# rules for resolving chords?



## johnfkingmatrix

Hi, maybe beginner question and im kind of self educating myself /trying to learn, so forgive me if my ideas are disjointed , and ty for you patience:

If i make a chord, like Dm7, how do i figure out what it resolves to? 
I get that you look at the tones, each one has a tendency.. but then i dont know the rules

what about complex chords like Cmaj7(#11)
is there a formula i can use to figure out any chords resolution!?

question 2: 
is this something i would be doing in a chord progression from one chord to the next/ or in a melody where im cycling between arpeggios , just picking the next chord based upon what it resolves to, or would that sound "trite" 


(also.. why does cmaj7#11 sound so dark? if its a major chord)

Thanks guys i appreciate the time you put into schooling me


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## Bwv 1080

Dm7 and Cmaj7#11 do not need to resolve in Jazz, in common practice classical, 7ths need to resolve down by step


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## Festus

Try this:
https://www.youtube.com
and search for resolving chords


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## johnfkingmatrix

Festus said:


> Try this:
> https://www.youtube.com
> and search for resolving chords


i did try that but they keep talking about 13 5 tonality thats why i asked about complex chords, and also the applications of song writing and maybe some quick tips for my shred solos

i seached a ton on resolving 7ths specifically everything keeps talking about the dominant and all i found was this

https://learnmusictheory.net/PDFs/pdffiles/02-10-SATBPartWriting6SeventhChords.pdf

TY bwv1080


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## vincula

johnfkingmatrix said:


> Hi, maybe beginner question and im kind of self educating myself /trying to learn, so forgive me if my ideas are disjointed , and ty for you patience:
> 
> If i make a chord, like Dm7, how do i figure out what it resolves to?
> I get that you look at the tones, each one has a tendency.. but then i dont know the rules
> 
> Thanks guys i appreciate the time you put into schooling me


Don't get it personal, mate. There are plenty of nice people here. Many are perhaps a bit confused by the nature of your multiple questions, pointing in all kind of directions, mainly because those questions clearly show that you must learn the fundamentals first, before embarking yourself in what you call complex chords.

Let's come with an example. Take the Dm7 chord you refer to. I come up with a few examples:

Dm7 is the iim7 chord in C major
Dm7 is the iiim7 in Bb major
Dm7 is the vi7 chord (relative minor) in F major

So depending on the chord progression, Dm7 will function/resolve in a different way. Here are some common ones:

*iim7* V7 Imaj7: *Dm7*---G7---Cmaj7

Imaj7 *vi7* iim7 V7 Imaj: Fmaj7---*Dm7*---Gm7---C7---Fmaj7

Imaj7 *iiim7* vi7 iim7 V7 Imaj7: Bbmaj7---*Dm7*---Gm7---Cm7---F7---BbMaj7

There are of course many other possibilities. Just an example!

Hope it helps... Hey, all "simple chords" 

Regards,

Vincula


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## Guest

Bwv 1080 said:


> [...] in common practice classical, 7ths need to resolve down by step


That's generally true, BWV, but with certain caveats: in the 2nd inversion of V7, the 7th rises.
Sorry to be the pedant in the ointment [sic] !!

*Note for Mr Penfold*: please submit my reply to Private Eye's _Pedants' Corner_ rubric. And if published, shall we split the tenner 50/50?


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## vincula

In jazz 3rd and 7ths of the chord are the basic _guidelines_ and you can connect the chords using _voice-leading_, resolving each chord smoothly into the next one. Great way of finding melodic lines for improvisation. Of course, it all depends what your intentions are.

This is an example based around the shells (3rd & 7th's) of a chord progression using the jazz standard "_All the things you are_":









Regards,

Vincula


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## Bwv 1080

TalkingHead said:


> That's generally true, BWV, but with certain caveats: in the 2nd inversion of V7, the 7th rises.
> Sorry to be the pedant in the ointment [sic] !!
> 
> *Note for Mr Penfold*: please submit my reply to Private Eye's _Pedants' Corner_ rubric. And if published, shall we split the tenner 50/50?


That does not make sense to me, The 7th in a dom 7 always resolves down by step


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## EdwardBast

______________________


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## EdwardBast

TalkingHead said:


> That's generally true, BWV, but with certain caveats: in the 2nd inversion of V7, the 7th rises.
> Sorry to be the pedant in the ointment [sic] !!


