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About This Author
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La Bene Vita
I am a professional musician  , worship leader , small business owner , songwriter , aspiring author and freelance nonfiction writer with a chemical engineering degree .
But that's just my resume.
My profile of qualifications is only one of the ways in which I am unique. Here I chronicle my personal and professional goals and my efforts to achieve them. Occasionally I fail. Mostly, I take daily baby steps toward all my long-term goals. Much like the stories I pen, the songs I compose, and the businesses I run, I am always a work in progress.
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I should get writing credit for this. A former adult student who may be geekier than I ( ) posed this question on Facebook:
Here's a bit of music theory to dabble with...
The fifth in a scale is called the "perfect fifth". The ear loves it with a passion: So much so that it has a vile hatred of the diminished fifth, or tritone. The fifth is even called the "dominant". Musical tuning and key signatures revolve around the fifth...literally. (circle of fifths)
But why is that? I wondered about the underlying math. The ear accepts an octave as the same note because it is double the frequency. A4 is 440 Hz. A5 is 880 Hz. A3 is 220 Hz. The chromatic scale has 12 progressive semitones (minor seconds), and the fifth happens to be 7 semitones above the tonic. (12 and 7 are Divine numbers.) What's 7 the number of? Divine completeness. Six is the number of man. The tritone is only six semitones above the tonic.
Does your ear really understand that? It might. But what is the fifth in terms of actual frequency?
Well, a minor second is 2^(1/12) Hz above its tonic. So it stands that the fifth is 2^(7/12) Hz above. And that power is almost exactly 1.5. (It's actually 1.49something). Incidentally, the tritone, being six semitones above tonic is exactly root two. That's right, the square root of two times tonic. Since A major has 3 sharps (F, C, G), and the fifth is E natural, it stands to reason that E4 is just under 440 x 1.5 Hz, or almost 660 Hz. The ear likes that interval.
My answer:
Andrew, you don't ask simple questions, do you?? First of all, consonance (the opposite of dissonance) is entirely subjective. Yes, we have centuries of study that show harmonics are pleasing to the ear of the average person, but that's still only the average person's opinion. Consider that different rules apply across the world; we are mostly familiar with Western music. Also, consonance would be boring without dissonance, which gives us the ability to color our music with emotion and expression.
Nonetheless, the perfect fifth is considered pleasing to the ear by general consensus. Mathematically, the perfect fifth has the simplest frequency ratio (see "pitch ratio" here https://en.wikipedia.org/wiki/Perfect_fifth) except for the unison and octave intervals. If you would like to conjecture about the spiritual basis for the consonance of the perfect fifth, I certainly enjoyed reading your theories. I can only add that if you believe that God made all things beautiful and all things unpleasant, then it follows He is responsible for the design of audio frequencies and their relative consonance or dissonance. I find it entirely believable that He would have a sense of humor or at least irony about the whole thing.
In your question, you correctly stated that the pitch ratio of the perfect fifth is 1.5, but consider it this way instead: 3/2. The octave is 2/1.The perfect fourth is 4/3, also considered a highly consonant interval, and the major third is 5/4. The augmented fifth, according to this chart (https://en.wikipedia.org/wiki/List_of_pitch_intervals), is 25/16.
When multiple audio frequencies are heard together, they do not remain independent. They interfere with one another. So the relative frequencies, and how simple or complex they are with respect to one another, will impact the resulting frequency that you hear. For the perfect fifth, independently, the fifth oscillates three times for every two oscillations of the root. This is why we consider pitch ratios in whole number fractions instead of decimals to evaluate their simplicity (where "simplicity" is an indicator of consonance.) |
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Thanks for sharing!
Even better if she can whistle to the tune of Mozart or something. 
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, also known as Michelle Tuesday, is a musician, educator and writer hailing from Columbus, Ohio.![Merit Badge in Music
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To a dear friend whose talent for writing music is sensational. May you have a fabulous New Year, (((Brandi)))!!! *^*Kiss*^*
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I don't know how you do it, but I assume there's magic involved *^*Bigsmile*^* I have really enjoyed this month of planning and preparation for NaNoWriMo and I love how organized it all is. Thank you for hosting a great challenge and for your dedication to helping so many of us prepare with confidence and trepidation for National Novel Writing Month (known to sane folks as 'November' *^*Laugh*^*) at your [Link To Item #1474311]](https://images.Writing.Com/imgs/writing.com/writers/badges/general-Organization-1150.gif)
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For your hard work, commitment, talent and innovation in running the October NaNoWriMo Preparation each year, which helps many of us get our scattered thoughts together for November's novel-writing. And also because this badge has ducks on it.](https://images.Writing.Com/imgs/writing.com/writers/badges/general-Leadership.gif)
