| A | B |
|---|
| Intervals | Exist in 2 dimensions= Horizontal (melodic) and Vertical (harmonic) |
| Numerical Size of an Interval | Depends on the number of letter names the 2 tones span |
| Quality | Describes the sound of an interval (e.g. G-natural sound different than G-sharp) |
| What does the complete identification of an interval depend on? | For both Horizontal (melodic) and Vertical (harmonic), depends on both its numerical size and its quality (e.g. C to G-natural/sharp/flat all have the SAME numerical size but sound different [i.e. have a different quality]) |
| Intervals: 5 Qualities | Major (M)= minor (m)= Perfect (P)= Augmented (A)= diminished (d)==== [occasionally you encounter DOUBLY augmented or DOUBLY diminished intervals] |
| For purposes of classification, how many groups do intervals divide into? | 2 groups |
| (Interval Classification) Group 1 | Unisons, 4ths, 5ths, octaves |
| (Interval Classification) Group 2 | 2nds, 3rds, 6ths, 7ths |
| Group 1: Describe these intervals | The intervals belonging to Group 1 are basically PERFECT= They are never major or minor= Intervals are sometimes augmented or diminished |
| Group 2: Describe these intervals | The intervals belonging to Group 2 are basically MAJOR or MINOR= They are NEVER perfect= Intervals are sometimes augmented or diminished |
| Group 1: When is the interval PERFECT | If the upper tone of the interval belongs to the major scale of the lower tone |
| Group 1: When is the interval AUGMENTED | If the interval is a chromatic half step larger than perfect |
| Group 1: When is the interval DIMINISHED | If the interval is a chromatic half step smaller than perfect |
| Group 2: When is the interval MAJOR | If the upper tone belongs to the major scale of the lower tone |
| Group 2: When is the interval AUGMENTED | If the interval is a chromatic half step larger than major |
| Group 2: When is the interval MINOR | If the interval is a chromatic half step smaller than major |
| Group 2: When is the interval DIMINISHED | If the interval is a chromatic half step smaller than minor |
| Compound Intervals | Intervals larger than an octave |
| According to the "Principle of Octave Equivalence", compound intervals... | Are functionally the same as the corresponding SIMPLE INTERVALS (e.g. A 12th is simply an expanded 5th= A 15th is an expanded 8ve)= Such intervals (e.g. 12th, 15th, etc.) are almost always called their corresponding simple interval name (e.g. 12th is called a 5th= 15th is called an octave)= The only compound intervals whose names we sometimes need are the 9th and the 10th |
| How do we invert an interval of an Octave or less? | By bringing the lower tone up an octave or the upper tone down an octave while leaving the other tone in place |
| How do we invert compound intervals? | One of the tones would have to be displaced by 2 or more octaves |
| What does the numerical size of an interval PLUS that of its inversion add up to? | [Numerical Size of an interval] + [the interval's inversion]= 9 |
| (Inversion) Unison=? | Octave (1+8=9) |
| (Inversion) 3rd=? | 6th (3+6=9) |
| Interval + Inversion =? | 9 |
| (Inversion) Perfect Interval | Perfect |
| (Inversion) Major | Minor |
| (Inversion) Minor | Major |
| (Inversion) Augmented | Diminished |
| (Inversion) Diminished | Augmented |
| What does interval inversion result from? Result? | Results from the octave displacement of one of the interval's tones= RESULT: An interval and its inversion form a related pair (this relationship is another consequence of "Octave Equivalence") |
| What are most musical tones? | Composite Sounds |
| Composite Sounds | (Most musical tones are Composite Sounds) Their pitch results from the frequency with which the sounding body (e.g. piano, violin string, etc.) vibrates= As it vibrates, the sounding body divides itself into segments that vibrate independently= The vibration of the segments produces OVERTONES |
| Overtones | Are individual tones that, when taken together, form the FUNDAMENTAL TONE (the pitch we hear)= The overtones blend into a single sound (the fundamental tone [the pitch we hear]) |
| When is it easier to hear overtones? | When the fundamental tone is in a lower register |
