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Avoid note - how do we identify them ?
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Arteinvivo
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PostPosted: Thu Mar 10, 2005 8:22 pm    Post subject: Reply with quote

Bjorn wrote:
....Have you tried it? and do you like it?

Sure, it's really interesting, so by using just the chord tones of these chords, different lines could be built.

If you have time, visit this site:
http://people.uncw.edu/russellr/diminished.html

It states something similar but with examples. This helped me to understand your post more fully.

Thanks
--
Arteinvivo
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Chrsitian
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PostPosted: Thu Mar 17, 2005 1:03 pm    Post subject: Reply with quote

So bjorn - basically what you are doing as adding a secondary dominant before each chord in a backcycling progression. I.e.:

Bm7 E7 Am7 D7 GM7

Bm7 B7 E7 Am7 A7 D7 D7 GM7

Then tritone substituting them

Bm7 F7 E7b9 Bb7 Am7 Eb7 D7 Ab7 GM7

Rather busy!
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Arteinvivo
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PostPosted: Thu Mar 17, 2005 8:59 pm    Post subject: Reply with quote

AT the beginning of this new topic, I asked how do we identify an avoid note in a particular scale when played against a particular set of chords or a simple chord though I have not had a specific answer I thought maybe some of you might be interested by what i found out on the WWW searching for something else.

If you visit this page (see link) there is a good article that explains how to deal with this mysterious avoid note that we find in every major scale. Here is a cue, this avoid note split every major scale into two families (Resolved/Unresolved).

http://www.guitar9.com/columnist244.html

see also http://www.guitar9.com/columnist322.html
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Christian
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PostPosted: Fri Mar 18, 2005 12:57 pm    Post subject: Reply with quote

That's what I though I said. Obviosuly I didn't say it clearly!

Indeed - it's a specific property of the 4th whch is found in the Ionian and Mixolydian modes, that splits the major scale into two segments.

All jazz cadences are based on the resolution of the 4th to a 3rd.
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PostPosted: Fri Mar 18, 2005 1:02 pm    Post subject: Reply with quote

The guy on the site is saying what I said - only simpler. Simpler is always better when explaining stuff, so tip of the hat.

However, the D triad doesn't contain a C, so must be resolved.

The theroy works for jazz. For common practice, you also resolve the 7th (F#) In jazz, the F# can be used to colour the tonic chord, (in a major 7th chord) so it must have a different function.

If anyones interested, there is a specific mathematical reason why the 4th sounds unresolved.
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Christian
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PostPosted: Fri Mar 18, 2005 1:03 pm    Post subject: Reply with quote

By common practice, I meant 'classical harmony.'
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Arteinvivo
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PostPosted: Fri Mar 18, 2005 8:41 pm    Post subject: Reply with quote

Quote:
If anyones interested, there is a specific mathematical reason why the 4th sounds unresolved.


Well, at this point of the discussion why not ? I am anxious to see the reason. Go ahead, let us know.

Thanks
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Christian
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PostPosted: Mon Mar 21, 2005 6:40 pm    Post subject: Reply with quote

OK - see if I can put this in the 5 minutes I have left!

Every chromatic interval can be found in the acoustic overtone sequence, transposed doiwnward by a relevant number of octaves. Mathematically, these ratios will have a power of two on the right hand side. The order of these ratios, gives you a set of intervals that boradly correspond to the order of inside and outsideness one would associate with the tonic major region of harmony. For example:

1:1 (Unison)
2:1 (Octave)
3:2 (perfect fifth)
5:4 (major third)
9:8 (major second)
13:8 (major sixth)
15:8 (maj 7)
25:16 (augmented fifth)
45:32 (augmented fourth)
75:32 (aug 9th)
135:64 (minor 9th)
75:64 (augmented second/minor third)

and so on (with some missong, cos I can't remember the ratios!)

I think - let me know of any errors in calculation.

