Harmony and Interval Chart — Model Answers for a 13-year-old (Ally McBeal-style teacher feedback)

Clear, student-friendly model answers and step-by-step explanations for a Harmony and Interval Chart activity. Includes interval ratios (just intonation), descriptions of how each interval sounds, answers to follow-up questions, and playful teacher feedback in an Ally McBeal cadence.

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Harmony and Interval Chart — Model Answers

Use these as examples after you try the TeachRock synth. I used just-intonation (simple whole-number) ratios, because they show why some intervals sound pleasant and others tense.

  • Interval: C : D — Description: a little bright, slightly eager; not as stable as a fifth. — Ratio: 9:8
    Teacher (Ally McBeal cadence): "Ooh, nice ear! You heard that gentle lift — good job!"
  • Interval: C : E — Description: warm and pleasant, sounds like 'happy' harmony (major third). — Ratio: 5:4
    Teacher (Ally McBeal cadence): "Ahhh — that's nice and sweet — keep listening for that sweetness!"
  • Interval: C : F — Description: steady and stable but a bit open (perfect fourth). — Ratio: 4:3
    Teacher (Ally McBeal cadence): "Mmm — stable, grounded — I like how you describe that!"
  • Interval: C : G — Description: very stable, strong and pleasing (perfect fifth). — Ratio: 3:2
    Teacher (Ally McBeal cadence): "Yes! That one feels like home — sing it out!"
  • Interval: C : A — Description: warm but a touch more open/tension than the third (major sixth). — Ratio: 5:3
    Teacher (Ally McBeal cadence): "Lovely — a little richer, a little more grown-up — good observation!"
  • Interval: C : B — Description: slightly tense, sounds like it wants to resolve to C (major seventh). — Ratio: 15:8
    Teacher (Ally McBeal cadence): "Ooo — you noticed the pull! That wants to go somewhere — great listening."
  • Interval: C : C (octave) — Description: exactly the same note an octave higher; very stable and 'complete'. — Ratio: 2:1
    Teacher (Ally McBeal cadence): "Bam! That’s a perfect fit — like a hug. Nice and clear."

Answers to the Questions (step-by-step)

  1. List the ratios of the note pairings that you liked. What do you notice about these ratios?

    Example liked ratios: 1:1 (unison), 2:1 (octave), 3:2 (perfect fifth), 4:3 (perfect fourth), 5:4 (major third).

    What I notice: These ratios use small whole numbers (1, 2, 3, 4, 5). Intervals with small-number ratios sound more consonant, stable, and pleasant.

    Teacher (Ally McBeal cadence): "Yes — short, simple numbers = cozy sounds. You’re connecting math and feeling — bravo!"

  2. List the ratios of the note pairings that you disliked. What do you notice about these ratios?

    Example disliked ratios: 15:8 (major seventh), 5:3 (major sixth) might feel less stable or a bit tense compared with the simplest ones.

    What I notice: Ratios with larger or more complex numbers tend to sound more tense, dissonant, or like they want to move to another note.

    Teacher (Ally McBeal cadence): "Mmm — good ear! The bigger numbers make your brain pay more attention — that’s tension, honey!"

  3. What two notes have the largest ratio?

    Using the list above, the largest ratio is C to the higher C (octave) = 2:1. (If you counted a very high octave or other ranges, that number could be bigger, but in this chart 2:1 is the largest.)

    Teacher (Ally McBeal cadence): "Simple and powerful — the octave stretches the frequency the most in our basic list."

  4. What two notes have the smallest ratio?

    The smallest ratio is C to itself (unison) = 1:1.

    Teacher (Ally McBeal cadence): "Tiny, tiny — same pitch, same everything. You can’t get simpler than that!"

  5. How does the complexity of the ratio relate to the sound of the two notes being played together?

    Step-by-step idea:

    1. Ratios with small whole numbers (1:1, 2:1, 3:2, 4:3, 5:4) line up the sound waves more often. When waves line up regularly, our ears hear them as consonant (pleasant and stable).
    2. When the ratio needs larger numbers (like 15:8 or other complicated fractions), the sound waves meet less often and in more complicated patterns. That makes the interval sound tense, dissonant, or like it wants to move (resolve).
    3. So: simpler ratios = more consonant/pleasant; more complex ratios = more dissonant/tension.

    Teacher (Ally McBeal cadence): "Yes — math makes music make sense. You heard the pattern — now put it in your pocket and use it!"

Quick experiment to try on the synth

Play C with each note, one at a time. Try to hum along with the C and notice which notes make your humming feel steady (consonant) and which make it wobble or want to move (dissonant). Write one short sentence for each interval describing how it felt.

Teacher (Ally McBeal cadence): "Play it, feel it, write it — and tell me what you heard!"

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