/improve/ - Self Improvement

>>43
I've seen this image posted around for YEARS, it is not only incredibly inaccurate but half of it reads like it was made up on the spot.

Your post isn't entirely accurate either because white keys are not necessarily natural tones, C flat F flat, B sharp and E sharp are all white keys, as are most double sharps and double flats.

I will take this opportunity to bring some clarity to this often misunderstood subject we call music, starting with why things sound good.

Whenever you pluck a string, or vibrate a column of air (like an organ, trumpet or flute) you produce a frequency which has a consistent rate of repetition. We measure this in hertz (reptitions per second). The lowest (and loudest) note is called the fundamental. This is not the only sound present, however, there are a series of softer and higher notes that help make up the overall sound. These are called overtones (also harmonics and partials but I won't get into the difference). The first overtone is twice the original frequency. So if our fundamental is 440 hz, the first overtone will be 880 hz. The next overtone is three times the fundamental (1320 hz), and the one after that four times (1760) and so on.

>>92
The combination of these tones (or lack of some of these tones) give instruments their particular sounds. Because of reasons that are related to physics (Fourier analysis), a string produces all of the harmonics aka overtones (triangle wave), a pan pipe or organ produces odd harmonics (omitting ever even numbered one) and a triangle or chime produces none (sine wave).

In the related pic you see how the distance between the overtones becomes smaller (the distance between keys, frets or flute holes, not the distance of the frequencies in hz), eventually it encompassing all 12 of the notes of our scale, and as you may have guessed, it is from these overtones our Western 12 note scale is derived.

>>93
Between two notes you have what is called an interval. An interval is merely the distance between two notes (even if the two notes are directly next to each other, or even the same note, it is an interval). The notes of the interval can be played simultaneously or one after the other.

Before I go in to the nature of intervals it would be helpful to understand how we notate.

The musical alphabet is as follows
A - B - C - D - E - F - G - A - B - C etc. extending infinitely in both directions. In a musical staff, Every line and space represents a letter in this alphabet. In the treble, the first line is E, the first space is F the second line is G etc. In music class the Treble lines can be remembered as: Every Good Boy Does Fine. The Treble spaces: FACE. The Bass Lines: Good boys do fine always. The Bass spaces: All Cows Eat Grass.

A line below the treble staff is middle C. A line above the Bass staff is the same middle C.

There are other staffs as well, which is represented by a 3 like symbol. The recess between the bumps of the 3 is
middle C (circled).

>>94
Between two notes you have what is known as an interval. Whether the notes are played at the same time, or one after another it is still an interval. It doesn't matter if the notes are right next to eachother, or even if they're the same note.

In this chart you have perfect, consonant and dissonant intervals. The perfect intervals are so called because they're the most consonant, and are in fact the first 3 harmonics (unison, octave and fifth). When you pluck a guitar string and it is a perfect interval to the string next to it, the unplucked string will begin vibrating in sympathy with it. Although they are the most consonant intervals, they are also a big headache which I will get into when I eventually talk about part-writing (some other day). When two such notes are played there is a small amount of beating between them. Try playing two notes on an untuned instrument (or better yet a two oscillator synthesizer) and you'll hear subtle vibrations between notes. The fewer of these vibrations the more consonant an interval is, and the more of them you hear the more dissonant it is. Consonance comes from the calmness you hear, dissonance from the jarring activity of this beating.

>>95
You may have noticed the fact that there are 12 notes on the piano (or any other instrument) before the sequence repeats itself, but there are only 8 letters. The other 'extra' notes have a function that will become apparent later on.

When you play a consecutive 8 step sequence along this musical alphabet you get a scale. The ancient Greeks called these modes, and in some countries they're called Church scales. If you play from C to C you get the Ionian mode. From D to D you get the Dorian, A - A is the Aeolin etc. Modes were the primary source of musical expression in the West up until the late Rennaissance/early Baroque. Two of these modes stuck out as being especially pleasing: the Ionian (which became the major) and Aeolian (natural minor).

On a piano, fretted instrumented or staff. Any scale or mode is a series of steps along the 12 notes of the scale. A half step is 1 key (or fret) and a whole step is 2 keys (or frets). Playing from C to C you get the sequence: (root) whole - whole - half - whole - whole - whole - half. Start this sequence on any note and you will always get a scale of the same proportion (major/ionian).

