I teach Music Theory (and piano) for a living-- this is an excellent introduction to the most practical concepts.
I was somewhat disappointed that the OP showed us a C Major scale without really explaining what a "major scale" is-- a collection of whole and half steps-- especially since they used a keyboard as an example, which is laid out in exactly the right pattern for teaching the major scale. (Notice that the black and white notes are arranged so that you skip some keys-- whole steps-- but sometimes you can't: half steps). I always teach how to build scales based on this pattern- WWHWWWH. Using this pattern, you can build any major scale beginning on any arbitrary note-- including notes that are sharped or flatted, which is neat. From here, you can figure out all of the scales, and thus all of the keys.
The advantage of learning in this fashion is that you can tackle intervals first, which are the distances between notes. (Note that major and minor intervals are named as such because they fit into our major or minor scales). Since a chord is simply collection of intervals, you end up with a more powerful understanding of them by learning which intervals (and which scale degrees) build which chords.
All the same, I really think the more "practical" approach here is really interesting, because you can start writing music earlier, albeit mostly in C Major.
Cool link, it really gives me insight as a fellow music educator.
Something to note: whole and half steps are not the only available type of steps, you can also move quarter steps. It's not common in Western music (if present at all) but very common in Middle Eastern music. Maqam world (http://maqamworld.com) provides a decent index of many Middle Eastern scales, some of them utilizing quarter tones.
I'm also a music theorist and educator. I'm interested in your perspective on whether it is a good idea to try to introduce students to the acoustic/mathematical derivation of the scale. To provide context for non-technical readers, the physical basis of harmonic intervals is integer ratios of frequencies, and European tempered tuning systems create scales and chords as a pragmatic adjustment of mathematically pure tuning to the necessity of using a finite number of predetermined pitches for instruments such as the piano.
I am still unsure as to whether the deeper understanding of scales, chords, keys, tuning, and temperament is something I should push to make students study and understand. Many students have a negative reaction to even the simplest math, but other students get a lot of benefit from understanding exactly how and why a given set of pitches fit together to form chords and scales. In the context of group instruction, deciding how much time to devote to this material is a dilemma for me.
I agree with you re: whole-steps and half-steps. When you teach "what makes a scale major?" in reference to the scales whole and half step pattern, it is then much easier to introduce minor, and scale modes (Ionian, Dorian, Phrygian).
Basic theory taught in this way is really not that hard (however, I majored in music in school).
If you introduce intervals, then you don't have to say "forget about B diminished. You won't miss it". You can say "B-dimished triad has a darker, more moody sound because it is made up of two-minor thirds. Or a Phrygian mode has an "eastern" sound because its scale starts with a half step.
That said, a lot of work went into the tutorial, and it is certainly well done.
The key-agnostic fretboard is a big part of the reason I enjoy playing guitar.
It's not a perfect tool for the application at hand because of the necessity of separating the second and third strings by a major third instead of a perfect fifth, which would confuse the issue.
However, I think it'd be more convenient to have a graphical representation of the major scale's construction on which a whole step is always clearly a whole step.
>I was somewhat disappointed that the OP showed us a C Major scale without really explaining what a "major scale" is-- a collection of whole and half steps...
I agree. I find it very frustrating that Western music breaks the twelve notes into two classes: the "naturals" (ABCDEFG), and "accidentals" (A# C# D# F# G#, and enharmonic equivalents). Playing guitar, I have come across people explaining barre chords -- a single fingering for a type of chord (e.g., major, minor) that you can shift up or down the fingerboard -- as "you can play any chord with this: E, F, G, A, etc.", and ignoring almost half of the possible chords. I'm convinced that the naming of notes to simplify playing in the key of C major or the relative A minor has inhibited players from gaining a real understanding of intervals.
To wit: when I play piano, I play in C. When I play guitar, I don't think about what key I'm in. I play in whatever fingering is easiest and what sounds best at the time.
It's a good intro, and music theory is one of those things that's quite hard to introduce well.
I'm a music educator, of a sort; this is a project of mine, build around interactive drills & concepts (click free resources if curious):
http://emusictheory.com
...but I've held off for a long time on writing a real online course, because, well, it's hard. The concepts don't always seem logical in isolation, the names of concepts sometimes overlap in weird ways (er, major 7th interval or major 7th chord?), and the general approach -- to lay down all the groundwork first, and only then get into anything remotely practical -- is deadly, deadly boring.
