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 09-19-2012, 02:02 PM #1 krm27 Registered User     Join Date: Mar 2012 Number of possible scales with musical potential - check my math or theorizing? I was trying to figure out how many possible scales have musical potential versus how many are simply modes of other scales. I did not think there could be that many, particularly with these parameters: 1) 7 intervals only (like major scale) 2) no interval of more than 3 semitones 3) no more than three consecutive intervals of only 1 semitone My result was 34 possible scales, each with 7 modes (238 possibilities). 3 of these use NO 3-semitone intervals (Heptanic prima, secunda, etc.) 20 of these use ONE-3 semitone interval 11 of these use TWO-3 semitone intervals I guess my concern is three fold: 1) Maybe I'm just wrong in my calculations. 2) Maybe I'm wrong to rule out scales with four 1-semitone intervals in a row as lacking musical potential. 3) Maybe I'm missing a bigger picture in trying to break it down this way, missing forest for trees or something like that. 4) Maybe there's a better website to go discuss or read about this stuff some one can point me to. Gracias, Ken Myers Student of Music Theory & Guitar (one year or so)
 09-19-2012, 02:10 PM #2 krm27 Registered User     Join Date: Mar 2012 Oh, in case anyone really has a lot of spare time, or is curious, here is how I worked this out: How many scale combinations in 12 note octave - using 7 intervals - using only intervals of 1 or 2 + Conclusion: Must have FIVE 2's and TWO 1's in order to add up to 12 using only seven 1's and 2's. 1 1122222 (7 MODES)HEPTONIA TERTIA / Neapolitan Major scale & modes 2 1212222 (7 MODES)HEPTONIA SECUNDA / Melodic Minor scale & modes 3 1221222 (7 MODES)HEPTONIA PRIMA / Major scale & modes + Conclusion: Only three unique scales with 7 modes each (21 total) How many scale combinations in 12 note octave - using 7 intervals - using only one interval of 3 and no higher intervals (all other 1 or 2) 3 _ _ _ _ _ _ 1 1 1 1 1 1 = 9 x 2 = 10x 2 2 = 11x 2 2 2 = 12 + Conclusion: Must have three 1's and three 2's. 1 3 1 1 1 2 2 2 2 1 3 1 1 2 2 2 3 1 1 3 1 2 2 2 4 1 1 1 3 2 2 2 5 1 1 1 2 3 2 2 6 1 1 1 2 2 3 2 + Conclusion: six possibilities keeping 1's grouped away from 2's 7 3 2 1 2 1 2 1 8 3 1 2 1 2 1 2 + Conclusion: two possibilities keeping 1's and 2's alternating Six remaining prefix options: 1st: 3 1 1 2 _ _ 2 (2 options) 2nd: 3 2 2 1 _ _ 1 (2 options) 3rd: 3 1 2 2 1 _ _ (2 options) 4th: 3 2 1 1 2 _ _ (2 options) 5th: 3 1 2 1 _ _ _ (2 unique options) 6th: 3 2 1 2 _ _ _ (2 unique options) 9 3 1 1 2 1 2 2 10 3 1 1 2 2 1 2 11 3 2 2 1 2 1 2 12 3 2 2 1 1 2 1 13 3 1 2 2 1 1 2 14 3 1 2 2 1 2 1 15 3 2 1 1 2 1 2 16 3 2 1 1 2 2 1 17 3 1 2 1 1 2 2 18 3 1 2 1 2 2 1 19 3 2 1 2 2 1 1 20 3 2 1 2 1 1 2 + Conclusion 20 unique scales (each w/ 7 modes) for 7 intervals, none higher than 3, using exactly one 3, for a total of 140 possibilities. How many scale combinations in 12 note octave - using 7 intervals - using two intervals of 3 and no higher intervals (all other 1 or 2) 3 3 _ _ _ _ _ 1 1 1 1 1 = 11 x 2 = 12 + Conclusion: Must have four 1's and one 2. 1) 3 3 1 1 1 1 2 - note four consecutive semitones 2) 3 3 1 1 1 2 1 3) 3 3 1 1 2 1 1 4) 3 3 1 2 1 1 1 5) 3 3 2 1 1 1 1 - note four consecutive semitones + Conclusion: five options keeping 3's together, 7 modes each. 6) 3 2 3 1 1 1 1 - note four consecutive semitones + Conclusion: one option putting just 2 between 3's 7) 3 1 1 1 3 1 2 8) 3 1 1 1 3 2 1 + Conclusion: two options putting three 1's between 3's 3 1 1 3 _ _ _ 9) 3 1 1 3 1 1 2 10) 3 1 1 3 1 2 1 11) 3 1 1 3 2 1 1 + Conclusion: three options putting two 1's between 3's 3 1 3 _ _ _ _ 12) 3 1 3 1 1 1 2 13) 3 1 3 1 1 2 1 14) 3 1 3 1 2 1 1 15) 3 1 3 2 1 1 1 + Conclusion: four options putting one 1 between 3's All others appear to be modes + Conclusion: FIFTEEN unique scales (each w/ 7 modes) for 7 intervals, none higher than 3, using exactly two 3's, for a total of 105 possibilities. It should be noted that three of these options include FOUR semitones in a row, and thus have less viability for melody / musicality, leaving ELEVEN unique scales (seven modes each) with seven intervals, two intervals of 3 semitones, without more than three consecutive intervals of 1 semitone, for a total of 77 possibilities. How many scale combinations in 12 note octave - using 7 intervals - using three intervals of 3 and no higher intervals (all other 1 or 2) 3 3 3 _ _ _ _ 1 1 1 1 = 13 x IMPOSSIBLE + Conclusion: NONE. CONCLUSION: Number of Scales with: - exactly 7 interval notes - no interval more than 3 semitones - no more than three consecutive intervals of only 1 semitone 21 (w/ no 3) 140 (w/ one 3) 77 (w/ two 3's) 238 unique scales
09-19-2012, 02:33 PM   #3
mrkeka
Lost in Translation

