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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 showe

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.

mycroftiv 16y ago
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.
- fab13n 16y ago
  My guess is that it would lose and scare all of the many people for whom mathematics aren't a native language. Do it for mathematically minded people, I'd say with at least a A level in sciences, but avoid it for "normal" people. There might be a non-mathy way to show that something fishy happens with Pythagorean scales, similar to the post, with well chosen computer-generated sounds; but this would mainly interest people with a couple years of musical practice.
- kbutler 16y ago
  > To provide context for non-technical readers, I love the fact that I'm a "non-technical" reader in this discussion!
- alexophile 16y ago
  >whether it is a good idea to try to introduce students to the acoustic/mathematical derivation of the scale I did this when I was teaching my roommate about theory, but he has a degree in math, so it seemed like the logical approach. That said, teaching theory is incredibly good practice, so I like to do it whenever possible, and in my experience, the best time to explain the mathematical foundations of music is when they start to ask questions about it. It's like the matrix - if they're not ready for it, it's just too much.
- icarus_drowning 16y ago
  I think it would be worth doing with older students as a supplement to the curriculum. One of the bad things about my "major scale-centric" approach is that I never explain why a major scale is WWHWWWH, which is actually a barrier to some students, who are either curious or who need more context for their information. I teach mostly middle-school and high-school kids, and we barely have enough time to get through what I have, so I skip it. I wish I didn't have to.
  - nitrogen 16y ago
    Do you ever tell them something like, "There's a bunch of cool stuff you can learn about this, if you go to the web site, or look for _____ on Wikipedia?"
hasenj 16y ago
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 http://maqamworld.com) provides a decent index of many Middle Eastern scales, some of them utilizing quarter tones. For instance: http://www.maqamworld.com/maqamat/rast.html http://www.maqamworld.com/maqamat/rast.html http://www.maqamworld.com/maqamat/bayati.html http://www.maqamworld.com/maqamat/bayati.html http://www.maqamworld.com/maqamat/sikah.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.
- ThomPete 16y ago
  There are many ways do divide an octave. Steve Vai created a scale called the Xavian scale wich is dividing the octave by 10. He used in on Deep Down Into The Pain http://www.guitarflame.com/2008/xavian-scale-steve-vais-own-10-unknown-notes-scale/ http://www.guitarflame.com/2008/xavian-scale-steve-vais-own-...
  - hasenj 16y ago
    I'm thinking about a music application that lets you place tones in arbitrary locations on a continuous line (representing the tone space) and assign them keys on the keyboard.
    - ThomPete 16y ago
      Something close is http://www.morphwiz.com/ http://www.morphwiz.com/ and http://misadigital.com/index.php?target=home&lang=en http://misadigital.com/index.php?target=home&lang=en They are both interesting because they are using touchscreen meaning that they are fretless.
      - gtani 16y ago
        Cool. I've started fretless bass, and reading about accommodations you make for playing with e.g. vocalists who run flat more often than sharp, or upper register of piano that are sharp.
defroost 16y ago
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.
zck 16y ago
>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.
- eftpotrm 16y ago
  > 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. I know what you mean, but I think that's significantly a keyboard-based hazard. I play the trumpet (mostly; I can do a very little on a few others and trying to improve) and I've frequently ended up jamming away in odd keys, switching between them as required. F# major is a relatively common key for me, I just hear the intervals and the fingers move quite automatically, even though trumpet harmonics are arranged around C major (well, concert Bb). I'm sure it's much the same on other wind instruments.
  - hernan7 16y ago
    Sax also favors the C major scale []. Back in the early 20th century, sax salespeople would take advantage of this to sell the sax as an "easy to play" instrument. You can hang a saxophone from your neck and in 5 minutes you are playing the C major scale, Twinkle Twinkle Little Star, whatever. Compare with the trumpet or the violin, where just playing your first major scale in tune scale in tune takes weeks of practice. [] Actually, sax is a transposing instrument. But it does favor whatever scale you read as C major when you play it.
presidentender 16y ago
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.
- SwellJoe 16y ago
  "separating the second and third strings by a major third instead of a perfect fifth" The other strings on a guitar are separated by a fourth, not fifth (perfect or otherwise).
  - pessimizer 16y ago
    Depends on which way you're counting.
    - nollidge 16y ago
      No, it depends on the distance between the notes, which in the standard guitar tuning is a fourth (except between G3 and B4, as mentioned). You can take the lower note an octave up or the higher an octave down to make a fifth, but that changes the interval.
    - SwellJoe 16y ago
      While guitarists, by necessity, have a loose approach to finding the right notes for a chord, and will often use an inversion to get them all (or at least the harmonically important ones, like the third) on the fretboard in a reasonable way, that doesn't change the meaning of fourth and fifth. It's a bit pedantic, sure, and the notes have the same harmonic meaning (sort of, though inversions do feel different sometimes), but when you lay out the standard tuning of a guitar out on a piano and ask someone the distance, it is a fourth. You have to jump through some hoops to convince them to tell you that the relationship between the G to the D below it is a "perfect fifth". I'll also point out that the post I was responding to had already established which way he was counting by describing the relationship between the G and B strings (which, if we're counting the other direction would be a flat 6th; and, as a musician of twenty years I had to do mental somersaults to make my brain think of it that way). One way or another the description of standard guitar tuning was incorrect. See what you made me do? I had to go all pedantic and stuff, and I hate doing that.
jtheory 16y ago
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 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. :)

mycroftiv 16y ago

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.

