17. Why does the Major Scale have 7 Notes?

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This video explores historical and mathematical reasons why the Major scale has 7 notes.

[@GlennFiddles]

I think the preference for the maximum interval size of a whole tone is more of a cultural construct than anything else. So many musical cultures, including Western folk traditions, make extensive and sometimes almost exclusive use of major pentatonic scales and I don't think they feel there is anything missing or "disjointed" about these melodies. And of course there is maqam which frequently uses intervals of approximately a tone and a half between adjacent notes in the western system, not to mention "1/4" tones like on maqam bayati or saba etc. I feel like our proclivity to want to explain music entirely as a result of mathematical interval ratios and formulas and formulas is useful up to a point but has largely become pernicious by the 21st century.

[@TotalDec]

We hear overtones close to 12-TET. That basically explains everything. The overtone series predates culture.

[@wiegraf9009]

Omg I had heard about Miller's Law before but never with a name attached to it! I'm definitely going to do a deep dive on the subject, thank you!

[@welhtataum]

additional ideas from the book "Geometry of Music" by Tymoczko. Smooth modulations (e.g. C major to F major) are very essential across genres of music. Notes which are nearly (but not exactly) evenly spaced apart allow for such smooth modulations. For example, augmented triads are exactly evenly spaced, so what we want are in fact the next most evenly spaced triads: the major and minor triads. Indeed, transitions such as C -> Am -> F are very smooth and familiar to us. 7 is coprime with 12: the number of semitones in a octave. This is key. It means that the most evenly spaced 7-note scale (being the major scale) and allows for smooth modulations (e.g. C major to F major) in a 12-cycle (resembling the circle of 5th). In contrast, 8 is not coprime with 12 and there are only 3 octatonic scales with no short modulations among them. (Additionally, 5 is coprime, so the pentatonic share these nice properties with the major scale.) 7 and 5 are the only numbers smaller and coprime to 12, apart from 1 and 11 which are rather uninteresting here. That's what makes the major and pentatonic scale stand out from the rest. These things in conjunction are part of what makes the major scale special and ubiquitous.

[@JESL_TheOnlyOne]

It is not necessarily true the major scale is the most "evenly spaced", which needs to be clarified. I would say all the modes of the major scale are, except Lydian and Locrian - and that's just one example, there's something like 33 modes of several scalar systems - there's a video in YT about it. I would say you need to define your terms and possibly study up on scales and modes a bit more.

[@welhtataum]

@@JESL_TheOnlyOne Modes are not taken into considerations here, which reflect the focal points on a scale, and has little to do with the spacing between notes (e.g. a semitone). Here, I'm just talking about a selection of 7 notes in the 12-notes equal temperament octave. The terms are well defined in the book, which I won't repeat in a KZbin comment. I'm trying to give an impression of the ideas, not to give very detailed expositions. Don't tell me to study, tell the author, if anyone at all. You would believe that we have studied.

[@JESL_TheOnlyOne]

@@welhtataum First of all, I didn't tell you to do anything. Please re-read what I wrote. I said, "I would say," and "possibly". That's called a polite suggestion. Modes don't have anything to do with "focal points of a scale", whatever that's supposed to mean. This is what is meant by clarification and definition. If you're trying to give an "impression of the ideas", you have failed entirely. I, for one, have no idea what you were talking about in your first comment and in this one. "Hazy" would be describing your efforts charitably. What little I did glean of your statements suggests a certain lack of comprehensive understanding, otherwise, you wouldn't have fallen back on pointing to your author with no other support. Perhaps he is wonderful, but the reader can't know this if you don't convey it. Seeing as I have more than a decent understanding of musical theory, musical history, and decades of playing experience, methinks you should ruminate on these things. Ciao!

[@welhtataum]

@@JESL_TheOnlyOne @John Lee your politeness is superficial. You are claiming superiority in knowledge by your last paragraph and end it with "ciao". If what you wanted to say is that things need more detail, then I don't deny it. Like I said, I'm trying to give impressions only. And if you also wanted to say that the impressions fail on you, just say that as you did, and I'd be fine with it. It's fine to point out where things are wrong or lacking. Polite suggestions are not strictly necessary.

[@JESL_TheOnlyOne]

@@welhtataum I'll thank you not to be condescending and patronizing - it's insulting. If you don't care for my mode of discourse, you can take a long walk off a short pier.

[@Vandalfoe]

Great series, BTW!

[@TotalDec]

Another way of saying this, is our perception is the same as the overtone series (hearing by peaks, troughs, and nodes). Breaking down the overtone series close to the start, would naturally give you 12 notes. You exclude 5 to get 7 by consonance. What is the "av" in "P8av" for? I'm guessing, Greek or something like that. Oct. is Latin, right?

