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Music Theory via Note Combinations

Music Theory via Note Combinations
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2020-11-09 04:27
PolygonFunctionCoordinate GeometryGeometric Construction
This example demonstrates the geometric representation of music theory using one note combinations via GeoGebra. It involves core math concepts like set theory, coordinate geometry, geometric construction, and function graphing. Key GeoGebra commands and objects used include Circle, Intersect, Polygon, Point, Area, and PointIn. Suitable for high school students and math enthusiasts exploring the intersection of music and mathematics.

GeoGebra Commands & Parameters

  1. Circle((0, 0), A) → a
  2. Circle((0, 0), Bb) → bb
  3. Circle((0, 0), B) → b
  4. Circle((0, 0), C) → c
  5. Circle((0, 0), Db) → db
  6. Circle((0, 0), D) → d
  7. Circle((0, 0), Eb) → eb
  8. Circle((0, 0), E) → e
  9. Circle((0, 0), F) → f
  10. Circle((0, 0), Gb) → gb
  11. Circle((0, 0), G) → g
  12. Circle((0, 0), Ab) → ab
  13. Intersect(a, yAxis, 2) → H
  14. Intersect(a, xAxis, 1) → I
  15. Intersect(a, yAxis, 1) → J
  16. Polygon(A, H, I, J) → q1, a_1, h, i, j
  17. Intersect(bb, yAxis, 1) → K
  18. Intersect(bb, yAxis, 2) → L
  19. Intersect(bb, xAxis, 1) → M
  20. Polygon(K, Bb, L, M) → q2, k, l, l_1, m
  21. Point(yAxis) → N
  22. Intersect(b, yAxis, 2) → O
  23. Intersect(b, xAxis, 1) → P
  24. Polygon(N, B, O, P) → q3, n, b_1, o, p
  25. Intersect(c, xAxis, 1) → R
  26. Point(yAxis) → S
  27. Polygon(C, Q, R, S) → q4, c_1, q, r, s
  28. Intersect(db, yAxis, 2) → T
  29. Intersect(db, xAxis, 1) → U
  30. Intersect(db, yAxis, 1) → V
  31. Polygon(Db, T, U, V) → q5, t, t_1, u, v
  32. Intersect(d, yAxis, 1) → W
  33. Intersect(d, yAxis, 2) → Z
  34. Intersect(d, xAxis, 1) → A_1
  35. Polygon(W, D, Z, A_1) → q6, w, d_1, z_1, f_1
  36. Point(eb) → B_1
  37. Intersect(eb, yAxis, 2) → C_1
  38. Intersect(eb, xAxis, 1) → D_1
  39. Polygon(B_1, Eb, C_1, D_1) → q7, g_1, h_1, i_1, j_1
  40. Point(e) → F_1
  41. Intersect(e, xAxis, 1) → G_1
  42. Polygon(E_1, E, F_1, G_1) → q8, e_1, e_2, k_1, m_1
  43. Intersect(f, yAxis, 1) → H_1
  44. Intersect(f, yAxis, 2) → I_1
  45. Intersect(f, xAxis, 1) → J_1
  46. Polygon(H_1, F, I_1, J_1) → q9, n_1, f_2, p_1, q_1
  47. Intersect(gb, yAxis, 1) → K_1
  48. Intersect(gb, yAxis, 2) → L_1
  49. Intersect(gb, xAxis, 1) → M_1
  50. Polygon(K_1, Gb, L_1, M_1) → q10, r_1, s_1, g_2, h_2
  51. Intersect(g, yAxis, 1) → N_1
  52. Intersect(g, yAxis, 2) → O_1
  53. Intersect(g, xAxis, 1) → P_1
  54. Polygon(N_1, G, O_1, P_1) → q11, i_2, g_3, o_1, j_2
  55. Intersect(ab, yAxis, 2) → Q_1
  56. Intersect(ab, xAxis, 1) → R_1
  57. Intersect(ab, yAxis, 1) → S_1
  58. Polygon(Ab, Q_1, R_1, S_1) → q12, k_2, l_2, m_2, n_2
  59. Area(ab) → u_1
  60. PointIn(ab) → Pointab
  61. Area(g) → v_1
  62. PointIn(g) → Pointg
  63. Area(gb) → w_1
  64. PointIn(gb) → Pointgb
  65. Area(f) → a_2
  66. PointIn(f) → Pointf
  67. Area(e) → b_2
  68. PointIn(e) → Pointe
  69. Area(eb) → c_2
  70. PointIn(eb) → Pointeb
  71. Area(d) → d_2
  72. PointIn(d) → Pointd
  73. Area(db) → o_2
  74. PointIn(db) → Pointdb
  75. Area(c) → p_2
  76. PointIn(c) → Pointc_{1}
  77. PointIn(q12) → Pointq12_{1}
  78. PointIn(q12) → Pointq12_{2}
  79. Area(a) → q_2
  80. PointIn(a) → Pointa
  81. Area(bb) → r_2
  82. PointIn(bb) → Pointbb
  83. Area(b) → s_2
  84. PointIn(b) → Pointb
  85. PointIn(q12) → Pointq12
  86. Area(c) → t_2
  87. PointIn(c) → Pointc

AI Drawing Prompt Reference

Draw 12 circles centered at the origin, each representing a note, then construct 9 quadrilaterals using the intersections of these circles with the axes, each quadrilateral representing a note combination.
The prompt above was compiled from the original drawing commands and is for reference only.