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Will
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PostPosted: Thu Jul 10, 2014 4:15 pm    Post subject: The Musician's Toolbox Reply with quote

A while ago in the music education thread, this came up:

"Looking forward to the day I can just think of music and there it is, fully realized." -- sonrisu

That's totally possible to do, it just requires a few skills and a lot of practice. These skills basically divide up into three areas: music theory, ear training, and sight singing. Ear training and sight singing are linked, but we won't be doing much sight singing here.

Common Practice Music Theory is about the analysis (which leads into the construction) of music from 1775 to 1885. We can break that down into vocabulary (the basics), tonality, and voice leading.

Vocabulary is probably the most boring part, so I'll go quickly here:

  • Pitch: How high or low a sound is. We use the first 7 letters of the roman alphabet and some symbols to distinguish these (C D E F G A B) C is usually the "home" pitch for everything. They can be raised and lowered, by being sharpened with "#" or flattened with something that looks like "b". We usually map A4 to 440hz, but technically you could map any note to any pitch, and derive the rest of the pitches from that.
  • Octave: the 8th note, going up the line. It's the same as the note you started on, just higher (literally vibrating at twice the frequency).
  • Steps: a half step (or semitone) is (usually) the smallest step between two pitches. A whole step is two half steps.
  • Intervals: The distance between two pitches. These'll be explained in the next section.
  • Scales: all 7 pitches, by name, going up and down. We'll usually be working with the major scale or a variant of the minor scale. For now, major is "happy" and minor is "sad". The note a scale starts on is called the tonic.
  • Time: We're still working on what this is, but we divide it into measures, beats, and divisions of beats for the sake of music
  • Notes: musical constructs. We use a lot of them. At their most basic, they have pitch, duration, and nebulous "style" qualities.
  • Rests: notes without sound; periods of silence in time.
  • Rhythm: a series of notes and rests analyzed without pitch; the rhythm of a passage is just the durations taken without the sounds. Can also be used to mean a specific pitch.
  • Other stuff I forgot about: probably not important.


Tonality is longer and harder, and means I have to get into more specifics than the quick definitions above.


Chromatic notes
First things first, there's more than 7 pitches. The distance between most notes is a whole step, which means we're missing out if we don't get the half step between them. To access that, we can sharpen, or raise, a note, or flatten, or lower, a note. Sharps look like "#", and flats kinda look like a lower-case "b". C#, Bb. This gives us twelve unique pitches: B#/C, C#/Db, D, D#/Eb, E/Fb, E#/F, F#/Gb, G, G#/Ab, A, A#/Bb, B/Cb. The notes separated by a slash are called "enharmonically equivalent": they sound the same, but, as in language, spelling in music matters. Also notice that some notes are a different distance apart. B and C are only a half step apart, as are E and F, but all the others are a whole step.


Scales
Going more in-depth on scales here: the C major scale looks like C D E F G A B C, but look at the steps between each note: notice it goes w, w, h, w, w, w, h. We can derive all the other major scales from this pattern, so E major would go:
E F# G# A B C# D# E. Scales have to use all the names in order, so we have to raise in some cases, and lower in others. C major has no sharps or flats in it. In a vacuum, all scales will sound the same, we only differentiate between them for a few reasons.


  • Range. People and instruments can only go up so high, and so low. If you want notes in a certain register, it's usually easier to pitch the whole piece higher than try to flip octaves
  • Sometimes we change keys for musical effect, so it's important to have keys at exact intervals higher and lower than others.


Sharps and Flats
We use these concepts in multiple ways. Here's a picture that I made to explain it:


Circle of Fifths
We usually organize the scales in something called the Circle of Fifths. A fifth (P5) is the interval between C and the G above it. Going clockwise, the Circle of Fifths goes C, G, D, A, E, B/Cb, F#/Gb, Db, Ab, Eb, Bb, F, C. Every time we move clockwise on the Circle of Fifths, we add a sharp (or remove a flat), and every time we move anticlockwise, we add a flat (or remove a sharp). The order we add sharps in is: F# C# G# D# A# E# B#, and the order we add flats in is: Bb Eb Ab Db Gb Cb Fb. Notice these also follow the Circle of Fifths--it's hiding everywhere in tonal music.