So I'm very much in favor of taking a practical approach, and trying to give the student something actual musical-sounding they can produce at the end of every mini-lesson... but if this were easy to do, I'd have it up on the site already. :)
A friend of mine here in Tokyo owns a small music company and recently launched a series of games to help with music training. They are flash-based, but I have been quite impressed with them and have enjoyed them quite a bit! He is using a freemium model, and you can try out the games on his website without even registering. (Free registration gives you progress tracking, and subscription gives you access to all levels and games.) For anyone interested in music training, I highly recommend them!
Really good stuff! Bug report: after I created an account, I was given a "Registration successful. You are now logged in." flash message in the middle of a "Cookies Required" page. It seems to have logged me in correctly, though. http://i.imgur.com/KMBPQ.png
I recently had a short-term stay at a place which had a piano. It seemed like a waste to let it just sit there, so I did a bit o' googling and found this site: http://www.pianobychords.com/
The information on music theory is similar to the post - but it also shows you how to play a few common songs. If you follow the fingering guide and play the same chords with both hands it sounds damn great! I thought only the guitar had that "pick it up, learn a couple of chords and you're good to go..." attitude!
One of the songs on the site was "Let It Be". I remembered that that song was in the Axis Of Awesome song "Four Chords" http://www.youtube.com/watch?v=qHBVnMf2t7w - now I know how to play hundreds of party-friendly songs on the piano. Damn satisfying for an outlay of just a few hours practice!
Fascinating read, but definitely not for beginners, at least for people like me, who have difficulty naming the notes (I have to go through "doe a deer..." each time, there are seven of them, right?)
My total music illiteracy really annoys me. However, whenever I try to pick up some knowledge I got held back by lots of questions that the usual music student (or teacher for that matter) has never thought about and no answer can be given. Here are a couple:
* Why are there seven notes? Is this due to an property of the ear?
* Ditto, for the octave concept, why should it be multiples of two?
* Why are there black keys between some white keys on the piano and not between others?
Is there a book that explains questions like these?
People sometimes guffaw at this, but I can't recommend Donald Duck in Mathemagic Land enough: http://www.youtube.com/watch?v=iEVGQKwKeCc They skip over several centuries of shifting and tweaking between the triad and the modern (western) major scale, but it's a great visual answer at least to your second question.
Why are there seven notes? Is this due to an property of the ear?
The 7 tones that make up a major scale are basically a cultural artifact of western music (which goes back to gregorian chant). Other cultures have more/fewer tones.
Ditto, for the octave concept, why should it be multiples of two?
Why are there black keys between some white keys on the piano and not between
others?
Well, IMHO this is a purely arbitrary cultural artifact resulting from the evolution of the keyboard (first in pipe organs). Since the octave is divided into 12 chromatic tones, you could in theory devise a keyboard with alternating white/black keys. However, the organ keyboard evolved in the middle ages, when chromaticism wasn't fully developed, hence, it appears the "white notes" of the keyboard appeared first, then later, the black notes added at the appropriate positions within the chromatic scale. See this, along with the accompanying picture, which clearly shows a small keyboard with the white keys only:
Modern western music is based on medieval church music, which in turn is based on ancient Greek music. These are two cultures that placed strong value on harmony and mathematical ratios, and it so happens that notes in ratios are harmonious to the ear. Mathematically speaking, the ratios between notes come mostly from low-order ratios in 5-limit tunings: https://secure.wikimedia.org/wikipedia/en/wiki/Limit_%28musi... .
In short, the Western scale is chosen to maximize the harmonic possibilities between different notes while having a reasonably even collection of whole-steps and half-steps between them. The black keys are the "in-between" half steps that do not appear in the C-major scale. The reason the ear likes harmony is probably due to our ears performing a Fourier transform on the incoming sound waves, and our brain blending together collections of multiples of some base frequency into one "note"--this lets us recognize the different characteristics of periodic oscillations from different physical sound sources.
That's basically the questions that music theory answers. As far as I understand things, it mostly relate to frequencies and harmonic resonance. The octaves are exact multiples of the same frequency (so a higher octave is 2x the frequency of the lower octave). The seven notes all fall out from that as well, but it is more complicated to explain and I don't know things well enough to break it down in a way that would be correct and make sense. But basically they resonate with each other.
