Behold the octave.

I've been known to rant on about CAGED and how I think it's most useful application to begin with is to see octave shapes all over the neck.

So I began to consider the lowly octave and as I did I came to have somewhat of a mystical perspective on it.

I will go as far as to say that the octave may just be the single most important interval in music. WHAAAAAAA??? Yes indeed. I say that the octave is to music as the concept of zero is to mathematics. Of course 'zero' is strictly a concept and the octave is a naturally ocurring phenomenon but in terms of importance and function I think they occupy pretty much the same space.

The octave wipes the slate clean. The octave is the interval that permits repetition to occur. If we didn't have the octave then we couldn't possibly have scales because there would be no restrictive element that creates a boundary whereby we begin a repetition of the previous notes.


The octave is king.

The octave definitely comes in handy when tuning the guitar. None of your fifth fret method - it's got to be tuned using octaves if you want all the chords to sound their best.

If you dig the octave, behold. It's the basic miracle of music:

http://en.wikipedia.org/wiki/Octave

The octave definitely comes in handy when tuning the guitar. None of your fifth fret method - it's got to be tuned using octaves if you want all the chords to sound their best.

If you dig the octave, behold. It's the basic miracle of music:

http://en.wikipedia.org/wiki/Octave

Well there ya go. I shoulda just looked on Wiki. The "basic miracle of music". I wish I had thought of that. :lol:

For me it's always been the minor 3rd. Divides the octave into 4 equal parts.
A lot of legit string players tune to a Dm triad. *No 'saddest key' jokes, it's the truth and most of them haven't even heard of spinal tap.

M3 is cool too - division of the octave by a triangle.

For me it's always been the minor 3rd. Divides the octave into 4 equal parts.
A lot of legit string players tune to a Dm triad. *No 'saddest key' jokes, it's the truth and most of them haven't even heard of spinal tap.

M3 is cool too - division of the octave by a triangle.

Yes but you're still using the octave as the reference point as to why the m3 and M3 are cool intervals. Sooooooo...octave is still the king. Check and mate. :mrgreen:

I know exactly what you're talking about. You double the frequency, and it's still the same note. So simple, but it blows my mind every time.

Classical music theorists often reduce pitches to their octave equivalents. For example, C4 = C5 = C6, etc. The equal sign means "is equivalent to" not "is equal to" in this post. I am short a couple of symbols, so am making do with this.

In some music, analysts use the integers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 to denote pitches. Here, 0 = C4 = C5 = C6, etc; 1 = C#4 = C#5, etc. Since it can be cumbersome to worry about octaves, theorists have incorporated the notion of pitch-class. A pitch-class is a pitch that does not have a specific octave.

Some theorists look at the pitch-class as equivalent to the integers mod 12. Those integers are not greater than 11. This has led theorists to consider pitch-classes as a mathematical group called Z12. The group Z12 has a subset of 0 3 6 9, also called a subgroup Z4. Extra credit for finding what the augmented triad is called in group theory.

0 4 8 - Z3?

Ive always felt that the advent of new textures in 20th century music must have been a major factor in this theory - atonality - melodies and chords that can cover two or more octaves very quickly - making the idea of intervals within the octave - and with names imbued with tonal meaning(min 3rd - P4th etc) , obsolete..


I'll go you halves BG - Im a big tritone fan!

Yes but you're still using the octave as the reference point as to why the m3 and M3 are cool intervals. Sooooooo...octave is still the king. Check and mate. :mrgreen:
Lol! True dat.
And I guess in nature, wherever a culture decides to place their intervals, the octave unambiguously is a dividing line. So you could say that the octave is the only universal interval.

That would be a cool band name: The Octave.

0 4 8 - Z3?

Ive always felt that the advent of new textures in 20th century music must have been a major factor in this theory - atonality - melodies and chords that can cover two or more octaves very quickly - making the idea of intervals within the octave - and with names imbued with tonal meaning(min 3rd - P4th etc) , obsolete..


I'll go you halves BG - Im a big tritone fan!

Z3 is right. Then there are Z2 and Z6. All of the numbers divide the octave into equal parts.

This leads to another concept, referred to as generating a group. A group Z12 can be generated by successively adding one integer to itself iteratively until it closes at the octave. There are four mod 12 integers that do this. Can you name them?

Hint: these four integers.

We are getting close to being able to make sense out of Pat Martino's sacred geometry.

A note contains the frequencies of its octave. So, the octave is embedded in any note. Also, the octave is embedded in the octave of the octave, and so on and so on.

Larry - do you mean Z2 Z3, Z4, and Z6 ? or am I barking up the wrong tree?

Im not sure I got the question but this is how I understood Pats view of geometry of the fretboard...

It's a powerful thing. It causes us unschooled plunkers to put a second "do" in every scale we play!

No no no no. The Major 7th. pitches notes that should clash being 1/2 step apart yet the seperation of 10 steps gives them a rich pleasantness.