Pedagogy benchmark · learner simulation
Can a beginner reach S60 in 12 weeks?
A deterministic simulator runs through the curriculum on behalf of three learner profiles. Each profile has explicit starting capacities (pitch production / discrimination, rhythm, breath, vocal quality, vowel stability, memory) and learning meta-parameters (motivation, learning rate). The simulator picks ready nodes session-by-session, simulates trials whose hit probability depends on capacity vs the node’s difficulty bar, advances mastery using the same gate the app uses live (≥ 80% hit rate AND ≥ 12 attempts), and reports whether the apex (S60 rescue-drill-selection) is reached within the 12-week window. Stubs (coach-only / formant-blocked / vibrato-blocked) are modelled as self-reported nodes whose pass-rate scales with motivation + learning rate.
Not in 12 wk
28 / 60
72
31.8 h
Verdict
Insufficient progress: only 28/60 interactive nodes mastered. This profile needs the foundation rebuilt — extend ear-training and pitch-production drills.
Trajectory
Cumulative mastered nodes by end of each week.
w1
w2
w3
w4
w5
w6
w7
w8
w9
w10
w11
w12
Starting capacity
Motivation 90% · Learning rate 85%
| Pitch production | 100 | ¢ median error |
| Pitch discrimination | 90 | ¢ JND |
| Rhythm | 200 | ms async |
| Breath | 3.0 | s sustain |
| Vocal quality | 35 | % clean |
| Vowel stability | 35 | % stable |
| Memory | 40 | % recall |
Ending capacity
Motivation 90% · Learning rate 85%
| Pitch production | 28 | ¢ median error |
| Pitch discrimination | 41 | ¢ JND |
| Rhythm | 61 | ms async |
| Breath | 7.5 | s sustain |
| Vocal quality | 86 | % clean |
| Vowel stability | 77 | % stable |
| Memory | 81 | % recall |
Per-phase mastery breakdown
How many nodes in each phase made it across the 80%-mastery / 12-attempts gate by the end of the 12-week window.
| Phase | Interactive | Stub | Total mastered |
|---|---|---|---|
| Foundation | 10 / 10 | 0 / 0 | 10 / 10 |
| Onset & solfège | 9 / 10 | 0 / 0 | 9 / 10 |
| Vowels & SOVT | 5 / 10 | 0 / 0 | 5 / 10 |
| Scale & dynamics | 1 / 10 | 0 / 0 | 1 / 10 |
| Bridge & range | 3 / 10 | 0 / 0 | 3 / 10 |
| A cappella | 0 / 10 | 0 / 0 | 0 / 10 |
Per-node trajectory
Which nodes the simulated learner mastered, when, and which stalled.
| Node | Phase | Skill | Attempts | Hit rate | Mastered |
|---|---|---|---|---|---|
| Red-flag self-screen and practice setup | Foundation | input-only | 1 | 100% | wk 1 |
| Alignment and release scan | Foundation | vocal-quality | 90 | 58% | wk 4 |
| Comfortable speaking-center map | Foundation | pitch-production | 18 | 78% | wk 2 |
| Silent inhale plus hiss exhale | Foundation | breath | 35 | 54% | wk 5 |
| Easy hum onset on /m/ or /ŋ/ | Foundation | pitch-production | 25 | 64% | wk 6 |
| Single-note match in comfortable range | Foundation | pitch-production | 60 | 67% | wk 7 |
| Same / higher / lower discrimination | Foundation | pitch-discrimination | 40 | 83% | wk 8 |
| Pulse clap with click | Foundation | rhythm | 96 | 68% | wk 1 |
| Single-vowel sustain on /u/ | Foundation | vocal-quality | 20 | 70% | wk 8 |
| Three-note siren within a fifth | Foundation | pitch-production | 15 | 93% | wk 7 |
| Coordinated onset on open vowel | Onset & solfège | vocal-quality | 30 | 80% | wk 8 |
| Smooth release / offset | Onset & solfège | vocal-quality | 20 | 85% | wk 10 |
| Two-note echo on neutral syllable | Onset & solfège | memory | 70 | 60% | wk 10 |
| so-mi with hand signs | Onset & solfège | memory | 30 | 73% | wk 11 |
| so-mi-la patterns | Onset & solfège | memory | 50 | 66% | wk 12 |
| Repeated-note stability in pulse | Onset & solfège | rhythm | 15 | 93% | wk 8 |