| What do overtones do? | They help determine the TIMBRE (tone color) of the various instruments= They make it possible to play harmonics on string instruments= They make it possible to play the technique of overblowing on wind instruments |
| Describe how overtones vary/are similar with different musical sounds of different pitch different instruments | The INTENSITY (loudness) of the different overtones will vary depending on the instrument and on how it is played= However, almost all musical sounds of any pitch contain the same group of overtones (called the OVERTONE SERIES) |
| Consonant Intervals | Stable Intervals= Intervals that produce the impression of stability |
| Dissonant Intervals | Unstable Intervals= Intervals that produce the impression of activity or tension |
| What are the Consonant Intervals | The Perfect Unison= The Perfect Octave= The Perfect 5th= The Perfect 4th (sometimes)= Major and minor 3rds= Major and minor 6ths |
| What are the Dissonant Intervals | All 2nds= All 7ths= All Augmented and Diminished Intervals= The Perfect 4th (sometimes) |
| In major-minor tonality, what are the consonant intervals? | The Unison and Octave, plus all the intervals that make up major and minor triads |
| What are the most stable triadic intervals? | (Those that lie between the lowest tone (root) of a triad and one of the upper tones)= These are Perfect 5ths, the Major 3rd, and the minor 3rd= The remaining consonances (the Major 6th, the minor 6th, and the Perfect 4th) result from the inversion of the more stable ones |
| What are the most stable intervals of all the consonances? Why? | The unison and octave= In the unison, the 2 tones agree completely= In the octave, the 2 tones differ only in register |
| How is the lack of tension in the unison and octave intervals reflected? | Composers tend to end pieces on unisons or octaves |
| When is the Perfect 5th uniquely important? Why | Is important in music based on the triad, for its upper tone defines the lower one as the root of a chord (e.g. if we hear the bare 5th F-C, we know F is the root, for F-C occurs in no triads except F major and F minor, in both of which F is the root) |
| What role does the 5th between scale degrees 1 and 5 play? | Because our feeling for a key rests partly on the stability of the tones of the tonic triad, the 5th between scale degrees 1 and 5 play an important role in defining the key |
| Which type of triad (major or minor) have composers tended to treat as the more stable of the 2? Result | Composers have tended to treat the major triad as more stable than the minor= Thus, the Major 3rd (which characterizes the major triad) is a more stable interval than the minor 3rd (which characterizes the minor triad) |
| Which intervals are more active than the 5th? | Both Major and minor 3rds |
| Which intervals are more active than the major/minor 3rd intervals? | The Major and minor 6ths (which are inversions of the 3rds)= Differences in stability between the 2 kinds of 6ths are not very significant |
| In what way/how is the fluid character of the Major/minor 6th intervals reflected? | Is reflected in the fact that Major/minor 6ths are NOT used to end pieces except for special and unusual effects |
| Describe the Perfect 4th | Is the only interval that is sometimes consonant and sometimes dissonant |
| Perfect Consonances | Name given to: Unisons, Octaves, and 5ths |
| Imperfect Consonances | Name given to: Major/minor 3rds and 6ths |
| In Two-Part-Textures, what do composers prefer for important Points of Articulation | In Two-Part Textures (music containing 2 melodic lines), composers prefer the more stable perfect consonances from important POINTS OF ARTICULATION (=beginnings and endings of phrases, sections, or pieces) |
| In Two-Part Textures, where do composers most often use imperfect consonances? Why? | Because of their less stable, more fluid character, the imperfect consonances normally predominate in places where the music moves from one point of articulation to another |
| In textures of more than two parts, where do composers most often use imperfect consonances? | In textures of more than 2 parts, imperfect consonances tend to occur between the highest and the lowest parts (the most prominent lines), except at points of articulation |
