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11/01/2022

Five of Stephen Sondheim’s best shows
A musical theatre legend has died. Stephen Sondheim, the greatest composer-lyricist of his generation, passed away on November 26 at the age of 91.

His dramatic genius combined a rare blend of elements, that of an astonishingly versatile and sophisticated composer, and an incredibly witty wordsmith. His extraordinary output includes a staggering 16 musicals as composer and lyricist, a further three as lyricist alone, as well as four musical revues featuring compilations of hit songs from his shows.

Sondheim’s principal contribution to musical theatre lies in having reinvigorated the Broadway show in the wake of Rodgers and Hammerstein. Among many accolades received, Sondheim’s songs for the film Dick Tracy (1990), starring Warren Beatty, Madonna, and Al Pacino, earned him an Academy Award.

Exceptionally, he has theatres named after him in both Broadway and the West End. Such is his far-reaching influence that he even appears as a fictionalised character in the new film Tick, Tick… Boom! on Netflix, based on the autobiographical musical by Rent composer Jonathan Larson.

When faced with such a prolific and fascinating output, it is difficult to single just a few shows out for praise, but here follow five of Sondheim’s best.

1. West Side Story

Shakespeare’s star-crossed lovers are given a contemporary twist in this celebrated retelling of Romeo and Juliet. Transposed to the setting of 1950s New York City, it saw the romance as a turf war between a white American street gang and Puerto Rican immigrants. Premiering in 1957, the show was something of a big break for the young Sondheim, who was latterly brought in as lyricist alongside the more established composer Leonard Bernstein, bookwriter Arthur Laurents, and director-choreographer Jerome Robbins.

The score is replete with hit songs, notable among them “Maria”, “Something’s Coming”, “I Feel Pretty”, and the “Tonight Quintet”, which features a remarkable five-way exchange between three principal characters plus the two gangs. The iconic 1961 film adaptation received a highly impressive ten Academy Awards and excitement is mounting over the soon-to-be-released remake directed by Steven Spielberg.

2. Gypsy

Following two years after West Side Story, Gypsy used the same creative team but substituted Jule Styne as composer. With its basis in the memoirs of Gypsy Rose Lee, the show tells the story of the eponymous burlesque performer and her overbearing mother, Rose.

Highlights include “Rose’s Turn”, one of the most demanding solos in the whole musical theatre repertory, in which Sondheim’s lyrics vividly depict the exploitative matriarch reflecting upon the consequences of past actions. Twice adapted for film, in 1962 and 1993, the musical was more recently televised in its 2015 West End revival production starring Imelda Staunton as Rose.

3. Company

Epitomising the “concept musical”, in which a show crystallises around a broad theme rather than an overarching story, 1970’s Company, with music and lyrics by Sondheim, presents a series of unrelated short scenes between the lead character, Bobby, and his best friends.

Notable productions include the 2006 revival starring Raul Esparza, in which the cast double as onstage instrumentalists; the 2011 New York Philharmonic concert version, with Neil Patrick Harris in the lead role; and the gender-flipped 2018 West End revival, featuring Rosalie Craig as Bobbie. “(Not) Getting Married Today”, one of the most challenging musical theatre songs of all time for its prominent use of patter, was breathtakingly performed by Jayma Mays in an episode of Glee.

4. Sweeney Todd

Inspired by the sinister character of the Victorian penny dreadful, Sweeney Todd: The Demon Barber of Fleet Street (to use its full name) has become arguably Sondheim’s best known musical. Premiered in 1979 with many subsequent high-profile revivals, including a concert version starring Bryn Terfel and Emma Thompson in 2014, it makes ingenious use of the show’s ensemble in a role akin to a classical Greek chorus, reflecting on the action throughout the musical without advancing it.

A gruesome tale of a barber intent on revenge and the piemaker who turns the men he murders into meat, it lent itself perfectly to Tim Burton’s directorial treatment in the acclaimed 2007 film, starring Johnny Depp and Helena Bonham Carter, who admirably tackled Sondheim’s taxing music and lyrics.

5. Into The Woods

My final selection on this list, from 1987, is Into The Woods. The musical creatively draws upon four well-known fairy tales – Jack and the Beanstalk, Cinderella, Little Red Riding Hood, and Rapunzel – intertwined with an original story of a baker and his wife, and the witch who has cursed them never to have children.

Sondheim’s music and lyrics coalesce most effectively in songs such as “Your Fault”, in which the constituent characters are artfully combined to recapitulate the complex set of circumstances that have brought them together. The use of fairy tales made the musical well suited to its 2014 Disney adaptation boasting an all-star cast led by Meryl Streep, James Corden, and Anna Kendrick.

Honourable mentionsof other Sondheim shows include: Follies (1971), A Little Night Music (1973), Merrily We Roll Along (1981), Sunday in the Park with George (1984), Assassins (1990).