The 4th is the last of these intervals that can be recovered in this way. You have to go a *long* way up into the overtones to find it. As a result, the ears find it even more tenuously connected to the fundamental than the tritone, dominant seventh or minor ninth. The addition of the fourth to any set of notes drawn from this 'acoustic major set' of tones will make a chord sound very dissonant. However, it can also, in the company of the right set of notes, give the effect of a different harmonic region. For example, ratios based on 3:

4:3 (P4)
5:3 (major sixth)
and so on

For minor, you use a different set of RHS - 5 - for example - gives you minor third 6:5 and minor sixth 8:5.

Obviously, these intervals are approximated in some way by Equal Temperament. The more approximate the interval and the more complex it's ratio (e.g. the tritone) the more dissonant it will sound. In fact for ET - for inaccrately tuned intervals, you will find a closer approximation higher up the overtone sequnece, but the interval will be more complex.

I'll post a more complete examination, when I have the ratios I worked out to hand.
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Arteinvivo
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PostPosted: Tue Mar 22, 2005 9:52 pm    Post subject: Reply with quote

Here is a place to get another point of view :
How Tones and Overtones REALLY Work
http://web.archive.org/web/20021215232312/http://completechords.com/Pages_Sidebranch_Free_Features/How_Music_Really_Works/How_Music_REALLY_Works_Full_Index.htm

I had to search the waybackmachine.org because the original site has remove this info from their site.

BTW it is a wonderfull tutorial on how music really works.

Have a nice reading (thousands of page to read there)
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Christian
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PostPosted: Wed Mar 23, 2005 1:36 pm    Post subject: Reply with quote

The site is a good primer on the basis of conventional music theory. It has no great insight on to how 'Music Really Works' no-one knows that, and I'm glad that this is so!

Many of the assertions seem unsupported. The site is similar to lots of articles and books I have read on the subject, some by extremely famous musicians - Paul Hindemith, Leonard Bernstein etc.

All these guys filled in the gaps in reasoning with wishful thinking. They were great musicians, but not very rigorous thinkers despite having all the brains you could wish for. This may sound arrogant, in that I will maintain that although I'm willing to admit I am not as good musician as Bernstein (putting it mild), I am a better trained reasoner, having trained as a physical scientist, and therefore feel I am in a position to attempt to refute the assertion, for example that the 'major pentatonic is common to all cultures' (Bernstein's assertion is simply wrong from the standpoint of empirical musicology)

Deriving traditional Western music from the overtone sequence is a) somewhat specious b) smacks of imperialism.

For example, Indonesian musicians use a 5 tone scale which is tuned equally over the octave. I would disagree that there is anything 'universal' about the major scale - its just that the scale has some properties which make it useful for writing dynamic harmony - for example the natural fourth dividing into two clear regions (as mentioned above.)

Also, the 7th overtone is often thought unmusical. Most musical instruments tend to minimise its prominence.

However - that's not to say that science and acoustics has no bearing on music - after all pitch and intervallic relationships are one of music's raw materials (though not the most important.) Acoustics does not dictate what shape music takes (e.g. - there is nothing universal about major scales) but it dictates how a certain set of materials - such as the Western scale - will behave.

Something worth adding is that even within Western Music the overtone sequence *does not* give the musical intervals. At risk of repeating myself, the overtone set is just one of a number of different sets of interval/ratios. Intervals based on the overtone set will have only right hand sides based on powers of 2.

Minor harmony, for example, involves ratios with 5 on the right hand side - e.g. 6:5 (minor third) and 8:5 (minor sixth.)

In 18th century temperaments these thirds and sixths were more exactly tuned in near keys, but in modern Equal Temperament they are rather sharp. My belief is that the adoption of ET circa 1860 changed the way the intervals sounded (before the intervals sounded different in each key) and put the fourths and fifths more or less in tune. Therefore, Hindemith/McTyner quartal chords, static extended chords and stacked fifths became popular - because they sounded good in the new tuning, whereas in the old they would have sounded out.

Of course ET can approximate only some of those - there are many musical sounds that fall between the cracks of the piano. Harry Partch, for example, devised new instruments so he could get at these different sounds.

None if this will help you play jazz though! Really it's all rather abstract... Like I say, we can argue about this stuff for ever, but it won't really help us play any worthwhile music... Music comes from the heart and instict, not cerebral calculation.
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