| What are all the "consonances" apart of? Result | All of the consonances form part of major or minor triads and thus function as CHORDAL ELEMENTS |
| What do Dissonant Intervals between two parts arise out of? | Dissonant intervals between 2 parts arise out of melodic activity in one or both of the parts |
| Passing Tones | Move by step from one stable tone to another |
| Neighboring Tones | Arise from the stepwise decoration of a single tone |
| Dissonant Intervals: Stepwise Motion | Approaching and leaving the dissonance by step ensures a close connection between it and the surrounding consonances= The stepwise connection channels the tension and energy of the dissonant intervals so that dissonance becomes a powerful force for musical direction |
| Dissonant Intervals: Isolated Dissonances | Those without a close connection to consonances= They run the risk of creating tensions that serve no musical purpose because they lead to no goals (unlike dissonances that arise from stepwise motion) |
| Active Tones | Scale Degrees [2, 4, 6, 7]= These tones tend to move to the Stable Scale Degrees [1, 3, 5] |
| What does the division of scale degrees into STABLE and ACTIVE tones directly relate to? How? | Directly relates to the phenomenon of consonance and dissonance because the active tones are those that form dissonances with one or more tones of the tonic chord, whereas Scale Degrees [1, 3, 5] (the tonic chord) are all consonant with each other |
| What is the simplest and most basic use of consonance and dissonance? | Scale Degrees [1, 3, 5] as consonances and the other scale degrees as dissonances against the other part or parts (i.e. this would mean that scale degrees 4, 2, and 7 form dissonances) |
| Because it would be far too limiting for composers to limit themselves to the simplest uses of consonance and dissonance, what do they do? | Stabilize the normally active tones by giving them the support of consonant intervals= At the same time, normally stable tones may become unstable by appearing as dissonances |
| When is the 4th Consonant? | It is consonant whenever the context shows it to function as an inverted 5th |
| In simple textures, when is the 4th mostly Dissonant? | When it occurs in a 2-part setting or between the lowest part and one of the upper tones in a setting of more than 2 parts |
| What does the special character of any scale degree partly depend on? | Depends partly on the intervals it forms with the other scale degrees (EX: In MAJOR, scale degrees [3, 6, 7] form a major 3rd, major 6th, and major 7th above scale degree 1= In minor, the corresponding intervals are all minor) |
| In any DIATONIC mode, the group of intervals formed y any scale degree sounding against all others..... | Is unique= Each group will differ from all the other groups by 2 or more intervals= Every scale degree generates a unique collection of intervals, which generates a unique collection of intervals, which gives each tone of a diatonic scale its own distinctive character |
| What intervals can be produced by combining the tones that belong to major, natural minor, and other diatonic scales? | [Perfect Unisons and Octaves], [Perfect and Diminished 5ths], [Perfect and Augmented 4ths], [Major and Minor 3rds and 6ths], [Major and Minor 2nds and 7ths] |
| Among the intervals found in major and in natural minor, describe the Perfect 5th and Perfect 4th | There are six Perfect 5ths and six Perfect 4ths (inversions of the 5ths)= However, there is only one Diminished 5th and only one Augmented 4th |
| Major Scale: Describe the Diminished 5th | Occurs between scale degrees 7 and 4 |
| Major Scale: Describe the Augmented 4th | Occurs between scale degrees 4 and 7 |
| Major Scale: What do scale degrees 4 and 7 tend to gravitate to? Why? | The stable tones 3 and 1= Because of the particularly intense character of the half-step relationship |
| Major Scale: Describe the melodic tendencies of scale degrees 4 and 7 when they occur at the same time | They are considerably enhanced by the tension of the dissonant interval they form |
