‘The Harmonious Blacksmith’ is a popular name given to the final movement, ‘Air and Variations’, of George Frideric Handel’s Suite No. 5 in E major, HWV 430, for Harpsicord. There are a few explanations as to why this movement became known as ‘The Harmonious Blacksmith’; however I want to talk about Pythagoras’ supposed role in musical theory.
Legend has it that Pythagoras passed a forge, noting the variances in pitch that the different hammers made on the anvil he estimated the consonance and dissonance from combining these sounds, gaining his first clue to the musical intervals on the diatonic scale. He entered the forge, making notes on the weights of the hammers, which were 12, 9, 8 and 6 pounds respectively.
Hammers A (12lbs) and D (6lbs) were in a ratio of 2:1, which is the ratio of an octave. Hammers B (9lbs)’s ratio with hammer A was 12:9 which equals 4:3 which is a musical fourth. Hammer C’s ratio with hammer A was 12:8 which equals 3:2 which is a musical fifth. The ratio of hammers B and C is 9:8 which is a musical whole tone or whole step interval.
This legend is demonstrably false, since these ratios are only relevant to string length, rather than weight. However Pythagoras may have had a role in discovering these properties in string length. But still, it’s an interesting legend.