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Music Theory for Beginners

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Re: Music Theory for Beginners

#31

Post by kbutler »

mycroftiv wrote: post #4
icarus_drowning wrote: post #3

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 bl…

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 t…

> To provide context for non-technical readers,

I love the fact that I'm a "non-technical" reader in this discussion!

Re: Music Theory for Beginners

#32

Post by Jun8 »

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?

Re: Music Theory for Beginners

#33

Post by zck »

icarus_drowning wrote: post #3

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 bl…

>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.

Re: Music Theory for Beginners

#34

Post by [deleted] »

Jun8 wrote: post #32

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…

[deleted]

Re: Music Theory for Beginners

#35

Post by eftpotrm »

zck wrote: post #33
icarus_drowning wrote: post #3

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 bl…

>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 sin…

> 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.

Re: Music Theory for Beginners

#36

Post by msluyter »

Jun8 wrote: post #32

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…

  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?
Can you clarify this question? Octaves result from the natural harmonic series: http://en.wikipedia.org/wiki/Harmonic_series_(music)

  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:

http://en.wikipedia.org/wiki/Pipe_organ#Keyboards

Re: Music Theory for Beginners

#37

Post by krig »

Jun8 wrote: post #32

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…

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.

Re: Music Theory for Beginners

#38

Post by pge »

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).

Re: Music Theory for Beginners

#39

Post by Jun8 »

msluyter wrote: post #36
Jun8 wrote: post #32

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…

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? Can you clarify this question? Octaves result from the natural harmonic series: http://en.wikipedia.org/wiki/Harmonic_seri…

I think an octave up (down) means double (half) the frequency of the tone. The usual explanation, I think, is that the Pythagoreans who invented it found this to be the "most pleasing" ratio.

I wonder if there are user studies to back this claim.

I am also at such a low level, that part of your explanation just goes over my head, i.e. what is chromatic scale? Wikipedia says: "The chromatic scale is a musical scale with twelve equally spaced pitches, each a semitone apart. A chromatic scale is a nondiatonic scale having no tonic due to the symmetry of its equally spaced tones." Now very helpful. I thought there were 7 notes! And I don't know any other terms in that sentence (checking their Wikipedia entries doesn't help either, leads to a loop)

Re: Music Theory for Beginners

#40

Post by doki_pen »

Jun8 wrote: post #32

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…

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.

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