interval tonics...

[motherlode]

CONSIDER THIS... WHEN WE HAVE AN INTERVAL OF TWO NOTES ...ONE OF THOSE NOTES WILL FUNCTION AS THE TONIC OF THAT INTERVAL... THE MAJ 2ND, MAJ 3RD, AUG 4TH, PERFECT 5TH, MAJ 6TH, AND MAJ 7TH, THE TONIC IS THE BOTTOM NOTE ( AS WELL AS THE OCTAVE). THE MIN 2ND, MIN 3RD, PERFECT 4TH, AUG 5TH, b7TH...THE TONIC IS THE TOP NOTE.

[lazaraga]

ok....

are you talking about overtonal relationships?

when you call one of these notes the tonic, do you mean it's considered the generating fundamental for the interval?

otherwise, please go on

 

 

 

 

peace

[motherlode]

consider this...because of our acceptance of the english alphabet and it's associated sounds, in time we aquired an accepted level of mastery and the ability to bend those truths into a personal form of self expression (the spoken word and the use of the dictionary)...even though we didn't invent the system!...NOW, in a musical context...the concept of interval tonics is fundamental (the alphabet) to the understanding and use (the dictionary) of Tonal Gravity... QUESTION: we all agree that there are 12 of each kind of interval, so the question is ...taking any type of interval, let's say the maj 2nd, C-D, now which maj 2nd would one step away? ...which maj 2nd is two steps away?...3 steps away?...4 steps away?...etc. until we have placed each maj 2nd in it's proper position according to it's tonal gravity. Remember, they are members fo the same family, now we see them in the same way that we our human relationships ie, Father, Mother, first born, etc. ...Interval tonics and tonal gravity is the tool that gives us the first step...

[motherlode]

Allow me to answer my own question by an example... tonal gravity for the maj 2nd from C ( keep the note sounding as you play through and you'll here it) : c-d,g-a,d-e,a-b,e-f#,f#-g#,eb-f,g#-Bb,Bb-c,f-g,b-c#,c#-d#...ther you have it, the 12 maj 2nd in their proper order according to ther TONAL GRAVITY...this only the beginning...

[lazaraga]

are you sure that's the correct order?

i was thinking more along the lines of

c d, g a, d e, a b, e f#, b c#, f# g#, c# d#, g# a#, d# f, a# c, f g.

or

c d, g a, e f#, Bb c, d e etc.

[motherlode]

consider this... TONAL GRAVITY IS NOT A CYCLE OF 5th! My example only started out that way because I happen to pick the maj 2nd in my example and that was the nature of that interval.NOW, let's look at the min 2nd (remember the tonic of the min 2nd is the top interval ...for the resolving tendencity in C once more: b-c,f#-g,g#-a,d-Eb,Eb-e,g-g#,f-f#,Bb-b,a-Bb,e-d#,c#-d,c-c#. Remember, there are 144 intervals, using Tonal Gravity , I can see the entire harnonic universe all at once, for example, you can play any interval and I'll know exactly where you are and how far you've traveled from the tonal center. Two things have not been discussed...(1) how is Tonal gravity derived and (2) what is the practical application? Finally this is not a paper concept, you have two examples (maj 2nd -and- min 2nd) play them and listen...I'm talking about mastering the tonal system, it took 20yrs to bring this to fruition...so,I'd be the first to admit it's not for everyone!

[lazaraga]

how is tonal gravity derived?

this seems like an interesting idea, but i don't understand how you generated these specrtra.

i've played your examples over tonic drones, and while they sound cool i don't hear these as being in their correct order according to a quality you call gravity.

please go on

 

 

 