Here's a picture:


At this point, you should be able to write out all the major scales. I won't get into reading/writing sheet music here, but you should be able to do that too. If you have a piano around, figuring out where the scales go on that would be useful too.

Intervals
Intervals represent the distance between two notes. They have a span and a quality. The span is the number of note names between the two notes, including those two. The quality is changed if you lower or raise one of the notes. The qualities are Major, minor, Perfect, diminished (*), augmented (+), marked with the first letter or the character in brackets. You can stack diminished or augmented modifiers, but you won't see that very often.

If you take the tonic of a major scale and look at the notes going up, they form these intervals: P1, M2, M3, P4, P5, M6, M7, P8. If you take the top of the scale and look at the notes going down, they form these intervals: P1, m2, m3, P4, P5, m6, m7, P8. Notice why unisons, fourths, fifths, and octaves get the perfect quality by default: when we invert the scale, they don't change quality. Intervals with perfect quality can't be Major or minor, only perfect, augmented, or diminished.

Here's how we derive the ascending intervals:


And the descending intervals:


There's one more interval, though. The diminished fifth (or augmented fourth), sometimes called the tritone, sounds sinister. You can find it between the 7th of the scale and the 4th of the scale.

And one more thing: you can measure all of these intervals with semitones, but that takes a long time. If you do enough work with this stuff, you just memorize them. However, there are times when, especially when you're working with computer music, you'll need to know the number of semitones in an interval, so I'll leave that as an exercise for you.

At this point, you should be able to write out all the intervals in a major scale, and be able to identify the interval between any two notes when given the bottom note.

Instead of moving into chords and finishing tonality, we're going to jump to sight singing and ear training. I'm not great at this stuff in practice, but this is where you start to pick up the skills to be able to write down what you hear, either in your head or off the radio.


Ear Training and Sight Singing
The goal of ear training is to identify what you hear. If I play you an interval, can you tell me what it is? The way to practice that is by 1) listening to all the intervals over and over and 2) singing them yourself. This is why we cover both at the same time. Why does singing help? Because if you can feel it in your vocal chords, then you have it.

Solfege
The tool we use to develop that is called solfege. There's several different ways to approach it, but where I live, movable-do solfege is standard. (I throw that in because if you live in Europe or Asia, you might well use fixed-do if you went to a music school, but that serves a slightly different purpose). What is solfege? It's basically just names for the degrees of the scale. If you start on C, the C major scale in solfege is "do re mi fa so la ti do." Same thing for E major, Bb major, anything. Names for scale degrees. There are also words for modified pitches. All twelve unique pitches would go: "do di/ra re ri/me mi fa fi/se so si/le la li/te ti do". Slashes indicate enharmonically equivalent pitches.

Singing tips: you will sound better and be in tune if you use enough air. Don't neglect the airflow!

At this point, you have all the knowledge you need to accomplish the initial goal: writing down what you hear. Practice identifying intervals, write down all the intervals, follow the intervals to the end of your idea. All you have to do is practice, which sounds easy, but is generally difficult. That's just how it is with music.

Practice Track
To start: sing along with this using solfege: https://www.dropbox.com/s/mflwpvsip9pwlf2/solfege101.wav (careful, might be loud)
The pattern is "do re mi fa so la ti ^do ti la so fa mi re do. do re do mi do fa do so do la do ti do ^do. ^do ti ^do la ^do so ^do fa ^do mi ^do re ^do do." where "^do" is the octave above the note you start on. That covers your major scale and all the intervals except the tritone, which is basically everything we've covered here. I made the practice track in famitracker. It's a pretty good tool for this sort of thing, but nothing beats a piano. You could also use a tone generator to make new exercises for yourself. Tuning apps like Tunable (android) and TonalEnergy Tuner (iOS) will have tone generators on them and also act as a way to check your abilities. There are programs like GNU Solfege and MacGamut (I don't recommend either; they're terrible), that'll provide you random intervals, scales etc to practice with; they're all just a pain to use though.

