harmonising the arpeggio?

**Alzo** · 08-08-2010, 07:29 AM

I don't know if anyone else has heard of this or not, it certainly isn't something that I'd heard of before, even though I've been playing this stuff for quite a while, which I guess is why it occurred to me.

It occurred to me a little while back that when/if you arpeggiate a scale, say the major scale, without resolving (eg. 1-3-5-7-9-11-13.. etc), that you get the scale harmonised and sequentially moving through all the scale tones. It's virtually impossible on the guitar, and even 88 keys don't quite make it, in fact I even wonder at the possibility, that at the top end of the sequence the notes could be completely inaudible to the ear, or the bottom end for that matter, if you adjusted it to allow for this problem.

So ok, here is the sequence: it is that same as the small example in the above paragraph, just more detailed.

ONE - 3 - 5 - 7 - TWO - 4 - 6 - 8 - THREE - 5 - 7 - 2 - FOUR - 6 - 8 - 3 - FIVE - 7 - 2 - 4 - SIX - 8 - 3 - 5 - SEVEN - 2 - 4 - 6 - ONE.

err.. ok, it is kinda easier to understand if you use ALL the extensions instead of repeating the octave, which is why I used 8 instead of 1 again. We don't have extensions for anything above 13, but we know they are there.

This means of course that as the extensions go higher and higher ALL these notes harmonise with each other, including block chords in combination.

Then of course it's apparent that there's really only 2 chords in a key, built from 1-3-5-7 or built from 2-4-5-8.

I just think this is interesting because it kinda poses the question: Why is music the way it is? like why do we use 3rds? or even how/why semitones, tempering? micro tones? music is culture based and our ears are too, and jazz is too, it's a system/framework that works, as is the micro-tonal system in India, but they don't have harmony.

**timscarey** · 08-08-2010, 01:53 PM

I don't really understand what this theory is all about guy.

**Reg** · 08-08-2010, 03:00 PM

Hey Alzo... you need to get a little better source for your information...I'm not sure where to start... music... has very physical tendencies, they call this science Acoustic, a fairly simple explanation can be found in "Acoustics of Music", by W.T. Bartholomew, can be found used and cheap. Your hinting at modal construction with harmonics or overtone methodology...??? Western music uses scales , the arrangement and order of rising pitches within the octave which can be transposed to any of the twelve notes or simi-tones from the chromatic scale or division of the octave which is the foundation of western music. There are other divisions of the octave and there were non repeating frequency patterns... but we don't use them... If you have specific questions I'll be glad to explain... Best Reg

**Alzo** · 08-08-2010, 08:47 PM

Well I wouldn't call it a theory it's just something that occurs, it just made sense one night while playing quietly on my own and I thought it was interesting. It's pretty basic really. Yeah I guess I'm talking about modal construction, it had just never before occurred to me in this way before, as it covers 9 octaves.

My sources are just me and my self with this, i don't understand why you would say that I should find another one, this is just me fooling around on the guitar while thinking a lot, for better or for worse.

I guess my question is, what is this?

With non tempering, as you go further away from middle C don't you lose "pitch"? So what's the Relationship between the overtone series and the tempered scale?

**timscarey** · 08-08-2010, 11:14 PM

After two octaves, you end up back where you started... right? how do you get 9 octaves?

The tempered scale was an invention of man, it is based on the first 6 overtones in the series. well, it's actually based on only the perfect 5th (the second overtone) but all of the first 6 overtones and the intervals created by them are found in a 12 tone equal tempered chromatic scale, the 7th overtone is too small and out of tune, we don't use it for harmonic purposes.

The actual system was started by the Greeks but was not "perfected" until the 1600's. The only intervals in the tempered system that are congruent with the overtone series are the octaves, all of the other intervals are "squeezed" to fit "evenly" within the octave, even a perfect 5th on an electric keyboard is slightly different from a naturally occurring 5th.

The entire point of this system is what is called "octave equivalence" meaning 2 notes an octave apart have the same harmonic function, in fact, this system is what allows one key to sound exactly like another, which then allows for modulation, which is what keeps music interesting.

a really good book for this stuff is Paul Hindemith's "the craft of musical composition" the whole first 2 chapters are about the origins of the tempered scale. Interesting stuff, especially when he breaks down the interval root system and the order of harmonic/melodic importance of each interval. I would recommend it highly.

**Alzo** · 08-09-2010, 12:56 AM

Tim,

Cool I'll check out that book, as well as the one Reg mentioned. I find this stuff very interesting, while I know that it's relevance these days is arguable.

As far as the octave's go, in my explanation I used the number 8 to represent the 1, but really it should just keep going into the extensions that we don't use in our terminology eg 9, 11, 13 and on though 15, 17 etc, if my math is right at the end of the 9th octave it resets back to the beginning, if you look at every 5th note starting from 1 it outlines the scale, in 9ths..