11/01/2022

Adele’s ‘30’: A mathematician explores number patterns in album titles
Adele, the 33-year-old British top-selling and award-winning recording artist, released her sensational new album, 30, in November. Reviewers are raving, with the New York Times calling it a “musical tour de force,” and Rolling Stone naming it her best album yet.

Besides how great the album is, everyone, it seems, is also talking about Adele’s numbers, as in: how many albums she has sold? But as a mathematician, I’m interested in how she has used numbers to sequence all of her albums. Her previous album was called 25. In fact, Adele’s album titles are always numbers, and they reflect the age that she wrote them. She wrote her debut album 19 at 19, followed by 21, then 25, and now, 30 Adele recently turned 33 but she started writing the album at 30.

‘Easy on Me,’ was the first single released from Adele’s new album, ‘30’
Is there a pattern to Adele’s albums? The chronological list of Adele’s album titles 19, 21, 25 and 30 was coined the “Adele sequence” by David Patrick, senior math and science curriculum director at the Art of Problem Solving.

Mathematicians love sequences, and they pop up all over the field. Sequences are simply numbers listed in a given order. The simplest sequence we learn about as children are the counting numbers 1, 2, 3, 4 and so on.

The '30' album cover features a profile photo of Adele.
Adele’s ‘30,’ album cover. (Columbia Records)
A vast, searchable catalogue of sequences is the On-line Encyclopedia of Integer Sequences, or OEIS, for short. The OEIS is your one-stop shop for everything on sequences, containing more than 340,000 entries.

As Patrick points out in his article on the Adele sequence, searching OEIS for 19, 21, 25, 30 uncovers the curious sequence with the catchy title A072666, whose first few numbers are: 2, 3, 4, 5, 6, 8, 10, 11, 13, 14, 18, 19, 21, 25, 30, 31, 36, 41, 43 and 44. The Adele sequence is there in the middle: 19, 21, 25, 30 and suggests her next album will be 31.

Adele’s sequence
A sequence of significant mathematical and real-world importance is the one consisting of prime numbers. Prime numbers and their properties form an expansive topic in mathematics, with applications from blockchains to encryption. A major open mathematical problem is to determine if there are infinitely many pairs of prime numbers whose difference is two (as is the case for 3 and 5 or 17 and 19).

A number is prime if it is larger than 1, and not the product of two smaller numbers. For example, 2 and 3 are prime, but 4 is not prime, as 4 is the product of 2 with itself. The primes form the sequence A000040: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67 …. The ancient mathematician, Euclid of Alexandria proved in 300 BC that the sequence of primes never ends.

A five-by-five grid of photographs of house numbers, mosaics, paintings and other sources.
A colourful grid of the first 25 prime numbers. (Chris/flickr), CC BY
To define the nth number in the A072666, we take the nth prime number (where “n” stands for a number), add it to the (n+1)th prime, and subtract 1. If the resulting number is prime, then we include n in the sequence. Otherwise, we skip it.

For example, the 19th prime is 67, and the 20th is 71. We then have 67 + 71 – 1 = 137, which is a prime number, and so 19 belongs to the sequence. In contrast, if we perform a similar check with the 20th and 21st prime, we have 71 + 73 – 1 = 143, which is the product of 11 and 13 and so is not prime. That tells us that 20 is skipped in the sequence.

OEIS lists a total of nine sequences containing 19, 21, 25, 30, such as A142958, whose next entry after 30 is 41. If, instead, Adele follows A142958, her next album will be 41. That would be sad news for her millions of devoted fans, as they’d have to wait almost a decade for more of those heartfelt ballads.

The inspiration of numbers
Adele may be unique in naming her albums only by numbers, but she is far from alone in using them in song and album titles. Musicians appear to often draw inspiration for their titles from numbers.

A tiny sample of popular songs with numbers in their title are “Eight Days a Week” and “When I’m Sixty Four” by the Beatles, “Edge of Seventeen” by Stevie Nicks, “Fifteen” and “22” by Taylor Swift, “99 Luftballons” by Nena, “10,000 Hours” by Dan + Shay and Justin Bieber, “99 Problems” by JAY-Z, “2 Become 1” by the Spice Girls, “Whalien 52” by BTS, “7/11” by Beyoncé, “Five Years” by David Bowie, “Three Times a Lady” by the Commodores and “7” by Prince.

Avant-garde techno artist Aphex Twin, aka Richard David James, went a mathematical step further and named one of his songs after an equation.

a mathematical equation
The Aphex Twin track, often referred to as the ‘Equation,’ after the mathematical formula pictured here, is the B-side on the single ‘Windowlicker. (Anthony Bonato), Author provided
Besides using numbers in their titles, some recording artists also completed advanced degrees in mathematics. There is Dan Snaith of the Polaris-winning band Caribou, whose doctoral dissertation at Imperial College London was entitled Overconvergent Siegel Modular Symbols, and Art Garfunkel, who holds a master’s in mathematics education from Columbia University.