I'll end part one here. The rest of this will be music theory with the sight singing/ear training tips that you need to go with it, but you have all the basics here! There will be a part two, just not today :)

Edit 7/29/14: Added some pictures, more explanation in parts.
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Edited by Will on Tue Jul 29, 2014 2:59 pm; edited 2 times
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sonrisu
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PostPosted: Fri Jul 11, 2014 4:09 pm    Post subject: Reply with quote

Quote:
"Looking forward to the day I can just think of music and there it is, fully realized." -- sonrisu

All interesting stuff, but I don't even want to have to write it. I just want to think it, and the output is there. :] Same could go for anything. Art. Programming. Would be amazing.

This theory stuff is interesting though. Keep going.
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Will
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PostPosted: Sat Jul 12, 2014 1:11 pm    Post subject: Reply with quote

Well, until we can get the electrodes hooked up, this is the closest thing you can get.
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Sirocco
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PostPosted: Sat Jul 12, 2014 1:18 pm    Post subject: Reply with quote

I do occasionally lament that I have no real aptitude for creating music. Although I did learn quite a bit when I ported SFXR to Allegro, but even then that was FM-specific stuff.
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Gil
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PostPosted: Sun Jul 13, 2014 4:22 am    Post subject: Reply with quote

Woohoo! A Will thread :)

Good stuff man
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Alex
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PostPosted: Tue Jul 29, 2014 10:43 am    Post subject: Re: The Musician's Toolbox Reply with quote

Will wrote:


  • Pitch: How high or low a sound is. We use the first 7 letters of the roman alphabet and some symbols to distinguish these (C D E F G A B) C is usually the "home" pitch for everything. They can be raised and lowered, by being sharpened with "#" or flattened with something that looks like "b"
I understand the pitch I think, but I don't understand the sharpening/flattening. Maybe it's because I'm not familiar with the sounds enough to recognize a flat or sharp sound. If you asked me if a sound was flat, or sharp, i probably couldn't say.
Quote:

  • Octave: the 8th note, going up the line. It's the same as the note you started on, just higher (literally vibrating at twice the frequency).
  • Steps: a half step (or semitone) is (usually) the smallest step between two pitches. A whole step is two half steps.
  • I briefly looked up sharp/flat notes, and it said they are halfsteps?, so I guess semitone is the same as a sharpened or flattened pitch?
    Quote:

  • Intervals: The distance between two pitches. These'll be explained in the next section.
  • Scales: all 7 pitches, by name, going up and down. We'll usually be working with the major scale or a variant of the minor scale. For now, major is "happy" and minor is "sad". The note a scale starts on is called the tonic.
  • why are there different scales? It also sounds like a scale can start anywhere. is the type of scale determined by where it starts?
    Quote:

  • Time: We're still working on what this is, but we divide it into measures, beats, and divisions of beats for the sake of music
  • Notes: musical constructs. We use a lot of them. At their most basic, they have pitch, duration, and nebulous "style" qualities.
  • Rests: notes without sound; periods of silence in time.
  • Rhythm: a series of notes and rests analyzed without pitch; the rhythm of a passage is just the durations taken without the sounds. Can also be used to mean a specific pitch.
  • Other stuff I forgot about: probably not important.


    Tonality is longer and harder, and means I have to get into more specifics than the quick definitions above.


