Page 1 of 4
#1
Now, this is just out of curiosity. There is a limited number of scales, right?
Why are we so wicked indecisive
Let's hit the streets with toy explosives
And let's enjoy what we have
#2
yes, theirs only 12 notes, obviously there only theres only a certain number of things you can do with them before you start repeating yourself
#4
'a guide to chords, scales & arpeggios' by al di meola has all the chords you'll ever need.

and about scales being infinite: no. there only exist a few hundred. maybe a thousand.

can a math nerd tell me the formula to calculating the possibility of scale numbers?
i just completely forgot pretty much everything i've learned on maths -.-
Last edited by RCalisto at Aug 28, 2008,
#6
Quote by RCalisto
can a math nerd tell me the formula to calculating the possibility of scale numbers?
D (I think) and I calculated it once under a certain set of conditions to assure that the scale wasn't just 7 chromatically ascending tones and such. The number was in excess of 50,000.

Quote by Shackman10
Ummmm...correct me if I'm wrong but there are 12 major scales and 12 minor scales
Kind of. There are 12 "regular" major and minor scales (24 total), but then harmonic and melodic minor as well as modes, synthetic scales, pentatonics, and the blues scale. However, those concepts are well above what should be discussed in this thread.

Quote by Shackman10
However...you can keep going up and up in octaves.
No. C D E F G A B C D E F G A B C is still just the C major scale.
#8
Quote by Shackman10
Ummmm...correct me if I'm wrong but there are 12 major scales and 12 minor scales

Enharmonically, there are 12, but some scholarly books say that there are "15" keys/natural scales, taking into account enharmonic notes. Example, Gb major/F# major. I've seen this in only a few books though, but these are old books, so I'm assuming this is the "correct" way.

/flame shield

EDIT: I mean 15 of each, 15 minor and 15 major.
#9
Quote by one vision
Enharmonically, there are 12, but some scholarly books say that there are "15" keys/natural scales, taking into account enharmonic notes. Example, Gb major/F# major. I've seen this in only a few books though, but these are old books, so I'm assuming this is the "correct" way.

/flame shield
There would be more than 15 if you took enharmonic tones into account.

Regardless, considering F#/Gb scales and chords different is useless for this topic, as a scale or chord should have its own unique sound; F# anf Gb sound exactly the same (ignore anyone who says otherwise unless they are talking about music a long time ago, like the 1500s or something).
#10
but what's the formula for finding this kind of stuff?
i tried looking it up, but have no idea what it is called.
#11
Quote by bangoodcharlote
There would be more than 15 if you took enharmonic tones into account.

Regardless, considering F#/Gb scales and chords different is useless for this topic, as a scale or chord should have its own unique sound; F# anf Gb sound exactly the same (ignore anyone who says otherwise unless they are talking about music a long time ago, like the 1500s or something).

Yeah, I know , the book is like 100 years old. I've never heard of anyone mention there being 15 of each. But yeah, it is pretty useless. To add to that, there are 12 of each on the circle of fifths. I just brought up the 15 for fun.
#12
Quote by RCalisto
but what's the formula for finding this kind of stuff?
i tried looking it up, but have no idea what it is called.
For finding how many scales there are? It's fairly basic conditional probability.
#14
Quote by RCalisto
but what's the formula for finding this kind of stuff?
i tried looking it up, but have no idea what it is called.

its an exponential formula which depends on how many notes you consider a scale to be.
#15
Well, between each pitch and its logaritmical relative pitch (which we perceive as the same, like A220 htz and A440) there are infinite frecuencies, and therefore infinite pitches..
There are infinite ways (combinations actually, since the order of pitches matters and it is usually done from lowest pitch to highest pitch) of arranging said pitches in a scale, since they are infinite...

Wouldn't scales be infinite then?
#16
Quote by gonzaw
Wouldn't scales be infinite then?
No. At most you could have 12! scales, most of which are useless.

