Two years ago today, Sound and Music made a public pledge to achieve gender equality across all of our work with composers and artists, under the headline “50:50 by 2020”. Anniversaries are an opportunity to reflect, and this one has not only led me to think about the headway we’ve made – but also the significant and systemic challenges that remain.

At one level, we’ve made good progress. This year, 44.5% of composers we – the UK’s national organisation for new music – are working with identify as women, as opposed to 33% two years ago. To reassure those who said that we were sacrificing considerations of artistic quality on the altar of tokenism, this has been artistically thrilling not only for us, but for everybody involved – the composers themselves, our partner organisations and indeed audiences.

It turns out that working with a wider range of composers and being interested in what they have to say leads to a greater variety of work, more distinctive programming and a very appealing energy. I see great examples of this across the sector, such as the recent SoundState Festival at the Southbank Centre, which had as its featured artists the composers Du Yun and Rebecca Saunders and the flautist Claire Chase and was buzzing with people and ideas for its entire duration.

One young black woman was told she 'didn’t look like a composer' in her first year at conservatoire

However, only roughly a third of applications to our programmes come from those who identify as women despite work to change perceptions about who can be a composer, and despite our very public commitments and comments on the subject. And I suspect that the percentage of female applicants to most other schemes across the sector is even lower. We’re still one of the very few organisations in the UK to release our data publicly.

One of the many arguments posed against gender balance (not only in music) is about the consistently lower percentage of applications from women in any competitive application process. More girls than boys are now taking GCSE music, but at some point between this and a professional career, many women drop off, lose heart and stop putting themselves forwards altogether.

Why? At what point are composers who happen to be women discouraged, and by who or what? What are the barriers to becoming a professional composer and do these affect one gender more than another?

Many of the answers to these questions, of course, are about wider society: about how women are portrayed in the media, about the weight of childcare and domestic arrangements disproportionately borne by women, about women being conditioned so often from a young age to “be nice”, “stop showing off”, leaving an embedded belief that shame, chastisement or punishment would follow any bold foray.

Clocking composers at the Proms … Joanna Ward. Photograph: Ruari Paterson-Achenbach

This plays out in the world of music in many different ways. Some are more obvious, such as the young black composer who was told that she “didn’t look like a composer” in her first year at conservatoire, or the established figure told that she couldn’t have written her large orchestral piece “without help”.

However, there is a more subtle edge to how composers who are women are treated. I’ve been talking recently to the brilliant young composer Joanna Ward, who has been researching gender equality in the field of composers. Part of her research has been to look at the programming of the BBC Proms 2013-18. The number of women being commissioned and programmed by the Proms is improving. However, her research reveals that women take up disproportionately less time in the programme. The average duration of a woman’s piece was 12 minutes, compared to 25 minutes for those by men. Even among world premieres (in other words, the Proms’ own commissions), the average duration of a world premiere by a woman was 11 minutes and the average duration of a world premiere by a man was 19 minutes.

In some ways it is unfair to single out the Proms. Their commitment to gender equality in commissioning is laudable, and their data is more readily available than that of many others. (I suspect other series and festivals would be no better and in many cases much worse.) And what the data doesn’t tell you is how this striking disparity has arisen. Are men being commissioned to write longer pieces? Are women more likely to compose shorter pieces? If so, why?

But it is a stark illustration that if you are an aspiring female composer, you will be looking at a future where, even if youcan avoid overtly sexist comments and behaviour, it seems likely that you will be allowed to take up less space than your male colleagues.

Targets are important. In my own organisation, I’ve seen how they can bring transparency and focus, and drive positive change. But achieving true gender equality in the music world will require us to go far beyond targets and take a long hard look at how we operate as a sector, including questioning our unconscious assumptions about what women are capable of.

At a time when the power of art to connect and move us feels more important than ever, this feels not only essential, but a tremendous creative opportunity.

• Susanna Eastburn is chief executive of Sound and Music.