    Chromatic notes
    First things first, there's more than 7 pitches. The distance between most notes is a whole step, which means we're missing out if we don't get the half step between them. To access that, we can sharpen, or raise, a note, or flatten, or lower, a note. Sharps look like "#", and flats kinda look like a lower-case "b". C#, Bb. This gives us twelve unique pitches: B#/C, C#/Db, D, D#/Eb, E/Fb, E#/F, F#/Gb, G, G#/Ab, A, A#/Bb, B/Cb. The notes separated by a slash are called "enharmonically equivalent": they sound the same, but, as in language, spelling matters. Also notice that some notes are a different distance apart. B and C are only a half step apart, as are E and F, but all the others are a whole step.
  • I reread this and I think I now understand their positions. the slashes were confusing me before, but the two notes have the same sound I guess.
    Quote:

    Next, scales. The C major scale looks like C D E F G A B C. Look at the intervals between each note: notice it goes w, w, h, w, w, w, h. We can derive all the other major scales from this pattern, so E major would go:
    E F# G# A B C# D# E. Scales have to use all the names in order, so we have to raise in some cases, and lower in others. C major has no sharps or flats in it.
    Okay, now I understand that part now that I understand the halfstepping. Essentially you just keep the same pattern of wholesteps/halfsteps and shift it up or down. I don't yet understand the purpose of this..
    Quote:

    Circle of Fifths
    We usually organize the scales in something called the Circle of Fifths. A fifth (P5) is the interval between C and the G above it. Going clockwise, the Circle of Fifths goes C, G, D, A, E, B/Cb, F#/Gb, Db, Ab, Eb, Bb, F, C. Every time we move clockwise on the Circle of Fifths, we add a sharp (or remove a flat), and every time we move anticlockwise, we add a flat (or remove a sharp). The order we add sharps in is: F# C# G# D# A# E# B#, and the order we add flats in is: Bb Eb Ab Db Gb Cb Fb. Notice these also follow the Circle of Fifths--it's hiding everywhere in tonal music.
    difficult for me to visualize this.. I think I understand what is happening but it is frustrating to solve. I think if I understand correctly, because the scale follows a pattern of wholestepping and halfstepping, when you make 4 whole or half steps from the starting note, the note you land on is where the next interval begins. And for some reason we add an extra halfstep on every firth cycle. I don't know why though..
    Quote:

    At this point, you should be able to write out all the major scales. I won't get into reading/writing sheet music here, but you should be able to do that too. If you have a piano around, figuring out where the scales go on that would be useful too.

    Intervals
    Intervals represent the distance between two notes. They have a span and a quality. The span is the number of note names between the two notes, including those two. The quality is changed if you lower or raise one of the notes. The qualities are Major, minor, Perfect, diminished (*), augmented (+), marked with the first letter or the character in brackets. You can stack diminished or augmented modifiers, but you won't see that very often.

    If you take the tonic of a major scale and look at the notes going up, they form these intervals: P1, M2, M3, P4, P5, M6, M7, P8. If you take the top of the scale and look at the notes going down, they form these intervals: P1, m2, m3, P4, P5, m6, m7, P8. Notice why unisons, fourths, fifths, and octaves get the perfect quality by default: when we invert the scale, they don't change quality. Intervals with perfect quality can't be Major or minor, only perfect, augmented, or diminished.
    I'm totaly lost here.. I don't understand the pattern to the intervals..
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    Gil
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    PostPosted: Tue Jul 29, 2014 2:12 pm    Post subject: Reply with quote

    Oh boy, that's tough to explain. Do you know the difference between a song written in a minor or a major key Alex?
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    Will
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    PostPosted: Tue Jul 29, 2014 3:02 pm    Post subject: Reply with quote

    Okay, I updated the OP with some pictures that might explain things better.
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    Alex
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    PostPosted: Tue Jul 29, 2014 4:01 pm    Post subject: Reply with quote

    Gil wrote:
    Oh boy, that's tough to explain. Do you know the difference between a song written in a minor or a major key Alex?


    nope.. all I know currently is that there is a major/minor.. and major starts with C?
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    Will
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    PostPosted: Tue Jul 29, 2014 4:34 pm    Post subject: Reply with quote

    Alex wrote:
    nope.. all I know currently is that there is a major/minor.. and major starts with C?


    I didn't go over the different types of scales yet, but if it's unclear: you can start any type of scale (the only type you know right now is major, following w,w,h,w,w,w,h) on any note. The other main types of scales are the minor scales, which I'll add to the post in a bit.
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