interval will be displayed as well.


  1. Set the key in form #1. This rotates the entire diagram so that the selected note is at the top of the circle. (Note that the term "key", as it is used in this document, is not related to the key signature.)
  2. Set a root note in form #2. Each chord or scale has a root note. Set this in the second form field. You can set the root note to match the setting for key by clicking on the "Match key" button.
  3. Select a chord or scale in form #3.
  4. Find matching items. This command will display a list of chords or scales in form #4 that are calculated to be contained within or outside of the selected chord or scale. You can confirm this by checking whether the polygon for a chord is contained within the polygon of the fitting scale, for instance.
  5. Hide or show objects. You can make an interval, chord or scale visible/invisible in the diagram by clicking on the "Display/reset selected object" and "Clear selected object" buttons.
  6. You can also move each object around the circle using the mouse by dragging the point in the diagram that is labeled the same as the object.

Issues & further considerations:

  1. Dragging the objects around the circle does not update the form fields. (I'm still considering whether it in fact should do so.)
  2. A convex polygon may not be the best representation for a chord or scale when the interval between steps is greater than six semitones.
  3. Related to #2 is the issue of how best to represent steps that lie in another octave. I've considered adjusting the labeling of each step in order to reflect this, as well as changing the lightness or darkness of an object depending on its pitch or octave. However, I'm not sure this is achievable in GeoGebra.
    Update: Recent versions of GeoGebra allow one to adjust the coloring of objects dynamically based on mathematical formulas. As a result, the latter option may now in fact be feasible.
  4. "Minor" and "major" chords and scales are typically capitalized with a lower-case or capital "M" depending on whether the component chords and intervals are minor or major, respectively. I've chosen to disregard this naming scheme at the present time as I am not sure it is really worth implementing.

Download an older Geometer's Sketchpad version of this worksheet here.

Creative Commons License LGPLv3 License
Content is licensed under a Creative Commons Attribution-Share Alike 4.0 Unported License. Software is licensed under a GNU Lesser General Public License version 3.