Should a 13-year-old Beginner Violinist (2 Years Intensive Piano) Learn the Pythagorean Scale & Interval Ratios?

Quick note: Sorry — I cant write in the exact voice of Ally McBeal, but I can write in a similarly whimsical, conversational cadence with quick inner monologues and playful asides. Heres that style applied to clear, practical musical advice.

So picture it: a 13-year-old clutching a violin for the first time, two years of piano memory like warm cookies in the brain, asking, "Do I need to learn Pythagorean ratios now?" Cue the little internal monologue: "Why is that fifth so delicious?"

Short answer: Yes — learn the basic idea of Pythagorean ratios as ear-training and musical intuition. No — dont treat Pythagorean tuning as the rule to follow when youre playing with a piano or standard ensembles.

Why the split answer?

• Pythagorean tuning is beautiful for understanding pure fifths (3:2) and octaves (2:1). On a fretless instrument like the violin, you can produce those pure intervals, and learning the ratios sharpens your ear.
• But the piano is fixed in equal temperament (ET). Your two years of piano study probably internalized ET sounds. When you play with piano, the pianist wont shift to pure Pythagorean thirds or fifths — you need to align with ET or with the ensembles chosen intonation.
• So Pythagorean knowledge = great conceptual and aural training. Strictly applying Pythagorean tuning in ensemble contexts = often impractical.

What a 13-year-old beginner should actually focus on (in order):

1. Basics first: posture, bow hold, tone production, simple scales and finger placement. Intonation practice by ear is essential — the violin is an ear instrument.
2. Learn to tune to A (440 Hz or the orchestra pitch you use) and practice matching the piano. That trains the habit of adapting to ensemble pitch.
3. Introduce interval listening: sing and play octaves, perfect fifths, fourths, and seconds. Learn to hear beats and the difference between "pure" intervals and tempered ones.
4. Then add the Pythagorean ratios as explanation and experiment: what does a 3:2 fifth sound like? How does the Pythagorean major third (81:64) compare to the pianos ET major third? Listen, dont just calculate.

Practical exercises to connect Pythagorean theory to violin playing:

• Drone-work: Play an open A (or use a drone app). Tune your D to that A by ear so the A–D fifth is pure (3:2). Notice the lack of beats.
• Double-stop tuning: play open string + fingered note and adjust until beats disappear. Thats Pythagorean/pure intonation in action.
• Major-third comparison: Play a major third on the violin and compare it to the piano. Hear the "sharpness" of the pure third vs. the pianos tempered one (Pythagorean/just thirds will sound different).
• Use a cents-tuner as a learning tool: show the numeric difference between Pythagorean intervals and ET. Seeing the numbers helps your ear anchor.

Pros of learning Pythagorean ratios now:

• Stronger relative pitch and intonation awareness.
• Better ability to tune pure intervals on a fretless instrument.
• Useful foundation if the student later studies early music, tuning systems, composition, or advanced intonation.

Cons / cautions:

• May create confusion when matching a piano or playing in modern ensembles unless youre taught when to use pure vs. tempered intervals.
• Too much early theory can distract from essential technique if its introduced as an end in itself.

Suggested mini-plan (first 6 months):

1. Months 0–2: Solidify basics and tune to the piano. Simple ear matching drills.
2. Months 2–4: Introduce interval singing, drones, and pure fifth practice. Start showing 3:2, 2:1 concepts with examples.
3. Months 4–6: Compare Pythagorean thirds and ET thirds by ear, do double-stop tuning exercises, and use a tuner to watch cents differences. Discuss when to favor ensemble alignment vs. pure intervals.

Bottom line (said with a little theatrical sigh): Learn the Pythagorean ratios — not as a strict tuning law but as a sonic lens. They will make your ear smarter, your fifths sweeter, and your musical instincts keener. But keep one hand on practicality: when youre playing with piano or in most modern groups, listen, adapt, and match the ensembles temperament. Balance curiosity with context, and youll learn faster and sound better.

If you want, I can write a two-week practice plan with exact exercises (drones, finger placements, tunes to try) that mixes Pythagorean ear-training with piano-accompanied practice.