# Extended theory question



## death of k (Oct 21, 2010)

okay, I'm not sure quite how to word this question, but i'll try my best.

i know with post-secondary education of music theory there's somewhat of a complete chart or understanding regarding all the potential musical intervals, and how they relate to eachother that goes into chromaticism as well as diatonic function. an example of this would be the use of a fifth interval to prepare the root or tonic in something like a cadence. 

i've been searching for some extension of this, something that might include interval relations of Maj and min seconds, thirds, P4ths and aug 4ths, sixths etc. as well as how these functions vary between the various modes, and ourside of key (ex. what would the effect of playing a perfect forth in lydian do?)

ANY advice, or direction would be greatly appreciated, thank you.


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## Mr. Big Noodles (Oct 21, 2010)

Are you asking for harmonic succession, or something more akin to modal theory? They share some basic concepts, so I guess it doesn't matter. I'm going to get breakfast, so I'm just going to cover harmonic theory right now.

For harmonic progressions, we can break it up by chord.

I - preceded by V, vii°, ii (linear), or bII (linear, or dominant-tonic relationship). iii happens occasionally, as a mediant relationship. The same functions are present in the minor mode.

V - preceded by a pre-dominant chord, including ii, IV, vi, I (especially the I6/4 in contrapuntal music), and a slew of chromatic chords, including the Neapolitan, the augmented sixths (really, any note can be ornamented by an augmented sixth chord), and secondary functions (V/V and vii°/V). Once again, the parallel functions from the minor mode apply, as they will in all of these.

vii° - same as V, excluding chromatic relationships, except those that are chromatically related to vii°, such as #vi°, i°, etc. These usually appear in relationship to a chromatic scale.

ii - preceded by I, IV, vi, or secondary chords, including augmented sixths. In jazz harmony, biii or bIII are also seen approaching ii (linear progression), and mediant relationship (or chromatic mediant).

IV - pretty much the same as ii. Preceded by I, vi, secondary functions, augmented sixths, V (blues), iii (linear), bV (also linear, but chromatically), and mediant relationship (or chromatic mediant).

vi - preceded by I, vii° (especially when encountered in a descending progression, such as I vii° vi V, etc., or when functioning as a dominant), V (deceptive cadence, or linear), bVI (chromatic linear), secondary functions, augmented sixths, mediant relationship (or chromatic mediant).

iii - preceded by I, ii, vii°, V, IV (linear), secondary functions, augmented sixths, and chromatic linear relationships.

Here are a couple diagrams of diatonic functions, using the circle of fifths progression:












This is a thing illustrating chromatic mediant relationships. I'll cover PLR relationships later:






Edit:

Okay, really quick explanation on PL, PR, LR, and PLR progressions. We're going to be dealing with three chord functions that avoid dominant to tonic relationships in a fashion that's called "parsimonious voice leading", which is a fancy way of saying that there's not a whole lot of note movement in this style. The way this is accomplished is by making cycles of chords that are related to each other by the parallel major or minor chord (P), two chords related by mediant that have a half-step between one chord tone and another in a progression called "leading tone exchange" (L) (For instance, between C and Em, B is the leading tone of C; between C and Ab, G is the leading tone of Ab), and two chords that form the relative major and minor tonics in their own key (R, for relative).

This involves making a cycle based on the four relationships stated above. A PL cycle contains a reference chord, its parallel major or minor, then a leading tone exchange, and repeats however long you want it. I warn you, this isn't the most applicable stuff. Examples:


```
C - Cm - Ab - Abm - E - Em - C
T - P  - L  - P   - L - P - L
```
Here's PR, alternating between the parallel and relative.


```
C - Cm - Eb - Ebm - Gb - Gbm - A - Am - C
T - P  - R  - P   - R  - R   - R - P  - R
```
And here's LR:


```
Cm - Ab - Fm - Db - Bbm - Gb - Ebm - Cm
T  - L  - R  -  L  -  R  - L  - R  - L
```
Finally, PLR:


```
C - Cm - Ab - Fm - F - Db - Bbm - Bb - Gb - Ebm - Eb - B - Abm - Ab - E - C#m - C# -
A - F#m - F# - D - Bm - B - G - Em - E - C
```
That last progression uses every major and minor chord in the 12TET system. I think I actually screwed up in there, because there shouldn't be any repetition. Oh, well. You don't see these sorts of progressions very often, because the complete cycle doesn't have a whole lot of application, and it's a pain in the ass to keep track of where these things are going, especially when you have twenty-four chords to worry about. I, also, am not a big fan of parallel major-minor relationships being used willy-nilly, and mediants tend to be pretty dramatic. John Coltrane used these sorts of progressions, but I don't know of many other examples.


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## bostjan (Oct 21, 2010)

death of k said:


> (ex. what would the effect of playing a perfect forth in lydian do?)



A lydian with a perfect fourth added would be the same as a major with a tritone added. There are octatonic blues scales that have tritones along with perfect fourths and fifths, as well as others with major and minor sevenths.

Ionian Tritone Blues (Octatonic) : 1 2 3 4 b5 5 6 7
Major Dominant Blues (Octatonic) : 1 2 3 4 5 6 b7 7
Aeolian Half Diminished Blues (Octatonic) : 1 2 b3 4 b5 b6 b7
Aeolian Major 7 Blues (Octatonic) : 1 2 b3 4 5 b6 b7 7


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## DatM (Oct 21, 2010)

death of k said:


> okay, I'm not sure quite how to word this question, but i'll try my best.
> 
> i know with post-secondary education of music theory there's somewhat of a complete chart or understanding regarding all the potential musical intervals, and how they relate to eachother that goes into chromaticism as well as diatonic function. an example of this would be the use of a fifth interval to prepare the root or tonic in something like a cadence.
> 
> ...



Are we talking melodies or chords here? Not quite sure what you're asking.


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## death of k (Oct 22, 2010)

thanks a ton to schecterwhore and Bostjan for the information, that will keep me busy for a while

in general my question is as open ended as possible. i suppose the most common practice of harmonic succession is in chord voicings, but would the same concepts not apply to to each mode's degrees in a melodic context? 

im sorry if im not being clear, i believe i'm searching for an understanding of the behaviour and general purpose of each mode and degree relative to every other mode and degree, in either a melodic of chordal context


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## Holy Katana (Oct 22, 2010)

I don't know if this is exactly what you're looking for, but here's a book that might provide some insight: Amazon.com: The Craft of Musical Composition: Theoretical Part - Book 1 (Tap/159) (9780901938305): Paul Hindemith: Books

I have it. It's really, really interesting.


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