[@gordengibson1]

In the week, we find seven days, Each one with its own special ways. From Monday to Sunday, they go by, A cycle that never says goodbye. In the sky, a rainbow's grace, Seven colors in perfect space. Red, orange, yellow, green, and blue, Indigo and violet, all in view. Continents on Earth's grand stage, Seven lands, from age to age. North and South, and East and West, Seven continents, all the best. In the periodic table, rows unfold, Seven times, a story to be told. Elements arranged, a structured art, Seven rows, a fundamental part. Music's symphony, enchanting to the soul, Seven notes, in harmony they roll. Do, Re, Mi, Fa, Sol, La, and Ti, Seven sounds that reach the sky. The number seven, a magical embrace, In these realms, it finds a place. From days to colors, continents, and more, Seven's presence, we can't ignore.

[@EndlessTeaz]

Most underrated comment… don’t forget 7 chakras … and/or the 7 gifts of the Holy Spirit

[@tatyanaiysckaya7579]

Thank you! This is great!

[@nikitanugent7165]

Hi there, I have been appreciating your videos, but your final statement has left me baffled. In what way are 3:2 and 4:3 the same ratio? And if you can define how they are the same ratio, how is that different from the way the ratios of 729:512 and 1024:729 are related to each other? I really am genuinely baffled. I've spent the last hour trying to figure out a way in which this makes sense, as I am new enough to music theory that I could very well be overlooking something. Also, Miller's Law doesn't apply here, as that principle talks about the number of objects you can remember, not the number of possible objects; i.e. you can remember a seven digit phone number, but each digit can have one of ten possible values.

[@user-qn2og5lg7p]

Same, really can't understand what part of it is "incosistancy".

[@TotalDec]

3:2 = 4:3 in "distance," as in moving your finger along an unfretted string; Same ratio. Technically, if you're going by length, it's the same ratio. He could have gone a bit further, and you'd have understood. I understand, cos ratios are something I worked with and read about a lot. The second set, the tritones aren't the same ratio. The numbers are the same, the interval name the same, you hear them the same. Part of this, is understanding a small "digit value" makes a big difference over a broad use. In 12-TET, every tritone is the same ratio. A real piano has a slight variation of this, but generally we say there the same. The numbers he gave, in-fact, are the two different ratios of 1.424 and 1.405. Hope that clears it up. Ask me anything. Ppl that make these types of vids typically don't stay awake at night going mad trying to understand ratios. They make cheap vids with the first thought that comes to mind, and it often is very incomplete or an incorrect guess. This one isn't bad. I'm just being honest about YT. It's about $, not ppl pouring their soul into it. Why does the Maj. Scale have 7 notes? You could write a thick book as an answer, or just say that's what sounds good. The real answer, is that by exclusion you form an exact sound. The Maj. Scale excludes 5 dissonant intervals leaving the consonant intervals to make a pleasant and harmonious sound. Exclusion is art. This particular exclusion gives the Maj. Scale a balance not otherwise possible, which is what is most remarkable about it. This is why in general, it's taught first. Without that balance, it takes more thought and taste to achieve a sound. There is no perfection in any other note system. They all borrow and mimic the perfection of the Maj. Scale. Anything else is broken and imperfect. I only click on these types of vids for the comment section.

[@TotalDec]

​​@@user-qn2og5lg7p, consistency, would be 12-TET, where every interval (the "decimal value" ratio) is the *exact* same when compared to it's inversion, or when when any interval is transposed. Decimal value, here, means the 3 or more numbers past/behind the decimal. It's kinda, a musician slang. Ask me anything... Glad to help.

[@MabookaMabooka]

Let's talk a bit more about frequencies and harmonics. Let us start (say) with base frequency 110 (A). Then, the octaves are: 220, 440, 880, 1760, etc. The Nth harmonic is our base frequency multiplied by N: >>> base_frequency = 110 >>> " ".join("%04s"%i for i in range(1,17)) ' 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16' >>> " ".join("%04s"%(i*base_frequency) for i in range(1,17)) ' 110 220 330 440 550 660 770 880 990 1100 1210 1320 1430 1540 1650 1760' >>> Note that in the octave between 880 and 1760 there are 8 basic, "natural" harmonics (from pure math / physics perspective). 8 notes that would be sounding the most "harmonically" as they all are natural overtones of our base frequency of 110 (from pure math / physics perspective). 8 notes, not 7. I think the 8th one was somehow "lost in translation" during the centuries when imperfect mucitians tried to somehow tune their instruments. It could as well be (and probably sounding better) this: 880 990 1100 1210 1320 1430 1540 1650 1760' A B C D E F G X A (Put "H" or "Z" or "Q" instead of "X" if you prefer).

[@MabookaMabooka]

PS: Unfortunately the spaces I used for alignment were thrown away by KZbin or the browser, so here are the same two rows (frequencies and their corresponding indexes) vertically: 1 110 2 220 3 330 4 440 5 550 6 660 7 770 8 880 9 990 10 1100 11 1210 12 1320 13 1430 14 1540 15 1650 16 1760

[@RandomRelapse]

I feel Barry Harris shaking his to this lol

[@hangarud]

7 is complete note 5 notes are just annoying

[@gordengibson1]

Not annoying if you quickly squirt the 5 notes with chromatic sounds.