Interactive piano reference to major and minor scales

There is an interesting "fudging" that has to happen, though, because 5/12 is not exactly equal to 3/7 (each of which should be the width of CDE relative to CDEFGAB.... 5 keys out of 12, or 3 white keys out of 7 white keys)

I actually discuss it in detail here (and all the weird ways people mess this up): https://youtu.be/xwKlKcymfDs?t=33

Here is some JavaScript code for calculating where each key should go. You can paste in the final numbers at bottom if that's easier. They start at the left of C (zero) and assume each white key is width of 1:

  var firstFiveWidth = 3/7; // c-e, 3 white keys
  var lastSevenWidth = 4/7; // f-b, 4 white keys

  // assume each of the 5 is equal width at back
  var cSharpMiddle = firstFiveWidth * (3/10);
  var dSharpMiddle = firstFiveWidth * (7/10);

  // assume each of the 7 is equal width at back
  var fSharpMiddle = firstFiveWidth + lastSevenWidth * (3/14);
  var gSharpMiddle = firstFiveWidth + lastSevenWidth * (7/14);
  var aSharpMiddle = firstFiveWidth + lastSevenWidth * (11/14);

  // average width of what a key in first five and a
  // key in last seven should be (then halve it)
  var halfBlackKeyWidth = (((firstFiveWidth/5) + (lastSevenWidth/7))/2)/2;

  var keys = [
    0,
    cSharpMiddle - halfBlackKeyWidth,
    1/7,
    dSharpMiddle - halfBlackKeyWidth,
    2/7,
    3/7,
    fSharpMiddle - halfBlackKeyWidth,
    4/7,
    gSharpMiddle - halfBlackKeyWidth,
    5/7,
    aSharpMiddle - halfBlackKeyWidth,
    6/7
  ]
  console.log("black key width: " + (halfBlackKeyWidth*2*7))
  console.log(keys.map(function(item){ return item *7}))

  black key width: 0.5857142857142857
  [
   0,
   0.607142857142857,
   1,
   1.807142857142857,
   2,
   3,
   3.564285714285714,
   4,
   4.707142857142857,
   5,
   5.85,
   6
  ]

And that's true! The trouble is, the last time I tried learning using techniques like this, I could never remember it with any amount of practice, and it made me so down about music that I quit for years. If I cared much about melodies, improvising, and/or performance, I might have the drive to invest effort past that hurdle, but I don't. I did have the drive for sound design--which is at least as complicated as foundational western music theory--because the whole thing fascinates me, so that's what I prioritize.

[0] Piano Companion Pro. Worth the lifetime purchase ($12). https://www.songtive.com/products/piano-companion

I come up with chord progressions in my DAW and use them as "ghost notes" to paint a melody over.

It's even easier in many cases to learn harmonic minor as a natural minor w/ a sharpened 7th, borrowed from the parallel major scale. (This doesn't work so well for Bb minor, since its relative major is a pretty exotic Db major; in this case, it's in fact easier to start from the parallel major and find the actual scale degrees.)

Major scale: 2 2 1 2 2 2 1 Minor scale: 2 1 2 2 1 2 2 etc

They sum up to 12 (octave)

Now that you got the theory, practice playing them evenly from every note and make sure they sound right.

Fingerings are a separate story though.

E.g. I just learned from my roommates that I can form the major chord for any note by adding the keys that are 4 half-steps and 7 half-steps higher. And then swap out the 4 half-steps higher key for 3 half-steps higher to make the minor chord. Very cool :)

A few years ago I made a similar site with many more scales and modes than this one:

http://www.dbmaj7.com/resources/piano

Although I do think I was initially taught the "minor scale" was the natural minor, so that may be where the OPs decision comes from.

Edit: Just saw info on the site. It is using natural.

Eh, just worry about Off Minor.

1. There is a major scale and a minor scale.

2. Actually, there are three minor scales: natural, melodic, and harmonic.

3. Actually, forget about those scales. Think instead more freely about tonality, modal mixtures, secondary dominants, and voice leading.

I think that anyone studying music is better off stopping at #1 or going all the way to #3. The problem with stopping at viewpoint #2 is that it's complex enough to make you really think, but not grounded enough in actual musical practice to make that thinking fruitful[1].

There are a lot of reasons why you might want a particular note to be sharp or flat. Sometimes you want a stronger resolution, like V -> i, rather than v -> i, which sounds weak. For that reason, to make better harmony, you may choose to make the 7th scale degree (B) a major 7th (B natural) instead of a minor 7th (B flat). You may also want to resolve a melodic line by half-step, which often sounds stronger, like B->C. But when you are stepping downwards, C->B, that's likely not any kind of resolution, so C->Bb is fine (it's likely not a resolution if you're in the key of C). These melodic concerns drive the "melodic" minor scale (and we drag in the 6th scale degree to avoid an augmented second interval).

The catch is... all we're really saying here is,

1. You are free to borrow notes from outside the key, for lots of reasons, and

2. There are lots of reasons in particular why you might want to borrow for the sixth and seventh scale degrees.

These deeper concepts get shoehorned into the notions of "melodic minor" and "harmonic minor". So much is lost by shoehorning these ideas into scales that I wonder why we even bother. I think it's really that people like categorizing scales and learning new names for things, which also drives people's fascination with modes, which is totally out of proportion to how much you'd actually want to use them in music. Modes and scales seem to have a particular fascination for hackers in the music scene.

I have a lot more to say on this subject, but I'm working on a blog post.

[1]: Please note that you definitely can choose to write music using one of these scales as a device, and many people do, and it's good stuff. It's just that most music that most people listen to doesn't make any sense to analyze as using particular minor scales.

https://www.masterclass.com/articles/minor-scale-guide#what-...

