Question

When adult beginners practise imitating pitches and vowels, does adding vibrotactile feedback that encodes their real-time pitch or formant error, under otherwise identical audiovisual conditions, reduce their pitch-imitation error 24 hours later, with no feedback of any kind, compared with wearing the same device switched off?

The framework’s question concerns “imitation learning of complex pronunciation or movement”. This protocol chooses vocal production: pitch (fundamental frequency) and vowel formants can both be measured objectively and automatically from recordings, with well-established algorithms (see the program below). Because a vocal task is closer to the author’s singing-training business, the protocol strengthens its arrangements for independence (see the ethics section).

Placing the primary outcome after feedback is withdrawn is deliberate. The “guidance hypothesis” from research on motor learning holds that frequent, immediate augmented feedback can raise performance during practice yet make learners depend on it, so that retention is worse once it is removed (Salmoni et al. 1984). The trial therefore looks not at how accurately people sing during training but at how they perform 24 hours later, without the device and without feedback.

The trial tests the idea in the hypothesis box of Chapter 3. It borders on the subjects of volume 10 (the biomechanics of phonation), volume 23 (deliberate practice) and volume 29 (auditory–motor feedback); it only cross-refers to them and does not repeat their material.

Measurement

On each trial the participant hears through headphones a target tone of about 1.5 s (a synthesised voice in the register of the participant’s sex, on the vowel /a/), and after a cue sings the same pitch on /a/ for about 2 s. The fundamental frequency is estimated over the stable middle second of each trial with the YIN algorithm (Cheveigné and Kawahara 2002), the median is taken and compared with the target:

$$e = 1200\,\log_2\frac{f_0}{f_t},$$

where $f_t$ is the fundamental of the target and $e$ is in cents, with 100 cents to a semitone. This measure (the stable middle, its median, conversion to cents, then the mean of the absolute values) is the one used in the pitch assessment of Chapter 8 of volume 10, which read the fundamental in Praat; it is not repeated here, and only the estimation algorithms for the fundamental and the formants are added as a sketch. Formants are estimated from the peaks of a linear-prediction (LPC) envelope (Makhoul 1975), and the vowel error is the Euclidean distance of the deviations of F1 and F2, each measured in semitones. The program below uses only the standard library to show how the two steps work: it synthesises a vowel with known fundamental frequency and formants, then estimates them back.

# How the Chapter 8 outcomes are measured: a SIMPLIFIED sketch, not lab software.
# A vowel is synthesised (pulse train -> glottal low-pass -> 4 formant resonators,
# sampling rate 10 kHz); f0 is recovered with YIN (de Cheveigne & Kawahara 2002:
# difference function, cumulative-mean normalisation, threshold 0.1, parabolic
# interpolation) and F1/F2 from the peaks of an order-12 LPC envelope (autocorrelation
# method, Levinson-Durbin; Makhoul 1975). Pitch error in cents = 1200 log2(f0 / target).
# Formant distance = Euclidean distance of F1 and F2 in semitones (st). Formant values and
# the "sung" errors are ILLUSTRATIVE; a real trial would use validated software.
import cmath, math, random, statistics

FS = 10000

def vowel(f0, formants, rng, dur=0.25):
    n = int(FS * dur); x = [0.0] * n; t = 0.0
    while t < n:
        x[int(t)] = 1.0; t += FS / f0
    for _ in range(2):                                   # glottal roll-off
        y = 0.0
        for i in range(n):
            y = 0.9 * y + x[i]; x[i] = y
    for f, bw in formants:                               # cascade of resonators
        r = math.exp(-math.pi * bw / FS); c = 2 * r * math.cos(2 * math.pi * f / FS)
        y1 = y2 = 0.0
        for i in range(n):
            y = x[i] + c * y1 - r * r * y2; y2, y1 = y1, y; x[i] = y
    peak = max(abs(v) for v in x)
    return [v / peak + rng.gauss(0, 0.002) for v in x]

