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#1August 12th, 2005 · 11:33 AM
6 threads / 4 songs
33 posts
United States of America
The Four Scale Theory
I have a new music theory that I want to share with the world. First, let's start off by defining a musical scale. The first rule that we can agree on is that it must have seven notes. But it cannot just have any notes. The notes must be regulated. This is the second rule, that no three notes can be semitones apart, ie three notes in a row. The third rule, just to make this simple, is that no scale can have a fifth that is not natural. Okay, now that we have this, we can proceed.

Think of the most simple musical scale, the C major scale.

C - D - E - F - G - A - B

To prevent confusion, the notes of any scale can be labeled as such:

1 - 2 - 3 - 4 - 5 - 6 - 7

The C scale has all natural notes. The is always natural, and defines the rest of the scale. The 2 is two semitones away from the one. This is the natural two. The three is two semitones away from the two. This is the natural three. The four is one away, the five is two away, the six is two away, and the seven is two away. So it could look like this:

1 - 2 - 3 4 - 5 - 6 - 7

Note how there is no dash after the 7, as the 7 and the 1's octave above have no separating tone. There are many coordinations of this particular arrangement of intervals. If we start at the 2 instead, we get:

2 - 3 4 - 5 - 6 - 71 -

If we move all the notes down two semitones on the 1's major scale, we get:

1 - 2 3 - 4 - 5 - 67 -

Compare this two the 1's original major scale, and we see that the 2 and the 7 have been moved down a step. This flatting of the notes creates a minor seventh scale. If we do this to all the numbers of the scale, we find:

1: 1 - 2 - 3 4 - 5 - 6 - 7
2: 1 - 2 3 - 4 - 5 - 67 -
3: 1 2 - 3 - 4 - 5 6 - 7 -
4: 1 - 2 - 3 - 4 5 - 6 - 7
5: 1 - 2 - 3 4 - 5 - 6 7
6: 1 - 2 3 - 4 - 5 6 - 7 -
7: 1 2 - 3 - 4 5 - 6 - 7 -

Notice how the places where the intervals are one semitone move to the left as the number increases. We can discount the 7 scale as a true scale, because the 5 is flatted. All others are true scales. They are the typical greek musical MODES.

Ionian (All natural)
Dorian (3b, 7b)
Phrygian (2b, 3b, 6b, 7b)
Lydian (4#)
Mixolydian (7b)
Aeolian (3b, 6b, 7b)
Locrian (2b, 3b, 5b, 6b, 7b)

If you arrange these starting with the lydian, and then go to the scale's fifth, you see that the change is a flat of a single note. First the 4, then the 7, then 3, then 6, then 2, then 5. The one never changes because it is a root note. Also, the order of the note flatting follows fourths in the same direction. Wierd, no?

Now, you might realize that they scales do not encompass all the scales. Take for example, a scale with just a flatted 3, or a sharp 4 and a flatted 7. To ascertain these scales, you could change the root scale. But how can you arrange it so all of the three primary rules stay intact? Notice the distance between the one semitone intervals of the C major scale. If you move them one closer, it creates a scale not known above. If you move them apart, however, it is really a reflection of the original scale, just a different orientation. Any closer, and the rules will be broken (rule 2). So similarly, you can make new modes with the new scale. These do not have names though.

Also, we haven't considered the possibility of having scales with 3 semitone gaps. these are possible, and to save trouble for anyone reading this, they are:

1 - 2 3 - 4 - 5 6 - - 7

and

1 - 2 - 3 4 - 5 6 - - 7



An entire listing of legal modes is below:

NATURAL MODES
1 2 3 4 5 6 7
1 2 3b 4 5 6 7b
1 2b 3b 4 5 6b 7b
1 2 3 4# 5 6 7
1 2 3 4 5 6 7b
1 2 3b 4 5 6b 7b

MINOR 3 MODES
1 2 3b 4 5 6 7
1 2b 3b 4 5 6 7b
1 2 3 4# 5 6 7b
1 2 3 4 5 6b 7b

MINOR 6 MODES
1 2 3 4 5 6b 7
1 2b 3b 4b 5 6b 7b
1 2 3b 4# 5 6 7
1 2b 3 4 5 6 7b

MINOR 3, 6 MODES
1 2 3b 4 5 6b 7
1 2 3b 4# 5 6 7b
1 2b 3 4 5 6b 7b
1 2# 3 4# 5 6 7

My favorites of these new scales are 3rd MINOR 3 MODE, the 4th MINOR 3 MODE, and the 4th MINOR 3, 6 MODE.

