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I'm currently reading The Complete Idiot's Guide to Music Composition by Michael Miller and in the "Composing With Chords" section, a reference chart for chord leading was provided and it looks like this:

These Chords       Lead to These Chords         
________________________________________
I                 | Any                 
ii                | IV,V,vii°          
iii               | ii,IV,vi            
IV                | I,iii,V,vii°        
V                 | I                   
vi                | ii,IV,V,I           
vii°              | I,iii               
----------------------------------------

However, the book does not explain why this is the case. Searching via Google does not seem to give any answers either.

Is there a scientific or logical explanation to why these chords "lead" to the specified chords, or is it simply just a result of common patterns in popular music?

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    This seems to be a very bad book as it says it is from an idiot. :) I wonder why you haven’t been linked to questions to answers here in this SE as this point has been mentioned again and again. Perhaps the the search machine was overflowed by the links to the lead guitar. But surely in the idiot’s book will be described the intervalls and the tensions of the lead tones, I hope so at least, otherwise it would fit for a fine chimney fire. – Albrecht Hügli Jan 26 at 22:31
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    The title of the book means the book is for idiots, not written by one haha. I have no knowledge regarding music composition, so the book so far has been helpful for me. – Alexander Sung Jan 26 at 22:40
  • This was a joke hehe. – Albrecht Hügli Jan 26 at 22:44
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    @piiperi This table is meant as a general guideline for creating chord progressions. Say you want to come up with a chord progression, you can start with I, then follow it with any chord as mentioned in the table. If you pick IV, then based on the table, you can follow it with I, iii, V, or vii*... etc. – Alexander Sung Jan 26 at 23:27
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    What might happen if someone decides to follow a chord with one not shown in that list - like V>vi, or V>IV, as happens in nearly every 12 bar blues?! Maybe the author hoped there were many idiots out there who would buy his book... – Tim Jan 27 at 12:40
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Your question can’t be answered without referring to the tension of the lead tones. The tones of a scale near the consonant intervals referred to the root have a tendency to lead to the next perfect interval. (Ti is tending to resolve into do, re to do, la to so, fi as augmented 4th toward so.) A similar tension show the steps near the 3rd and the 6th. (Fa leads to mi) The tension for a solution of a halftone step is stronger the the tension of whole tone.
That means that the altered tones have a stronger tendency to resolve into the next consonant interval (ri will lead to mi, si to la, ta to la).

These are just examples, you’ll find others by yourself.

According to Ernst Kurth (1913, 119–736) the major and minor thirds contain "latent" tendencies towards the perfect fourth and whole tone, respectively, and thus establish tonality. However, Carl Dahlhaus (1990, 44–47) contests Kurth's position, holding that this drive is in fact created through or with harmonic function, a root progression in another voice by a whole-tone or fifth, or melodically (monophonically) by the context of the scale. For example, the leading tone of alternating C chord and F minor chords is either the note E leading to F (if F is tonic), or A♭ leading to G (if C is tonic).

The leading-function of a chord and its tendency to resolve into another chord is a similar function as the function of the leading-tones it is consisting of.

In the link below is explained how this tension of the leading-tones as an element of chords are functioning.

The rest is up to developing as you surely are not what the title of your book says.

https://en.wikipedia.org/wiki/Leading-tone

and here is just another link explaining the doremi as relative scale that can be transferred to all scales and keys:

Movable do solfège

  • Forgive me for my ignorance, but what is "ti", "fi", "so", "ri', and "ta"??? – coconochao Jan 28 at 13:09
  • They are like explained in the link the relative names of the degrees or steps of the scale. You can relate them to the scale of major C: If C=Do so you can count either 1,2,3,4,5,6,7, or C,D,E,F,G,A,B or use the relative names of the do re me en.wikipedia.org/wiki/Solf%C3%A8ge Do Re Mi is finally nothing else than numbering the steps but the difference is do vowels are expressing the lead tone function better than just numbers do. Look at the altered names: all sharpened # become an i (e.g. Fa -> Fi, and all flattened become an a or u (Ti->Ta). Try it out. I'll show it later. – Albrecht Hügli Jan 28 at 13:31
  • Oh, I didn't realize that the link would explain this. Thank you for the explanation! – coconochao Jan 28 at 13:42
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Is there a scientific or logical explanation to why these chords "lead" to the specified chords,

Albrecht already answered as to the musical logic regarding 'leading.' Basically, half steps have a strong pull.

But I think something should be said about 'common patterns.'

or is it simply just a result of common patterns in popular music?

Yes, common patterns are important. In fact I think several of the options for progressions in the chart come from common patterns. But the chart doesn't explain the connection to such patterns.

This the following is a loosely organized list of some patterns you might look into:

  • 'functional harmony' which groups chords in predominant, dominant, and tonic categories and defines a syntax of progressions from predominant to dominant to tonic.
  • 'strong progressions' generally considered root movement by descending fifth, descending third (from the tonic), or ascending step (from IV to V)
  • hugely important are 'harmonic sequences' where typically a two chord progression like a descending fifth or fourth is then repeated a step higher or lower, one very well known sequence is the circle of fifths.
  • root progression by step is also used, but in classical style the chords will be in first inversion some refer to this as 'fauxbourdon', root position chords can also move by step but it is probably more common with pop styles bVI bVII i is one example.

That isn't a complete list of patterns. It's just a starting point. But even from that short list certain things can be seen.

For example, iii ii is considered a weak progression compared to a strong progression like roots by descending fifths. But, in the context of root movement by step it's a fairly common pattern.

Of course we need more than two chords to establish a clear pattern.

And that is what I think the potential pitfall of the chart is. It doesn't explain how some of those potential progressions fit into common patterns.

Nearly any two chords could could be used in succession depending on the surrounding musical context. In that sense the chart is both obvious and meaningless, because it doesn't explain how to create the context that gives chord progressions meaning. It's a kind of musical anti-pattern!

Some might say the chart is a kind of 'harmonic training wheels' for a beginner, but I actually think it will just lead to a beginner becoming confused.

Without some knowledge of common patterns there is the risk of the chart producing weak, meandering progressions like... I ii viio iii ii IV iii ii.

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