def yin(x, start, fmin=70, fmax=600, w=300, thr=0.1):
    tmin, tmax = int(FS / fmax), int(FS / fmin) + 1
    d = [0.0] + [sum((x[start + j] - x[start + j + t]) ** 2 for j in range(w))
                 for t in range(1, tmax + 2)]
    cm, run = [1.0], 0.0
    for t in range(1, len(d)):
        run += d[t]; cm.append(d[t] * t / run)
    t = next((t for t in range(tmin, tmax) if cm[t] < thr), None)
    if t is None:
        t = min(range(tmin, tmax), key=lambda k: cm[k])
    while t + 1 < tmax and cm[t + 1] < cm[t]:
        t += 1
    a, b, c = cm[t - 1], cm[t], cm[t + 1]
    return FS / (t + 0.5 * (a - c) / (a - 2 * b + c))

def lpc_formants(x, start, p=12, w=300):
    s = [x[start + i] - 0.97 * x[start + i - 1] for i in range(w)]
    s = [v * (0.54 - 0.46 * math.cos(2 * math.pi * i / (w - 1))) for i, v in enumerate(s)]
    r = [sum(s[i] * s[i + k] for i in range(w - k)) for k in range(p + 1)]
    a, e = [1.0] + [0.0] * p, r[0]
    for i in range(1, p + 1):                            # Levinson-Durbin recursion
        k = -sum(a[j] * r[i - j] for j in range(i)) / e
        a = [a[j] + k * a[i - j] if 0 < j < i else a[j] for j in range(p + 1)]
        a[i] = k; e *= 1 - k * k
    def gain(f):
        w0 = -2j * math.pi * f / FS
        return 1 / abs(sum(aj * cmath.exp(w0 * j) for j, aj in enumerate(a)))
    fs_ = list(range(150, 4000, 5)); g = [gain(f) for f in fs_]
    peaks = [fs_[i] for i in range(1, len(g) - 1) if g[i - 1] < g[i] > g[i + 1]]
    return peaks[0], peaks[1]

def semis(a, b):
    return 12 * math.log2(a / b)

if __name__ == "__main__":
    rng = random.Random(34)
    A = [(700, 80), (1200, 90), (2500, 120), (3500, 150)]   # illustrative /a/-like vowel
    comfort = 150.0                                       # participant's comfortable f0
    sung_err = [+35, -20, +60, -45, +10]                  # illustrative "true" errors
    print("target  steps  true err  YIN f0   measured err (cents)")
    meas = []
    for st, err in zip((-4, -2, 0, 2, 4), sung_err):
        target = comfort * 2 ** (st / 12); sung = target * 2 ** (err / 1200)
        x = vowel(sung, A, rng)
        f0 = statistics.median(yin(x, s) for s in (800, 1100, 1400))  # stable middle
        meas.append(1200 * math.log2(f0 / target))
        print(f"{target:6.1f}  {st:+4d}  {err:+8d}  {f0:6.1f}  {meas[-1]:+8.1f}")
    print(f"mean absolute error: true {statistics.mean(map(abs, sung_err)):.1f},"
          f" measured {statistics.mean(map(abs, meas)):.1f} cents")
    print("formants of the same vowel (true F1 700, F2 1200) as f0 rises:")
    for f0 in (110, 220, 330, 440):
        f1, f2 = lpc_formants(vowel(f0, A, rng), 1200)
        dist = math.hypot(semis(f1, 700), semis(f2, 1200))
        print(f"  f0 {f0:3d} Hz: LPC F1 {f1:4d}, F2 {f2:4d}; distance {dist:4.2f} st")
# target  steps  true err  YIN f0   measured err (cents)
#  119.1    -4       +35   121.6     +36.1
#  133.6    -2       -20   132.0     -21.0
#  150.0    +0       +60   155.4     +61.6
#  168.4    +2       -45   164.0     -46.0
#  189.0    +4       +10   189.9      +8.1
# mean absolute error: true 34.0, measured 34.6 cents
# formants of the same vowel (true F1 700, F2 1200) as f0 rises:
#   f0 110 Hz: LPC F1  690, F2 1200; distance 0.25 st
#   f0 220 Hz: LPC F1  665, F2 1175; distance 0.96 st
#   f0 330 Hz: LPC F1  665, F2 1225; distance 0.96 st
#   f0 440 Hz: LPC F1  455, F2  895; distance 9.02 st

