The three main types of martingale are the standing martingale, the running martingale and the Irish martingale. The market harborough (German martingale) is a modification of the running martingale.
Although there is a great deal of discussion around the origin of the word martingale, it’s possibly an Anglicism based on the Persian word mughal. A painting of a horse currently on sale at Sotheby’s and labelled as ‘A falconer mounted on a dappled horse, Mughal, late 17th or early 18th century’, distinctly shows the horse wearing a martingale (see https://shorturl.at/bowDH).
The fact that English lexicographer Mayhew proposed the Spanish word (which was of Arabic origin) as the etymology of the word martingale strengthens this contention. Modern Arabian horses can be shown under saddle in ‘traditional costume classes’ wearing a version of a martingale. It consists of a light leather collar around the neck, with a metal ring on each side through which the reins can be threaded. Pulling both reins slightly upward, when riding at