These are all the possible scales ever. Please comment on this theory.
#2August 12th, 2005 · 05:34 PM
31 threads / 1 songs
434 posts
United States of America
ok, lets play chess but lets make the queen only able to move 3 spaces diagonally and 6 spaces rank/file wise no more no less... and while we're at it lets make cars only allowed to have pistons pointing at 32.9485 degrees apart from each other... and lets make yoghurt illegal and lets make the consumption of 3 pounds of cheese per day mandatory or you go to jail... and hell... lets declare that you can only look at the moon between the hours of 9 and 11pm...

ok, i'll comment

there are many many more than just 18 scales/modes

maybe you should actually read up on this section of theory about which you speak. the subject is well documented.

it's all well and good to be imaginative and stuff... but why anyone would ever want to put the kinds of restrictions on music that you just proposed is beyond me. MAYBE, maybe... for the sake of learning, but this doesn't seem to be aimed in that direction.

If you do this then jazz goes right out the window. There is no longer a chromatic scale, there is no longer a pentatonic scale, there is no longer a blues scale. Asian music ceases to exist. Polytonality is virtual impossible and you're left with a landscape of utterly predictable musical possiblities.
#3August 12th, 2005 · 11:13 PM
3 threads / 2 songs
27 posts
United States of America
If I may be so bold as to recommend the book ,The Guitar Grimoire. If you are unfamiliar with it, a "grimoire" was a magicians book of spells and that is exactlly what the book is. It contains every scale I have ever come across and many more. It has them in traditional as well as swept fingerings and in every key. It's a must for any serious theroretical guitarist.
#4August 13th, 2005 · 12:14 PM
6 threads / 4 songs
33 posts
United States of America
It's really just a theory, not a mandate for music. It may still need improvement. On the contrary to what entheon said, pentatonic and chromatic scales aren't prohibited by the theory. The theory is only to point out strange and beautiful similarities in scales, not to outlaw those not in the theory. But if you look closer, pentatonic and chromatic scales are really aural tricks, played out mathematically and beyond much human comprehension. Chromatic scales are based on assumed chord changes or transposition on the diminished scale. For example, if you were to play big band and swing music, you would encounter many times when a single note would straddle between the note one semitone below it and the note one semitone above it. Say it's an E, like in the song "Can't Let You Loose". When the E drops to an Eb, it's like taking the C7 chord it's playing, and transposing it on the C diminished scale, which includes those notes. When you go back to the E, and then to the F, you're playing back on the C7 scale again. It's like playing two scales at once, but without the dissonance achieved by playing all three notes at the same time. The blues scale is similar, really the C blues scale is a combination of the C dorian and the C diminished. Pentatonic scales are the so called "opposites" of major scales, scales which include all the notes the major scales don't. This forms a sort of irony for the brain. Indian music, as was pointed out, is similar to the blues scale and poly-tonality in general, just using different notes other than the common 3 and 5. And of course, we can't forget about our friend, the whole tone scale, which can be considered a modulation from the 1 to the flatted 5. But all these really fit into musical order with the 18 modes of mine, if you think about it the right way.
#5August 23rd, 2005 · 01:32 PM
8 threads / 4 songs
246 posts
United Kingdom
ok ... this thread is giving ME a headache and I'M about to start a 3 year music degree!!  I think we ALL need to get out much more! 
#6January 18th, 2006 · 09:18 PM
163 threads / 18 songs
2,320 posts
United Kingdom
re: The Four Scale Theory
please explain this thread to J S Bach........................im sure he might have sothing to say..


'Bollocks' probably.

splash.....the fish
#7January 19th, 2006 · 04:24 AM
118 threads / 55 songs
3,081 posts
Netherlands
I have an interesting lead on a new music theory myself, and it deals with geometrical frequency modulation patterns.

