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Alex_
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so every V/V just descends a 5th..

so V/V in C.. V = G and therefore V/V = 5 and then V/V/V  = F.. and then V/V/V/V = Bb...

and mixolydians are played over these because mixolydians go over the 5th.. and this is The Cycle of fifths

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vii ?? tritone?? cricket bat?? can someone explain.

argus
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I can't explain the cricket bat, but if you want a popular example of the circle of fifths, listen to "Hey Joe"

It's in E and the verse progression is

C - G - D - A - E

or

IV/IV/IV/IV - IV/IV/IV - IV/IV - IV - I

Musenfreund
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hbriem
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[quote author=Alex_ link=board=theory;num=1063250195;start=45#45 date=09/11/03 at 11:17:33]vii ?? tritone?? cricket bat?? can someone explain.[/quote]

The V7 (the dominant) is almost the same chord as the vii diminished.  They can reliably substitute for each other and have the same harmonic function, i.e. leading you back to the I in a perfect cadence.

How so?  Well, look at the notes in the V7 : 5-7-9-11 and the vii: 7-9-11.  3 common notes.  In C major, the G7 has the notes G-B-D-F and the Bdim has B-D-F.

Now the important thing about these 2 chords and what gives them their restless, yearning quality, is the tritone interval (#4, b5, 3 whole steps,diabolus in musica) between the 11 and the 7 (F-B).

It is the tritone interval in the dom7 chord and its resolution to the I (or i)  that is the most important element in Western key-based music.

Oh, yes, argus said that each key contains only one dominant chord (the V7).  He joked that if Notepad pointed out that the vii is a kind of dominant chord too, he would get struck with a cricket bat.  A cricket bat is a flat wooden implement used in the sport of cricket.  In the US you might threaten people with a baseball bat instead.
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argus
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[quote author=Helgi Briem link=board=theory;num=1063250195;start=45#48 date=09/12/03 at 06:05:21]
diabolus in musica[/quote]

Where did this term come from? I heard that it came from the Middle Ages where a diminished 5th interval was considered sacreligious.

Musenfreund
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What a fascinating term.  It is apparently also called a "wolf fifth".

Indeed, your explanation seems to be the case.  In the very early church, rhythm was essentially banned as well -- too sensual, too diabolical.  Hence the use of chants.

At any rate, though I've no idea how reliable it is, here's a link to a site on devilish music, from which the Bosch image above was taken:

http://music.research.home.att.net/Bosch_Music.htm
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hbriem
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Where did this term come from? I heard that it came from the Middle Ages where a diminished 5th interval was considered sacreligious.
I've heard the same story.

On the other hand I've also heard that this story is just urban legend and that the interval was never actually banned, just avoided because of its general nastiness.

I have been unable to find out which is true, as eminent authorities swear to both.
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NoteBoat
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There were several things structurally different about the middle ages that led to the naming of the 'wolf' interval, or 'diabolus in musica' (the devil in music) as it was also referred to...

First, the music of the middle ages wasn't polyphonic, so these intervals occurred melodically, rather than harmonically

Second, it's not the same interval we play today. Â They didn't have equal temperment (or its predecessor, well temperment), so the interval C-F# wasn't the same as C-Gb.

In our tuning systems today, we measure chromatically in half steps, and each half step can be divided into 100 increments called 'cents'. Â Having 12 tones in a chromatic octave, the wolf interval is 600 cents above the tonic.

If we rely on Pythagorean tuning, F# is 588 cents above C, and Gb is 612 cents above C... a difference of almost 1/4 of a half step between the two!... so the wolf interval sounded a lot more out of tune then than it does today.

It's also incredibly difficult to sing, which is probably the major reason it was avoided -- the vast majority of music in the middle ages was vocal.

Unfortunately, I don't read Latin or Greek, and I don't have any primary resources dated before 1725, so I can't definatively say if it's legend or not... but in modern translation I find references to this interval's use for composition dating back to 1555. Â As this roughly corresponds with efforts to create a temperment system, I suspect that the use of 'wolf' intervals came about because they weren't the same sound as they were a few years earlier!

I don't find any prohibitions, just cautions against using them. The earliest one I've found dates to the early 1300s, with Jacobus of Liege.
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