Edit: And let's not bring up microtonality.
#17
Quote by RCalisto
'a guide to chords, scales & arpeggios' by al di meola has all the chords you'll ever need.

and about scales being infinite: no. there only exist a few hundred. maybe a thousand.

can a math nerd tell me the formula to calculating the possibility of scale numbers?
i just completely forgot pretty much everything i've learned on maths -.-

If a scale was anything longer than 1 note (so there could be two note scales)
It might be
(12x11)+
(12!/9!)+
(12!/8!)+
(12!/7!)+
(12!/6!)+
(12!/5!)+
etc.. until you get to just 12!/1. You would be able to skip octaves and such but this is the best way I could calculate it.
#21
Quote by bangoodcharlote
Octaves don't count. The max is 12! with most of the scales being useless.

no scale is useless, however writing something for a 10 tone scale would more than likely require you to view many of the notes as passing tones. i personally have a couple things im working on that are 9 and 10 tone scales that are based off of this.
#22
Quote by z4twenny
however writing something for a 10 tone scale would more than likely require you to view many of the notes as passing tones.
But you don't form chords from passing tones, and that's the reason to have scales...to form chords!

Quote by RCalisto
care to explain how you reached that value?
I didn't do the calculation, but I assume it is the answer to 12!.
#24
how did you do the math though? i'm probably doing it all wrong because i'm not getting millions of scales.
#27
scales are note patters (half and whole steps). You can even make up you're own scale with up to 12 notes (if you dont want to repeat any) using a 12 tone matrix. (check this online generator http://www.dancavanagh.com/music/matrix.php )

3 Octatonic scales
4 hexatonic scales
whole notes

There is so many you can do if you repeat notes, so I dont think they are endless.
Last edited by Pabli7o at Aug 29, 2008,
#28
oh i get it. i never knew that ! meant what you just said. i had never seen it used so far.
#29
Quote by RCalisto
oh i get it. i never knew that ! meant what you just said. i had never seen it used so far.
! is pronounced "factorial." So 12! is 12 factorial which equals 12x11x10x9...x2. You're supposed to include x1 as well, but it doesn't change the number so I leave it out.
#30
X!=x*(x-1)*(x-2)..*(x-(x-1))

Damn, you beat me to it.

I feel like I just realized why it wouldn't be 12 factorial though and then I lost my thought....

Oh yeah, because factorial is for permutations when we want combinations--with scales, the order doesn't matter for this purpose as it'll always be organized back into an sequential order of lowest to highest (eg. R, 3, b2, 4, 7, R would become R, b2, 3, 4, 7, R)

Looks like I have more math to do.
Last edited by TheShred201 at Aug 29, 2008,
#31
so you guys over there are taught that till 9th grade or something? cus i've heard several times on portugal we're taught the same thing you are taught 2 years earlier
#33
Quote by bangoodcharlote
No. At most you could have 12! scales, most of which are useless.

Edit: And let's not bring up microtonality.


No microtonal music then, huh?


Well, you have to notate how much notes there are in the scale (max being 12).
But if you do 12!, you are only considering the pitches, not intervals (which would be 29 intervals I suppose).
BUT...some intervals are enharmonical, they can't be put in the same scale, but count as different scales when done separated (like having 1 2 3 5 and 1 2 b4 5, etc).
Also, the order doesn't matter (like having 1 2 3 4 5 and 1 4 3 2 5 since the first one is the one that matters only, because of ascending pitches)....

So at first glance it seems to be 29!/17!12!+29!/18!11!+29!/19!10!+...+29

Now, you have to take out all the ones with enharmonical intervals (I don't know how), and the ones with succeded intervals with pitches not according to their degree hierarchy (like having a #2 and a bb3, the #2 has a higher pitch than bb3)...

After taking out all of them, you have all the possible western scales...
If I'm not wrong..

EDIT:Oh, I forgot...

THe ones with the Unison (1) always have to be present, so that means that in reality it is 28!/16!12!+28!/16!11!+...+28
Oh, and the whole (28!/16!12!+...+28-[scales with enharmonical intervals]-[scales with uneven intervals]) is all multiplied by the quantity of different notes. These would be Cbb Cb C C# CX with all 7 so it is 5*7=35 different notes. SO you multiply everything by 35 in the end...

I think it is way higher than 480000000 (or whatever the number that was posted before)
Last edited by gonzaw at Aug 29, 2008,
#34
Quote by RCalisto
so you guys over there are taught that till 9th grade or something? cus i've heard several times on portugal we're taught the same thing you are taught 2 years earlier


What?

I assume you are talking about the US and Portugal? So are you saying that in portugal they are taught that in 9th and in the US it is at 7th or in the US it's at 9th and in portugal is 7th....

For me, that stuff was part of the math I took in 7th grade. I'm in the US.
#35
i mean we're late here.
you proved me right too. i hadn't even heard of such thing so far.

no actually i did. i just remembered. but not from school, it was from some news paper cross word type of thing.
#36
Quote by gonzaw
No microtonal music then, huh?