I'm going to see if I can produce a computer program which will then prove that my theory works by automatically composing tunes for me, using formulas I put into it.

I'm not telling exactly what I have in mind just yet, but playing with this theory on my guitar is quite convincingly supporting my ideas.
 
I may write a book about it and publish it accordingly.

I'm afraid it won't sell though.... 
#8January 19th, 2006 · 02:55 PM
163 threads / 18 songs
2,320 posts
United Kingdom
????
i sincerely hope your tongue is being bitten very hard on this one ................

               
#9January 26th, 2006 · 04:10 PM
118 threads / 55 songs
3,081 posts
Netherlands
re: ????
swordfish wrote…
i sincerely hope your tongue is being bitten very hard on this one ................

               :D

indeed, there are a many angles of perspective one could take on that previous post of mine... I suggest, to any, to try a few..........................................






#10March 17th, 2006 · 02:48 PM
4 threads / 1 songs
16 posts
Canada
All possible scales
There are (if I counted right) 357 scales using the chromatic notes.

each scale or chord (depending how you use them) has 12 possible roots (keys) and as many inversions (modes) as there are notes.

There are:
1 1-note scale (note)
6 2-note scales (intervals)
19 3-note scales (chords)
43 4-note scales
66 5-note scales
86 6-note scales
66 7-note scales
43 8-note scales
19 9-note scales
6 10-note scales
1 11-note scale
1 12-note scale
and for good measure
1 0-note scale (rest)

for example
2 note systems with root C

C Db
C D
C Eb
C E
C F
C Gb

when you get to C G note that a 5th is an inverted 4th.

XenosX's regulated theory is useful as the 'muisically accessible' subset of all possible 7 note chords but it does omit useful scales such as byzantine (with 3 consecutive semitones), whole tone (6 note)and diminished (8 note).

the list of all 66 7-note scale systems (but remember each has 12 roots and 7 modes) starts with the hideous

1234567-----
123456-7----
123456--7---
123456---7--
123456----7-

and ends with the useful

12-34-56-7--   derived from diminished
12-34-56--7-   derived from diminished
12-34-5-67--   7th mode of minor harmonic
12-34-5-6-7-   7th mode of minor melodic
12-3-45-67--   7th mode of 'major harmonic'
12-3-45-6-7-   7th mode of major

Another useful system to consider is the list of 43 4-note chords (20 of which are diatonic to the western system).  Playing the other 23 'outside' chords demysifies the frightening idea of 'unlimited harmonic variation' one feels looking at a piano.  Yes there are unlimited variations when you allow notes to fall in any octave but if you condensed them back into close voicing they would be an inversion of one of the 357 possibilities.

The reason I point this out is not for the construction of atonal music, but rather because most textbooks tell you to make up, for example, 4 note scales in order to improve soloing (a valuable excercise).  Then they go on about unlimited variation.  None of them say 'after you get to 43 combinations (and their 4 inversions, 12 roots and as many voicings as your instrument can handle) you are finished'.
#11August 1st, 2007 · 12:06 PM
19 threads / 15 songs
84 posts
United States of America
The theory of scales allows for the construction of large numbers of possible scales. For the idea of the 7 note scale I count 462 possibilities - or more precisely, 66 groups of 7 modes. The usefulness of all of these possibilities are debatable, but there is no denying the numbers. Please note that the 462 I list are for one key only. If you want them for every possible root note (from C to B) you would have 5,544 possibilities.

For the pentatonic, there are 330 possibilities for a single root note: 66 groups of 5 "modes". These are a little harder to categorize, but very straightforward to arrange.

As for explaining the theory to J.S. Bach, I suggest that explaining matters to the living is far more appropriate.

If you want verification of the numbers, I am willing to supply some but the files are very large and will have to be filtered into text files from the original excel docs.