The five targets in the program lie 2 and 4 semitones above and below the participant’s comfortable pitch (150 Hz in the example), and the “sung” errors are illustrative settings. The errors estimated by YIN differ from the settings by 1.0 to 1.9 cents (from simplifications in both synthesis and estimation, for instance pulses that can fall only on whole samples), and the mean absolute error over the five trials is 34.6 cents against a true 34.0, far below the smallest effect of interest of 20 cents used below. Formants are another matter: at a fundamental of 110 Hz the LPC estimates of F1/F2 are off by only 0.25 semitones, but at 440 Hz the harmonics are sparse and the envelope peaks are “captured” by them (F1 455 Hz, F2 895 Hz, close to the harmonics at 440 and 880 Hz), a distance of 9.02 semitones. The protocol therefore keeps formants as a secondary outcome, has every vowel trial sung at the participant’s comfortable pitch, and specifies in advance that estimates are spot-checked against spectrograms by staff unaware of allocation. The real trial uses validated speech-analysis software, with all settings published before enrolment.

Design

The mean absolute error in cents was chosen as the single primary outcome because it is a common measure of imitation accuracy in research on singing, computed automatically with algorithms such as YIN and needing no raters (Hutchins et al. 2014); and because, as a continuous measure, it keeps more information than a dichotomous measure such as “the proportion within ±50 cents” and does not hit a ceiling for people who already sing fairly accurately. Formant measurement depends on the fundamental (see the program above), so formants are a secondary outcome.

Pilot and re-estimation of the sample size

The author found no published effect size for “training pitch with vibrotactile feedback” that could be borrowed, and the between-person standard deviation of the error can only be roughly inferred from published means. Most published studies report means: 78 adults imitating single pitches had a mean absolute error of about 66 cents (Demorest and Pfordresher 2015); in the second experiment of Pfordresher and Brown (2007), 7 of 45 people (16 %) were poor-pitch singers, with a mean absolute error of 229 cents against about 30 cents for 7 matched accurate singers (Pfordresher and Brown 2007). In another study, 22 participants imitating five target pitches with their voices had a mean absolute error of about 38 cents (Hutchins et al. 2014). Such distributions are strongly right-skewed: a minority of poor-pitch singers raises both the mean and the standard deviation. The trial in Chapter 8 of volume 10 used the same outcome (mean absolute pitch error over five target notes) and assumed a between-person standard deviation of 20 cents, to be checked in a pilot; on the figures above that assumption is probably too low for unselected adult beginners, so this book takes a more cautious planning value (below) and leaves it to the pilot to re-estimate.

The protocol therefore has two steps. First, a small external pilot with n = 20 (10 per arm, same protocol as the main trial) tests the procedures and estimates the standard deviation of the 24-hour error and its correlation with baseline. Pilot data do not enter the main analysis. Second, the sample size of the main trial is recalculated by a rule written as code in advance:

