Intervals

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Syscrusher
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Intervals

Post by Syscrusher » Wed Apr 13, 2011 3:44 pm

There has been a lot of talk so far about 3rds and 4ths etc.. Seeing as they are so necessary in the description of Music Theory concepts I figured I'd jot something down about intervals.

Any discussion of intervals should include a discussion of the "Octave". The octave is perhaps the only cross-cultural musical concept. Every culture's music references the octave - how it is divided into smaller intervals however is different from culture to culture. Studies show that even animals (such as birds) share the concept of the octave. An octave is basically a doubling of frequency. A4 is 440Hz. Double that frequency and you get 880Hz and the pitch A5. This can be visualized as two waves - one with twice the number of peaks as the other. There is essentially an infinity of frequencies within the octave (ie. 440.1, 440.2, 440.3 etc...) so we divide it up into intelligible (and audible) intervals. In Western musical tradition the octave is divided into twelve even "slices" we call Semi-Tones. This is the smallest interval available in our notation and the smallest available interval on the piano keyboard. The succession of the 12 Semi-Tones within the octave is called the "Chromatic Scale". It contains all the colours - "Chroma" - of the octave as we have divided it. The succession of Tones (the interval of two Semi-Tones - ST+ST) is called the Whole-Tone scale. Thus the octave is divided into 12 Semi-Tones and 6 Tones.

Basically an interval is the particular distance between two notes. Like almost everything else, these distances are explained through the Major Scale (it's difficult not to cross reference threads as everything is so interrelated):

Do Re Mi Fa So La Ti Do or 1 2 3 4 5 6 7 8(1)

1(Do) - T - 2(Re) - T - 3(Mi) - ST - 4(Fa) - T - 5(So) - T - 6(La) - T - 7(Ti) - ST - 1(Do)

This gives us what is called the Major Scale formula. (T - T - ST - T - T - T - ST). Start on any of the 12 pitches in the octave and follow this formula and you will get the corresponding Major Scale.

The only Major Scale that can be expressed without using sharps and flats is the C Major Scale so we will use this for our examples. The C Major Scale is all the piano's white keys from C to C. C D E F G A B C. These are called our "natural" notes. Notice that all the natural notes are a Tone apart except for E-F and B-C; these are a Semi-Tone (there is no black key between them).

The smallest interval name we have is the "2nd". This is the distance from one note of the Major Scale to the next. You will quickly realize that there is two types of 2nd - the Tone (T) and the (ST). The Tone is the larger division and is called a "major 2nd" ( often written +2nd ). The Semi-Tone is a "minor 2nd" ( -2nd ). Thus C to D is a major 2nd interval as is D to E, F to G, G to A, and A to B. The remaining pairs E to F and B to C are -2nd intervals.

The next interval is the 3rd. That is skipping a distance of a third within the scale - C to E, D to F, E to G etc...
Thirds are very important as they are used to construct chords (that is another thread altogether).
Here you will notice that there are two types of 3rd as well. C to E, F to A, G to B are all two Tones apart (T+T) while the remaining 3rds - D to E, E to G, A to C, B to D - are a Tone and a Semi-Tone (T+ST) apart. Again the wider interval (T+T) is given the "major" designation (+3rd) and the smaller (T+ST) the minor (-3rd).

This continues through 4ths, 5ths, 6ths, and 7ths each one having two identities. There are major and minor 6ths and 7ths however 4ths and 5ths are given different designations:

C to F is the distance of T+T+ST and is called a "perfect 4th". The 4th's dual identity is called the "augmented" 4th. In a major scale it only occurs between the 4th(Fa) and 7th(Ti) degrees ( F to B in the key of C ) all other 4ths are "perfect". An aug4th is the distance of T+T+T. Note that the augmented (aug) 4th is "stretched" by a ST.

The 5th's two flavours are called "perfect" and "diminished". A perfect 5th interval is the distance of three Tones and a Semi-Tone (T+T+T+ST). The diminished (dim) 5th is one ST less in distance ( T+T+T). Note that the dim5th is the same distance as the aug4th but is "squished" down from the perfect 5th. B to F is the only natural (white key) dim5th. Note that it is the inversion of the sole natural aug4th (F to B).

The 6ths and 7ths return to major/minor designations.
A major 6th is T+T+T+T+ST where a minor 6th is T+T+T+T (one ST less). C to A is a maj6th. E to C is a min6th T+T+T+T.

A major 7th is T+T+T+T+T+ST. ie C to B. A minor 7th is T+T+T+T+T (one ST less). G to F is a min7th.

Note that intervals can be counted beyond the octave. G to F crosses over C but is still a minor 7th: G-A-B-C-D-E-F.

An interval that crosses over the octave but exceeds the distance of a 7th is called a "compound" interval. For instance: C to D is a maj2nd but crossing over the octave it becomes a maj9th. C-D-E-F-G-A-B-C-D. This becomes useful especially when naming chords with extensions (chords beyond triads).

That is basically it for now unless one of you intrepid readers has something to add.
Last edited by Syscrusher on Wed Apr 13, 2011 8:21 pm, edited 3 times in total.

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Cfgk24
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Re: Intervals

Post by Cfgk24 » Wed Apr 13, 2011 4:18 pm

Brilliant!
Yes, I can see a visit to 'Chords' is coming up.

Also - just to clarify the methods we have of writing Tones and Semitones when describing the intervals between notes in the scale.

I use T to represent a Tone and S to represent a Semitone.

ST is used here in this thread to describe a Semitone.. In some instances TS or ST may represent 3 semitones . . . .

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Decktonic
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Re: Intervals

Post by Decktonic » Wed Apr 13, 2011 4:40 pm

Learning intervals changed my life...
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Snakecharmer
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Re: Intervals

Post by Snakecharmer » Wed Jul 20, 2011 4:43 pm

Decktonic wrote:Learning intervals changed my life...
Amen!
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