As to why the human ear finds harmonic resonance pleasing is a more difficult question to answer. Why do we find order pleasing, and chaos frustrating? Speaking generally, the human brain functions as an advanced pattern seeking machine. What we do is take in chaotic and diverse information and make sense of it in some way, piecing individual facial features together into a specific face, and so on. Information that is ordered to begin with requires less work for the brain to process, so perhaps we find it pleasing because it is easy to sort and label mentally?
The intervals of black and white keys relate to the major scale. Basically, the major scale has the property of consisting of two whole steps, one half step, three whole steps and finally one half step. So the piano is constructed based on that scale.
Again, I can't explain it much better than that, but any book on the mathematics of music and signal processing / frequencies would have more information.
But yeah, the reason why you can't answer those questions is because you don't know music theory. That's where the answer to them is. It's not that they can't be answered.
Get a list of tone frequencies and do math with them. You will see patterns, called harmonics by musicians. Doubling the frequency (octave) can be thought of as the same tone playing twice, with an even offset. Our brains can pick up on that and notice that 440Hz is the same as 880Hz (only and "octave" higher)
Interesting fact: The tones of the scale aren't exactly evenly spaced, because of math. Some instruments use true tones and are made specifically for a certain key. Other instruments that can play in any key (like guitar) are never truly in tune.
One of the music theory things it took me a while to understand is why different major keys matter. In an idealized world, one can start a scale on any frequency and move up in whole and half steps (WWHWWWH) and have a scale. So why talk about the "key of G" vs the "key of C" if all that denotes is the frequency of the note we start on (which can be shifted up or down arbitrarily to suit the range of the instrument or vocalist)? The answer lies the physics of frequencies. The notes are not exactly the same from key to key because the whole and half steps are not exactly the same width. A perfect "fifth" (e.g., C & G played together) from a frequency perspective (meaning the two frequencies that resonate together creating a harmonic one octave above the lower) has a frequency ratio of 3/2 meaning the G is 1.5x the frequency of the C. The octave has a ratio of 2 (the high C is twice the frequency of the C below it). G is 7 half steps above C and the octave is 12 half steps. So if we walk our way up the piano in fifths, after 84 half steps, we would have a note (3/2)^12 = 129.75x the original frequency. But if we do the same on the octaves, we get 2^7 = 128x the original frequency, so the note we need to make all the major fifths sound right is different from the note we need to make the octaves sound right. The two are diverging slightly. So the result is that we can tune an instrument perfectly in one key only or we can tune it in a compromise of all the keys which sounds okay over a short range but sounds worse as we try to cover a wider range. If you're interested, there's lots of good reading on the subject (google "well-tempered" or "meantone").
EDIT: I realized I assumed a key concept in there. When two notes are played together, a third is heard (the "beat" frequency). If f1 and f2 are the frequencies of the notes being played, f2 - f1 = the beat freq. An octave sounds nice because the beat disappears (2f - f = f, so the beat is the same as the lower note of the octave). Other "pleasant" chord combinations are ones in which the beat does not clash with the first two note (e.g., is an octave of one of the notes).
Almost every instrument nowdays is tuned in equal temperament. Tuning matters most for old keyboard music, as in, pre-Beethoven.
The reason keys are important is because many instruments have different sound qualities for different notes. Keys close to E minor or G major allow guitarists to get that "twangy" open string sound. You can get a richer sound tuning up, or a thinner "heavy metal" sound tuning down. Keys close to B-flat allow brass players to use more basic tones on their instruments. All singers have certain sound qualities that are only available on certain notes. "Every Breath You Take", for example, would sound different even a semitone off, because Sting's transition from his creepy baritone to his high-pitched whine happens at a very specific part of his range, and the creepy quality of his voice contrasted with the high-pitched pleas for love is one of the most important qualities of the song.
But, yeah, temperament nowdays is almost irrelevant.
If you're really interested in this, I highly recommend checking out the book How Equal Temperament Ruined Harmony (and Why You Should Care) by Ross Duffin.
