Practising

I highly recommend watching this short TED Ed video about how the brain changes when we practise, and how we can use this knowledge to practise more effectively.
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I have been a subscriber to The Bulletproof Musician newsletter for years. Written by Dr. Noa Kageyama, a performance psychologist who teaches at The Juilliard School, this free, weekly newsletter and the online blog offer handy tips for performers backed by research. Each newsletter typically focuses on one topic, such as memorising, setting practise targets, and dealing with nerves. There is also a podcast with the same name.

Breathing

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Hixon, T. J. (2006). Respiratory function in singing: A primer for singers and singing teachers. Redington Brown.
This short book was written by the pre-eminent speech scientist, Thomas J. Hixon "to provide readers with the best scientific information available and encourage them to use that information to evaluate their current beliefs about respiratory function in singing."
It is written in plain, simple English (with copious dad jokes), and although it could never be called a page turner, it will give you a good understanding of the facts of breathing and how to use the respiratory system efficiently when singing.

The information on anatomy and physiology can be found worded almost identically in the following speech pathology textbooks (and their previous editions). Unlike the Primer, they have colour images, but they don't contain the chapters on breathing for singing and breathing exercises.
  • Hoit, J. D., Weismer, G., & Story, B. (2022). Foundations of speech and hearing: Anatomy and physiology (Second edition). Plural Publishing, Inc.
  • Hixon, T. J., Weismer, G., & Hoit, J. D. (2020). Preclinical speech science: Anatomy, physiology, acoustics, and perception (Third edition). Plural Publishing.
Breathing for singing is also explained in Titze, I. R. (2000). Principles of voice production (2nd printing). National Center for Voice and Speech.
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Inspiratory muscle trainer (IMT)

As the name suggests, this device is designed to strengthen the muscles involved in inspiration (inhalation). It is particularly helpful for students whose external intercostal muscles are not strong enough to prevent their ribcage from collapsing when they start singing. I have both the Philips Respironics Threshold IMT and the EMST 150 with the inspiratory adapter, though any clinical-grade device should be fine.

Vocal Acoustics

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Bozeman, K. (2022). Practical vocal acoustics: Pedagogic applications for teachers and singers. Rowman & Littlefield Publishers.

Charts and other supplementary materials are available at: http://www.kenbozeman.com/Pedagogic-Resources.php

This book revolutionised my teaching. If you want to teach the acoustic vocal registers to others, you should study this book; treble and bass voices use different strategies, so don't assume that what works for you applies to other voice types. If you are struggling with the scientific explanations, try reading chapter 3 of this book first:
Behrman, A., & Finan, D. (2023). Speech and voice science (Fourth edition). Plural Publishing, Inc.
It explains sound waves and resonances in a way that is thorough and easy to understand.

If you want to take your study of vocal acoustic pedagogy further, Professor Bozeman's follow-up book, Kinesthetic Voice Pedagogy is another wonderful resource. You could also take the asynchronous online course or 5-day in-person course (which I attended) run by the New England Conservatory of Music, USA.

SOVTs

In this short video, Dr. Ingo Titze, inventor of "the straw exercise" (and my voice science professor at the SVI) demonstrates how to use straw phonation to combat vocal fatigue.
This series of 3 short videos explains the benefits of SOVTs for vocal technique.

Karin Titze Cox and Dr. Titze have also just published a book on SOVT methods: Voice is FREE after SOVT
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I've tried metal, glass, paper…even bucatini pasta! Unfortunately, I'm yet to find an eco-friendly, 3mm-diameter straw as good for SOVTs as these lightweight, plastic, coffee stirrer straws (5" length). Since disposable straws are now banned in most parts of Australia, you might have trouble purchasing these here, but they are for sale on Amazon.com. I clean the straws I use myself with a thin, straw brush (such as the one available here) so I can safely reuse them.

Auditioning

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Legge, A. (2017). The art of auditioning: A handbook for singers, accompanists and coaches (Revised Ed.). Edition Peters.

This little book is an invaluable resources if you're looking for audition arias (they're all from standard repertoire) or you're looking for a description of the different Fächer (voice types). It also describes a good system for learning repertoire. I was fortunate to receive regular coachings with Tony Legge when he was music director of Opera Australia, and I am forever grateful to him for teaching me to perform subtext.
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The Wolf Trap Opera website and blog contain heaps of useful advice on auditioning, particularly for young artist programs. The aria frequency lists are a great resource if you're looking for aria ideas.