 

peace

[motherlode]

background: RECALL that the first partial of the overtone series is the octave, the second partial is the perfect 5th, followed by the perfect 4th,(and so on...) stop...if the fundamental tone was 'C', that would be C-C-G-C...of the first 3 intervals, the 5th is the fundamental 'harmonic' interval (the 4th inverted is a ...5th), and of the first 4 tones...3 are the same, that is 'C'. Now, based on this, new tones were generated using the cycle of 5th's...So, C goes to G (a 5th), to D(a 5th),to A, to E, to B, to F#, to C#...Stop! We started with 'C' ! If we take our tones from the cycle of 5th's and place them within the octave, we get...c-d-e-f#-g-a-b-(add another 'C' for the octave)...look familiar? It's the LYDIAN mode (scale)...remember interval tonics? The maj 2nd,maj 3rd,aug 4th, per 5th, maj 6th, maj 7th...the tonic of the interval is the bottom note, in addition, the octave is split equally at f#! All of this is contained with Lydian. So why is the ionian mode called the maj scale? Not lydian? Because the 2 PERFECT intervals (4th & 5th) contain all the notes of the mode. Now here is the rub...of the 7 notes played in the scale , how do the 5 notes that we didn't play(C#,D#,F,G#,A#) relate? what is their proper position?...thus inters TONAL GRAVITY. Play this: c-g-d-a-e-b-f#-g#-Eb-f-Bb-Db...all the notes in music in their proper order according to their TONAL GRAVITY...(play & listen)...I'm waiting...

[lazaraga]

i was thinking along those lines

but i have some questions

how is the placement of the non lydian tones determined?

why is it not a stack of 5ths?

shouldn't the interval gravity for maj2 be

c d, g a, d e, a b, e f#, b c#, f# g#, g# a#, Eb f, f g,Bb c, Db Eb

 

and for min2

b c, f# g,c# d, g# a, d# e, a# b, f f#, g g#, d eb, e f, a Bb, c Db

 

why are your scales different?

whya are the non lydian tones arrranged the way they are, why not in order by 5ths?

 

interesting idea though, please go on

 

 

 

 

peace

[motherlode]

there is more than one scale of lydian derivation...lydian,lydian augmented (which is the 3rd mode of the melodic minor scale), lydian diminished, aux dim, aux aug, and the so-called, lydian chromatic...each one of these new scales introduces ONE new tone of the 5 tones that were not sounded when we played the lydian, please note, the lydian aug scale introduces the the aug 5th(g#); the lydian dim introduces the min 3rd(Eb); the aug dim introduces the perfect 4th(f); the aux aug introduces the b7th(Bb) and the lydian chromatic introduces the min 2nd (Db)... NOW TO ANSWER YOUR QUESTION, go back the the PRIMES that I listed c-g-d-a-e-b-f#-g#-Eb-f-Bb-Db...remembering that the 5th was the most important HARMONIC interval in music...start with a tone, we'll use 'C', travel a 5th, which brings us to 'G', travel a 5th,which brings us to 'D', and so on, remember this is how we derived the lydian scale, now this were some thing funny happens, when we get to f# we have used up ALL the lydian tones but there are 5 LEFT! NOW WHAT? move to the next lydian scale---lydian aug---which brings in one of our unused tones the g#! So in keeping with the logic, our last lydian tone 'f#' is followed by 'g#'...There are 4 tones left...move to the next lydian scale---lydian dim--- Lo and Behole, it contains another unused tone, the 'Eb', it assumes the next position, move to the next scale---aux dim---and there's another unused tone 'f', it takes the next spot...move to the next scale---aux aug---there's the Bb, so it takes the next spot...NOW, at this point we have all the tones of the chromatic scale... except one, Db,so we kindly add it, thus giving the so-called Lydian Chromatic Scale...(play & listen)

[lazaraga]

groovy

 

so are my two interval gravity scales i posted in my previous post correct? did you make some typos when your were originally posting yours?

please double check as i like this idea.

 

 

 

peace

[motherlode]

