Pythagorean hammers
Encyclopedia
According to legend, Pythagoras
discovered the foundations of music by listening to the sounds of four blacksmith
's hammers, which produced consonance
and dissonance
when they were struck simultaneously. Supposedly, he noticed that hammer A produced consonance with hammer B when they were struck together, and hammer C produced consonance with hammer A, but hammers B and C produced dissonance with each other. Hammer D produced such perfect consonance with hammer A that they seemed to be "singing" the same note.
Ostensibly, Pythagoras rushed into the blacksmith to discover why, and he found that the explanation was in the weight ratios. The hammers weighed 12, 9, 8, and 6 pounds respectively. Hammers A and D were in a ratio of 2:1, which is the ratio of the octave. Hammers B and C weighed 9 and 8 pounds. Their ratios with hammer A were (12:9 = 4:3 = musical fourth) and (12:8 = 3:2 = musical fifth). The space between B and C is a ratio of 9:8, which is equal to the musical whole tone, or whole step interval
.
The legend – which can be traced as far back as Nicomachus
' Enchiridion harmonices, from the 2nd century CE – is demonstrably false, at least with respect to the hammers. These proportions are indeed relevant to string length (i.e. that of a monochord
) – using these founding intervals, it is possible to construct the basic seven-tone diatonic scale
used in modern music, and Pythagoras might well have been influential in the discovery of these proportions - but the proportions do not have the same relationship to hammer weight and the tones produced by them.
Pythagoras
Pythagoras of Samos was an Ionian Greek philosopher, mathematician, and founder of the religious movement called Pythagoreanism. Most of the information about Pythagoras was written down centuries after he lived, so very little reliable information is known about him...
discovered the foundations of music by listening to the sounds of four blacksmith
Blacksmith
A blacksmith is a person who creates objects from wrought iron or steel by forging the metal; that is, by using tools to hammer, bend, and cut...
's hammers, which produced consonance
Consonance and dissonance
In music, a consonance is a harmony, chord, or interval considered stable, as opposed to a dissonance , which is considered to be unstable...
and dissonance
Consonance and dissonance
In music, a consonance is a harmony, chord, or interval considered stable, as opposed to a dissonance , which is considered to be unstable...
when they were struck simultaneously. Supposedly, he noticed that hammer A produced consonance with hammer B when they were struck together, and hammer C produced consonance with hammer A, but hammers B and C produced dissonance with each other. Hammer D produced such perfect consonance with hammer A that they seemed to be "singing" the same note.
Ostensibly, Pythagoras rushed into the blacksmith to discover why, and he found that the explanation was in the weight ratios. The hammers weighed 12, 9, 8, and 6 pounds respectively. Hammers A and D were in a ratio of 2:1, which is the ratio of the octave. Hammers B and C weighed 9 and 8 pounds. Their ratios with hammer A were (12:9 = 4:3 = musical fourth) and (12:8 = 3:2 = musical fifth). The space between B and C is a ratio of 9:8, which is equal to the musical whole tone, or whole step interval
Interval (music)
In music theory, an interval is a combination of two notes, or the ratio between their frequencies. Two-note combinations are also called dyads...
.
The legend – which can be traced as far back as Nicomachus
Nicomachus
Nicomachus was an important mathematician in the ancient world and is best known for his works Introduction to Arithmetic and Manual of Harmonics in Greek. He was born in Gerasa, in the Roman province of Syria , and was strongly influenced by Aristotle...
' Enchiridion harmonices, from the 2nd century CE – is demonstrably false, at least with respect to the hammers. These proportions are indeed relevant to string length (i.e. that of a monochord
Monochord
A monochord is an ancient musical and scientific laboratory instrument. The word "monochord" comes from the Greek and means literally "one string." A misconception of the term lies within its name. Often a monochord has more than one string, most of the time two, one open string and a second string...
) – using these founding intervals, it is possible to construct the basic seven-tone diatonic scale
Diatonic scale
In music theory, a diatonic scale is a seven note, octave-repeating musical scale comprising five whole steps and two half steps for each octave, in which the two half steps are separated from each other by either two or three whole steps...
used in modern music, and Pythagoras might well have been influential in the discovery of these proportions - but the proportions do not have the same relationship to hammer weight and the tones produced by them.
See also
- Diatonic scaleDiatonic scaleIn music theory, a diatonic scale is a seven note, octave-repeating musical scale comprising five whole steps and two half steps for each octave, in which the two half steps are separated from each other by either two or three whole steps...
- Equal temperamentEqual temperamentAn equal temperament is a musical temperament, or a system of tuning, in which every pair of adjacent notes has an identical frequency ratio. As pitch is perceived roughly as the logarithm of frequency, this means that the perceived "distance" from every note to its nearest neighbor is the same for...
- Interval (music)Interval (music)In music theory, an interval is a combination of two notes, or the ratio between their frequencies. Two-note combinations are also called dyads...
- Just intonationJust intonationIn music, just intonation is any musical tuning in which the frequencies of notes are related by ratios of small whole numbers. Any interval tuned in this way is called a just interval. The two notes in any just interval are members of the same harmonic series...