| Four-beat entry after count-in | Onset & solfège | rhythm | 20 | 85% | wk 8 |
| Five-note descending hum | Onset & solfège | memory | 32 | 59% | wk 11 |
| Hum-to-vowel transfer | Onset & solfège | vocal-quality | 16 | 88% | wk 11 |
| Short echo after 2-second delay | Onset & solfège | memory | 0 | 0% | — |
| Five pure vowels on one pitch | Vowels & SOVT | vowel-stability | 115 | 50% | wk 11 |
| Vowel switching on one pitch | Vowels & SOVT | vowel-stability | 30 | 67% | — |
| Jaw / tongue release while sustaining | Vowels & SOVT | vocal-quality | 0 | 0% | — |
| Straw or lip-trill sustain (SOVT) | Vowels & SOVT | breath | 40 | 68% | wk 7 |
| SOVT glide across a sixth | Vowels & SOVT | vocal-quality | 16 | 94% | wk 8 |
| Detect and reduce register event in a glide | Vowels & SOVT | vocal-quality | 15 | 87% | wk 9 |
| 1–3–5 arpeggio on trill or hum | Vowels & SOVT | pitch-production | 20 | 100% | wk 11 |
| Resting-tone / tonic finding after cadence | Vowels & SOVT | pitch-production | 0 | 0% | — |
| 4–5 note phrase from memory | Vowels & SOVT | memory | 0 | 0% | — |
| Degree prompts from tonic: do, re, mi, sol, la | Vowels & SOVT | pitch-production | 0 | 0% | — |
| Major pentachord up and down | Scale & dynamics | pitch-production | 0 | 0% | — |
| Minor and major third echo | Scale & dynamics | pitch-production | 0 | 0% | — |
| Perfect fourth and fifth echo | Scale & dynamics | pitch-production | 0 | 0% | — |
| Glide-to-discrete-note landing | Scale & dynamics | pitch-production | 0 | 0% | — |
| Soft vs medium contrast | Scale & dynamics | vocal-quality | 0 | 0% | — |
| Simple swell and decrescendo | Scale & dynamics | vocal-quality | 0 | 0% | — |
| Two-syllable legato phrase | Scale & dynamics | vocal-quality | 0 | 0% | — |
| Consonant-to-vowel clarity | Scale & dynamics | vowel-stability | 15 | 67% | — |
| Breath grouping for 6–8 second phrase | Scale & dynamics | breath | 15 | 93% | wk 8 |
| Two-phrase memory with clean restart | Scale & dynamics | memory | 0 | 0% | — |
| Siren across the main bridge / passaggio | Bridge & range | vocal-quality | 15 | 93% | wk 9 |
| Vowel modification on upward motion | Bridge & range | vowel-stability | 0 | 0% | — |
| Bright / narrow resonance cue | Bridge & range | vocal-quality | 30 | 67% | — |
| Speech-to-song three-note transfer | Bridge & range | pitch-production | 15 | 80% | wk 11 |
| One-octave scale fragment | Bridge & range | pitch-production | 0 | 0% | — |
| Tonic-dominant arpeggio | Bridge & range | pitch-production | 0 | 0% | — |
| Sing target degrees against tonic drone | Bridge & range | pitch-production | 0 | 0% | — |
| Straight-tone then optional natural vibrato release | Bridge & range | vocal-quality | 0 | 0% | — |
| Staccato in tempo | Bridge & range | rhythm | 24 | 79% | wk 9 |
| Five-note melisma | Bridge & range | pitch-production | 0 | 0% | — |
| Phrase transposition up or down a whole step | A cappella | memory | 0 | 0% | — |
| Call-and-response with one-note variation | A cappella | memory | 0 | 0% | — |
| A cappella eight-beat phrase resolving to tonic | A cappella | pitch-production | 0 | 0% | — |
| Verse-length breath planning | A cappella | breath | 0 | 0% | — |
| Emotional contrast via dynamics and vowel colour | A cappella | vowel-stability | 0 | 0% | — |
| Unison with guide voice | A cappella | pitch-production | 0 | 0% | — |
| Simple harmony line over drone | A cappella | pitch-production | 0 | 0% | — |
| Eight-bar simple song from memory | A cappella | memory | 0 | 0% | — |
| Self-diagnosis of miss type | A cappella | input-only | 0 | 0% | — |
| Independent rescue-drill selection | A cappella | input-only | 0 | 0% | — |