Musical Scales

ROUGH, INCOMPLETE, EDIT IN PROCESS......

[last updated: 2026-09-16]
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• What is a 'scale' ?
  • A scale is a set or collection of notes, almost always ascending.
    They most often have just 7 notes, though lots of scales have fewer notes.
    So for example, the "C-major" scale is composed of the notes: C, D, E, F, G, A, and B.

    Scales are used to compose and play musical pieces.
    That is, a given song will usually only have notes from a single scale,
        though of course that 'rule' gets violated all the time.
    The notes are chosen because they 'fit together' well with each other
    and provide the emotional character that the composer desires.

• Scale types:
  • The complete 12-note "chromatic scale" that makes up a keyboard octave is composed of all the notes from some starting note (the "tonic" or "root")
    up to the next occurrence on the keyboard of that tonic note.
    So the complete chromatic scale is composed of:
    A, A#, B, C, C#, D, D#, E, F, F#, G, and G#
    Notice that changing the tonic does not change the notes included in the complete chromatic scale, they are still those same 12 notes, it only changes the pitch.

    The full chromatic scale is almost never used for music composition.

  • Scales used in music composition are most often 7 notes, a subset of the full chromatic scale.
  • Scales are named with a descriptor phrase that starts with the root or tonic note, followed by the words that describes the type of scale.
    eg. C-major, or C-minor, or C-minor-7th
    The 'C' is the root or tonic, and will be the first note in the scale.
    The 'major' designates the 'type' of scale.
  • It happens that all scales of a given type will have a similar "sound", "character", or "emotional quality"
    So for example, all major scales will have a similar sound,
    which will be a different emotional character to the sound of a minor scale, and all minor scales in turn will have a sound similar to each other.
  • (partial) List of scale types:
    Major
    minor
    7th
    major blues
    minor blues
    pentatonic

    many others ...

• Construction of scales:
  • There are two methods that can be used to create a scale:
    • follow the characteristic pattern of number of semitones between notes,
    • or follow an algorithm.

  • The first scale, conventionally used as a reference point for all others,
    is the C-major scale.
    • It is built with the algorithm:
      Start with your desired tonic C,
      and play all the white keys up to the next C

      So the C-major scale is composed of the notes:

      C, D, E, F, G, A, and B.
    • From this starting/reference C-major scale you can extract the semitone pattern
      that is characteristic of and in fact defines all major scales.
    • Notice that the pattern of semitone increments for the C-major scale is:
      2, 2, 1, 2, 2, 2, 1
      That is, C-to-D is 2 semitones,
      D-to-E is 2 semitones,
      E-to-F is 1 semitone,
      F-to-G is 2 semitones,
      G-to-A is 2 semitones,
      A-to-B is 2 semitones,
      B-to-C (the tonic one octave higher than starting point) is 1 semitone.

      If this semitone pattern is used to construct a different scale, starting from a different tonic note,
      it will still be a "major" scale, but now with the new tonic.

• Semitone interval patterns for scale types:
  • major: 2 - 2 - 1 - 2 - 2 - 2 - 1
  • minor: 2 - 1 - 2 - 2 - 1 - 2 - 2
  • major-pentatonic: 2 - 2 - 3 - 2 - 3
  • major-blues: 2 - 1 - 1 - 3 - 2 - 3
  • minor blues: 3 - 2 - 1 - 1 - 3 - 2
  • ...

• Construct a scale using the semitone-interval-pattern method:
  • Choose your desired tonic note.
  • Choose the scale type you want, eg. "minor"
    Get the semitone pattern that defines that scale type from the list above.
  • Starting with your tonic note, build each successive note in the scale
    by adding the number of semitones from the pattern.

  • So for example, to construct a B♭-minor scale,
    which will use the semitone pattern:
    2 - 1 - 2 - 2 - 1 - 2 - 2

    The notes will be:

    B♭ (the tonic),
    C (2-semitone increment),
    C# (1-semitone increment),
    D# (2-semitone increment),
    F (2-semitone increment),
    F# (1-semitone increment),
    G# (2-semitone increment),
    A# (2-semitone increment to return to the tonic - A# = B♭ - one octave higher)

    
    .

• Construct a scale using the algorithm method:
  • ...

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• The major scale is the foundation of western music, and is used as a reference point for constructing other scales.
  • The algorithm for creating the C-major scale is:
    Start with the C, and play all the white keys up to the next C.
  • To build a major scale using the step-interval method:
    start from the root or tonic note,
    add successive notes that are increased by some increment,
        either a whole step (2 semitones), or a half step (1 semitone)
  • Each scale type (see list above) has a characteristic pattern of steps between each of the notes.
  • Major scales are built with the pattern:
    whole or half steps: w - w - h - w - w - w - h
    OR: number of semitones: 2 - 2 - 1 - 2 - 2 - 2 - 1
    Note: This method requires a total of 12 semitones,
    which return you to the tonic note, one octave higher.
  • So for example:
    The C-major scale will start with the root or tonic C.
    The second note will be D, an increase of 2 semitones.
    The third note will be E, an increase of 2 semitones.
    The fourth note will be F, in increase of 1 semitone.
    etc...
  • All major scales can be built using this pattern.
    Start with the tonic note, and add successive notes, increasing by the number of semitones as specified by the pattern.
    Other possible scales in addition to C include all the notes of the piano: C#, D, D#, E, F, F#, G, G#, A, A#, and B
• Construction of other scale types:
  • For example: If you want to create a C-minor scale,
    • The first method is to start with the tonic, and follow the pattern of intervals for minor scales, which is:
      2 - 1 - 2 - 2 - 1 - 2 - 2

      This will produce the C-minor scale:

      C, D, D#, F, G, G#, A#
    • The second method is to follow an algorithm,
      which are unfortunately poorly documented and can be confusing.
      But for a minor scale, the algorithm is straight-forward, and says:
      "Starting with the major scale (C-major = C, D, E, F, G, A, B)
      flat the 3rd, 6th, and 7th degree notes"

      So in C-major, the 3rd degree note is E, so flatting it, ie. replacing it with its 'flat' (E♭ = D#),
      the 6th degree note is A, so its flat is G#,
      and the 7th degree note is B, so its flat is A#,
      resulting in:

      C, D, D#, F, G, G#, A#
      ie. the same result as from following the interval pattern.

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• Other stuff...
  • Each 'complete' scale will contain 7 notes, (not including the duplicated octave note)
    with a total delta, from the first tonic to the next octave of the tonic, of 12 semitones.

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