Intervals

What types of sounds can be established when notes are played simultaneously?
Feb 22: Took notes on Generic and Specific intervals and used the generic and specific interval trainers.

Feb 23: Took notes on Writing intervals and studied Freebern's theory tricks

Feb 24: Reviewed and did exercises on key signatures, scales, and intervals.

Feb 28: Reviewed and did exercises on intervals. Took notes on interval inversions and copied notes on consonance and dissonance. Worked on ear training with intervals.

March 1: Reviewed and did exercises on ear training with intervals.

March 2: Reviewed consonance and dissonance and intervals, and did exercises on ear training with intervals and other ear training.

March 3: Did more ear training exercises and did unit 3 theory vocabulary.

March 4: Did more ear training exercises.

March 8: Did more ear training exercises and took quizzes.

Unit 3 Macro Concepts

 * Intervals and their inversions
 * Consonance vs. Dissonance
 * Melodic tendencies of scale degrees.
 * 18th. Century principles of rhythm used inmelody.
 * Principles of great melodic writing

__**INTERVALS:**__


 * Generic Intervals:**

An interval measures the distance between two notes...generic intervals are measured on the staff...when two notes occupy the same line or space, they are a **first (or a prime)** apart (C-C)...accidentals are ignored when measuring musical intervals, only staff position matters (C-C#)...as the notes become further apart on a staff, the interval type increases (C-D, D-E are **seconds**)...(C-E are **thirds**)...thirds share the same position type, either both on a line or both on a space...(C-F, D-G are **fourths**)...(C-G, D-A are **fifths**)...(C-A, D-B are **sixths**)...(C-B, D-C are **sevenths**)...(C-C, D-D are **eighths**)


 * Specific Intervals:**

Specific Intervals are measured on both the staff and in half steps on the keyboard...(C-D and C-Db are both generic seconds, however C-D is one half step larger than C-Db)...a **major second** is made up of two half steps (C-D, E-F#)...a **major third** is made up four half steps (C-E, E-G#)...a **perfect fourth** is made up of five half steps (C-F, F-Bb)...a **perfect fifth** is made up of seven half steps (C-G, B-F#)...a **major sixth** is made up of nine half steps (C-A, Eb-C)...a **major seventh** is made up of eleven half steps (C-B, D-C#)...a **perfect eighth**, or perfect octave, is made up of twelve half steps (C-C)...the terms "major" and "perfect" refer to the interval's quality...only seconds, thirds, sixths, and sevenths can have a major quality...firsts, fourths, fifths, and eighths use "perfect" instead...//a minor interval has one less half step than a major interval// (for example, since C-E is a major third, four half steps, C-Eb is a minor third, # half steps)...since minor intervals transform from major intervals; only seconds, thirds, sixths, and sevenths can be "minor"...//an augmented interval has one more half step than a perfect interval// (since C-F is a perfect fourth, 5 half steps, C-F# would be an augmented fourth, 6 half steps)...//major intervals can be augmented by adding a half step// (for example, since C-A is a major sixth, 9 half steps, C to A# is an augmented sixth, 10 half steps)...//a diminished interval has one less half step than a perfect interval// (since C-G is a perfect fifth, 7 half steps, C-Gb would be a diminished fifth, 6 half steps)...//minor intervals can also be diminished by subtracting a half step// (recall that C-B is a major seventh, 11 half steps, and C-Bb is a minor seventh, 10 half steps...C-Bbb is a diminished seventh, 9 half steps)

