Standard canvas and stretcher sizes satisfying golden and silver ratios as well as optimal use of material

TL;DR

This paper derives a general formula for standard canvas and stretcher sizes that satisfy the golden ratio, porte d'harmonie, and optimal material use, proposing new sizes for various painting formats.

Contribution

It introduces a unified formula to determine canvas sizes aligning with aesthetic ratios and manufacturing efficiency, correcting misconceptions about existing standards.

Findings

New sizes satisfy golden ratio and porte d'harmonie

Formula applies to all painting formats

Optimizes material usage in production

Abstract

The sizes of canvases and stretchers for oil painting have been standardized in France in 19th century and widely accepted in many countries in Europe as well as in Japan so far. These standard sizes do not follow the golden ratio and porte d'harmonie number as has been often claimed. In this work, a general formula is derived to calculate the sizes of painting canvases and stretchers, which satisfy exactly the golden ratio and the porte d'harmonie number as well as the rule for optimal use of material in their mass production. Based on this formula new canvas and stretcher sizes are calculated for all three figure, landscape and marine formats.