1. The standard deviation is the one-sided 80 % upper confidence limit of the pooled within-arm pilot standard deviation (18 degrees of freedom) (Browne 1995). Sim and Lewis (2012) also used the upper-confidence-limit approach, but with a 95 % limit, and argued that the size of a pilot should be set by considerations of precision and overall efficiency; their analysis points to pilots of about 55 people or more in total (Sim and Lewis 2012). By the author’s decision this protocol uses only 20, at the cost that the upper limit inflates the standard deviation 1.183-fold and the sample size about 1.40-fold.
2. The correlation with baseline is the pilot estimate, but no higher than the planned 0.6 and no lower than 0.
3. The effect size is not estimated from the pilot. The smallest effect of interest is fixed in advance at 20 cents (about one fifth of a semitone) and does not change with the pilot. With 10 per arm the standard error of the difference between arms is about 27 cents, larger than the smallest effect of interest itself; a sample size based on such an estimate would be randomly too large or too small, and proceeding only when a pilot “looks effective” leads later studies systematically to overestimate the effect and underestimate the numbers needed (Kraemer et al. 2006). The pilot statistician therefore reports only the pooled standard deviation and the correlation, and neither computes nor reports the difference between arms.
4. The final number of analysable participants per arm is bounded between 150 and 350: the lower bound protects against a pilot standard deviation that happens to be small making the trial too small; the upper bound is a constraint of feasibility. If the rule gives more than the upper bound, the trial runs with 350 per arm, and the registration states that the actual power at the pilot values is below 90 %.

# Sample size for the Chapter 8 trial, with a pre-registered re-estimation rule.
# Primary outcome: mean absolute pitch error (cents) when imitating 5 target notes,
# 24 h after training, without feedback. Planning values, all ASSUMED:
#   SD between people 75 cents (published means only; see the check below),
#   correlation with baseline r 0.6, smallest effect of interest (SESOI) 20 cents,
#   two-sided alpha 0.05, 90 % power, 15 % loss. ANCOVA on the baseline shrinks the
#   variance by (1 - r^2) (Borm, Fransen & Lemmens 2007).
# Pilot rule: external pilot, n = 20 (10 per arm), never in the main analysis. An
# independent statistician reports only the pooled within-arm SD (df 18) and r.
# SD used = one-sided 80 % upper confidence limit (Browne 1995); r used = pilot r, but
# never above the planned 0.6 nor below 0. SESOI stays 20: the pilot never estimates
# the effect. Final n is clamped to [150, 350] analysable per arm.
import math, random
from statistics import NormalDist
N = NormalDist()
SESOI, LOSS, N_MIN, N_MAX = 20.0, 0.15, 150, 350

def per_arm(sd, delta, r, alpha=0.05, power=0.90):
    z = N.inv_cdf(1 - alpha / 2) + N.inv_cdf(power)    # +1 below ~ t correction z_a^2/4
    return math.ceil(2 * z ** 2 * sd ** 2 * (1 - r ** 2) / delta ** 2) + 1

def chi2_cdf(x, k):                          # regularised lower gamma P(k/2, x/2), series
    a, y = k / 2, x / 2
    term = total = 1 / a
    for i in range(1, 500):
        term *= y / (a + i); total += term
    return total * math.exp(-y + a * math.log(y) - math.lgamma(a))

def chi2_ppf(p, k):
    lo, hi = 1e-9, 10 * k + 100
    for _ in range(100):
        mid = (lo + hi) / 2
        lo, hi = (mid, hi) if chi2_cdf(mid, k) < p else (lo, mid)
    return (lo + hi) / 2

def reestimate(s, r, df=18, conf=0.80):
    s_up = s * math.sqrt(df / chi2_ppf(1 - conf, df))
    r_use = min(max(r, 0.0), 0.6)
    n = per_arm(s_up, SESOI, r_use)
    return s_up, r_use, n, min(max(n, N_MIN), N_MAX)

def simulate(rng, n, true_diff, sd=75.0, r=0.6, sims=3000):
    benefit = strongest = 0
    for _ in range(sims):
        arms = []
        for shift in (0.0, -true_diff):                     # arm A lowers the error
            xs = [rng.gauss(0, sd) for _ in range(n)]
            ys = [r * x + rng.gauss(shift, sd * math.sqrt(1 - r * r)) for x in xs]
            arms.append((xs, ys))
        cx = [[x - sum(xs) / n for x in xs] for xs, _ in arms]   # centre within arms
        cy = [[y - sum(ys) / n for y in ys] for _, ys in arms]
        b = sum(x * y for a, c in zip(cx, cy) for x, y in zip(a, c)) \
            / sum(x * x for a in cx for x in a)
        adj = [sum(y - b * x for x, y in zip(xs, ys)) / n for xs, ys in arms]
        d = adj[0] - adj[1]                       # B minus A: positive = A better
        rss = sum((y - b * x) ** 2 for a, c in zip(cx, cy) for x, y in zip(a, c))
        lo = d - 1.96 * math.sqrt(rss / (2 * n - 3) * 2 / n)
        benefit += lo > 0; strongest += lo >= SESOI
    return benefit / sims, strongest / sims