Why would it rise?


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## Guest

Bwv 1080 said:


> That does not make sense to me, The 7th in a dom 7 always resolves down by step


* William Lovelock*, _First Year Harmony_ (page 45): The second inversion may also resolve to I6 (1B), the bass rising a step. In this case the 7th also _rises a step_.


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## Guest

EdwardBast said:


> Why would it rise?
> 
> View attachment 151741


*William Lovelock*, _First Year Harmony_ (page 45): The second inversion may also resolve to I6 (1B), the bass rising a step. In this case the 7th also _rises a step_.


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## BabyGiraffe

johnfkingmatrix said:


> If i make a chord, like Dm7, how do i figure out what it resolves to?
> I get that you look at the tones, each one has a tendency.. but then i dont know the rules
> 
> what about complex chords like Cmaj7(#11)
> is there a formula i can use to figure out any chords resolution!?
> 
> question 2:
> is this something i would be doing in a chord progression from one chord to the next/ or in a melody where im cycling between arpeggios , just picking the next chord based upon what it resolves to, or would that sound "trite"


There are no universal rules... I recommend to use your ears instead. Use small melodic steps - outside of bass register, but even there you can do it, if you are writing melodic bass parts. Harmonic series segments over first harmonic will be the most stable chords, resolve to them in cadences, so: major chord (flatten the third around 14 cents), barbershop seventh (dominant with around 30 cents flat seventh and flat major third) and 9th chord (again flat sevenths and third). 11th and 13th harmonic are out of tune in 12 equal by around 1/4 tone=> unusuable, 15th is OK, but I would use it only as a suspension (for example: standard major-major seventh chord). 
Create your own piano/guitar reductions, if you want to study particular composer/style.


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## EdwardBast

TalkingHead said:


> *William Lovelock*, _First Year Harmony_ (page 45): The second inversion may also resolve to I6 (1B), the bass rising a step. In this case the 7th also _rises a step_.


Hmm. I'm dubious about Lovelock's position and wonder about its basis. Is it based on practice? Or does he believe that as a general rule doubling the 5th is better than doubling the 3rd? I've mocked out three scenarios comparing Lovelock's suggested resolution with one where the 7th descends:









In the first scenario Lovelock's solution might be a little stronger. In the second scenario, however, the downward resolution of the 7th is clearly superior. To my ears the third scenario is a toss up; neither sounds very good because of the octaves (F-F and A-A respectively).

I know this sounds like quibbling but discussing the minutia of voice-leading is actually fun for me.


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## Bwv 1080

It works for me if the V43 is in close position, so in C: DFGB - EGC, but that is because your ear hears the F-E half step, even though technically they are different voices


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## Roger Knox

TalkingHead said:


> *William Lovelock*, _First Year Harmony_ (page 45): The second inversion may also resolve to I6 (1B), the bass rising a step. In this case the 7th also _rises a step_.


Talking Head, I am entirely with you on this and I'll explain why: it eliminates confusion. I taught harmony for many years to hundreds of teenagers and post-secondary students. I believe Lovelock is a British _classical_ harmony manual of the kind we use in Canada for conservatory harmony exams (usually pre-university). In this system you learn elementary harmony by rules, and then practise them with written exercises. The example you refer to is called the Exceptional Resolution or the Rising Resolution of the dominant seventh, 2nd inversion. It is used harmonizing a melody where the leading tone goes to the tonic in the middle of a phrase, or harmonizing a bass line that rises from the 2nd to 3rd scale degree. You end up doubling the fifth of the chord of resolution, which is exceptional, but applies here. In my traditional way of thinking you don't need to ask _why_, just learn to do it and keep advancing. Once you've mastered this you finish up with other elementary dominant seventh resolutions, and move on to the next topic as efficiently as possible. Dominant seventh resolutions are especially common and important in elementary harmony, but harmony becomes more fun and less rule-bound as you advance.

Of course this is classical harmony in the four-part chorale format, as you might find in 18th- or 19th-century church hymns. Everyone learns this format, because it is a kind of template for all harmony in 18th-19th century classical music, not only church hymns. It is a good beginning for arranging music too. There are differences in format for keyboard harmony and even more for guitar harmony. Jazz/pop harmony has similarities, but also differences from classical harmony. One thing I oppose is learning from two different sources at the same time. Another thing I oppose especially, is learning both classical and jazz/pop harmony at the same time. In fact my response to teachers who do this is this: "#^&*^*&[email protected]!!! etc. ..."