You'll find that listening to music in a single key for extended periods of time can become extremely tiring. Most (not all people) need fresh tonality, or they get bored. (Obviously all of this depends on what kind/style of music you are listening to, etc., but I would wager that even if you switched from "classical" music to "pop" music and stayed in the same key, most people would find it aurally tiring).
There's also Renoise (http://www.renoise.com/) which is inspired by old school mod trackers. There's a free demo, and the full version is really cheap.
Reaper: http://reaper.fm/ is excellent, very cheap ($40) and has an unlimited trial. Unlimited both in time and scope, you get the full software. I use it, works great.
I personally use FL Studio/Sibelius (FLS trial won't let you save your song in an editable format, but you can export in ogg/wav/midi/mp3). It depends on what you want to do, for music production Pro Tools/Logic Pro are a must (though it's more about the instrument library and external hardware quality).
Overall I'm not a fan, but I come from a background in more complex/full-featured DAW's like Logic and ProTools. I also find the UI lacking. That said, it's a great way to get off the ground when starting out with digital audio.
I hope the author turns this into a series, introducing additional theory. When I was first learning basic music theory, it was either all text or text along with notation. I took lesson on snare drum when I was younger, so I can read rhythms fine but never bothered to learn to read the pitches correctly. When I started playing guitar and piano, having something with embedded content and "piano roll" images would have helped immensely.
on a similar note (and because there's some great links being posted here), this video by walter lewin covers the physics of sound and how it relates to music, it could be good secondary material for someone learning about music theory:
I really love the idea behind this article, but I didn't like the execution. I was confused and intimidated after the "scales" section (and that's the first part).
Also, I don't know what the difference between a key, note and a few other words mean.
Trying to be constructive, I hope the article gets edited because I'm genuinely interested in learning these things.
It's only somewhat related, but This Week's Finds in Mathematical Physics #234 discusses some of the math behind music theory. It's a nice article if you're familiar with basic group theory.
http://math.ucr.edu/home/baez/week234.html
This is so white! lol I can relate because it's how I first approached music, but most mature musicians in the Western world begin with rhythm, yet there is no mention of rhythm in this article.
[+] [-] icarus_drowning|15 years ago|reply
I was somewhat disappointed that the OP showed us a C Major scale without really explaining what a "major scale" is-- a collection of whole and half steps-- especially since they used a keyboard as an example, which is laid out in exactly the right pattern for teaching the major scale. (Notice that the black and white notes are arranged so that you skip some keys-- whole steps-- but sometimes you can't: half steps). I always teach how to build scales based on this pattern- WWHWWWH. Using this pattern, you can build any major scale beginning on any arbitrary note-- including notes that are sharped or flatted, which is neat. From here, you can figure out all of the scales, and thus all of the keys.
The advantage of learning in this fashion is that you can tackle intervals first, which are the distances between notes. (Note that major and minor intervals are named as such because they fit into our major or minor scales). Since a chord is simply collection of intervals, you end up with a more powerful understanding of them by learning which intervals (and which scale degrees) build which chords.
All the same, I really think the more "practical" approach here is really interesting, because you can start writing music earlier, albeit mostly in C Major.
Cool link, it really gives me insight as a fellow music educator.
[+] [-] hasenj|15 years ago|reply
For instance:
http://www.maqamworld.com/maqamat/rast.html
http://www.maqamworld.com/maqamat/bayati.html
http://www.maqamworld.com/maqamat/sikah.html
For those interested, each scale is accompanies by several audio samples to hear what it sounds like.
[+] [-] mycroftiv|15 years ago|reply
I am still unsure as to whether the deeper understanding of scales, chords, keys, tuning, and temperament is something I should push to make students study and understand. Many students have a negative reaction to even the simplest math, but other students get a lot of benefit from understanding exactly how and why a given set of pitches fit together to form chords and scales. In the context of group instruction, deciding how much time to devote to this material is a dilemma for me.
[+] [-] defroost|15 years ago|reply
That said, a lot of work went into the tutorial, and it is certainly well done.
[+] [-] presidentender|15 years ago|reply
It's not a perfect tool for the application at hand because of the necessity of separating the second and third strings by a major third instead of a perfect fifth, which would confuse the issue.
However, I think it'd be more convenient to have a graphical representation of the major scale's construction on which a whole step is always clearly a whole step.
