Comment by snorkel | Hacker News Reader

Comment by snorkel | Hacker News Reader

For non-musicians, here's some terminology behind this:

There are 7 natural notes in (western) music: A, B, C, D, E, F, G (the white keys on a piano keyboard)

... plus 5 accidental notes that half-way between: A#, C#, D#, F#, G# also known as Bb, Db, Eb, Gb, Ab ... the black keys on a piano keyboard.

# means sharp (go up in pitch one-half step)

b means flat (go down in pitch one-half step)

7 naturals + 5 accidentals = 12 notes in the chromatic scale. These are the primary colors in music.

Chords are like secondary colors. Chords are combinations notes that harmonize well when played together. Typically chords are 3 or more notes spaced at one note or one-and-half notes apart. So the C Major chord is C + E + G played together.

Minor chords, noted with the lowercase "m" are made by dropping the "third" note down a half-step, so "C minor" or "Cm" is C + Eb + G, can also be expressed as C + D# + G

So put it all together, F#m means "F sharp minor" so the root note of the chord is "F sharp" and the next note from the F major chord, A#, is dropped down a half step from its major position to A natural, so the notes are F# + A + C#

Fortunately when playing an actual instrument you only memorize your finger positions to make the entire common chord shapes rather than thinking about the individual note under each finger.

The hook melody of song, the chord sequence that is repeated throughout the verse or chorus, is expressed as chord progression in Roman numeral 1 to 7:

I II III IV V VI VII

Why did we switch from letters to numerals now? Because lettered notes A, B, C, D, E, F, G are fixed positions (ie. hard-coded) and the numerals are relative positions (ie. abstracted) So the Roman numeral expression is a more general form of the melody structure. This lets you takes a progression like

C–G–Am–F (repeated over and over until you get a Grammy)

and expressed it as

I–V–vi–IV

.. which you can just shift up or down to another key and everybody loves your new hit song, you win another Grammy, and few people realize it's same damn song as before with new tempo and new lyrics!

http://en.wikipedia.org/wiki/I%E2%80%93V%E2%80%93vi%E2%80%93...

...

But the question is, what's natural about the Naturals, and whats accidental about the Accidentals? Because taken together they are just 12 equally spaced notes.

Good question. I don't know the exact answer, but yes I think there's nothing special that distinguish naturals and accidentals from a "listening" point of view. However, this distinction is handy for written music. For example, when you play a piece of music in a given key, let say G major, the notes are G A B C D E F#, there's only one accidental, so you can put this information in the key signature at the beginning of the score, and you can use only 7 natural notes on your staff. And this works for all "diatonic" keys (where notes belong to a major scale). You can always write your music with 7 naturals.

But you're just describing a notation, and the notation works OK because of the convention that in any given key you only use 7 of the available 12 tones. But why 7, and why those 7?

Sounds that sound good together have frequencies that are whole number ratios of each other. (This means they have harmonics that align. If they don't align, you get a beat frequency which sounds objectionable.)

A 3:4:5 ratio is a major triad. A good scale should have as many major triads as possible with the least number of notes.

So, let's call the root of our scale 1/1. You might want to build a major triad there, so you have 1/1, 5/4, and 3/2. If you build a triad off of 3/2, you'll end up adding a couple more notes: 15/8 and 9/4. If you add 4/3 as a note and build a triad there, you'll end up adding 5/3 and 2/1. 2/1 is the octave, so we can pretend it's equivalent to 1/1, and 9/4 is an octave above 9/8, so we can substitute 9/8.

So, our scale is 1/1, 9/8, 5/4, 4/3, 3/2, 5/3, and 15/8, and we have the major scale. It is possible to construct 3 major chords and 2 minor chords (10:12:15 ratio) from those seven notes. If you add 10/9 (slightly flat of 9/8), you can add one more minor chord.

By a mathematical coincidence, we can approximate these values pretty closely with various powers of the twelfth root of 2:

x = 2^(1/12) 1, x^2, x^4, x^5, x^7, x^9, x^11

The latter scale is equal tempered, whereas the former is "just" (untempered). The ET scale has very accurate fourths and fifths, but thirds and sixths are far enough off that they don't sound quite as nice in chords. We tend to put up with that in modern music, though.

Accidentals are notes outside of a scale, and a scale is an arbitrary concept chosen by some ancient people who decided certain notes sound good together.

http://en.wikipedia.org/wiki/Accidental_%28music%29

I don't see a good online reference, maybe I read this a guitar book somewhere, but essentially the tones for A, B, C, D, E, F, G notes were picked out by the ancient Greeks (who referred to them as Alpha, Beta, Gamma ... so on) In fact Pythagoras came up with a mathematical tuning system http://en.wikipedia.org/wiki/Pythagoras#Musical_theories_and...

The 7 natural notes are based on a 7-tone equal temperament (equal tonal spacing), which gives you enough equal spacing between notes to make nice harmonies (nice complimentary resonance) so this sort of a 7-tone minimal palette, and 5 "accidentals" fill the spaces in between those 7 tones to make a fuller 12-tone equal temperament palette.

The 7 natural notes are based on a 7-tone equal temperament (equal tonal spacing), which gives you enough equal spacing between notes to make nice harmonies

But they are not equally spaced. The tonal gap between A and B is twice as big as the gap between B and C, for example (look at the frequencies on a logarithmic scale).

The parent is being slightly confusing by bringing temperament into the discussion. They mean that the 12 notes are evenly spaced on an evenly tempered instrument, which means of course that you don't get the 'perfect' fourth or fifth you would get on a naturally tempered instrument (the frequencies are very slightly off).

Nearly all music we hear now is evenly tempered, but that is a pretty recent innovation.

Harmonics. They resonate well together because they have some common frequency. 13 equally spaced notes wouldn't match on multiples of 2, 3, 4 and 6.

Example: The major scale (C, D, E, F etc) are the notes 0/12, 2/12, 4, 5, 7, 9 and 11. You'd expect the 6th note to sound nice, wouldn't you? Wrong: The scale is logarithmic.

A nice C chord is made of 0th, 4th, 7th/12, which are 523Hz, 659Hz, 783Hz. Notice how the second frequency is 125% higher and the last 150% higher. So they have harmonics in common and it makes them sound well together.

Yes (from the little I know) a major aspect in our hearing is that nature doesn't produce pure sinusoids. Mechanical vibration materials is bound to have a series of resonances multiples of some basic frequency. So if you have a single person, or single object, emitting sound, you expect to see this nice harmonic lineup. When the fundamental frequencies don't have a pair (a,b) s.t. a * f1=b * f2, their harmonic multiples don't match and you can tell something is odd.

For f2=125% f1, for example, every 4th harmonic from f2 lines up perfectly; for f2=150% f1, every 2nd harmonic lines up; for f2= 200% f1, every harmonic actually lines up. I guess it's like looking at combs with different spacings and finding ones that superpose neatly.

The notes of the scale evolved gradually. Originally only the 7 notes of the diatonic (major) scale were used, sometimes fewer than seven. But if you take one of the notes in a diatonic scale other than the first and try to start a new scale starting with this note, you will find that you need new notes, the existing 7 don't allow you to create a new scale that "sounds the same" (has the same ratios between the frequencies of each note). The new notes that need to be added to allow these new scales became what are today the accidentals.

This link has some information about this:

http://en.wikipedia.org/wiki/Accidental_%28music%29#History_...

For some reason this is the first explanation of Roman numerals used in chord progression that made sense to me. Thank you!

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