You need to decide whether you are studying classical or jazz/pop harmony first, based on what instrument you play, where you are now, and where you might be headed musically. Do try to be specific, and good luck!


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## Guest

EdwardBast said:


> Hmm. I'm dubious about Lovelock's position and wonder about its basis. Is it based on practice? Or does he believe that as a general rule doubling the 5th is better than doubling the 3rd? I've mocked out three scenarios comparing Lovelock's suggested resolution with one where the 7th descends:
> 
> View attachment 151771
> 
> 
> In the first scenario Lovelock's solution might be a little stronger. In the second scenario, however, the downward resolution of the 7th is clearly superior. To my ears the third scenario is a toss up; neither sounds very good because of the octaves (F-F and A-A respectively).
> 
> I know this sounds like quibbling but discussing the minutia of voice-leading is actually fun for me.


It's not just Lovelock, there is also *Sten Ingelf*, _Learn from the Masters_:


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## Guest

EdwardBast said:


> Hmm. I'm dubious about Lovelock's position and wonder about its basis. *Is it based on practice? Or does he believe that as a general rule doubling the 5th is better than doubling the 3rd?*


I think it's both. Lovelock is against doubling the third in major chords (they sound too "harsh") and there are examples in the literature (which I will have to dig out).


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## mikeh375

I learnt CP via Lovelock and as a result, have a fondness for his books. I did all 3 years of his Harmony course and also his Examination Fugue and Free Counterpoint texts. Highly recommended.


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## Guest

EdwardBast said:


> [...] I know this sounds like quibbling but discussing the minutia of voice-leading is actually fun for me.


No problem! The finer points of voice-leading are all about more "effective" writing, what works better "aesthetically".


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## mikeh375

EdwardBast said:


> ..........I know this sounds like quibbling but discussing the minutia of voice-leading is actually fun for me.


You're not alone in your geekiness Edward....


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## Guest

Roger Knox said:


> Talking Head, I am entirely with you on this and I'll explain why: it eliminates confusion. I taught harmony for many years to hundreds of teenagers and post-secondary students. I believe Lovelock is a British _classical_ harmony manual of the kind we use in Canada for conservatory harmony exams (usually pre-university). In this system you learn elementary harmony by rules, and then practise them with written exercises. The example you refer to is called the Exceptional Resolution or the Rising Resolution of the dominant seventh, 2nd inversion. It is used harmonizing a melody where the leading tone goes to the tonic in the middle of a phrase, or harmonizing a bass line that rises from the 2nd to 3rd scale degree. You end up doubling the fifth of the chord of resolution, which is exceptional, but applies here. In my traditional way of thinking you don't need to ask _why_, just learn to do it and keep advancing. Once you've mastered this you finish up with other elementary dominant seventh resolutions, and move on to the next topic as efficiently as possible. Dominant seventh resolutions are especially common and important in elementary harmony, but harmony becomes more fun and less rule-bound as you advance.
> 
> Of course this is classical harmony in the four-part chorale format, as you might find in 18th- or 19th-century church hymns. Everyone learns this format, because it is a kind of template for all harmony in 18th-19th century classical music, not only church hymns. It is a good beginning for arranging music too. There are differences in format for keyboard harmony and even more for guitar harmony. Jazz/pop harmony has similarities, but also differences from classical harmony. One thing I oppose is learning from two different sources at the same time. Another thing I oppose especially, is learning both classical and jazz/pop harmony at the same time. In fact my response to teachers who do this is this: "#^&*^*&[email protected]!!! etc. ..."
> 
> You need to decide whether you are studying classical or jazz/pop harmony first, based on what instrument you play, where you are now, and where you might be headed musically. Do try to be specific, and good luck!


Yes, the Lovelock harmony books (First Year Harmony & Second Year Harmony) were staple fare for secondary school classical harmony lessons when I was young. I still use them today in my courses, believe it or not!


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## EdwardBast

TalkingHead said:


> It's not just Lovelock, there is also *Sten Ingelf*, _Learn from the Masters_:
> View attachment 151793


Piston and others have this as well.