[+] [-] zck|15 years ago|reply
I agree. I find it very frustrating that Western music breaks the twelve notes into two classes: the "naturals" (ABCDEFG), and "accidentals" (A# C# D# F# G#, and enharmonic equivalents). Playing guitar, I have come across people explaining barre chords -- a single fingering for a type of chord (e.g., major, minor) that you can shift up or down the fingerboard -- as "you can play any chord with this: E, F, G, A, etc.", and ignoring almost half of the possible chords. I'm convinced that the naming of notes to simplify playing in the key of C major or the relative A minor has inhibited players from gaining a real understanding of intervals.
To wit: when I play piano, I play in C. When I play guitar, I don't think about what key I'm in. I play in whatever fingering is easiest and what sounds best at the time.
[+] [-] jtheory|15 years ago|reply
I'm a music educator, of a sort; this is a project of mine, build around interactive drills & concepts (click free resources if curious): http://emusictheory.com
...but I've held off for a long time on writing a real online course, because, well, it's hard. The concepts don't always seem logical in isolation, the names of concepts sometimes overlap in weird ways (er, major 7th interval or major 7th chord?), and the general approach -- to lay down all the groundwork first, and only then get into anything remotely practical -- is deadly, deadly boring.
So I'm very much in favor of taking a practical approach, and trying to give the student something actual musical-sounding they can produce at the end of every mini-lesson... but if this were easy to do, I'd have it up on the site already. :)
[+] [-] 1331|15 years ago|reply
http://trainer.thetamusic.com/
[+] [-] ThomPete|15 years ago|reply
1. Send him this presentation: http://fury.com/2010/02/jesse-shells-mindblowing-talk-on-the...
2. Tell him to do it for the iphone and ipad where people can also practice on the ipad.
3. Set up achievement levels
Khan Academy for music education.
[+] [-] shawndrost|15 years ago|reply
[+] [-] mrspeaker|15 years ago|reply
The information on music theory is similar to the post - but it also shows you how to play a few common songs. If you follow the fingering guide and play the same chords with both hands it sounds damn great! I thought only the guitar had that "pick it up, learn a couple of chords and you're good to go..." attitude!
One of the songs on the site was "Let It Be". I remembered that that song was in the Axis Of Awesome song "Four Chords" http://www.youtube.com/watch?v=qHBVnMf2t7w - now I know how to play hundreds of party-friendly songs on the piano. Damn satisfying for an outlay of just a few hours practice!
[+] [-] kranner|15 years ago|reply
Ralph Towner calls the guitar a "portable piano".
[+] [-] Jun8|15 years ago|reply
My total music illiteracy really annoys me. However, whenever I try to pick up some knowledge I got held back by lots of questions that the usual music student (or teacher for that matter) has never thought about and no answer can be given. Here are a couple:
* Why are there seven notes? Is this due to an property of the ear?
* Ditto, for the octave concept, why should it be multiples of two?
* Why are there black keys between some white keys on the piano and not between others?
Is there a book that explains questions like these?
[+] [-] alexophile|15 years ago|reply
[+] [-] msluyter|15 years ago|reply
http://en.wikipedia.org/wiki/Pipe_organ#Keyboards
[+] [-] cynicalkane|15 years ago|reply
In short, the Western scale is chosen to maximize the harmonic possibilities between different notes while having a reasonably even collection of whole-steps and half-steps between them. The black keys are the "in-between" half steps that do not appear in the C-major scale. The reason the ear likes harmony is probably due to our ears performing a Fourier transform on the incoming sound waves, and our brain blending together collections of multiples of some base frequency into one "note"--this lets us recognize the different characteristics of periodic oscillations from different physical sound sources.
[+] [-] kreek|15 years ago|reply
There's also a great TV series from England called 'How Music Works' which gives more of a historical background. http://www.youtube.com/watch?v=PnbOWi6f_IM
[+] [-] krig|15 years ago|reply
As to why the human ear finds harmonic resonance pleasing is a more difficult question to answer. Why do we find order pleasing, and chaos frustrating? Speaking generally, the human brain functions as an advanced pattern seeking machine. What we do is take in chaotic and diverse information and make sense of it in some way, piecing individual facial features together into a specific face, and so on. Information that is ordered to begin with requires less work for the brain to process, so perhaps we find it pleasing because it is easy to sort and label mentally?