I know this is a flaky idea in many respects, it's just something that I found to be rather curious, it's hard to explain in way, it does point to some practical, albeit experimental application.

I hope that explains it better, it's made me think a lot more about it just writing it here. When I originally thought of this I was kinda playing with the idea that every chord movement is 2-5, so I was in a very reductionist headspace, reducing everything down to some common denominator, like I said, it's experimentally practical and it must be a result of the tempering.

Time to do some book shopping

**bako** · 08-09-2010, 10:07 AM

Alzo,

I understand what you were saying but I also understand why it's confusing.
Traditionally these are extensions in 3rds based on each degree of a 7 note scale.

C E G B D F A (C)
D F A C E G B (D)
ect.

After you reach the 13th, game over.
You were working in a context of 7th chords and although the notes are repeating it takes 9 octaves to complete all seven 7th chords. If you used the triad as your model it would complete itself in 6 octaves. Using 3rds it completes itself in 2 octaves and building 13th extensions on each degree within 3 octaves which is much more compatible for guitar and voice leading in general than 9 octaves.

Here's on possible 23rd chord made up of 4 augmented triads from the 2 whole tone scales.
C E G#// Bb D F#// A C# E#// G B D#

For some people what is called microtones and semitones are real notes. They are not notes in between or a slightly flat major 3rd, they are the intended sound. The terminology is used to explain to those of us who believe the musical universe is made up of 12 notes.

**Alzo** · 08-09-2010, 10:49 PM

Bako, man thanks! -for spending a little time with my roundabout explanation yes it is hard to explain, but really once you get it it's a very simple idea.

however: Now you've confused me! -how do triads complete the sequence in 6 octaves? As the way I'm thinking is that triads implies that the triad is self contained, but if it's stacking 3rds it must continue until completion? damn it's hard to explain this stuff in english..

4ths don't work with a 7 note scale. However using 4ths on the pentatonic scale will result in a 7 octave completion. (this is all making me think of fractal geometry and mandelbrot sets, basically when punched into a computer program certain equations either calculate to become finite, or they shoot off into infinity never to repeat the same way, always permeating). yeah the rule is that whatever the interval between the first note and the first note that represents the next scale tone, will determine the amount of octaves that will occur until completion, eg major scale: 1 to 9 = 9 octaves. This appears to be idiosyncratic to each scale, as in like I just said about the pentatonic in 4ths, 4ths make sense when applied to the 12 tone canvas, but really, to the pentatonic as it's own entity it's in 3rds.

Yeah it seems to want to build gigantic chords that are basically unplayable on anything but some kind of synth. So your augmented triads are from combining 2 scales, is the second group of triads based on the other scale up the octave, how are you combining the scales? harmonising triads using large intervals, allowing for the extensions to harmonise notes that are semi-tones apart.

The reason I said, in the initial post, that music is cultural is that I think we have been conditioned to hear things stacked in 3rds, triads, 7ths, as well as 9ths etc. However a good friend of mine informed me that once upon a time vocal choir music, which would be largely religious (I think gregorian, or maybe even before, I'm not a full bottle on this) used to use 4th based harmony, I can't remember what else he said about this, it was very interesting though.

**bako** · 08-10-2010, 01:20 AM

CEGBDFACEGBDFACEGBDFAC

I applied what I interpreted to be your methodology to triads.
My impression is that you 7th chord were your basic unit.

Your sequence with 7ths:
Cma7 Dm7 Em7 Fma7 G7 Am7 Bm7b5 (C note)

With triads:
C Bdim Am G F Em Dm (C note)

What insight are you hoping to gain with these observations?

**Alzo** · 08-10-2010, 05:08 AM

Ah yes, of course! It's just backwards

I really don't know what insight I hope to get from this, apart from what it is to itself and my own fascination. However I think I will experiment and compose some music using this idea. I'm thinking it's possible to combine keys and borrow chords, could be great for experimental soundscape type stuff.

Something that it does relate to I think, is chord substitution and reharmonisation, in a reductive way. Take a tune like Autumn Leaves for example, which is diatonic, chords are either built from the 1-3-5-7 or the 2-4-6-1(8). There's a certain economy in this, plus it keeps common tones and voicings. then we have the 9th. By altering the 5 chord to be b9 in the major 5-1 change it creates the same movement as the minor 5-1, combine this with the diminished/b9 relationship and you have a very economic way of comping and voice leading. You and many probably play this way anyway, I do, it's how I thought of it.

**bako** · 08-10-2010, 07:23 AM

Originally Posted by Alzo

Take a tune like Autumn Leaves for example, which is diatonic, chords are either built from the 1-3-5-7 or the 2-4-6-1(8).

Autumn Leaves (1st section)
Bb
IIm7 V7 Ima7 IVma7
Gm
IIm7b5 V7 Im

I don't follow this description in reference to this song. Can you elaborate on your way of thinking about this song?
Thanks.

