What the book covers

1. Self-sustained oscillation: why the phase difference between the glottal margins is the key; the threshold formula checked against Titze 1988; the evidence on hydration.
2. Nonlinear source–filter coupling: Titze’s two levels of interaction; inertive and compliant reactance and the threshold; straws and water.
3. The singer’s formant and masking: a band signal-to-noise calculation under stated assumptions.
4. Registers and nonlinear dynamics: the asymmetric two-mass model, period doubling and chaos, throat singing and rock distortion.
5. The auditory-motor loop: the pitch-shift reflex, DIVA, and a delayed internal model with a Kalman filter.
6. The Lombard effect and mixed monitoring: air and bone conduction in one cochlea; ear plugs and in-ear monitors.
7. Reading the classics: the Record of Music, the Zhuangzi, two treatises on singing and the Śūraṅgama Sūtra (echoing Volume 2, Turning the Hearing Inward).
8. Practice and a pre-registered trial: a four-step checklist and a randomised trial of straw phonation plus bone-conduction self-monitoring against a usual reading warm-up.

What Volume 10 already covered is only recapped here, marked “see Volume 10 of this series”; rather than repeat its programs, this book builds new calculations on them.

Claims corrected on checking

Several statements in the author’s framework for this book needed correcting or qualifying once checked. Each chapter says so where it arises; they are collected here.

1. The threshold pressure formula. Titze’s 1988 general form (as reproduced by Zhang 2010 and by Fulcher and Scherer 2011) is $P_{\text{th}} = 2k_t B c\,\xi_{01}^2 / [T(\xi_{01}+\xi_{02})]$, where $\xi_{01}$ and $\xi_{02}$ are the prephonatory half-widths at the lower and upper glottal margins and $B$ is tissue damping per unit area. For a rectangular glottis, $\xi_{01} = \xi_{02} = \xi_0$, the factor 2 cancels and $P_{\text{th}} = k_t B c\,\xi_0/T$, as in Volume 10. The framework’s $2k_tBc\xi_0/T$ mixes the coefficient of the general form with the simplified $\xi_0$ and overstates the threshold by a factor of two.
2. “Hydration lowers vocal fold viscosity.” The direct link between hydration and viscosity comes from excised canine larynges, in which hydration was changed with osmotic solutions and the change in tissue viscosity was assumed. The human experiments had 6 and 12 participants: in the first, the fall in threshold pressure with hydration appeared mainly at high pitches and the rise with mild dehydration mainly at low pitches, with speaking pitch unaffected; in the second, double-blind study the effects appeared mainly in high-pitched tasks. The evidence supports “hydration affects how easily phonation starts”, but viscosity was never measured directly in people.
3. “F0 crossing F1 into the compliant region causes voice breaks.” For an open vocal tract it is true that the tract is inertive below the first formant and compliant in a band above it; and Titze, Riede and Popolo (2008, 18 participants) found that bifurcations such as frequency jumps and subharmonics were more frequent when F0 crossed F1, concluding that nonlinear source–filter coupling is “partly” responsible for source instabilities. But register transitions (M1/M2) depend mainly on laryngeal muscle and tissue mechanisms; acoustic loading is one contributing factor, and voice breaks cannot be attributed wholesale to F0 crossing F1.
4. “Straws raise inertive reactance.” More precisely, a straw lowers the first resonance of the tract to about 200 Hz, with a compliant band just above it and a wide inertive band higher up (the program in this book gives 208 Hz, compliant from about 210 to 390 Hz and inertive from about 390 to 1130 Hz). Semi-occlusion also raises the mean pressure in the mouth. A three-dimensional computational study suggests that the benefit of these exercises may not lie in directly raising vocal efficiency, and the clinical evidence remains limited and inconsistent.
5. The area ratio behind the singer’s formant. What matters is the ratio between the cross-sections of the epilarynx (laryngeal vestibule, or larynx tube) exit and the pharynx: about 1:6 in Sundberg’s 1974 model and only about 4.5:1 in his 1995 magnetic-resonance measurements, which showed the fourth and fifth formants to be “strongly, though not exclusively,” dependent on the larynx tube. It is not the laryngeal ventricle, nor “a pharynx-to-ventricle-exit area ratio above 6:1” as the framework had it.
6. “A signal-to-noise gain of 10–15 dB.” This is not an established measurement. Under the assumptions stated in this book, the gain in the 2.5–3.2 kHz bands is roughly the number of decibels by which the formant cluster rises above a speech-like spectrum (8.8 dB for a 10 dB cluster, 12.9 dB for a 15 dB cluster), and the absolute ratio depends strongly on how fast the orchestral spectrum falls at high frequencies.
7. “Chaotic attractor = vocal fold polyp.” This cannot be written. Researchers have observed subharmonics and irregular vibration in some pathological voices and have described them with the tools of nonlinear dynamics; such descriptions are not diagnoses, and the same phenomena occur in healthy voices (at register transitions, for example) and in deliberate singing techniques.
8. “Attending to bone conduction and resonance sensations stabilises pitch instantly.” This is the author’s hypothesis; the book marks it as such and drops “instantly”. The auditory-motor loop has a delay of about 100–150 ms, and the program in Chapter 5 shows that even a perfect internal model cannot remove the drift that occurs during the delay. A physical fact also needs stating: air- and bone-conducted versions of one’s own voice add up in the same cochlea, and outside noise masks both, so “listening by bone” is not an independent channel that escapes masking.
9. Classical quotations. The author’s quotation from Yannan Zhi’an’s Treatise on Singing, “凡唱曲有地所……有声不散”, could not be found word for word in any text that could be checked, and the book does not quote it; the quotation from Xu Dachun’s Transmitting the Sound of Yuefu, “出声之法，必先明乎口齿喉舌唇五音之部位”, could not be verified word for word either, so the book only paraphrases the sections “Mouth Rules for Producing the Sound” and “The Five Sounds”, and asks the author to check them against the original.

How to read the boxes

As in other 5D Library books, different kinds of statement are marked separately.

When the book applies concepts from physics and control theory (impedance, inertive reactance, bifurcation, chaos, Kalman filtering) to real singers, they are simplified models: they help us see structure, but a model that reproduces a phenomenon does not show that real larynges and brains work that way.

About this edition

This is version 1.0.0, the first complete edition: a preface and eight chapters, in Chinese and English, with 16 programs and 4 vector figures. The text, boxes and code were drafted with an AI writing tool from the author’s title, framework and notes; the author is responsible for reviewing and revising them and for checking every source. Corrections and missing references are welcome through the 5D Library website.