Someone once said," for every complex question, there's always one answer that's SIMPLE, OBVIOUS...AND WRONG!" All musical questions are not answered so simply by the cycle of 5ths (unfortunately) HOWEVER, I can see that you have enough understanding to grab this concept, if you can bear with me you'll see how nicely this fits with what you know already! Now, let's look again at the min 2nd...remembering the concept of interval tonics, you'll recall the tonic of the min 2nd is the TOP INTERVAL...So back to 'C' lydian, is there a min 2nd in lydian where the first tone in the scale is the TONIC---YES! the min 2nd from b to c! Now look at the next step---'g'(according to the order of Primes) , is there a min 2nd?---YES!, f# to g go to the nex step---'d', is there a min 2nd?---NO!, go to he next step---'e', same question,---NO!, continue until we've use all the lydian tones...Now move on to the next scale---lydian aug (which brings in a new tone 'g#'),do we find a min 2nd---YES!, g# to a, are there any more in the lydian aug scale---NO!, move to the next scale lydian dim, same process, con't,con't, At this point I'm going to introduce something new---if we combine all the notes of the 'pure' lydian scales (lydian,lydian aug, lydian dim) also known as the Consonant Nucleus, it produces something called the '9 tone scale' ie, c-d-Eb-e-f#-g-g#-a-b, this is important because it can produce intervals that not obtained from 'pure' lydian scales but belong to the world of music at large---so the '9 tone scale' produces the min 2nd on Eb and G---out of space, consider what has been said...I'm waiting...

[lazaraga]

brilliant

i dig it

 

thanks for explaining this more.

i like this idea very much.

 

it reminds of something i do, where i stack a scale in fifths

ex C G D A E B F#

and take the first group of 5

C G D A E

the 2nd group

G D A E B

and the 3rd

D A E B F#

 

now i got three pentatonic scales associated with a scale, which drift further from the chord of the tonic.

 

 

so yeah i like your idea alot for how it presents this spectrum/rainbow of intervals. where did you pick it up?

have you tried it for other scales, or only in a pure overtonal universal sense?

 

 

 

peace

[motherlode]

" drift further...", this is the phrase that you used that let's me know that you really do understand, because without a sense of drifting ie,gravitation, the abstract beauty of the concept is loss...from the example's you gave, yes, you were already headed in the direction of tonal mastery...you have the PRIMES, min 2nd, and maj 2nd, allow me to share the rest of TONAL GRAVITY with you for your examination...MIN 3rds (I'll type the root of the interval using Arabic numbers---just play the interval under investigation from that degree of the scale) :6 3 7 +4 +5 -3 1 4 2 5 -2 -7. MAJ 3rd: 1 5 2 3 +5 7 -3 4 +4 -7 6 -2. PERFECT 4th: 5 2 6 3 7 +4 -3 1 -7 4 -2 +5. AUG 4th: 1 +4 2 +5 6 -3 7 4 3 -7 5 -2. PERFECT 5th: 1 5 2 6 3 7 +5 4 -3 -7 +4 -2. AUGMENTED 5th: 3 7 +4 +5 1 -3 5 6 -7 2 -2 4. MAJ 6th: 1 5 2 6 7 +4 -3 +5 4 -7 3 -2. MIN 7th: 2 6 3 7 +4 +5 4 -7 1 5 -2 -3. MAJ 7th: 1 5 6 -3 3 +5 +4 7 -7 4 2 -2. There you have it---all 144 intervals in music arranged in their proper order and relationship to each other! It goes without me saying that their are numerous wonderful applications for this bit of knowledge...but a closer look at the associated scales would be in order first...

[lazaraga]

nice

 

 

so your interval tonics idea has some basis in overtonal ideas, like the generative power of the fifth (the 3rd partial).

where does the power of the third come into play (5th partial)?

for example, which is more closely related to the tonic "C"

the fifth of the fifth, D

or the third of the tonic, E

which has more gravity?

 

the way i hear the major/ionian mode

C the tonic/fundamental

D the fifth of the fifth

E the third, aka the 5th partial

F an "undertonal" tonic, of which C is the fifth

G the fifth, aka 3rd partial

A the fifth of the fifth of the fifth, or is it the major third of undertonal F?

B the 5th partial of the third partial, or the major third of the fifth of the tonic.

 

or in the lydian, would you hear F# as a close approximation of the 11th partial, or would it be the major third of the fifth of the fifth?

 

lately i've been trying to arrange these tones in their appropriate order according to their "closeness" to the tonic/fundamental.

should it be

C G D E A B F?

which is closer gravitationally to C, A or B?