Vocal Pedagogy

This is by no means a complete list of the pedagogy books and resources I have found useful, but if you're looking for an explanation of how the voice works, evidence-based vocal exercises, or ideas for expanding your teaching toolkit, these are great places to start (in no particular order).
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Ragan, K. (2020). A Systematic Approach to Voice: The Art of Studio Application. Plural Publishing.
This book was written by Dr. Kari Ragan, who first proposed (and continues to help define) Evidence-Based Vocal Pedagogy. As the name suggests, it offers a methodical and structured approach to teaching vocal technique. Since it is so well organised, it could also be used as a reference book of vocal exercises or literature reviews. Like many pedagogy books, it breaks down singing into component parts: respiration, phonation, registration, articulation, and resonance. Each of the main chapters reviews the research literature, identifies the takeaways that teachers would benefit from knowing, and offers practical suggestions and exercises.
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Brown, O. (1996). Discover your voice: How to develop healthy voice habits. Singular Pub. Group.
Despite its name, this book covers topics beyond just vocal technique (e.g., interpretation, putting together a concert program, and requirements for a professional career). It also covers anatomy, physiology and basic acoustics, although more up-to-date information can be found in other places). What I love about this book (apart from the many gems of wisdom it contains) are the exercises and concepts at the beginning. They get to the very foundation of how to make a vocal sound in a free and healthy manner, and, most importantly, how to make the transition from primal sound into singing. I have used these exercises with beginner students and also professional and post-tertiary singers who wanted to work on their vocal technique "from scratch" (and who probably appreciated the benefit of the exercises more). There is an accompanying recording of the exercises.
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McCoy, S. (2019). Your Voice: An Inside View 3: Voice Science & Pedagogy. Inside View Press.
I wish this book (or 2-book set) existed when I was a student. Widely used as a pedagogy textbook in the USA, it includes heaps of multimedia content and, I think, is very easy for singers to read. Like many textbooks, it doesn't include citations (which I would have found helpful as a researcher), but for someone wanting to get a comprehensive overview of voice science, this is an excellent choice.

There is also a condensed version of this book called The Basics of Voice Science & Pedagogy.
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Austin, S. F. (2017). Provenance: Historic voice pedagogy viewed through a contemporary lens. Inside View Press.
This book is a collection of excellent articles originally published in the NATS' Journal of Singing. They identify gems from the historical vocal pedagogy literature for teaching vocal technique, and explain why they work in a scientific, yet easy to understand, manner.
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If you can cope with watching videos of real human specimens, Acland's Video Atlas of Human Anatomy is well worth watching to gain a greater understanding of the muscles and structures relevant to singing. Aimed primarily at medical students, it is, nevertheless, easy to understand and quite fascinating. When I was studying vocal anatomy, I found this far more effective than drawings, 3D models, or animations. The videos on the larynx, pharynx, soft palate, neck muscles, torso, jaw, and tongue are particularly useful. Be warned: once you see it, you can't unsee it…but you won't forget your vocal anatomy either!

Advice for Singers

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Fleming, R. (2004). The Inner Voice: The Making of a Singer. Penguin.

Renée Fleming's autobiography is not just an account of her journey from student to superstar. It was written with the intent of helping young singers, and it is full of great advice and frank insight.
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Dr. Ian Howell (whose classes I had the pleasure of attending at the Acoustic Vocal Pedagogy Workshop) recently published a book: Advice for Young Musicians: "Laid out like a book of poems meant to be dipped in and out of, this book covers how careers unfold; how music, practice, and performance work; business, networking, and relationships; becoming who you are; necessary skills, behaviors, and outlooks; academia and education; and mentors and teachers."

Dr. Howell has also produced this useful technology guide for teaching singing online.

CCM Pedagogy

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Dr. Matt Edwards is one of America's leading CCM and Musical Theatre pedagogues. I had the good fortune of attending his lectures at the Summer Vocology Institute and would highly recommend checking out his website, blog posts and books if you're looking for non-classical vocal pedagogy resources.

Topic Theory

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Of all the music analysis techniques I was taught at uni, topic theory is the one I find most useful as a performer. First proposed in 1980 as a way to approach 18th-century music "in much the same way a listener of the time would have done" (Leonard Ratner in Classic Music: Expression, Form, and Style), it essentially teaches you the melodic, harmonic, and rhythmic formulas used by composers up to the late 19th century, and their meanings. I find it particularly useful when a singer has to stand through an awkwardly long instrumental introduction (e.g. "Porgi, amor") or I'm looking for ways to make a performance more nuanced and expressive. The Oxford Handbook of Topic Theory is the most comprehensive book on topic theory. It is a large collection of scholarly essays covering subjects such as analysing, performing, and listening to topics. The examples are mostly from instrumental repertoire, so this book would be for learning the principles of topic theory rather than seeing it applied in action to vocal repertoire.