Join Date: Aug 2006
Location: São Paulo
You know, you could have used all that time you spent doing this math learning how to build chords, harmonize the major scale, and use chord tones and approach notes... You would have a far more practical and usable result.
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Quote:
 Originally Posted by Xiaoxi The Byzantine scale was useful until the Ottoman scale came around and totally annihilated it.

09-19-2012, 02:35 PM   #4
:-D
hi

Join Date: Dec 2007
Location: Earth
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 Originally Posted by rockaholic97 Thanks! I wish everyone on Ultimate Guitar could be more like you!

 09-19-2012, 02:40 PM #5 MaggaraMarine Slapping the bass.     Join Date: Oct 2009 Location: Finland There's just one: The major scale. /Thread __________________ My motto: Play what the song needs you to play! Gear: Charvel So Cal (MIJ) Digitech RP355 MXR Micro Chorus Laney VC30 Tokai TB48 Hartke HyDrive 210c
09-19-2012, 02:42 PM   #6
mrkeka
Lost in Translation

Join Date: Aug 2006
Location: São Paulo
Quote:
 Originally Posted by :-D don't care, had sex

with a llama?
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Quote:
 Originally Posted by Xiaoxi The Byzantine scale was useful until the Ottoman scale came around and totally annihilated it.

 09-19-2012, 02:49 PM #7 tappooh Registered User     Join Date: May 2011 A minor pentatonic. __________________ Fernando Alonso 2012 WDC My Buckethead covers (I don't dress up like him)
09-19-2012, 03:13 PM   #8
krm27
Registered User

Join Date: Mar 2012
Quote:
 Originally Posted by mrkeka You know, you could have used all that time you spent doing this math learning how to build chords, harmonize the major scale, and use chord tones and approach notes... You would have a far more practical and usable result.

Thanks, this is sort of the feedback I was hoping for, as I can go off on tangent way too far. And it gives me some thought as to what to focus on next. Though the above math took under an hour, so it's not like I could have done all the stuff you listed in that time. It all started as I was trying to learn chord building, which then led me to first trying to understand intervals better, which led to thinking about scales. Then it seemed like wrapping my head around scale potential was pre-cursor to wrapping my head around chord potential.

Ken

 09-19-2012, 03:41 PM #9 macashmack Spongethug Moneypants     Join Date: May 2011 Location: New York, NY in the end, there is only one scale. The scale of music. With this scale, one can mold the energy of sound into anything they want, without limit, and infinite potential. __________________ We're forever stuck waist deep We can still breath but we can't move We can still see but we can't choose
 09-19-2012, 03:48 PM #10 Sethis Registered User   Join Date: Dec 2011 Chromatic scale is the best.
09-19-2012, 03:52 PM   #11
wolflen
Registered User

Join Date: May 2008
Location: los angeles
Quote:
 Originally Posted by krm27 Thanks, this is sort of the feedback I was hoping for, as I can go off on It all started as I was trying to learn chord building, which then led me to first trying to understand intervals better, which led to thinking about scales. Then it seemed like wrapping my head around scale potential was pre-cursor to wrapping my head around chord potential. Ken

for the chord part..try ted greenes' chord chemestry...modern chord progressions (2 vols)

(who knew there were that many A chords !!)

