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  #1  
Old 2005-11-17, 15:03
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Unanything Unanything is offline
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Scale Possibilities

Here's a cool octatonic for you all.

1 - m2 - m3 - M3 - b5 - 5 - M6 - dim7

Oh, I'll bet no one can work out how many heptatonics there are with:

a 1st and perf. 4th,
and one of each of the 2nd, 3rd, 5th, 6th, and 7th notes.
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Quote:
Originally Posted by fatdanny
Also, check out Autopsy, the vocalist sounds like hes about to eat your grandmother while fucking you in the eye. Brutal.


Quote:
Originally Posted by floridadude
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  #2  
Old 2005-11-18, 13:48
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I'll tell you now, then.

There are 32, because 32 = 2 to the power of 5.

If 1 and 4 are constant, then you only need to worry about the 2nds, 3rds, 5ths, 6ths and 7ths. As each has two notes inherent, one and one only are included in these scales. Therefore you can count using base two like you do in gate logic diagrams in technological studies, or, as it is popularly known, BINARY. Using this, you can find all the combinations of figures and find all the scales possible in the stated condition.

0 - minor/flattened
1 - major/perfect

2nd 3rd 5th 6th 7th
0 0 0 0 0 - Locrian mode
0 1 1 0 0 - Phrygian Dominant scale
1 0 1 1 0 - Dorian mode

That means there would be 16 possible scales made up of two adjoined tetrachords.

Clever?
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Quote:
Originally Posted by fatdanny
Also, check out Autopsy, the vocalist sounds like hes about to eat your grandmother while fucking you in the eye. Brutal.


Quote:
Originally Posted by floridadude
I coated the end of a toothpick with Satan's blood and simply wiped it across the top of an omelet. PERFECT!
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  #3  
Old 2005-11-18, 16:25
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Damn...

That's heavy. I'm a computer science graduate, so that makes killer fuckin sense. I was always told there's a correlation between programming and music. You just told me...it's all about base 2. Nice.
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  #4  
Old 2005-11-19, 05:19
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Quote:
Originally Posted by davie_gravy
Damn...

That's heavy. I'm a computer science graduate, so that makes killer fuckin sense. I was always told there's a correlation between programming and music. You just told me...it's all about base 2. Nice.


Glad I could be of service.

That means there are 2 to the 11 one octave scales of all possible number of degrees and intervals. Use eleven digits (ROOT is constant therefore excluded) with 0 - excluded, 1- included.

This means 11111111111 is the chromatic scale.

Which is... 4096/2
Which equals... 2048.

WHOA...

I'm not sure how many heptatonics there are. Mr. Gravy, can you figure a binary system? You could look through all 2048 posibilities and filter out all possibilities with more than six 1's, but that'd be way too time-consuming. Although I did make a point of writing out all the 32. And I have tabbed a lot of Meshuggah's I...

Like my octatonic by the way?

You could have this as wll for a similar sound.
1 - m2 - M3 - 4 - m6 - M6
A hexatonic, like the blues scale. Made up of adjoined Gypsy tetrachords.
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Quote:
Originally Posted by fatdanny
Also, check out Autopsy, the vocalist sounds like hes about to eat your grandmother while fucking you in the eye. Brutal.


Quote:
Originally Posted by floridadude
I coated the end of a toothpick with Satan's blood and simply wiped it across the top of an omelet. PERFECT!
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  #5  
Old 2005-11-19, 15:22
vivaldi vivaldi is offline
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wtf?
didnt understand a thing.
mate could ya explain in simple words
cheers
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  #6  
Old 2005-11-19, 16:46
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He's just showing you the relationship that scales and music take in relation to binary.

Code:
0 - minor/flattened 1 - major/perfect 2nd 3rd 5th 6th 7th 0 0 0 0 0 - Locrian mode 0 1 1 0 0 - Phrygian Dominant scale 1 0 1 1 0 - Dorian mode


See, the root and perfect 4 are constant, the 1's and 0's represent whether it's a minor tone or major tone for that particular degree (2nd, 3rd, 5th, etc).

1 1 1 1 1 - Major Scale (Ionian Mode) because the major scale contains all major scale tones. Therefore, they would all be 1's which represent major/perfect scale tones

1 0 1 0 0 - Minor Scale (Aeolian Mode) because the minor scale contains a flattened 3rd, 6th, and 7th scale tone.

See how all scale possibilities are in relation to binary now?
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  #7  
Old 2005-11-19, 23:46
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thnaks dude
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  #8  
Old 2005-11-21, 06:31
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Quote:
Originally Posted by Unanything
I'm not sure how many heptatonics there are. Mr. Gravy, can you figure a binary system? You could look through all 2048 posibilities and filter out all possibilities with more than six 1's, but that'd be way too time-consuming.


To arrive at a figure for the number of included notes you would permutate the number of notes to be included among the total number of notes available according to the following formula.

C(m,n) = m!/(n!)(m-n)!

where n is the number of notes to be included and m is the total number of notes for the permutation to be applied to. In all cases m =11 but in the case of heptonics, n = 7.

Now:

C(11,7) = (1x2x3x4x5x6x7x8x9x10x11)/[(1x2x3x4x6x7)x(1x2x3x4)]

C(11,7) = 8x9x10x11/1x2x3x4

C(11,7) = 7,920/24

C(11,7) = 330

Similarly, the permutations for all scale lengths are as follows:

C(11,0) = 1
C(11,1) = 11
C(11,2) = 55
C(11,3) = 165
C(11,4) = 330
C(11,5) = 462
C(11,6) = 462
C(11,7) = 330
C(11,8) = 165
C(11,9) = 55
C(11,10) = 11
C(11,11) = 1

Which gives a total of 2,048 scale combinations. However, the true number of scale combinations is 2,036 if a scale is to include at least two notes.