 

 

peace

[motherlode]

If I remember correctly,,, the overtone series runs...octave,perfect 5th,perfect 4th,maj 3rd, min 3rd, (min 3rd), perfect 4th, maj 2nd, maj 2nd,maj 2nd, min 2nd, maj 2nd, min 2nd,min 2nd, min 2nd, etc...corresponding to c c g c e g (Bb) c d e f# g a Bb b c, etc...Now the answer to your questions are found in the order of the 'Primes' in Tonal Gravity...But please, the Ionian and it's associated laws haven't been a part of my music vocabulary in almost almost 40 years, I'm now in the business freeing the truth to work it's magic on my behalf...Oh yes, Tonal Gravity only answers the riddle of the interval...no mention of chords and their 'Close to Distant Relationship' has been made...

[lazaraga]

well, if not ionian then try lydian. instead of the undertonal 4th(F in the example) replace it with the 11th partial F#.

do you get what i'm saying about the generative powers of both the fifth and the third? do you consider the power of the third (5th partial) at all in your concept of gravity?

hey spill the beans on any more insights you got

 

 

peace

[motherlode]

Lydian is what we've been taking about for the last couple of days...a closing note: of the 144 intervals ---49 belong to Lydian,13 to Lyd aug, 13 to Lyd dim,with 6 more added by the '9 tone Scale', that's 81 intervals or just over 56% of ALL the intervals! Lydian is perfectly symmetrical---for example, look at, for instance, the maj 3rd...inverted it becomes an augmented 5th...so look at the first maj 3rd formed in Tonal Gravity, it's formed on '1', now look at the aug 5th...the first one is formed on '3' , just what you'd expect (the inversion)! And you'll this holds true all thru the concept...and where is the cut off? at the Aug 4th, in other words all intervals ABOVE the aug 4th is a perfect reflection of all the intervals below it! In addition, Lydian is the only mode that the TONIC tone is also the TONIC of all the Intervals contained in the scale! That's why I don't rely of the Ionian as the basis of MY harmonic vocabulary...that interval of the perfect 4th ( I-IV) sounds like (V-I) in the key of the subdominant (remember the TOP note is the tonic of the perfect 4th)...now look at the perfect 4th's in Tonal Gravity, the first one is built on '5', so in the key of 'C' , that's G to C (V-I), I hope you can comprehend all of this...it's a new way of looking about what you already kown, for most people it's easier to learn something COMPLETELY NEW than to think of what they know in a NEW way! Answer this , and you will have answered your own question regarding the 3rd (5th partial) , the extentions of the major chord (take 'C') are: maj 7, maj 9th, aug 4th, and 13th...that aug 4th is 'f#', but THERE IS NO 'F#' in the key fo 'C', so why not 'F' ?!...Ummmm...

[lazaraga]

yeah i'm hip to lydian, its been my basic source for a while now too. why did i bring up the ionian scale? i guess its because my girlfriend has been practicing sargam lately, so i hear alot of perfect fourths, and i began thinking about its undertonal origins. listening to her sing, i heard more and more the overtonal relationships in the scale. i've been trying to put them in order, like you have with interval gravity. that's what brought ionian to mind.

 

as far as the question you end with, do you mean that you hear the F# as being the third of D in the key of C?

see that's my question,

which is closer: the third of D in C lydian (F#)

or

the 11th partial of C (F#)

which one is more accessible to the listener, by being more closely related to the tonic?

 

so you only hear the perfect 4th as being V-I in the key of the subdominant? how does an 11th chord sound to you? as a mispelled inversion?

i sometimes hear that perfect 4th almost as a blue note, and i like using it at times as so

 

this conversation is getting too involved for my patience with the computer. im gonna have to print all this out to make sure i havent missed anything. thanks for sharing your insights

 

 

peace

[motherlode]

Yes you're Right!! that's why we're musicians...one peice of music can say it all so much more eloquently!...peace

[lazaraga]

is this from george russell's concept?

 

 

peace

[dumb donnie]

 

Originally posted by lazaraga is this from george russell's concept? peace

 

 

Yeah, that is pretty much straight from the book.

[motherlode]

Eric Dolphy first explained this to me in 1962...later such a concept was being taught at the Metro Arts Complex in Detroit...after studing music in the university I saw the beauty in the thinking and embraced it totally until this day!