1. Identify what key you’re in (I.e what scale you want to use to build the harmonies from) 2. Start with the note you’re looking to harmonize, and play that note and every other note from the scale in step 1. 3. Do some final touch up work:

eg the chord you made in step 2, should probably be inverted to space the notes out more

eg playing a chord for “every” note in your melody will be too much. So choose the chords that work best over all, but you can always add chords back in as passing chords

eg once you’ve plaid the first three notes of the harmonization (root, third, fifth) you can be more liberal with the next notes and leave the pattern I described. So for example you can flatten/sharpen the next note in the sequence, or even play an entirely different note. Having the first 3 notes will ground the chord strong enough harmonically to let you do whatever you want with the rest and still retain the character of the chord. This helps you create more interesting and tense sounds and also let’s you harmonize notes in less traditional ways than before.

I typed this on my phone but I hope that helps. Last thing is just try harmonization of the c major scale. It will sound like you’re playing the scale with “chords”. Then try harmonizing Mary had a little lamb and so on. You can basically play anything by ear once you get a hang of this.

This is a challenging task, almost as hard as composition itself! It's easier if you have a matching baseline to go with the melody, since there are often idiomatic chords that can be played with a given bass note. (Such as the famous "rule of the octave", that has you playing root-position chords on the tonic and dominant, and first inversion chords (i.e. harmonizing with thirds and sixths over the bass) in all other scale degrees.)

Of course you could improvise a baseline for your melody and then harmonize that, but this requires a lot of familiarity with the rules of counterpoint.

When you think you've got it right, look up the `official' chords in a book or online (be careful online, I've found some hilariously wrong chords for pop songs).

Developing your ear is the most important thing. `Rules' for harmony just summarise what many people have thought sounds good. Theory also provides a language for talking about what the music is doing (whether or not the music is conventional).

Work the other way around too: take a chord progression (whether from an existing song, or of your own creation), and improvise singing a melody over the top. The singing is important because it forces you to just use the natural notes that come into your head against each chord.

Also, investigate different notes against a given chord. While just keeping on playing the same chord, taking each of the twelve chromatic notes in turn, play it over the chord: does it sound `resolved' or `normal', or `unresolved' / `weird' / `tense', if the latter try using it in a melodic phrase between two `normal' sounding notes.

The chord for a given bit of melody often contains most or all of the melody notes. It often contains all of the stronger notes in the melody. A melody note can be `stronger' by being on a strong beat, by lasting longer, by being first or last in a phrase, etc.

Although, in a given key, every chord contains all the notes of the scale. For example, in C major, chord I fully extended is: C (root), E (major third), G (perfect fifth), B (major seventh), D (major ninth), F (perfect eleventh), A (major thirteenth). But that's all the notes of the scale, just organised in a particular way (in scale-wise thirds, starting on C). So any bit of a C major melody contains `only' notes from a (fully extended) C major chord. (Fully extending the C major chord in another key which contains it will give different extended notes, for example, in G major, the C major chord is chord IV and will have F# as the (augmented or sharp) eleventh.)

But each note of the scale has a different `sound' or `meaning' in the context of a given chord. A melody using Cs, Es and Gs over a C major chord will sound `grounded' and `normal'. A melody using Ds, Fs and As over a C major chord will sound `jazzy' or `floaty'. A melody using Cs, Es and Gs over a Bb major chord will sound `jazzy' or `floaty. A melody using Ds, Fs and As over a D minor chord will sound `grounded' and 'normal'.

But you can't look at each part of the melody and a chord for it in isolation. You probably want the chord progression on its own to have some sense to it: to feel like its going somewhere, telling a story, sometimes unsurprising, sometimes surprising.

Different styles of music harmonise their melodies in different ways. A hymn tune, versus a jazz bebop tune, versus a Joni Mitchell song. Within the same style, different harmonisations are possible. E.g. here is Chick Corea reharmonising his own Spain: https://www.youtube.com/watch?v=XsQRFgU2fz4 .

Harmonization is the right word.

http://openmusictheory.com/

(But, as the name suggests, it's not a shortcut rules-of-thumb bypassing the theory kind of resource.)

Edit: most awesome would actually be an animation of the hand playing the scale with cross-unders and whatnot but that sounds like a lot of work.

https://developer.mozilla.org/en-US/docs/Web/API/Web_MIDI_AP...

Tone.js is great. I’m using it to convert MIDI files and sync visuals on a jazz piano tutorial website I’m building[2].

[0] https://tonejs.github.io

[1] https://archive.org/details/SalamanderGrandPianoV3

[2] https://www.jazzkeys.fyi

See my comment about how to calculate the piano key geometry (or just paste in my numbers) if you want your piano diagram to have correct placement of the keys (black keys shouldn't bisect the two adjacent white keys.... it makes the white key "stems" really narrow between black keys and looks weird).

Such as the fact that the circle of fifths also determines the type of sharps or flats found in the matching key signature, and that the last-added "sharp" in the key signature pertains to the leading tone in major (G major has an F#, and so on) or the second scale degree in minor. Conversely, the last-added flat in a key signature pertains to the fourth scale degree in the major mode, and the next-last (if any) to the tonic.

For you maybe. None of music theory makes even a smidgen of sense to me. Absolutely none of it.

FTA:

>First, a reference chart of the major scales, with keys in order of 5ths, as with the circle of fifths. This illustrates that there's just one note difference (at the 7th scale degree) between scales formed from keys that are separated by a fifth.

Uh.. nothing about the circle of fifths illustrates anything. Also it's plain to hear that all those scales have different notes given that they all start on different notes, so clearly they differ by more than just the seventh degree.

I dunno, I hate music theory