No one, not even possibly Adele, knows her next album title. Her love of literature, ignited early in school by an English teacher, may also point to an appreciation of math (or maths as she might say).

For whatever reasons, musical artists like Adele, Taylor Swift and the Beatles drew on inspiration from numbers for their song and album titles. Adele herself may be doodling with numbers and mathematical sequences as you read this, plotting her next sonic masterpiece.

11/01/2022

What’s your school closures playlist? Why music should be part of parents’ pandemic survival strategy
With pandemic school closures in place in Ontario, Québec, Nova Scotia and Prince Edward Island until Jan. 17, and other provinces on watch, music could be important for maintaining the well-being of children and families.

Many are concerned about the effects of closures on student and family well-being. While scientists and government officials are busy developing strategies to defeat the Omicron variant, young children — whom UNICEF has cautioned could be a “lost generation” — yet again find themselves asked to attend a virtual classroom from inside their homes.

Early childhood researchers, children’s rights advocates, health experts and parents continue to point out that the psychological well-being of children seems to be getting lost in policy-making and public debate.

Read more: Child and youth mental health problems have doubled during COVID-19

Listening to music at home or participating in musical activities might be an important way for parents and children to reduce stress, find ways to regulate their emotions and experience joy together.

Music and self-regulation
How can participation in musical activities be therapeutic? Experts argue that music is at the very centre of what it means to be human. Stephen Malloch and Colwyn Trevarthen, who have respectively researched psychology, movement and music, and child psychology, argue music comes from how human bodies, from birth, explore their environment using habitual patterns of action — a kind of “communicative musicality.”

On a physiological level, the connections between different brain areas are still developing in young children, yet these areas all become involved simultaneously when a child is performing a musical activity. This means that music might help sustain and regulate emotional well-being by engaging all these brain areas, and thus help to make sense of otherwise incomprehensible situations.

‘Good Morning America’ segment featuring a child who sings about hating COVID-19.
Express yourself
Even though we don’t know now the extent to which children globally have been affected by isolation during the pandemic, many undoubtedly are processing stress and grief from missing daily routines.

Music allows children to safely express emotions that might otherwise manifest in persistent nightmares, violence or trauma which may be correlated with mental health challenges, PTSD and substance abuse later in life. Psychiatrists note that an important part of recovery from trauma is being able to articulate one’s feelings.

Given the opportunity to express themselves musically with instruments or simply in choosing songs, children may find venues to express emotions that are common responses to traumatic experiences, such as disappointment, anger, passion and sadness. These can all be poured into a song that has no need for linear narrative.

Instead, music can simultaneously be a compassionate witness and a medium capable of encapsulating and expressing what a child might experience while missing friends and routines. Adults can listen to how children may hum a favourite song or make up a new tune to give their feelings a voice.

Singing about pandemic and enforced safety measures might help children make sense of a scary situation. Psychologists suggest that sharing songs and singing games together as a family can strengthen relationship between children and their parents and ultimately bring a smile whether through simple fun or looking to music to put our current situation in a larger context across generations. Listening to relaxing music can also promote mental wellness.

‘Totally Fixed Where We Are,’ based on ‘Total Eclipse of the Heart,’ adapted by the Marsh Family, February 2021.
Younger children
During lockdown, interaction with peers is constrained for most children, and even more so for younger ones who don’t have access to social media and cannot reap the psychological benefits of digitally mediated communication with their friends.

Some research suggests that some caregivers have been turning to music while being isolated in COVID-19 shutdowns. For example, a study of caregivers of children aged between three and six years old in Brazil found that about 60 per cent of caregivers were listening to music to relax or feel excited during social distancing.

Read more: Parenting in a pandemic: How to develop stronger family relationships during COVID-19

But if this does not happen, how can caregivers benefit from music or facilitate children’s engagement with music? They could start by simply sharing their favourite playlists with children or choosing music they think could support a positive mood. They can strategically help evoke positive emotions that may help families keep an optimistic outlook through our pandemic winter.

There is a great variety of ways in which both parents and children can engage with recorded music: dancing or tapping, singing along, making up another melodic line or even creating a funny parody.

A child's fingers are seen on a keyboard.
Participating in virtual music groups can be one way of maintaining a connection to communities. (Pexels/Ron Lach)
Importance of connections
Finally, to restore the lost sense of belonging and community connection, which is crucial to maintaining psychological health, parents can encourage children’s participation in virtual music groups.

This type of collective music-making has been found to promote self-expression, help manage emotions and bring a comforting sense of belonging. For children who have memories of attending school and activities before the pandemic, it can also help remind them of who they were before the pandemic.

Music can help children adapt to difficult situations by binding families together.

Most importantly, music can help revive the belief that everything will eventually be well, despite this seemingly never-ending series of lockdowns that many of us feel are damaging the spirits of adults and children alike.

11/01/2022

11/01/2022