Dominant 7th tuning

Ray Tomes wrote:

>Subject: Re: blues scale
>
>monz@juno.com wrote:
>
>>It's important to emphasize that in the blues, the '7th' is
>>used as a *harmonic 7th* (7:4) in virtually every chord.
>
>I Agree.
>
>>I feel this rational interpretation is valid because these
>>chords *do not* follow the type of 'dominant 7th' resolution
>>rules that classical music uses (which require a non-harmonic
>>'7th').
>
>I have been in this argument before, but I don't think that the chord
>C-E-G-Bb can possibly mean anything other than the ratios 4:5:6:7 in any
>system of music. It may be classically correct that Bb is 16/9 times C
>or whatever (which it would be if played with an F) but the raios would
>then be 36:45:54:64 which is impossibly complex to be "intentional".
>IMO the old theory does not match the composers "real musical intention"
>which must be 4:5:6:7 even if the instrument cannot produce that as
>ratios of 36:45:54:64 can have no meaning at all.

This may well be true of the blues, but I suspect that in most cases if you
presented a composer who had assumed a 12-tET or meantone keyboard, with a
4:5:6:7 chord where he or she had specified a dominant 7th chord, they
would find it quite strange. I tend to think of it as an augmented 6th
chord or a harmonic 7th chord and quite different from a dominant 7th.

You are ignoring the possibility of chords which, although they have quite
high numbers when represented as a subset of the harmonic series, contain
intervals or sub-chords, all of which are low on the harmonic series. i.e.
multiple virtual fundamentals.

One such possibility for the dominant 7th is
C E G Bb Errors in 12-tET
------------------------------
4:5:6 +13.6c, -15.6c, -2.0c
5:6 -15.6c
5 : 7 +17.5c
5 : 9 -17.6c

Note that the last 3 lines above can be abbreviated to 1/9:1/7:1/6:1/5, not
that I think this gives any added consonance over the individual intervals
involved, unlike the 4:5:6.

Note also that this version of the dominant 7th cannot be consistently
tuned in JI, the 5:7 being inconsistent with all the others. So it doesn't
even _have_ a representation as x:y:z:w. However the resulting 36/35
quarter-tone error is extremely well distributed in 12-tET.

In contrast, the proposed 4:5:6:7 has 12-tET errors of 31 and 33 cents in
the 4:7 and 6:7.

>The problem is that
>apart from the main notes in the key the others have multiple possible
>different meanings and so a strict rule will often be wrong.

Indeed. Which is one reason I'll stick to working on adaptive meantone
without ratios of 7, for now.

Regards,
-- Dave Keenan
http://dkeenan.com

I wrote:
>>It may be classically correct that Bb is 16/9 times C
>>or whatever (which it would be if played with an F) but the raios would
>>then be 36:45:54:64 which is impossibly complex to be "intentional".

Monz and Dave Keenan said I am wrong, and they are right.
These ratios are possible. I take it all back. Thanks guys.

-- Ray Tomes -- http://www.kcbbs.gen.nz/users/rtomes/rt-home.htm --
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