While we're talking pedagogy: I had a crazy but highly proficient organist and an alcoholic composer for undergrad theory. Neither used a text. The former just handed out xeroxed harmonization exercises and then showed us what Bach had done with the same melody or bass. The composer would do odd things like giving us a passage in reduction by Wagner or Hugo Wolf (or some such), remove a few measures, and see if we could fill in the blanks.  In both cases it was sink or swim. I ended up buying a couple of texts on my own.

With counterpoint it was just as strange. For the Renaissance we used Gioseffo Zarlino's istitutione harmoniche (1558) Part Three(?), the Art of Counterpoint, as a text, including the original exercises and cantus firmi. So for us it was Josquin, Willaert and Lassus rather than Palestrina.


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## mikeh375

...for early contrapuntal technique the texts I went through were Swindale's 'Polyphonic Composition' and then R.O.Morris's 'Contrapuntal Technique in the 16thC'. The Morris took a general approach to style, focusing not only on Palestrina, but others too such as Byrd and Morely and even someone called Bugsworthy! (anyone heard of him?).

I'm guessing that John probably needn't concern himself with species counterpoint unless he wants to delve deeper into the art and artifice of music and should definitely heed Roger's advice above about deciding one way or another imv. Trying to learn two approaches to harmony, jazz/pop or CP, although possible (I did it inadvertently, coming from jazz guitar initially), is not necessary if he is aiming to be creative in popular music.


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## Guest

mikeh375 said:


> ...for early contrapuntal technique the texts I went through were *Swindale's 'Polyphonic Composition'* [...]


 Me too. Happy days!! Nah, I found Owen's PC a bit too dry. A propos, I was toying with the idea of offering a polyphonic course here at my local University but I really couldn't find a teaching resource that I was 100% happy with. On reflection, I'm glad I dropped that idea, TBH.



mikeh375 said:


> [...] and then R.O.Morris's 'Contrapuntal Technique in the 16thC'. The Morris took a general approach to style, focusing not only on Palestrina, but others too such as Byrd and Morely and even someone called *Bugsworthy*! (anyone heard of him?)


No, never heard of him. Great name, though!


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## mikeh375

TalkingHead said:


> Me too. Happy days!! Nah, I found Owen's PC a bit too dry. A propos, I was toying with the idea of offering a polyphonic course here at my local University but I really couldn't find a teaching resource that I was 100% happy with. On reflection, I'm glad I dropped that idea, TBH.
> 
> No, never heard of him. Great name, though!


TH has _anybody_ ever been able to sex up species counterpoint... The Morris is worth a look though as it is jam packed with examples. I didn't find it dry, but see below.
Re Bugsworthy, well look what a google turned up....LOL

_Nicholas Bugsworthy

A "previously unknown Tudor composer," until author Reginald Owen Morris needed some invented examples and a chance to add a bit of fun in his otherwise dry work, Contrapuntal Technique in the Sixteenth Century, Oxford University Press 1922.
The samples of his work given at the end of the book, Conceits and Vapours are also funny, one is actually a contrapuntal version of Irving Berlin's 1911 hit song "Everybody's Doing It." The samples are also numbered no. 10,001, and no. 10,002, which would mean Bugsworthy cranked out more music than the notably prolific J.S. Bach.
Morris did not fool all the experts, some who pointed out Bugsworthy in reviews. Further, British classical music magazine The Dominant wrote up a whole article on Bugsworthy for their April Fool's edition of 1928. The article, by real musicologist Sir Richard Terry, posited his birth circa 1540.
_

....my excuse, I was young, impressionable and not always sober.


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## Guest

mikeh375 said:


> TH *has anybody ever been able to sex up species counterpoint*... The Morris is worth a look though as it is jam packed with examples. I didn't find it dry, but see below.


Yeah, that's true enough. That said, I teach _*Baroque*_ counterpoint (up to 3rd species) and I'm able to sex that up quite a lot, though it does help that my main resource is Bach!!

As to Nicholas Bugsworthy, that's a hilarious story, thanks so much for explaining that, you had me worrying I was missing out on an old master!!


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## Haydn70

TalkingHead said:


> It's not just Lovelock, there is also *Sten Ingelf*, _Learn from the Masters_:
> View attachment 151793


When I took the three-semester lower division harmony sequence in the 1970s the books used were _Harmony and Melody, Vols. I and II_ by Elie Siegmeister. (I still have them although I think they are pretty bad.)

In volume I, chapter 14, "The Dominant Seventh" Siegmeister gives the example below.