PS: I knew the Combinatorics module I opted for in my final year of university would come in handy!
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  #9  
Old 2005-11-21, 16:25
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Very Impressive mansley!
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  #10  
Old 2005-11-22, 03:53
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Cheers!
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  #11  
Old 2005-11-22, 14:30
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Quote:
Originally Posted by johnmansley
To arrive at a figure for the number of included notes you would permutate the number of notes to be included among the total number of notes available according to the following formula.

C(m,n) = m!/(n!)(m-n)!

where n is the number of notes to be included and m is the total number of notes for the permutation to be applied to. In all cases m =11 but in the case of heptonics, n = 7.

Now:

C(11,7) = (1x2x3x4x5x6x7x8x9x10x11)/[(1x2x3x4x6x7)x(1x2x3x4)]

C(11,7) = 8x9x10x11/1x2x3x4

C(11,7) = 7,920/24

C(11,7) = 330

Similarly, the permutations for all scale lengths are as follows:

C(11,0) = 1
C(11,1) = 11
C(11,2) = 55
C(11,3) = 165
C(11,4) = 330
C(11,5) = 462
C(11,6) = 462
C(11,7) = 330
C(11,8) = 165
C(11,9) = 55
C(11,10) = 11
C(11,11) = 1

Which gives a total of 2,048 scale combinations. However, the true number of scale combinations is 2,036 if a scale is to include at least two notes.

PS: I knew the Combinatorics module I opted for in my final year of university would come in handy!


I know what the ! does in Maths but we haven't reached that yet in it. There was a freak question on it in my exam last year and no one but me had a shitting clue. I lost a couple of marks though because I forgot the quadraric formula. I think I'll open a thread on it in Chit chat. I was breaking up algebraically while the teacher rattled on about circle and tangent equations because everone (but me) is failing at it. i seem to be the only one who knows what a negative reciprocal is. In fact I got called a smartarse by a co-Higher Maths student for mentioning it when we did the gradients of perpendicular lines.

I'm gonna be a-noting that formula.
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Quote:
Originally Posted by fatdanny
Also, check out Autopsy, the vocalist sounds like hes about to eat your grandmother while fucking you in the eye. Brutal.


Quote:
Originally Posted by floridadude
I coated the end of a toothpick with Satan's blood and simply wiped it across the top of an omelet. PERFECT!
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  #12  
Old 2005-11-22, 14:42
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Yea,


I always hated fuckin factorials. Thank god for powerful calculators.
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  #13  
Old 2005-11-22, 16:23
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Are we writing an analysis program? What's the point of this?

Manx
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  #14  
Old 2005-11-23, 09:04
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It's of interest to me and therefore has a point.
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  #15  
Old 2005-11-23, 11:33
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Uhhh, sorry to burst your bubble Unanything, but there are only two real octatonic scales--the major octatoc (0-2) and the minor octatonic (0-1). In some weird cases, there may be a third, and that is 1-2.

Major:
D-E-F-G-Ab-Bb-B-C#-D

minor:
D-Eb-F-F#-G#-A-B-C-D

You gave only the minor one, and the last note is a half step up, making it a m7 from the root, not a dim7. If it was dim, it wouldv'e been Cb.
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  #16  
Old 2005-11-23, 15:37
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Quote:
Originally Posted by powersofterror
Uhhh, sorry to burst your bubble Unanything, but there are only two real octatonic scales--the major octatoc (0-2) and the minor octatonic (0-1). In some weird cases, there may be a third, and that is 1-2.

Major:
D-E-F-G-Ab-Bb-B-C#-D

minor:
D-Eb-F-F#-G#-A-B-C-D

You gave only the minor one, and the last note is a half step up, making it a m7 from the root, not a dim7. If it was dim, it wouldv'e been Cb.

Yeah. Isn't a dim7 just the same thing as an M6?
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  #17  
Old 2005-11-23, 16:02
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Quote:
Originally Posted by Rattlehead
Yeah. Isn't a dim7 just the same thing as an M6?


It is in terms of the actual note your playing, but it's all about the chord type that determines if it's a dim7 over major6.
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  #18  
Old 2005-11-24, 14:03
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That's another way of saying it's "enharmonic."
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  #19  
Old 2005-11-24, 14:54
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Music theory can extend beyond the established you know. You should know that. I called it an octatonic because there are 8 notes in it.

You should some of the chords I'm using... I've been getting Mr. oRg to name them and he's been using powertab to name some. In fact cred' to the man.
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Quote:
Originally Posted by fatdanny
Also, check out Autopsy, the vocalist sounds like hes about to eat your grandmother while fucking you in the eye. Brutal.


Quote:
Originally Posted by floridadude
I coated the end of a toothpick with Satan's blood and simply wiped it across the top of an omelet. PERFECT!
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  #20  
Old 2005-11-26, 14:03
Rattlehead Rattlehead is offline
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Quote:
Originally Posted by Unanything
Music theory can extend beyond the established you know. You should know that. I called it an octatonic because there are 8 notes in it.

Yeah but the reason I was asking is because if there are enharmonic notes in an octatonic scale, like in
1 - m2 - m3 - M3 - b5 - 5 - M6 - dim7
Then it technically should be called septatonic, on account that there are only 7 actual notes.
I'm confused. Is there something I'm missing here?

Quote:
Originally Posted by Unanything
You should some of the chords I'm using... I've been getting Mr. oRg to name them and he's been using powertab to name some. In fact cred' to the man.
I didn't understand this passage at all.



Edit: Cool, I just found out that you can set Calculator to binary and octal number systems! Then I thought I'd share this useless information with you kind folks, so I desecrated my post by adding this. Enjoy!
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Last edited by Rattlehead : 2005-11-26 at 14:28.
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