>>96
Now the subject of accidentals (sharps and flats) becomes relevant, because we always want our 8 scale steps to occur within our musical alphabet sequence (ABCDEFGABC etc). If we start our major scale sequence on G, we end up playing a new key instead of F. Since we still want a F in the sequence, and it is one half step above, we'll give it a sharp marking to signify it as F sharp (an F that's been raised a half step). Our scale sequence is now G A B C D E F# G. For clarity's sake we never want a letter omitted from our alphabet sequence. When we need to modify a note to be lower we give it a flat (b) sign.

Next post will be about the single most beautiful diagram you may ever see.

>>97
When you play our major scale sequence ((root) whole - whole - half - whole - whole - whole - half) in C we have no accidentals. If you start it on the fifth scale degree (the fifth letter in our alphabet) of C, which is G you end up with one accidental (F#). Play it one fifth above that, on D, you add another raised accidental (F#, C#), one fifth above that, A major you have 3 accidentals (F#, C#, G#). For every fifth you add, you add a new accidental.

Going in the opposite direction from C, one fifth down, you get the key of F major, where you lower the B to a Bb. The next fifth down, Bb major, has 2 flats, Bb and Eb.

The reason we have two different accidentals is that if you keep raising by fifths, you eventually get to a point where every note is an accidental, such as C# major, in the next key signature, G# major you have to raise the F# into an F double-sharp. And keep going until you get to B# major (which resembles C major, but is notated confusingly). Hence the need for two opposite accidnetal functions.

>>98
Another point of interest is that every sharp you add is also one fifth above the previous one, and every flat you add is one fifth below the previous one.

Within our major scale, you'll notice there being two places where a half step occurs. In our C major scale, F and B are one half step away from E and C. These notes create tension, and are the last stable in the sequence. They are called tendency tones because they have a tendency to lead the ear to closest tone. F->E and B->C. The seventh scale degree, in this case B is not just a tendency tone, it is also the leading tone, because it leads us to the root tone (the tonic) of our C major scale.

The Aeolian mode ((root) - whole - half - whole - whole - half - whole - whole - whole) is most often called the natural minor. This scale is unsatisfactory for achieving certain harmonic resolutions I will explain when I envtually talk about harmony. Essentially the scale lacks a leading tone that can draw the listener back to the root note (tonic). When it is needed the seventh scale degree can be raised to provide this function. A scale with a permanently raised seventh is called the harmonic minor scale, which is the stereotypical Middle Eastern. The sixth scale degree of the minor scale can be raised as well to when leading up to the seventh. If you are descending from the tonic, to the seventh then to the sixth you may flatten these notes again. This variable step approach was popular during the rennaissance and baroque era, but is rarely if ever used today. A classic example is Bach's E minor bourré.

https://www.youtube.com/watch?v=APNI2CC0k6A

A misconception is that you have to pick a minor scale and strictly adhere to it. The sixth and seventh scale degrees are variable and can be altered to suit whatever harmonic and/or melodic needs you have.

That's about it from me for tonight but I'll be back to explain parallel major/minor scales, tonic, dominant and subdominant, chords, dissonance resolutions and a bunch of other topics as well as answer questions if anyone bothers to read this.

>>106
Two elements define the consonance of an interval. First, the size of the numbers in the ratio. For example, 5:4 (the just major third) will sound more consonant than something like 81:64 (the Pythagorean major third). Second, how close are the notes to the actual interval. On a piano and most modern western instruments that uses equal temperament, octaves (2:1) are pure, perfect fifths are almost pure, but major thirds (5:4) less so, even if we got used to it over the time.

3:2, the perfect fifth, was the interval that Pythagoras used to build his Pythagorean scale, which served as the base for the western tuning system. It's using the Pythagorean tuning the modes mentioned at >>96 were made.

5:4, the major third, and 6:5, minor third, were "discovered" in the Renaissance, and a tuning called meantone was invented to have these intervals as pure as possible to go with the music written at that time. The problem with meantone was that you could play in only a certain number of keys without the intervals sounding badly out of tune.

Meantone was eventually replaced by what we now call Well-Temperament (as in Bach's "The Well-Tempered Clavier") and later by Equal Temperament so that the music could be played in any key without sounding out of tune.

The notes in 12 tone Equal Temprament can be mathematically calculated by the formula 440Hz*2^(x/12) where x is the number of notes higher or lower than middle A. It also happens sometimes that the 440Hz is changed a bit for whatever reason.

This information probably has little value to someone that's trying to learn modern music theory, but I find it interesting anyway.

Is there going to be a test on this?
I really am not good at remembering any details to how the theory works, I just try to play by ear.