Speaking of doubling we were taught to double the root (except for the vii chord) or fifth and never the third. There is another school of doubling wherein the acceptable pitches are the 1st, 4th, and 5th scale steps…and sometimes the 2nd. Thus, for example, in the key of C, it would be OK to double the G in an e minor chord. I believe this was/is the doubling technique in Piston's _Harmony_.

Sorry I can't get rid of the first image.


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## Roger Knox

johnfkingmatrix said:


> i seached a ton on resolving 7ths specifically everything keeps talking about the dominant and all i found was this: https://learnmusictheory.net/PDFs/pdffiles/02-10-SATBPartWriting6SeventhChords.pdf


Did we help with your problem?


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## mikeh375

johnfkingmatrix said:


> Hi, maybe beginner question and im kind of self educating myself /trying to learn, so forgive me if my ideas are disjointed , and ty for you patience:
> 
> If i make a chord, like Dm7, how do i figure out what it resolves to?
> I get that you look at the tones, each one has a tendency.. but then i dont know the rules
> 
> what about complex chords like Cmaj7(#11)
> is there a formula i can use to figure out any chords resolution!?
> 
> question 2:
> is this something i would be doing in a chord progression from one chord to the next/ or in a melody where im cycling between arpeggios , just picking the next chord based upon what it resolves to, or would that sound "trite"
> 
> (also.. why does cmaj7#11 sound so dark? if its a major chord)
> 
> Thanks guys i appreciate the time you put into schooling me


Cmaj7(#11) can also be thought of as a composite of two chords - b minor and c maj i.e. bitonal and assuming the 9th is included. Funnily enough, it doesn't sound dark to my ears.

Thanks to earlier genres like House and Acid Jazz, where short samples of scored or studio-produced chords could be played chromatically on a keyboard, thereby transposing the original chord up to 12 times, modern popular music ears are used to one type of harmony shifting chromatically almost anywhere. The same principle could be applied to resolving chords.
A good way to get a sense of were you could resolve Dm7 in a non CP and more acidy jazzy way might be to resolve it to every common chord and common 7th (or higher) chord throughout every key and hear the result. For example, resolve Dm7 to a Db major chord, or to Ab13, or perhaps a B maj7sharp9th chord. This way of thinking is akin to the cut 'n' paste way of composing with sample blocks in a DAW, but you may find it useful and more immediate than learning CP conventions. In fact, it can be less restrictive than CP and can open up many more possibilities if one isn't too concerned with formal procedure - considerations that might be important to you.

As an added bonus, experimentation like the above will help train your ears and you may also find a progression that might be compositionally useful.


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## johnfkingmatrix

vincula said:


> Dm7 is the iim7 chord in C major
> Dm7 is the iiim7 in Bb major
> Dm7 is the vi7 chord (relative minor) in F major
> 
> Vincula


oOOOOH. thats a good way to look at it ! So basically i look for strong resolutions like IV V I, and ask myself, "ok the chord im on is the IV chord of WHAT".. and then resolve it from there ?!

So SAY IM in the key of Cmaj... i pick a common resolution, IV V I because i know its strong.. the chord im on is Gmaj, i ask myself "What is Gmaj the IV of?" .. its Dmajor.. so now my resolution goes Gmaj-->Amaj-->Dmaj ?


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## johnfkingmatrix

BabyGiraffe said:


> There are no universal rules... I recommend to use your ears instead. Use small melodic steps - outside of bass register, but even there you can do it, if you are writing melodic bass parts. Harmonic series segments over first harmonic will be the most stable chords, resolve to them in cadences, so: major chord (flatten the third around 14 cents), barbershop seventh (dominant with around 30 cents flat seventh and flat major third) and 9th chord (again flat sevenths and third). 11th and 13th harmonic are out of tune in 12 equal by around 1/4 tone=> unusuable, 15th is OK, but I would use it only as a suspension (for example: standard major-major seventh chord).
> Create your own piano/guitar reductions, if you want to study particular composer/style.


you're saying western music being in 440hz and the inherent out of tuneness needs to be taken into account? O_O


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## johnfkingmatrix

Roger Knox said:


> You need to decide whether you are studying classical or jazz/pop harmony first, based on what instrument you play, where you are now, and where you might be headed musically. Do try to be specific, and good luck!





mikeh375 said:


> I'm guessing that John probably needn't concern himself with species counterpoint unless he wants to delve deeper into the art and artifice of music and should definitely heed Roger's advice above about deciding one way or another imv. Trying to learn two approaches to harmony, jazz/pop or CP, although possible (I did it inadvertently, coming from jazz guitar initially), is not necessary if he is aiming to be creative in popular music.


actually i started exclusively with baroque piano and counterpoint, its all i listened to/tried to write/studied for a long time. Then when i switched to guitar everything i wroute sounded like something a midieval lute player would write. I actually am trying to work really hard to make myself not sound neoclassical, or like im playing a lute.. so thats kind of the direction i was/am trying to sound more "modern/poppy" : /

Fugues make a lot of sense and the structure is very straightforward (at least, at a surface level - not saying i write anything beyond elementary) .. i almost feel like you could program a computer to write counterpoint.. pop/rock/metal.. not so much, at least as far as rules i can come up with


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## johnfkingmatrix

mikeh375 said:


> This way of thinking is akin to the cut 'n' paste way of composing with sample blocks in a DAW, but you may find it useful and more immediate than learning CP conventions. In fact, it can be less restrictive than CP and can open up many more possibilities if one isn't too concerned with formal procedure - considerations that might be important to you.
> 
> As an added bonus, experimentation like the above will help train your ears and you may also find a progression that might be compositionally useful.


ACTUALLY thats what led me down this rabbit hole.. i do stuff like that, then i find something that sounds great.. but then i dont know what to do next, because i dont know what got me there in the first place. !! thats exactly the root of my question..

So what happens is, i do something randomly through cut and paste/experimentation, it sounds great, then i get stuck. .. so i ask questions here to try to figure out what the hell i did lol


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## johnfkingmatrix

Roger Knox said:


> Did we help with your problem?


its opening a lot of rabbit holes, and im incredibly grateful to eveyones input !

I guess the thing im trying to accomplish is:

When im randomly experimenting, and i come up with an idea that sounds good, i suspect if i know what it is im doing, i would know where to go next ? otherwise i just have a short idea that dead ends : / which is what happens to me all of the time. i have a good idea then dead end. If you're all patient enough, i can submit a sample of where i hit a wall

I also suspect that "resolutions" are the natural next step? or am i grasping at straws

SO yes, ultimately im just trying to help my composition/songwriting skills by knowing intellectually what would most likely sound good next. am i going about this the right way?

the complex chord thing came up because, in solos if im playing an arpeggio ive created that has like 4-5 tones in it, i just analyze what "chord" those notes form.. and generally its a complex chord.. so my logic is .. ok if this arpeggio forms a cm13b9 (just made up example) ... the arpeggio that will sound GREAT next will be whateve a cm13b9 resolves to... and so on so forth? is this appropriate approach? otherwise im kind of just randomly switching arpegios and its aimless and sounds like crap until i accidently find the next one that sounds good.

a rule i have discovered is : if im playing a 3 tone arpeggio, any arpeggio that contains 2 of the original 3 tones will sound great. like FAC ->ACE -->ECg etc etc. ganted thats INCREDIBLY trite and overdnoe.. i get that generally results in some cycle of 5ths circling thing.. was tying to extend that logic to complex chords, which i thought ultimately is derived from voice leading/which tones resolve to what *Shrug*


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## vincula

johnfkingmatrix said:


> So SAY IM in the key of Cmaj... i pick a common resolution, IV V I because i know its strong.. the chord im on is Gmaj, i ask myself "What is Gmaj the IV of?" .. its Dmajor.. so now my resolution goes Gmaj-->Amaj-->Dmaj ?


Good way of thinking to get you started. In the key of C major a IV V I progression will go G7(or maj) A7 Dmaj7. In jazz and common pop/rock (eg. Stevie Wonder) that progression would be a "backdoor ii V I":

https://en.wikipedia.org/wiki/Backdoor_progression

The V is a dominant chord with a flattened 7th resolving to the tonic. In jazz the above-mentioned progression would probably go like iv7 V7 Imaj: Gm7 A7 Dmaj7. (instead of iim7 V7 Imaj7 Dm7 G7 Cmaj7)

There are no short-cuts or fancy easy ways to look at harmony. it takes time, patience, humbleness and practice. Enjoy the _baby steps_ like we all do No one's ever "done" with it.

Regards,

Vincula


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