if __name__ == "__main__":
    p, good, poor = 7 / 45, 30.0, 229.0           # Pfordresher & Brown 2007, Exp. 2
    print(f"check: {p:.0%} poor-pitch singers (229 c), rest 30 c -> mean"
          f" {p * poor + (1 - p) * good:.0f} c; split alone gives SD"
          f" {math.sqrt(p * (1 - p)) * (poor - good):.0f} c")
    n = per_arm(75, SESOI, 0.6); rec = math.ceil(n / (1 - LOSS))
    print(f"plan: SD 75, r 0.6, SESOI 20 (d = {20 / 75:.2f}), 90 % power: {n} per arm,"
          f" recruit {rec} ({2 * rec})")
    print("analysable per arm      SESOI 15     20     30")
    for sd in (60, 75, 90):
        for r in (0.4, 0.6):
            print(f"  SD {sd}, r {r:.1f} {'':8s}"
                  + "".join(f"{per_arm(sd, dl, r):7d}" for dl in (15, 20, 30)))
    se = 75 * math.sqrt(2 / 10) * math.sqrt(1 - 0.36)
    print(f"pilot of 10 per arm: SE of an arm difference about {se:.0f} c (SESOI 20)")
    k = math.sqrt(18 / chi2_ppf(0.20, 18))
    print(f"80 % upper limit with df 18: SD x {k:.3f}, so n x {k * k:.2f}")
    print("pilot SD, r -> SD used, r used -> n per arm -> clamped -> recruit (all)")
    for s, r in ((50, 0.65), (60, 0.70), (75, 0.60), (90, 0.45)):
        s_up, r_lo, raw, n2 = reestimate(s, r)
        rec2 = math.ceil(n2 / (1 - LOSS))
        print(f"  {s:4d}, {r:.2f} -> {s_up:5.1f}, {r_lo:.2f} -> {raw:4d} -> {n2:3d}"
              f" -> {rec2} ({2 * rec2})")
    rng = random.Random(2026)
    for true in (0.0, 20.0, 40.0):
        p_any, p_top = simulate(rng, n, true)
        print(f"true benefit {true:4.1f}: P(some benefit verdict) {p_any:.3f},"
              f" P(benefit >= SESOI shown) {p_top:.3f}")
# check: 16% poor-pitch singers (229 c), rest 30 c -> mean 61 c; split alone gives SD 72 c
# plan: SD 75, r 0.6, SESOI 20 (d = 0.27), 90 % power: 191 per arm, recruit 225 (450)
# analysable per arm      SESOI 15     20     30
#   SD 60, r 0.4             284    160     72
#   SD 60, r 0.6             217    123     55
#   SD 75, r 0.4             443    250    112
#   SD 75, r 0.6             338    191     86
#   SD 90, r 0.4             637    359    160
#   SD 90, r 0.6             486    274    123
# pilot of 10 per arm: SE of an arm difference about 27 c (SESOI 20)
# 80 % upper limit with df 18: SD x 1.183, so n x 1.40
# pilot SD, r -> SD used, r used -> n per arm -> clamped -> recruit (all)
#     50, 0.65 ->  59.2, 0.60 ->  119 -> 150 -> 177 (354)
#     60, 0.70 ->  71.0, 0.60 ->  171 -> 171 -> 202 (404)
#     75, 0.60 ->  88.7, 0.60 ->  266 -> 266 -> 313 (626)
#     90, 0.45 -> 106.5, 0.45 ->  477 -> 350 -> 412 (824)
# true benefit  0.0: P(some benefit verdict) 0.028, P(benefit >= SESOI shown) 0.000
# true benefit 20.0: P(some benefit verdict) 0.908, P(benefit >= SESOI shown) 0.026
# true benefit 40.0: P(some benefit verdict) 1.000, P(benefit >= SESOI shown) 0.894