 09-19-2012, 03:53 PM #12 J-Dawg158 UG's Resident Dhampyr     Join Date: Nov 2008 Cool, now using the same criteria can you figure out how many unique scales there are in 53-TET? Edit: Inquiring minds want to know! __________________ I'm an Engeneer Enginear Enginere I'm Good at Math Last edited by J-Dawg158 : 09-19-2012 at 03:54 PM.
 09-19-2012, 04:15 PM #13 Xiaoxi busy passing you     Join Date: Nov 2007 Location: on the autobahn What you're really trying to accomplish is how much time you can possibly waste. __________________ Modes and scales are dumb and useless. Stop learning them. No, seriously. Analyzing Brahms: Insights to Help Us Improve Our Music My New Workstation
09-19-2012, 04:28 PM   #14
macashmack
Spongethug Moneypants

Join Date: May 2011
Location: New York, NY
Quote:
 Originally Posted by Xiaoxi What you're really trying to accomplish is how much time you can possibly waste.

Xiaoxi, You probably don't even know who I am on this website, but i looked at your profile, and you're a young guy! I always imagined you to be an old black guy!
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We're forever stuck waist deep
We can still breath but we can't move
We can still see but we can't choose

09-19-2012, 04:38 PM   #15
Xiaoxi
busy passing you

Join Date: Nov 2007
Location: on the autobahn
Quote:
 Originally Posted by macashmack Xiaoxi, You probably don't even know who I am on this website, but i looked at your profile, and you're a young guy! I always imagined you to be an old black guy!

That's because I am! You flatter me too much.
__________________
Modes and scales are dumb and useless. Stop learning them. No, seriously.

Analyzing Brahms: Insights to Help Us Improve Our Music

My New Workstation

09-19-2012, 04:58 PM   #16
:-D
hi

Join Date: Dec 2007
Location: Earth
old black guys named xiaoxi are few and far between
__________________
Quote:
 Originally Posted by Archeo Avis You just won.

Quote:
 Originally Posted by rockaholic97 Thanks! I wish everyone on Ultimate Guitar could be more like you!

 09-19-2012, 07:10 PM #17 AlanHB Godin's Resident Groupie     Join Date: Aug 2008 Location: Canberra, Australia The error in your theorizing TS concerns the application and harmonic context in which you intend to use these scales. I bet most of them will be heard as minor variations to the major or minor scale, because that's what they will function as. __________________ And no, Guitar Hero will not help. Even on expert. Really.
 09-20-2012, 02:15 AM #18 Hail kill both bass players     Join Date: Jan 2010 Location: Dallas
09-20-2012, 04:37 AM   #19
A cornucopia of trivia

Join Date: Jul 2011
Location: Butt****, SY
Quote:
 Originally Posted by krm27 I was trying to figure out how many possible scales have musical potential versus how many are simply modes of other scales.

What everyone else said.

Plus: Musical potential has nothing to do with modes or scales. It has to do with the potential to make music.

You can make music on a snare drum.

How many notes does that have?
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Quote:
 Originally Posted by Hail oh shut up with that /mu/ bullshit. fidget house shouldn't even be a genre, why in the world would it deserve its own subgenres you twat

 09-20-2012, 03:26 PM #20 Blind In 1 Ear Git-Man     Join Date: Jun 2006 i literally have no idea what the point of this thread is, or what the premise is, or what the first line you wrote is supposed to mean. all that stuff you calculated does nothing in actually WRITING a good MELODY. and as you figured out, there are a lot of possibilities of note choices. and it's all subjective anyway so i'm sorry to say but, you kinda just wasted your time on something that will probably never help you. not to mention you can just learn theory. that's what it's there for. so you don't waste time calculating things like this. just look up the scales, learn the intervals and theory that goes with them, and apply where you see fit. __________________ http://www.youtube.com/user/timmy47?feature=mhee check out my youtube page for some songs.

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