3 ms·

>Let's consider the major sixth. >It is the 27th harmonic of the fundamental. This is the problem I have with discussions concerning the harmonic series, it i

>Let's consider the major sixth. >It is the 27th harmonic of the fundamental. This is the problem I have with discussions concerning the harmonic series, it is presented as equivalent to the notes of the scale, even though no musician before the 19th century was even aware of it. Even in the heyday of just intonation (in theory not in practice), no theorist used the Pythagorean ratio for it, the very simple reason being that the intervals were obtained via dividing the octave and subsequent ratios. This is how it was done in the most important treatises such as Zarlino, Galilei etc, and subsequent theorist followed in their footsteps. The 5:3 major sixth differs from the ET and Pythagorean one for one very good reason: it was the one derivation that theorists actually used. Though how the major sixth was used in practice is a much more difficult question, and that was the reason for Galilei's break with Zarlino showed. I just want to re-iterate that all these musical concepts have existed long before the discovery of the harmonic series, and were justified differently. The harmonic series definitely does not "explain fully" any ratio as this comment thread has amply shown. It is an invention of the 19th century that people have tried to bolt on to existing concepts which nevertheless requires significant contortions and even so come up deficient. For the audience, I highly recommend reading through the first chapter of Galilei's Dialogo which presents a historical derivation of the intervals of the scale and the many difficulties attending to just intonation. https://digital.library.unt.edu/ark:/67531/metadc500437/ https://digital.library.unt.edu/ark:/67531/metadc500437/

PaulDavisThe1st 5y ago
It seems to me that you are confusing two claims. 1. a claim about the history of how common western pitches were selected over time. 2. a claim about acoustics and physics shaping the overall process of how humans (and some other animals) select pitches. I am not suggesting for one second that the actual history of the 12T scale has been explicitly rooted in an understanding of the actual physical harmonic series. I am suggesting that many of the choices made throughout time, both in western europe and other cultures, and also by some other species that sing (e.g. some birds) have been shaped by the physics of the harmonic series.

PaulDavisThe1st 5y ago

It seems to me that you are confusing two claims. 1. a claim about the history of how common western pitches were selected over time. 2. a claim about acoustics and physics shaping the overall process of how humans (and some other animals) select pitches. I am not suggesting for one second that the actual history of the 12T scale has been explicitly rooted in an understanding of the actual physical harmonic series. I am suggesting that many of the choices made throughout time, both in western europe and other cultures, and also by some other species that sing (e.g. some birds) have been shaped by the physics of the harmonic series.