The Euclidean Algorithm Generates Traditional Musical Rhythms

What do African rhythms, spallation neutron source (SNS) accelerators in nuclear physics, string theory (stringology) in computer science, and an ancient algorithm described by Euclid have in common? The short answer is: patterns distributed as evenly as possible. For the long answer please read on…

http://cgm.cs.mcgill.ca/~godfried/publications/banff.pdf

Chord Formulas and ‘Feel’

Where R=root note and the ascending numbers are semitone intervals. 7th note extensions in parenthesis.

Chord Formula  ‘Feel’
Semitone Root+1 Suspenseful, threatening
5th R+7 Solid, ‘power chord’
Major R+4+3(+3) complacent, satisfied, optimistic
Minor R+3+4(+3) Sad (but not always)
7th  R+4+3+4 Tough, bluesey jazzy rocky
Major 7th  R+4+3+4 Happy, almost jazzy
Minor 7th R+3+4+3 Airy, melancholy, ‘Not quite’ sad
Min/Maj 7th R+3+4+4 Softer still
Augmented R+4+4*(+3) Blues, country, jazz
Diminished R+3+3*(+3) Classical, jazz, gospel
Sus2 R+2+5 ‘Open’ sound , hanging there
Sus4 R+5+2 As above
Major 9th R+3+3+3+4 Open, soaring, airy
9th (dom 9th) R+4+3+3+4 Open, soaring, airy
m9th R+3+7+10+14 Tragic, hopeless
6th R+4+3+2 Jazzy-bossa playfulness
m6 R+3+7+9 Suspenseful, mysterious

To find the desired chord on the keyboard: Place a finger on the root note, count-up the semitones to the next position, place your finger and count-up again for the next position, etc. Example: A Maj7th = R+4-3-4 = A – Csharp – E – Gsharp.

To find the first inversion of any chord, take your finger off the root and place it on the note one octave above (in our example, still an A, just an octave higher).

To find the second inversion, move your lowest finger up to the next available note in the chord.

This way you can cycle up and down the keyboard, in the process using the same notes – = A – Csharp – E – Gsharp in different order.

[youtube http://www.youtube.com/watch?v=_sb3DwU6ZK4&w=400&h=255]

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The Role of the Bass Line

In almost all musical forms, the bass has two important functions to fulfill. First, the bass defines the chords being played and guides the movement of the music from one chord to another. This role is usually shared with a guitar or a piano. Second, the bass provides the rhythm of the music being played. This role is usually shared with the drums. Because it links the two functions of rhythm and harmony, the bass is often the instrument around which the rest of the music is organized.

via Bass Lesson. Part 2 – The Role of the Bass Line | Lessons @ Ultimate-Guitar.Com

Mixolydian scales

The mixolydian scale contains all four notes of the seventh chord (1-3-5-b7). The additional tones are scale degree two, scale-degree four, and scale-degree six. Scale-degree [b]seven is the most characteristic tone of the mixolydian scale, and uniquely identifies mixolydian. The basic quality of mixolydian is major.

Mixolydian scales.