The first line of the program makes a rough check with Pfordresher and Brown’s numbers: if 16 % of people have a mean error of 229 cents and the rest 30 cents, the overall mean is about 61 cents (of the same order as the 66 cents reported by Demorest and Pfordresher), and the difference between these two kinds of singer alone produces a standard deviation of about 72 cents. On this basis the book takes as planning values a standard deviation of 75 cents, a correlation with baseline of 0.6, and a smallest effect of interest of 20 cents (about 0.27 standard deviations). All three are the author’s assumptions, not published estimates. Analysis of covariance uses the baseline to multiply the required number by $1 – r^2$ (Borm et al. 2007). Under these assumptions 191 analysable participants are needed per arm; allowing for about 15 % loss and exclusion, 225 per arm are recruited, 450 in all. The sensitivity table shows that with a standard deviation of 90 and a correlation of 0.4, 359 per arm would be needed; with 60 and 0.6, only 123.

In the re-estimation examples, a pilot that returns exactly the planning values (standard deviation 75, correlation 0.6) yields 266 per arm (313 recruited, 626 in all), more than the plan, because the upper confidence limit is deliberately conservative; a pilot standard deviation of 50 yields 119, raised to the lower bound of 150; a pilot with 90 and 0.45 yields 477, cut to the upper bound of 350 (412 recruited, 824 in all).

The last three lines of the program check the statistical properties of the decision rule with 3,000 simulations, consistent with the conclusion of volume 33: “90 % power” means the probability of reaching some verdict of benefit when the true effect equals the smallest effect of interest (simulated: 0.908); in that case the strongest verdict, “at least the smallest effect of interest”, appears only about 2.5 % of the time (simulated: 0.026, with Monte Carlo error of about 0.003); to reach the strongest verdict with about 90 % probability, the true effect must be about twice the smallest effect of interest (simulated at 40 cents: 0.894). When the true effect is zero, the probability of wrongly reaching a verdict of benefit is 0.028, close to the nominal 2.5 %. The simulation assumes normally distributed errors; real data are right-skewed, which is one reason for the pilot and the sensitivity analysis.

Decision rule

# Decision rule fixed before enrolment. D = arm B minus arm A in 24-h pitch error (cents),
# adjusted for baseline and stratum; 95 % CI; positive = arm A (vibrotactile error
# feedback) more accurate. SESOI 20 cents. Gates: more than 25 % of randomised people
# excluded, or a fidelity check fails (median voice-to-vibration latency above 60 ms in
# the device log, or under 90 % of planned training minutes delivered in either arm)
# -> NOT INTERPRETABLE. Secondary outcomes never decide the verdict.
SESOI = 20

def verdict(d, lo, hi, excluded=0.10, fidelity_ok=True):
    if excluded > 0.25:
        return f"D = {d:+.0f}: NOT INTERPRETABLE - {excluded:.0%} excluded (limit 25 %)"
    if not fidelity_ok:
        return f"D = {d:+.0f}: NOT INTERPRETABLE - fidelity check failed"
    if lo >= SESOI:   v = "A beats B by at least the SESOI (20 cents)"
    elif lo > 0:      v = "A beats B; size not shown to reach 20 cents"
    elif hi < 0:      v = "A is WORSE than B"
    elif lo >= -SESOI and hi <= SESOI: v = "no difference worth acting on"
    else:             v = "unclear: the interval is too wide to decide"
    return f"D = {d:+.0f} ({lo:+.0f} to {hi:+.0f}): {v}"