Well, you have to notate how much degrees there are in the scale (max being 12).
But if you do 12!, you are only considering the pitches, not intervals (which would be 29 intervals I suppose).
BUT...some intervals are enharmonical, they can't be put in the same scale, but count as different scales when done separated (like having 1 2 3 5 and 1 2 b4 5, etc).
Also, the order doesn't matter (like having 1 2 3 4 5 and 1 4 3 2 5 since the first one is the one that matters only, because of ascending pitches)....

So at first glance it seems to be 29!/17!12!+29!/18!11!+29!/19!10!+...+29

Now, you have to take out all the ones with enharmonical intervals (I don't know how), and the ones with succeded intervals with pitches not according to their degree hierarchy (like having a #2 and a bb3, the #2 has a higher pitch than bb3)...

After taking out all of them, you have all the possible western scales...
If I'm not wrong..
This post makes no sense from either a math or music perspective. If your scale can contain 12 notes makes, note one can be any of 12, note 2 can be any of the remaining 11, note 3 can be any of the remaining 10, etc, hence 12!=479,001,600 scales, nearly half a billion.

When I did this with conditional probability, making all the scales actually useful, the answer was still very large, but more like 50,000 rather than half a billion.
#39
And here's mine:
The total number of scales you can get is equal to the total number of groups from 1 to 12 that you can take from the set of 12 tones. Each size of group is a combination, written as 12c1, or 12c2, etc. meaning 12 (tones) Choose 2, etc.

So, say you wanted to see how many groups of 1 you can take from 12...The answer? 12 of course, and here's the math for a combination done to express this situation.
(12!/((12-1)!*1!))

Since you want the total of all of the independent group sizes that can be selected from 12, you would do:
12c1+12c2+12c3+12c4+12c5+12c6+12c7+12c8+12c9+12c10+12c11+12c12
Without that shorthand notation, it looks something like this::
(12!/((12-1)!*1!))+(12!/((12-2)!*2!))+(12!/((12-3)!*3!))+(12!/((12-4)!*4!))+(12!/((12-5)!*5!))+(12!/((12-6)!*6!))+(12!/((12-7)!*7!))+(12!/((12-8)!*8!))+(12!/((12-9)!*9!))+(12!/((12-10)!*10!))+(12!/((12-11)!*11!))+(12!/((12-12)!*12!))

The answer to which (If I didn't make any typos, which I believe that I didn't) is 4,095. Less than we got earlier by a lot, but still a large number. Although, that's for each root note as a key....Since all of them can be sharp or flat, we have:
C, C#, Cb, D, D#, Db, E, E#, Eb, ...
Giving us 24 total root notes for these scales.
By multiplying 24 times 4,095 we get 98,280. So there are 4,095 sets of intervals you can stack with no repetition in a scale, and no scales repeated with different interval names (b5 vs.#4). I feel like I worded that poorly--you can make 4095 combinations of 12 tones. As you can use each of 24 notes as the root when writing these, there are 98,280 scales that you can write.
#40
Quote by bangoodcharlote
This post makes no sense from either a math or music perspective. If your scale can contain 12 notes makes, note one can be any of 12, note 2 can be any of the remaining 11, note 3 can be any of the remaining 10, etc, hence 12!=479,001,600 scales, nearly half a billion.

When I did this with conditional probability, making all the scales actually useful, the answer was still very large, but more like 50,000 rather than half a billion.


But on scale can contain 12 notes, then another scale can contain 11 notes, and another pentatonic scale can contain 5, etc...
But, this is because of the enharmonical intervals (like what I said), since the max number of notes in a scale would be that of the chromatic scale, like:
C C# D D# E F F# G G# A A# B there are 12 notes.
BUt what if the scale was C C# D D# E F F# G G# A Bb B?? It would be a different scale. Or what about maybe C C# CX Eb E E# EX G G# GX Bb B? There are a lot of possibilities, only with a 12-note scale using C as the tonic (you multiply it by 35 in the end)...
Then you have undecatonic (sp?) scales, like C C# D D# E F G G# A A# B, so you do the same...
Then with decatonic scales, then with nonatonic (sp?) scales, then octatonic, eptatonic, hexatonic, pentatonic, tetratonic, propatonic, diatonic, atonic...
I suppose the scales made of 3, 2 and 1 notes are left out, but still, I think it is way over 500.000.000
Page 1 of 4