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 Post subject: Re: The Scale Fingerings
PostPosted: Sat Nov 12, 2011 12:36 am 
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In major scales the simplest description of key progression is to say that every time you go up a fifth you have to either add one more sharp or subtract a flat (or if you go down a fourth you either subtract a sharp or add a flat). If tetrachords in any way "caused" that, this leaves absolutely no explanation as to why an identical rule holds together the progression between natural minors- despite an absence of tetrachords. We have similar cases (when viewed in terms of how key signatures progress), only one of which involves the notion of a tetrachord.

I think this is most concise proof I can think of, that the tetrachord is not a concept that causes anything- but rather an observation of an incidental detail. Quite why it does work out in a way where you end up keeping the same sharps and flats (plus or minus one) every time you move up a 5th or down a 4th, is probably one for an extremely advanced mathematician.

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 Post subject: Re: The Scale Fingerings
PostPosted: Sat Nov 12, 2011 2:49 am 
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Joined: Mon Nov 29, 2010 7:28 am
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Location: Springfield, Missouri, USA
Quote:
In major scales the simplest description of key progression is to say that every time you go up a fifth you have to either add one more sharp or subtract a flat (or if you go down a fourth you either subtract a sharp or add a flat).
You meant down a fifth, not a 4th. Interestingly this is one of the reasons that the subdominant is called such: it is the interval of the 5th below the tonic, hence sub-dominant.

It has been a refreshing discussion on things theoretical.

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 Post subject: Re: The Scale Fingerings
PostPosted: Sat Nov 12, 2011 2:55 am 
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Joined: Sun Oct 30, 2011 1:07 am
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musical-md wrote:
Quote:
In major scales the simplest description of key progression is to say that every time you go up a fifth you have to either add one more sharp or subtract a flat (or if you go down a fourth you either subtract a sharp or add a flat).
You meant down a fifth, not a 4th. Interestingly this is one of the reasons that the subdominant is called such: it is the interval of the 5th below the tonic, hence sub-dominant.

It has been a refreshing discussion on things theoretical.


Oops- yep, up a fourth or down a fifth for the second of those statements.

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