for case in ((36, 24, 48), (19, 7, 31), (2, -10, 14), (-18, -30, -6),
             (10, -22, 42), (30, 18, 42, 0.31), (25, 13, 37, 0.12, False)):
    print(verdict(*case))
# D = +36 (+24 to +48): A beats B by at least the SESOI (20 cents)
# D = +19 (+7 to +31): A beats B; size not shown to reach 20 cents
# D = +2 (-10 to +14): no difference worth acting on
# D = -18 (-30 to -6): A is WORSE than B
# D = +10 (-22 to +42): unclear: the interval is too wide to decide
# D = +30: NOT INTERPRETABLE - 31% excluded (limit 25 %)
# D = +25: NOT INTERPRETABLE - fidelity check failed

The example results are invented. If more than 25 % of those randomised are excluded, or a fidelity check fails (the device log shows a median delay from voice to vibration above 60 ms, or either arm completes less than 90 % of the planned training time), the report says “not interpretable” whatever the primary outcome. Only when the lower bound of the confidence interval for the difference is at least 20 cents does the report say “arm A is better by at least the smallest effect of interest”. Secondary outcomes are reported only as estimates with confidence intervals and do not change the verdict.

What this trial cannot show

First, it compares “vibrotactile error feedback” with “the same device not vibrating”, all else equal, so it can say whether adding this tactile feedback helps; but it cannot compare it with other kinds of feedback, such as a visual pitch trace or a teacher’s guidance, nor separate the effect of the error information carried by the vibration from the attention or expectation that “something vibrating” may itself produce; that would need a further control arm receiving vibration unrelated to the error. Second, a sustained /a/ on five pitches in the comfortable range and two unfamiliar vowels cannot stand for singing, speech intonation or foreign-language pronunciation as a whole. Third, retention in the laboratory at 24 hours and 7 days says nothing about the level reached months later. Fourth, the participants are adults without formal vocal training, and the results cannot be extended to children, professional singers, or people with voice disorders or hearing impairment (including cochlear-implant users). Fifth, participants know whether they feel vibration, so expectation effects cannot be wholly excluded. Sixth, whatever the result, it cannot be used to support or oppose any particular course, device or the author’s teaching methods.

Ethics and conflicts of interest

The trial carries little risk but must still be approved by an independent ethics committee, with informed consent from participants.

Vocal load. No training block lasts more than 10 minutes and training totals no more than 30 minutes a day, with 5-minute breaks between blocks; drinking water is provided and participants are encouraged to drink during breaks; every target lies within 4 semitones of the participant’s comfortable pitch and is sung at a comfortable loudness, with no demand to sing loudly or with effort; people with a voice disorder, persistent hoarseness or laryngeal surgery do not take part, and anyone with an acute upper respiratory infection on a test day is rescheduled; participants stop at once, without consequence, if they notice a sore throat, hoarseness, coughing or any discomfort; anyone still hoarse the next day is followed up by the research staff and advised to see a doctor.

Vibration safety. The bands use low-power vibration elements of the kind found in the haptic alerts of phones and smartwatches; pulses are brief, and total vibration time is a small fraction of the 30 minutes of training, far below the levels that occupational limits for hand–arm vibration address (EU Directive 2002/44/EC sets an action value of 2.5 m/s² as an 8-hour equivalent); people with broken skin or sensory loss on the forearm or wrist, or with implanted electronic medical devices, do not take part; and participants may remove the bands or withdraw at any time without consequence.

Independence. Because the vocal task is closer to the author’s singing-training business, the training materials use no content from the author’s courses, no participants are recruited from the author’s students, and the trial is run and analysed by independent researchers. The protocol, the target and vowel materials, the device’s encoding program and the analysis code are publicly registered before the first participant is enrolled; if possible the study is submitted as a Registered Report, so that publication does not depend on the result. After the trial, participants in arm B are offered arm A’s training. Recordings and data are stored anonymously.