The intervals of black and white keys relate to the major scale. Basically, the major scale has the property of consisting of two whole steps, one half step, three whole steps and finally one half step. So the piano is constructed based on that scale.
Again, I can't explain it much better than that, but any book on the mathematics of music and signal processing / frequencies would have more information.
But yeah, the reason why you can't answer those questions is because you don't know music theory. That's where the answer to them is. It's not that they can't be answered.
[+] [-] doki_pen|15 years ago|reply
Interesting fact: The tones of the scale aren't exactly evenly spaced, because of math. Some instruments use true tones and are made specifically for a certain key. Other instruments that can play in any key (like guitar) are never truly in tune.
[+] [-] unknown|15 years ago|reply
[deleted]
[+] [-] pge|15 years ago|reply
EDIT: I realized I assumed a key concept in there. When two notes are played together, a third is heard (the "beat" frequency). If f1 and f2 are the frequencies of the notes being played, f2 - f1 = the beat freq. An octave sounds nice because the beat disappears (2f - f = f, so the beat is the same as the lower note of the octave). Other "pleasant" chord combinations are ones in which the beat does not clash with the first two note (e.g., is an octave of one of the notes).
[+] [-] cynicalkane|15 years ago|reply
The reason keys are important is because many instruments have different sound qualities for different notes. Keys close to E minor or G major allow guitarists to get that "twangy" open string sound. You can get a richer sound tuning up, or a thinner "heavy metal" sound tuning down. Keys close to B-flat allow brass players to use more basic tones on their instruments. All singers have certain sound qualities that are only available on certain notes. "Every Breath You Take", for example, would sound different even a semitone off, because Sting's transition from his creepy baritone to his high-pitched whine happens at a very specific part of his range, and the creepy quality of his voice contrasted with the high-pitched pleas for love is one of the most important qualities of the song.
But, yeah, temperament nowdays is almost irrelevant.
[+] [-] caryme|15 years ago|reply
[+] [-] icarus_drowning|15 years ago|reply
[+] [-] jonp|15 years ago|reply
[+] [-] psawaya|15 years ago|reply
There's also Renoise (http://www.renoise.com/) which is inspired by old school mod trackers. There's a free demo, and the full version is really cheap.
[+] [-] krig|15 years ago|reply
[+] [-] eagleal|15 years ago|reply
Consider looking at the See also section for a list of DAWs: http://en.wikipedia.org/wiki/Digital_Audio_Workstation#See_a...
[+] [-] RyanMcGreal|15 years ago|reply
[+] [-] daydream|15 years ago|reply
http://audacity.sourceforge.net/
Free/open source, for Windows, OS X, and Linux.
Overall I'm not a fan, but I come from a background in more complex/full-featured DAW's like Logic and ProTools. I also find the UI lacking. That said, it's a great way to get off the ground when starting out with digital audio.
[+] [-] frou_dh|15 years ago|reply
[+] [-] nitrogen|15 years ago|reply
Sony ACID (I use ACID Pro extensively, free trial, free lite version)
Ableton Live
FL Studio
energyXT (Linux and Mac versions available)
Other stuff to check out: console.jp, Audiomulch
[+] [-] MrJagil|15 years ago|reply
[+] [-] unknown|15 years ago|reply
[deleted]
[+] [-] Qerub|15 years ago|reply
http://cs.lth.se/english/course/edan40_functional_programmin...
[+] [-] ssharp|15 years ago|reply
[+] [-] whoeverest|15 years ago|reply
[+] [-] sethg|15 years ago|reply
[+] [-] thesystemis|15 years ago|reply
http://mitworld.mit.edu/video/168
what's great is that it's a serious physics lecture, but designed for kids, and there's plenty of funky experiments within the one hour.
[+] [-] psykotic|15 years ago|reply
http://www.maths.abdn.ac.uk/~bensondj/html/maths-music.html
[+] [-] tieTYT|15 years ago|reply
Also, I don't know what the difference between a key, note and a few other words mean.
Trying to be constructive, I hope the article gets edited because I'm genuinely interested in learning these things.
[+] [-] drbaskin|15 years ago|reply
[+] [-] pinchyfingers|15 years ago|reply
Rhythm is our soul, get some soul, crackers!
[+] [-] baddox|15 years ago|reply
[+] [-] TheSOB88|15 years ago|reply