Theory. Modes, Part One

I've been working on this a bit, so it's time to test my understanding by writing it down.

The key question: what are modes?  (And for later, what does it mean to observe that the seventh chords come from the modes?)

The octave is the starting point.

A musical octave is a neat convergence of physics and psychology. Two notes that are an octave apart are perceived as equivalent; the notes are at a 2 to 1 ratio (eg, tuning A is pereived as a perceptual high A; tuning A is 440 Hz and high A is 880 Hz).

Western music divides the octave into 12 equal intervals, called semitones. (Mathematically, the term is cent.). Note carefully, the intervals are ratio's. The ratio's thus are the same, no matter what octave they apply to.

Here's where things get a bit strange.

Subsets of intervals, called collections or incorrectly sometimes called scales, form the basis of Western music. Conventionally-- which is to say, in common practice for over 1000 years – however, only two collections are used, and they each consist of 7 intervals.  We know them as major and minor.

And as final twist, the intervals between notes in a collection are not equally or uniformly spaced. Rather, 2 intervals are closer together than the other 5.

Here is C major, the most familiar of all collection, expressed in semi-tones.

note:        C   D   E   F   G   A   B   C  

semi-tones     2   2   1   2   2   2   1

symbol         T   T   S   T   T   T   S
(T = whole tone, S = semi-tone)

 The technical description as a mode is Ionian.

And here it is for C minor, which is technically described as the Aeolian mode.

note:        C   D   E   F   G   A   B   C  

semi-tones     2   1   2   2   2   1   2

symbol         T   S   T   T   T   S   T

Here's the whole set.

Ionian      T,T,S T,T,T,S  Major

Dorian      T,S,T,T,T,S,T

Phrygian    S,T,T,T,S,T,T

Lydian      T,T,T,S,T,T,S

Mixolydian  T,T,S,T,T,S,T

Aeolian     T,S,T,T,S,T,T  Minor

Locrian     S,T,T,S,T,T,T

The piano keyboard is anchored to these, but more on that later too.  As well as how it relates to keys (as in key of C, or A-flat minor, or whatever.)

Oh, one more thing:  A mnemonic for remember the names of the modes is 'I Don't Punch Like Mohammed ALi'.