When writing intervals on the staff, it is common to confuse intervals with he same number of half steps (fox example, one may accidentally write C to F#, an augmented fourth, instead of C to Gb, a diminished fifth...look and sound identical, but one is fourth and one is fifth)...3 step process to reduce the risk of this mistake: write note and generic interval on staff, figure out number of half steps on the keyboard, compare results and add accidentals
 * ~ Semitones ||~ Common Name ||~ Alternate Names ||
 * 0 || **perfect unison** || diminished second ||
 * 1 || **minor second** || augmented unison ||
 * 2 || **major second** || **diminished third** ||
 * 3 || **minor third** || **augmented second** ||
 * 4 || **major third** || diminished fourth ||
 * 5 || **perfect fourth** || augmented third ||
 * 6 || **tritone** || **augmented fourth, diminished fifth** ||
 * 7 || **perfect fifth** || diminished sixth ||
 * 8 || **minor sixth** || augmented fifth ||
 * 9 || **major sixth** || **diminished seventh** ||
 * 10 || **minor seventh** || **augmented sixth** ||
 * 11 || **major seventh** || diminished octave ||
 * 12 || **perfect octave** || augmented seventh ||
 * **Writing Intervals:**


 * __FREEBERN'S THEORY TRICKS:__**

Intervals: think of scale...M2 M3 P4 P5 M6 M7

Maj+1=Aug Maj-1=Min-1=Dim P+1=Aug P-1=Dim

Key Signatures: For flats, go back one flat, for sharps, go up one sharp

CDAEB pencil trick

FACEGBD f-a,c-e,g-b is M3 a-c,e-g,b-d is m3

TO find minor key, go up a 6th from major or go down a m3

For relative minor: 1, 2, b3, continue scale

2+7=9 3+6=9 4+5=9 ||


 * __INVERTING INTERVALS:__**

To invert intervals, move the lowest note an octave higher...a perfect fifth C-G becomes a perfect fourth G-C, a perfect fourth F#-B becomes B-F#...perfect intervals will always invert to other perfect intervals...fourths and fifths will invert to each other....a major third C-E becomes a minor sixth E-C, a minor third E-G becomes a major sixth G-E...minor and major intervals invert to each other...thirds and sixths invert to each other...a major seventh C-B becomes a minor second B-C...seconds and sevenths invert to each other...diminished an augmented intervals invert to each other...an augmented fourth C-F# becomes a diminished fifth F#-C


 * __Consonance and Dissonance:__**

If you have a chord and a note that doesn't fit in the chord, that note is a dissonance...in two voices, thirds, fifths, sixths, and octaves are consonances...seconds, fourths, and sevenths are dissonances...Some of the rules governing various types of motion imply, at least to Schenker, important relationships between these different groups of intervals (see the full explanation of species counterpoint for more on these rules):


 * __The rules governing dissonance__ - Dissonant intervals are only allowed on weak beats in between consonant intervals (although fourth species introduces an exception). Intervals of seconds, sevenths and Despite being a perfect interval, the fourth is paradoxically considered to be a functional dissonance. For whatever reason, the vertical fourth is treated as an unstable interval in the tonal repertory - it always resolves either up to a fifth or down to a third. If it is not at the bottom of a chord, however, its dissonant function ceases.


 * __The rule probiting parallel fifths__ - Schenker gives a number of reasons why parallel fifths are not allowed. The most important is that counterpoint requires two independent voices and, because the fifth and octave are the first and second overtones of the harmonic series, parallel motion involving these intervals sounds like a shadowing of the lower voice. The same point could conceivably be made about thirds, but Schenker considers the perfect fifth a special case. He calls it a 'boundary interval' because it, 'demarcates the harmonic content of the bass note' (Schenker,//Counterpoint //, p. 125) - in other words because it spans the interval between the top and bottom notes of a root position triad, it **implies** that triad in a way that other intervals (such as a third) do not. What, you may ask, is wrong with that? Schenkerian theory explains tonal music as harmonic units (i.e. triads) decorated and extended through time according to the principles of counterpoint ... parallel fifths imply a succession of undecorated triads which perhaps upsets this model.

__**THEORY VOCABULARY UNIT 3:**__


 * Interval: the relationship between the pitches of two notes **
 *  Diatonic Interval: intervals between the notes of a diatonic scale **
 *  Chromatic Interval: intervals between the notes of a chromatic scale **
 *  Consonance: a harmony, chord, or interval considered stable **
 *  Dissonance: ** a harmony, chord, or interval considered unstable