fab13n 16y ago
My guess is that it would lose and scare all of the many people for whom mathematics aren't a native language. Do it for mathematically minded people, I'd say with at least a A level in sciences, but avoid it for "normal" people. There might be a non-mathy way to show that something fishy happens with Pythagorean scales, similar to the post, with well chosen computer-generated sounds; but this would mainly interest people with a couple years of musical practice.
kbutler 16y ago
> To provide context for non-technical readers, I love the fact that I'm a "non-technical" reader in this discussion!
alexophile 16y ago
>whether it is a good idea to try to introduce students to the acoustic/mathematical derivation of the scale I did this when I was teaching my roommate about theory, but he has a degree in math, so it seemed like the logical approach. That said, teaching theory is incredibly good practice, so I like to do it whenever possible, and in my experience, the best time to explain the mathematical foundations of music is when they start to ask questions about it. It's like the matrix - if they're not ready for it, it's just too much.
icarus_drowning 16y ago
I think it would be worth doing with older students as a supplement to the curriculum. One of the bad things about my "major scale-centric" approach is that I never explain why a major scale is WWHWWWH, which is actually a barrier to some students, who are either curious or who need more context for their information. I teach mostly middle-school and high-school kids, and we barely have enough time to get through what I have, so I skip it. I wish I didn't have to.
- nitrogen 16y ago
  Do you ever tell them something like, "There's a bunch of cool stuff you can learn about this, if you go to the web site, or look for _____ on Wikipedia?"

hasenj 16y ago

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 http://maqamworld.com) provides a decent index of many Middle Eastern scales, some of them utilizing quarter tones. For instance: http://www.maqamworld.com/maqamat/rast.html http://www.maqamworld.com/maqamat/rast.html http://www.maqamworld.com/maqamat/bayati.html http://www.maqamworld.com/maqamat/bayati.html http://www.maqamworld.com/maqamat/sikah.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.

ThomPete 16y ago
There are many ways do divide an octave. Steve Vai created a scale called the Xavian scale wich is dividing the octave by 10. He used in on Deep Down Into The Pain http://www.guitarflame.com/2008/xavian-scale-steve-vais-own-10-unknown-notes-scale/ http://www.guitarflame.com/2008/xavian-scale-steve-vais-own-...
- hasenj 16y ago
  I'm thinking about a music application that lets you place tones in arbitrary locations on a continuous line (representing the tone space) and assign them keys on the keyboard.
  - ThomPete 16y ago
    Something close is http://www.morphwiz.com/ http://www.morphwiz.com/ and http://misadigital.com/index.php?target=home&lang=en http://misadigital.com/index.php?target=home&lang=en They are both interesting because they are using touchscreen meaning that they are fretless.
    - gtani 16y ago
      Cool. I've started fretless bass, and reading about accommodations you make for playing with e.g. vocalists who run flat more often than sharp, or upper register of piano that are sharp.

defroost 16y ago

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.

zck 16y ago

>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.

eftpotrm 16y ago
> 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. I know what you mean, but I think that's significantly a keyboard-based hazard. I play the trumpet (mostly; I can do a very little on a few others and trying to improve) and I've frequently ended up jamming away in odd keys, switching between them as required. F# major is a relatively common key for me, I just hear the intervals and the fingers move quite automatically, even though trumpet harmonics are arranged around C major (well, concert Bb). I'm sure it's much the same on other wind instruments.
- hernan7 16y ago
  Sax also favors the C major scale []. Back in the early 20th century, sax salespeople would take advantage of this to sell the sax as an "easy to play" instrument. You can hang a saxophone from your neck and in 5 minutes you are playing the C major scale, Twinkle Twinkle Little Star, whatever. Compare with the trumpet or the violin, where just playing your first major scale in tune scale in tune takes weeks of practice. [] Actually, sax is a transposing instrument. But it does favor whatever scale you read as C major when you play it.

presidentender 16y ago

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.

SwellJoe 16y ago
"separating the second and third strings by a major third instead of a perfect fifth" The other strings on a guitar are separated by a fourth, not fifth (perfect or otherwise).
- pessimizer 16y ago
  Depends on which way you're counting.
  - nollidge 16y ago
    No, it depends on the distance between the notes, which in the standard guitar tuning is a fourth (except between G3 and B4, as mentioned). You can take the lower note an octave up or the higher an octave down to make a fifth, but that changes the interval.
  - SwellJoe 16y ago
    While guitarists, by necessity, have a loose approach to finding the right notes for a chord, and will often use an inversion to get them all (or at least the harmonically important ones, like the third) on the fretboard in a reasonable way, that doesn't change the meaning of fourth and fifth. It's a bit pedantic, sure, and the notes have the same harmonic meaning (sort of, though inversions do feel different sometimes), but when you lay out the standard tuning of a guitar out on a piano and ask someone the distance, it is a fourth. You have to jump through some hoops to convince them to tell you that the relationship between the G to the D below it is a "perfect fifth". I'll also point out that the post I was responding to had already established which way he was counting by describing the relationship between the G and B strings (which, if we're counting the other direction would be a flat 6th; and, as a musician of twenty years I had to do mental somersaults to make my brain think of it that way). One way or another the description of standard guitar tuning was incorrect. See what you made me do? I had to go all pedantic and stuff, and I hate doing that.

jtheory 16y ago

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 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. :)