It is a common Japanese myth, based on Chinese literary traditions, that Japan has four seasons. In fact, it has five (5). The so-called 'rainy season', (or 'Tsuyu', etc.), which in most of the country lasts from mid-June to the end of July, is in fact the tail-end of the Asian monsoon. Temperatures drop from late May, and the frequency and intensity of rain gradually increase, until, by late July, hot and heavy rain is falling. The 'Tsuyu' is definitely a distinct season, which every year causes deadly landslides. This is most people's least favourite season.
'Summer proper' ('honkakuteki na natsu') does not begin until the end of July or early August. Summer --with its heat and typically Asian high humidity-- then continues right though September and even into early October. In central and western Japan, Autumn leaves do not turn or fall until late October-November, and some remain on the trees until Christmas. It follows that the other seasons are likewise skewed, Winter not beginning until late December, Spring lasting through to early May, the Tsuyu following, and --once again--Summer not beginning until late July-early August.
All of the four 'normal' ones.