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E-mail from a friend of mine. She has a PHD in Music Theory. My question is how is the term 'fifth' derived?

Ah, there are so many things to say about music and fifths...  :)

I don't have a reference for you, but here's what my answer would be:

1) The music came before the math. Natural overtones were found naturally and then were explained mathematically (the chicken or the egg?). Music was part of art, philosophy, and science, and the thinkers looked for ratios common to the order of the universe. The musicians didn't necessarily think about the math; they performed the music.

2) Unison and octave-displaced singing came first. Next came "organum" - parallel 5ths of the type you are talking about...not that they were called fifths then...the singing of the music also came before the notating of the music. Most music was performed and taught in the church, which is significant because of the acoustics in the churches and in medieval castles...the natural overtone series was amplified in these spaces. The first harmonic in the overtone series is the octave; the second is the perfect fifth (not that it was called that back then...medieval music was often notated between the span of the 4th , or the tetrachord, with various names for the different combinations). When the intervals of the harmonic series are sung in acousticaly live spaces, the remaining tones in the series are amplified naturally, providing a fuller, resonant, more "colorful" sound. So you have the octave, the fifth, the repeating octave, the next interval is a third, the repeating fifth, and finally other notes begin to enter into the basic sound.

3) These early parallel fifths and later thirds, along with the 4th (inverted 5th) became the basics of early modes. These intervals naturally resonated vocally, but also because of the underlying mathematical properties, early musical instruments would naturally divide along these same intervals - trumpets without valves would be able to produce octaves and fifths more easily than smaller divisions of the octave.

4) Since the dawn of Medieval modes, Western music has been based on a series of steps between the octaves - some half steps and some whole steps, based on the mode of choice, but always 7 tones and then the repeating octave at #8. These eventually evolved into the major/minor harmonic system, scales with 7 tones....really long story behind this evolution, with consonant and dissonant sounds equated with good, evil, and various emotions; earlier tetrachords being combined to create the modes. Also, because information from the early Greeks is so sparse, there is much about their systems we don't know. The 12-note chromatic scale became possible only after equal temperament - the natural qualities of instruments and voices lent themselves to various 7-note divisions of the octave before mathematics made the 12 chromatic notes more equi-distant.

(As an aside, there is now a whole field within musicology dedicated to the study of early instruments, early tuning, etc. For example, A has not always equaled was not standardized until way later into music history.)

5) Finally...if you sing "do re mi" in numbers, "1 - 2 - 3," with a number for each note of the 7-note scale or mode - voila, thirds and fifths...the "contrived" naming you so rightly refer to after they "filled in the notes." Some schools teach sightsinging using numbers instead of the syllables, because kids instinctively know that 1 - 5 is bigger than 1 - 3. It drives the purists crazy because of the missing half-steps. Also, they will tell you that learning to sing solfeggio - do, re, mi, fa, sol, etc. - allows the singer to tune to the overtone series instead of to the mathematically-based equal temperament scale. Theoretically, singers who sing a cappella can tune to the harmonic series rather than to the equal temperament scale...another whole area of interest and study.

So - the concept and practice of thirds and fifths long pre-dates us calling them that; it's based on the mathematical ratios because the ratios explain the naturally occurring phenomenon of the harmonic series...the music of the universe...and the contrived names help us mere mortals communicate about it.

If you want, you can wade through any music history textbook and gain a basic understanding of the order of things - the one I used was by Grout, "A History of Western Music." Any music theory textbook should explain more about tetrachords and the harmonic series, out of which early scales grew. I wouldn't know where to go on-line; I'm still old-school when it comes to textbooks!

And I loved trying to answer your question - I hope it helped. Thanks for asking!



Hope all is going well!

I have a music question and perhaps you can point me in the right direction.

I subscribe to Flat Picking Guitar magazine and this month they have an article about creating 2 part harmonies. The idea is to play something different than the 100 other guitarists at jam sessions. They start with some basic theory and describe creating a parallel harmony (3rds and 5th). Then show how it's kind of an art as to the final decision for a harmonized note. So I started brushing up on basic music theory, which lead me back to some basic questions. .. which I can't seem to answer.

Why is a fifth called a fifth? Is this a contrived term after they got done filling in the notes? I read all the stuff about Pythagoras and the subsequent agreement on equal temperament, but I still don't understand how you derive the term 'fifth' starting from the basic 3:2 ratio.

So far, I've read several web sites, including some rather complex explanations.

For example:


Can you provide a reference I can study? This could be a case that I'm just not seeing the obvious.