How many notes are there in an octave?
Many music theory teachers would start by saying that there are 12 chromatic notes in the octave, this would be a modification of the truth.
This early stand point has led many aspiring musicians to give up understanding music theory.
What really is the answer was discover in ancient Greece, thousands of years ago, this is what they realized:
If you took a string, tightened it hard enough and plucked it, you would get a note. The pitch of this note is irrelevant since all notes behave in the same way.
When this was discovered (thousands of years ago) there was no pitch reference, all was done on the relationship between notes, what we today call intervals.
Once the string had made a noise the experimentation begun!
From one note to intervals
Half the length of that string and you would get the octave, which is the same note, but an octave higher.
Using /2, /3, /4, /5 and /8 to shorten the string you’d find more intervals:
- Fifth: 2/3 of original length.
- Fourth: 3/4 of original length.
- Major Third: 4/5 of original length.
- Minor Third: 5/6 of original length.
- Major Sixth: 3/5 of original length.
- Minor Sixth: 5/8 of original length.
By altering the length of the string in various degrees of /2 /3 /4 /5 /8 you get musical notes. Not a 12 note chromatic scale.
Instead, the 12 note chromatic scale is a product of what happens when we build a 7 note scale and then transpose it to all possible root notes via the cycle of 5ths and 4ths.
So the answer to the “chicken and egg” like question:
What came first, the 12 note chromatic scale or the 7 note scale?
The answer is that a 7 note scale is a product of nature (well, almost!), the chromatic scale a product of the 7 note scale in different keys.
In the next music theory lesson you’ll find out how every note has overtones consisting of a major triad!
This will then pave the pave for what was to become the major scale.
Music Theory in The whole Enchilada!
These days my latest eBook Music Theory is now only available in the package The Whole Enchilada which is only £74.95 (a combined value of £105.69).
In this package few stones are left unturned as you get 8 eBooks, 29 videos and 254 Jam Tracks!
-Dan (your guitar guru)
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I guess i see 7 but I hear 8 in the solfege.
So 7 different notes.
I did not even think I made a point, did mention the name of stacking thirds from the scale to make all the chords and it makes the 7th degree chord or bump in the road chord as well.
The question ask how many notes in a Octave??????????
I thought even the word octave in English meant 8.
Absolutely, octagon, it all says 8.
But if you harmonise a major scale you wouldn’t say you get 8 chords, you’d get 7.
I guess this is why it’s an important question to ask, how many notes are there?
Music theory is full of so many contradictions like this that it’s important to get to the bottom of them all.
Your question is very valid!
I hope this lesson series will put us all on the same page!
I’m well excited about how this will all be received
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Just a few minor points. If someone is starting with theory from scratch, they may not know what a Major 3rd is, or the other intervals mentioned.
Some people might also like know that because this string theory stuff hadn’t be formalized, music was more about melody and monophonic than homophonic and using chordal harmony.
I think it was our friend Pythagoras who found that the simple ratios gave us these fundamental notes.
As is music on the guitar today, music was at that time by necessity an aural tradition as music notation couldn’t really be achieved..
For interested ones and history buffs, the earliest surviving Grecian example of notated music was the Epitaph of Seikilos. It shows how music was often one vocalist who accompanied them self on one string in unison or near unison.
http://en.wikipedia.org/wiki/Seikilos_epitaph
Maybe put that in later, like in an more advanced theory section.
The stuff about The Well Tempered Clavier is definately interesting, but yes could be a distraction for budding theorist.
Personally, I found that history put a lot of things into context. If you get the history, u can get the principles and this is more important than ‘rules’.
So go for it I say!
Wow… I am the guy you speak of that knows little to no theory… I’m thinking my avatar is pretty accurate. It’s all very interesting, I’ll try to keep up!
Cheers Jim, I hope I can clear the mist with this series of music theory lessons.
If there is anything you don’t get, or need clarified, don’t be afraid to ask!
i am a little confused with the math on shortening strings.
“Shorten it by 4/3 and you would get a fourth”
How do you shorten something by a greater amount than it’s original length? 4/3 is 1/3 longer than 3/3=1
Lol! Now that’s what I call a good point!
Have a look at these links, my head hurts after a while…
http://en.wikipedia.org/wiki/Pythagorean_interval
http://www.silkqin.com/08anal/tunings.htm#f8
http://frank.mtsu.edu/~wroberts/scales.htm
I guess my explanation is a bit too simplified, suggestions welcome!
It’s pretty clear why it took so long for everyone to agree…
As another example, it took until 1939 for everyone to agree that an A is 440…
http://www.piano-tuners.org/history/pitch.html
My understanding is that those ratios relate to frequencies of the notes, rather than the length of the string per se.
For example, if we say “open” is 0 and it’s “octave” is 12 (i.e. as in a guitar), then according to what was written above, then to get a fifth you should shorten the string by 2/3, by fretting at 8, however, we know this is not a 5th. In fact, a 5th would be on fret 7…
In fact, looking at some of the sources you linked Guru, a fifth (up) actually has frequency 3/2 times that of the root note. Using the example of “A” having a frequency of 440hz, a fifth up would be 660 (440/2 = 220, 220 x 3 = 660), we hear this frequency as an “E”.