**Alzo** · 08-10-2010, 07:58 AM

Yeah, ok it's not perfect, because what I'm saying is that the F7 is the same chord as the D7, which it's not, but if you use F7b9 it's closer, and then 5th in the root gives you Cdim, which then resolves into Bbmaj, which is Gm. Ok I am being liberal here, the trick would be to use the F# to create the tension before each of the resolutions, either minor 5-1 or maj 5-1, using G harmonic minor. First chord Cm7 should really be a Cm6, just for the sake of explanation anyway. So you could say that the first 2 chords are the same and the second 2 chords are the same (5-1), Bb and Eb both inversions of Gm and built from the 2-4-6-8 degrees, and the first two (as long as the C is a Cm6..) are built from 1-3-5-7. I know the Cm6 thing isn't great but I'm not by any means trying to say that this is anything near a perfect or even grounded idea at all.

The more I think about this I realise that it's very reductionist, it's interesting but there are problems, like the Cm6, if the guide tones aren't working, because it should be a m7 chord, well.. then again who says it should be a m7.. Ok well the melody of the tune will probably slap me about for saying that, but I think this topic is aside from melody, this is, if anything, an improv idea, comping, voice leading etc. *phew*!

**bako** · 08-10-2010, 09:20 AM

There are theorists that like to look at everything as either a V7 and I. Others will include the idea of pre dominant and non tonic material.
There are some insights to be gained by reductionist approaches as well viewing the individual details microscopically.

**Reg** · 08-10-2010, 10:41 AM

Hey Alzo... wasn't trying to rain on your approach... sorry. There are centuries of material on these subjects. And in the last 75 years some pretty solid facts... This subject is fairly complex and usually requires a good amount of research, (I don't mean Wikipedia). I'm not a Musicologist, do have few degrees and and understand traditional and jazz harmony. Anyway musicology is divided into three main divisions, 1st; history, 2nd; folk and non-western music, called ethnomusicology and 3rd; all the rest, acoustics, physiology, psychology, aesthetics, sociology, pedagogy and theory. These areas will help you have a better understanding of where your trying to go. Bako is obviously great and much easier... Best Reg

**Alzo** · 08-10-2010, 11:19 AM

Bako,

Yeah I've heard of the 5-1 idea before, I kinda understood it but never really bothered to look into it, till I discovered this.

This definitely has helped me with aspects of my playing, but it's hard to say what came from what, but what I was working on at the time did lead me down the path. I think it may help to think more like a piano player, to be able to see the inversions clearly and break away from the trappings of the guitars fretboard.

Whats your thoughts on this? Have you had any insights in this general area that may have contributed something?

I don't know much about non-tonic stuff, I know it's used in classical music. I actually think I need to read books about this rather than tempering etc, do you have any good ideas for some reading?

I'd also like to say thanks for hearing me out with an open mind, it's actually been very helpful for me to have this dialog and put my thoughts on paper, so to speak.

**Alzo** · 08-10-2010, 11:34 AM

Originally Posted by Reg

Hey Alzo... wasn't trying to rain on your approach... sorry. There are centuries of material on these subjects. And in the last 75 years some pretty solid facts... This subject is fairly complex and usually requires a good amount of research, (I don't mean Wikipedia). I'm not a Musicologist, do have few degrees and and understand traditional and jazz harmony. Anyway musicology is divided into three main divisions, 1st; history, 2nd; folk and non-western music, called ethnomusicology and 3rd; all the rest, acoustics, physiology, psychology, aesthetics, sociology, pedagogy and theory. These areas will help you have a better understanding of where your trying to go. Bako is obviously great and much easier... Best Reg

Reg, no worries there. My general theory knowledge is pretty good, it was just hard to explain, and I'm kinda new here so who's to say what that new crazy guy is on, or on about!

**bako** · 08-10-2010, 02:20 PM

Originally Posted by Alzo

I think it may help to think more like a piano player, to be able to see the inversions clearly and break away from the trappings of the guitars fretboard.Whats your thoughts on this? Have you had any insights in this general area that may have contributed something?

Thinking in the context of piano (10 fingers and one location for each note and each octave resembling the other)
can bring new insights. So can the act of arranging for various size horn or string sections or even full big band or orchestra.

Seeing inversions clearly is a reflection on our knowing the note spelling of chords, the intervallic function of each note, how well we know the fingerboard and finding creative alternative solutions when something is impossible to play.

**Alzo** · 08-11-2010, 03:30 AM

Yeah I think I'll write some stuff whilst attempting to apply this approach. I will have to use piano of course, and not in the jazz vein, I think I'll go for a more textural soundscape thing. On a slightly side note I've always liked the Scofield album "Quiet", love the way he did the horns, even though there appears to be dissonance at times.