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Tony Deff
Joined: May 25, 2008 Posts: 51 Location: Suffolk, UK
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Posted: Sun Feb 03, 2013 12:12 pm Post subject:
Mystery of the Minor Chord Subject description: an interesting new viewpoint |
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Seeing the references to Musical Mathematics and Music - a mathematical offering on this forum, reminded me of a time I played detective with the mathematics of chords.
I was too ill to move around and so bored out of my skull that I got to doodling with chord ratios.
I had long known, as is common knowledge, that the major chord is (or, at least, should be) the ratio 4:5:6.
I had also known, as is not uncommon knowledge, that the minor chord is the ratio 10:12:15.
I think you would agree with me that the minor chord is the next most concordant cluster of notes to a major chord, but why should that be?
That would mean that 10:12:15 is the next simplest ratio to 4:5:6, wouldn't it?
It is easy to deduce that 5:6:7 is Nature's diminished chord (from the top of a Just seventh chord — and one not available from tempered scales).
As to what 6:7 and 7:8 sounded like, I built switchable dividers to listen to these ratios.
I could convince myself that 7:8 was acting as a whole tone, and that 6:7 was a form of minor third.
So, where does that leave 10:12:15?
A musical apple dropped on my head when I realised that a major chord upward from a note is "mirrored" downward from the same note. I calculated the reciprocal of 10:12:15. It comes to 180:150:120 = 6:5:4
That is, a minor chord is the reciprocal of a major chord! (Not many people know that.)
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On close inspection of the ratios, the mystery is easily solved. |
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blue hell
Site Admin
Joined: Apr 03, 2004 Posts: 24075 Location: The Netherlands, Enschede
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Posted: Sun Feb 03, 2013 12:50 pm Post subject:
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I didn't know it - interesting! _________________ Jan
also .. could someone please turn down the thermostat a bit.
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Antimon
Joined: Jan 18, 2005 Posts: 4145 Location: Sweden
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Tony Deff
Joined: May 25, 2008 Posts: 51 Location: Suffolk, UK
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Posted: Wed Feb 13, 2013 3:46 pm Post subject:
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Antimon wrote: | - you can't explain music |
You can't explain what some people call music. |
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