It’s been a long while since I studied anything to do with waves, but I believe I will be doing some stuff on them this semester, so hopefully I will be able to confirm that I’m correct and update you on the whole story
Note: I’ve found something on the internet that say due to the nature of guitar strings, the lengths vary slightly from what their mathematical value says they should be… I’ll look more into this – perhaps this is a reason why stuff is so convoluted…
Source:
http://hyperphysics.phy-astr.gsu.edu/hbase/waves/string.html#c2
Obviously, the size of frets changes progressively the further down the nexk you go, again convoluting the matter.
Source:
http://entertainment.howstuffworks.com/guitar4.htm
Yes, but then again, it’s not in perfect tune, this image shows a guitar attempting to get closer to being in “perfect tune” http://www.ricktoone.com/feather/
Right! I think I’ve sorted it, but some of the fractions are upside down Guru…
Fifth: 2/3 of original length.
Fourth: 3/4 of original length.
Major Third: 4/5 of original length.
Minor Third: 5/6 of original length.
Major Sixth: 3/5 of original length.
Minor Sixth: 5/8 of original length. (The last bullet also has a typo! third -> sixth)
The problem is that this is hard to translate to guitar because fret sizes change, which I believe is to account for the properties of strings. So, you can’t do what I did before and say that 2/3 of string length (between 0 and 12) is fret 8, because it isn’t!
AND, just to confuse people, the frequencies depend on the reciprocal fraction (i.e. you flip the fraction). To demonstrate:
Fifth: 3/2 of original frequency.
Fourth: 4/3 of original frequency.
Major Third: 5/4 of original frequency.
Minor Third: 6/5 of original frequency.
Major Sixth: 5/3 of original frequency.
Minor Sixth: 8/5 of original frequency.
I believe this is where the confusion in your fractions, and my original post, come from Guru
Nice one!
I knew someone brainy would sort this
I’ll amend accordingly!
Oh and yes, it’s not in perfect tune, the lengths given on that website are actually just approximate to my exact calculations
You are a legend Jonny!
Oh and to be clearer, if you go on the wikipedia & silkqin links you posted before Gu, I’ve worked out that the frequences (and therefore lengths) I’ve listed based on what you had written are actually approximate, for example;
Minor Third: 6/5 (actual numerical value is 1.2)
The true value for the minor third is apparently 32/27 (actual numerical value is 1.185).
So comparing, the approximation is 1.2, the true value is 1.185… Not much in it!
You can see on silkqin (point 7) that the “Just Intonation” are actually just approximations of the Pythagorean – which is basically what I showed above.
Do you want a full list of lengths/frequencies of all “12″ notes or is the explanation enough?
Thanks Guru, but in all honesty I did this as much for myself as anyone else… I’m the curious type, don’t like it when things don’t match up properly!
I think I’ll check these when I’m less sleepy, just in case I’ve made a cock up!
The thing is, it seems simple at first, for example, 440 is A, 880 is the octave so it would be easy to think that to divide the difference in 12 would give you a number which every time added would give you the next note, but this is not the case at all.
It’s like steveo said somewhere: c e g, f a c, g b d, the three major chords put together spells the major scale, it would be great if it was that simple!
The only thing everyone seem to agree with is that moving up in 5ths give you all notes.
@Paul
The list has been revised, there’s a lot of confusion around this topic it seems, you can read more further down the blog comments.
I’ve updated the eBook now as well
@jonnys777 I think this deep info is perfect to further discuss in the group:
http://spytunes.com/groups/music-theory/
Ok, I’ll look into it tommorrow!
Btw, what does the ebook cover? I can’t afford to buy it right now so I haven’t
Well as you know, I’m really into my updates.
At the moment the eBook has 20 chapters, the first 4 you have seen here in the blog
I have a feeling it will become bigger, following on from what is in chapter 20, so basically more sight reading.
Check preview for complete index: http://spytunes.com/news/music-theory-preview
The final test is an eyeopener, I’ve tried it on a couple of guitarists, it’s a proper wake up call. If you follow it you will actually learn how to read music, this is the goal of this book.
If I can teach guitar players how to read I will be a very, very happy guru
I think I shed a bit more light on this…
Pythagoras first found that the simple ratios gave you the perfect intervals.
He started off with he ratio for the 4th, 5th and octave.
One day he heard a blacksmith’s hammer and there were two distinct sounds. He initially thought that these two sound were related to the force used, but later realized it was weight/length.
So he rigged up some strings on a board and started experimenting, and found the 4th, 5th and octave ratios.
Using only these ‘two’ rules, he was able to find the other notes of the scale.
Going around the circle of fifths, you eventually get all the notes until you are back where you started, except, you are not in the same octave. So he used the octave rule to bring each note back into the range of an octave.
The only thing was, because we are dealing with inexact ratio, you had some intervals that weren’t pleasing to the ear.
As usual, just my two cents worth.