Have you heard about the Major Scale Formula? :)
View the full lesson at Major Scale Theory | JustinGuitar
I am definitely having trouble with the F sharp and C sharp major scales work sheetā¦I have stalled on those two for sureā¦
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Not sure if Iāve missed something but the formula TTSTTTS. Where did that come from?
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Itās just a major scale pattern - someone invented it in the past thought it sounds good and a whole music industry relies on it until today 
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Wellā¦yes and no. Iād call the origins of the formula TTSTTTS a combination of physics/math and history/tradition.
The physics part comes in from the frequency of notes. Every time you double the frequency you get the āsameā note an octave higher. So if you have a note at 200Hz, an octave higher is 400Hz, and an octave beyond that is 800Hz. Note that this isnāt a linear pattern. As the frequency increases the spread between octaves increases as well.
Then you have overtones relative to your fundamentalās frequency. One can look at those as fractions or ratios. If you imagine a vibrating guitar string, the fundamental is the whole string vibrating, or 1:1. The octave is 1:2. The fifth is 2:3, the fourth is 3:4, the major third is 4:5, the minor third is 5:6, and so on. So the tones of the harmonic series actually are rooted in mathematical ratios applied to the fundamental frequency. The overtones of a given fundamental frequency line up with the āstepsā of the major scale for that key. Butā¦to allow for harmonious modulation between keys you have to make some compromises.
History and tradition come in when you consider how all that gets used in Western music. The Western tradition divides the octave up into 12 notes. Back in the day they didnāt really understand all the physics, but they knew that certain notes sounded pleasing together and this scheme worked well. (Of course, the reason behind this was the physics.) One reason 12 notes works well is because it uses a single ratio (allowing modulation between keys, for example) to divide up the octave. The problem is that no one ratio is a perfect match. However, using a ratio of 3/2 is pretty close when using 12 steps within the octave.
Historically, you then get into different temperaments (e.g., Pythagorean, Just, Mean, etc). But today, modern Western music tends to use equal temperament, which is convenient, but is a compromise. Some notes are slightly out of tune (i.e., not perfectly matching the ratios) even when theyāre āin tuneā according to the equal temperament scheme. However, equal temperament is pretty close, allows modulation, and avoids really bad āwolf intervalsā that are present in some earlier temperament schemes. (Itās also worth noting that some instruments allow for perfect intonation of any note to its fundamental: fretless instruments are a good example.)
While the Western tradition uses 12 notes within the octave, thatās not the only way to divide it up. Itās just a way that works out well with the math and the desire to enable modulation, etc. Other musical traditions divide it up other ways. And even within the Western tradition there are examples of composers who delve into āmicrotonalā divisions.
Sorry for the TL;DR post. Itās a big question with a big answer. The math and history behind it is kind of fascinating: well-worth researching if youāre interested in that kind of thing.
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Iāll just memorize your entire post for an off-the-cuff response the next time someone tells me thereās no relationship between music and math 
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Lol. 
Yeah, I know.
āWhy?ā is one of best questions ever, in my opinion, and one that Iāve spent way too much time chasing down in all sorts of contexts over the years. @Flickās question just happened to be one that Iāve looked into quite a bit. And fairly recently, too. I think I started looking at temperaments and the reasons and history behind them when I got more interested in playing baroque and classical music and instruments that donāt necessarily use equal temperament. One thing leads to anotherā¦
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This is a pretty cool video on the history of guitar that touches on this. The History of Guitar - YouTube
One thought, the historian briefly mentions the 12 notes in the western scale as āthe church notesā during a large period of history until perhaps the 16 th century (trying to remember, I may be off a bit), anyway, I was wondering about how the western church influenced music and the very notes we use, whereas non-western cultures may have quite a different view.
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Itās probably not possible to overstate the influence of the Church on Western music. During the medieval period the Church developed the use of 12 tones within the octave (mostly used with chant, at first). The Church also codified modes of the major scale. All that didnāt happen ex nihilo, though. The concept of modes existed in antiquity (e.g., in Greece), although the Churchās use of modal theory wasnāt exactly the same as what had gone before. The Church also developed polyphony in the Western tradition, expanding upon the earlier monophonic style of chant. Western secular music developed alongside sacred music, and no doubt pulled in other influences, but largely built on the foundations the Church laid. In the early to mid Middle Ages the Church was uniquely positioned as a source of musical thought and instruction in the Western world.
Edited to add: As a tangent, Iāve watched that video, and others from Rob Scallon and Brandon Acker. Great stuff. Pretty much all of Ackerās videos are right up my alley. I like a lot of Rob Scallonās, too: especially the ones where he tries out unusual instruments.
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Thanks! Very cool you know this history.
Now I want to learn music history, too! As if there isnāt enough to learn. Why didnāt I pay attention to this kind of cool stuff when I was in college?
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Lol. College is wasted on youth. (Only half jokingā¦although I guess it might be more accurate to say that youth tend to waste college. I speak from personal experienceā¦)
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I resemble thatā¦
Not sure I would go back. The nice thing about being older is we can self motivate for the things that interest us and learn anyway Unfortunately, that really is no longer my career. Sighā¦some day.
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I agree on both counts. Iāve always been better at learning on my own (with books), anyway, rather than in a classroom situation. This particular subject is one that represents a confluence of my major interests (i.e., music and history) so itās an easy one as far as motivation goes.
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Wow! Iām almost sorry I askedš I guess I should reach for my abacus the next time I reach for my guitar!
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Jason, if you havenāt seen these videos I think you may like them ā¦
Building the Major Scale from Scratch on Guitar - Why These Notes: Building the Major Scale from Scratch on Guitar - Why These Notes - YouTube
Building the Major Scale on Paper - Why These Notes: Building the Major Scale on Paper - Why These Notes - YouTube
Visualizing the Notes as Ratios - Why the Major Chord is Happy & The Minor Chord is Sad: Visualizing the Notes as Ratios - Why the Major Chord is Happy & The Minor Chord is Sad - YouTube
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Thanks Richard; I hadnāt seen those videos. I just watched the first one, and it does seem like good video series.
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Is there a reason that the Notes in Column 1 are ordered CGDAEBā¦instead of just CDEFGA?
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This is the order of the Circle of fifths. G is the 5th of C
D is the the of G and so on.
It is also the order of sharps C has 0# G has 1# D has 2# on so on
This is how you know what Key sheet music is writen.
If you see ### 4/4 at the beginning of sheet music it is in the key
of A and 4/4 time
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You can order the scales any way you like, but as @stitch explained, this way you will see the relationship between the scales immediately (i.e. you start with C major and continue with degree V, and so on) and it will make major scale theory much much easier to understand.
Besides, the order of the scales is uncannily similar to that of the open strings 
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