Or, you could save time by assuming there is only one scale: the chromatic C and that all of the variations are the result of omitting notes.
#12August 1st, 2007 · 01:04 PM
159 threads / 32 songs
1,956 posts
United States of America
wow now I'm confused again
so  I take it that the scales you mention are from the downsized pythagora's 12 chromatic scale ........but then what about the Chinese that break up the octave into just 5 parts or India  the octave is broken up into  22 parts to create an Indian scale........hmm some of you mathematicians can go to work on that one.....lol....we have notes because the human ear responds mostly to these certain vibration speeds but in reality there are vibrations speeds or tones between the ones we write about...most of the music and notes played today are an adjusted tuning and not true tuning...... what if you had an instrument that could play a real slide between all tones...hmm like the trombone ..or slide guitar.......you could break up the octave into hundreds of parts if you had the technology...the  human ear couldn't register the difference but it would still be there.....

     Aaak now my head hurts...... hmm I'll think I'll play with a tone generator and create a new scale in between the steps of the 12 note chromatic scale.......naaa I'll just turn on the radio and relax.......lol.......
#13August 1st, 2007 · 01:35 PM
19 threads / 15 songs
84 posts
United States of America
Scaling the fish...
Not trying to be confusing here. I was a math major (big surprise here...) before diving into music. I took all of the possibilities for scales and sorted them. I was only dealing with the heptatonic (7 note) and the pentatonic. I do not deal with micro tonal scales because I believe we are not finished with the 12 note scale system by a long shot.

We are dealing with a form of abstraction here in order to get to the heart of the matter. Take for instance the Ionian mode of the major scale. C D E F G A B C. If we reduce this to numbers where the semitone = 1, this can be represented as 2 2 1 2 2 2 1 (read M2 M2 m2 M2 M2 M2 m2 with M2 = Major 2nd and m2 = minor 2nd): if you add all of these together, you get the number 12. Careful examination of a number of scales show that when returning to the root note, it always adds up to 12.

I took every possible group of 7 sets of numbers that added to 12 and sorted them. I got 462 possibilities. Dividing that by 7, as every scale belongs to a group of modes (just like the melodic and harmonic minor scales), and you have 66 groups. Granted, you get nearly useless groups like C Db Ebb Fbb Gbbb Abbbb Bbbbbb and its modes, but this is for completeness, not usability.

I am sure that if I declare a given scale useless, some musician more talented (or more reckless) will create a piece of music that justifiably uses the scale.

Hope this clears up where my numbers came from.

PS, there is a real instrument that does in fact slide between the notes. It is the Transperformance self tuning guitar and it can retune in performance live by pressing a button with the pitch of strings going up and down simultaneously. I have played it. Too rich for my blood, however.
#14August 1st, 2007 · 02:21 PM
159 threads / 32 songs
1,956 posts
United States of America
huh ?
I can't believe you responded I was just joking...... really there are a lot of instruments that slide between notes...
trombone......slide guitars...the humane voice....for that matter even a ruler....you remember this trick take a ruler hold one end down on the table and stike the ruler the slide in or out off the table top.....hmm a string tied to a bent piece of wood then put pressure on the bent piece of wood strike the string and release or add pressure hmm the old hunting bow musical insturment...plucking a rubber band and stretching or releasing it   ...or  ahh crap I'm done ..I'll go play my guitar now....in a simple 7 note major scale......lol
#15August 1st, 2007 · 02:52 PM
19 threads / 15 songs
84 posts
United States of America
Between the notes
I only mentioned the Transperformance as it was an instrument that slides between the notes, but more explicitly, it does so as a performance instrument coincidentally as opposed to by explicit design. This instrument was meant to facilitate the use of alternate tunings for the guitar. It has, among other features, a refresh button where strum the strings and touch the button and it resets the tuning to accurate pitch very quickly. However, it was discovered that by pressing the presets to change tunings while sounding the strings it functioned like an automated slide guitar.

Dave Beegle used the Transperformance in the album "See What I See" (the band is "Fourth Estate") on the song Poets lament. Hearing natural harmonics glide simultaneously in opposite direction is unusual even for pedal steel guitars, and is possibly unique to this instrument. You can find Dave Beegle written up as one of the "10 best guitarists you've never heard of" I think in Guitar Player Magazine.

But I do not mean to go on too long about irrelevancies. My original intent was to clarify what I was doing with the 12 tone scale. I am familiar with many varieties of microtonal scales: I merely choose to ignore them until I have finished my research about how to carve up the 12 note scale. I have some other research published under the title 2,985,984 Guitar Tunings. It can be found in the Elderly Instruments online catalog.
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