| Resolution | Is the motion of a dissonant interval to the consonance that acts as its goal |
| Major Scale: How does the Diminished 5th resolve? | Resolves by moving in to a 3rd |
| Major Scale: How does the Augmented 4th resolve? | Resolves by moving out to a 6th |
| Major Scale: What does the resolution of the Diminished 5th and Augmented 4th to scale degree 1 and 3 create? | Creates a strong drive toward the tonic triad and helps orient the listener to the position of the tonic |
| Major Scale: Key-Defining Progression | Is the resolution of the Diminished 5th and Augmented 4th to scale degrees 1 and 3 |
| Major Scale: What is the Key-Defining function of the Diminished 5th and Augmented 4th connected to? | Connected with the fact that any particular Diminished 5th or Augmented 4th occurs in only 1 major key (EX: the minor 2nd E-F occurs in 2 major keys [C and F]= The Major 3rd C-E occurs in 3 major keys [C, F, and G]= HOWEVER, the Diminished 5th B-F (and the Augmented 4th F-B), unlike any other interval, occurs in 1 Major Key [C-major]) |
| Major Scale: Tritone | (Means 3 whole steps) Is the name of the Augmented 4th in the Major Scale (=Thus, F-G, G-A, and A-B)= Strictly speaking, the diminished 5th is not a TRITONE, for it contains NOT 3 whole steps but a Diatonic Half Step, 2 WHole steps, and Another Diatonic Half Step (B-C, C-D, D-E, and E-F)= However, for convenience, the term "TRITONE" is often used to mean the Diminished 5th as well as the Augmented 4th) |
| Minor Scale: Describe the Diminished 5th | Lies between scale degrees 2 and 6 |
| Minor Scale: Describe the Augmented 4th | Lies between scale degrees 6 and 2 |
| Minor Scale: What does the Diminished 5th and Augmented 4th resolve to? | Resolve to scale degree 3 and 5, expressed as a 3rd (Resolution of Diminished 5th) or as a 6th (resolution of Augmented 4th) |
| Minor Scale: How well does the resolution of an Diminished 5th and Augmented 4th define the key? | Although scale degrees 3 and 5 are members of the tonic triad, these resolutions do not define the key nearly as successfully as do the corresponding resolutions to scale degrees 1 and 3 in Major= When scale degrees 3 and 5 are heard without scale degree 1, scale degree 3 tends to be heard as the root of a triad= RESULT: It is partly because of this implication that the minor mode tends to gravitate to its MEDIANT DEGREE (or Relative Major) |
| What is the result of raising scale degree 7 in the Harmonic and Melodic Minor? | Creates an "artificial" tritone between scale degrees 4 and 7 that resolves to scale degrees 1 and 3 as in Major= The use of this Tritone (or Diminished 5th) lends to Minor the clear definition of the key that occurs naturally in Major |
| What is the result of the raised scale degree 6 in the Ascending Melodic Minor Scale? | Creates another Tritone (in this case with scale degree 3)= This tritone occurs much less often than the other two and has no significant influence on key definition |
| Describe the interval between raised scale degree 7 and natural scale degree 6 in the Harmonic Minor | Is a Diminished 7th= Inverted, it becomes an augmented 2nd= Like all Diminished and Augmented Intervals, these are DISSONANT |
| What does the Diminished 7th and Augmented 2nd resolve to? | They resolve to scale degrees 1 and 5 |
| Between the Diminished 7th and Augmented 2nd, which is more useful? Why? | The Diminished 7th is more useful because it resolves to a 5th= The interval of the 4th (to which the Augmented 2nd resolves) is itself often dissonant= Therefore, the Augmented 2nd cannot occur very freely |
| When is an Augmented 2nd used? | Because the interval of the 4th (to which the augmented 2nd resolves) is itself often dissonant, the augmented 2nd cannot occur very freely= RULE: It is used in those situations where the 4th to which it resolves is consonant |
| Describe the Key-Defining Power of the Diminished 7th and Augmented 2nd | This pair of dissonant intervals has a very strong Key-Defining Power= The resolution to scale degrees 1 and 5 points out the location of the tonic= Also, among the intervals in Major and Minor Scales, the Diminished 7th and Augmented 2nd appear ONLY between raised scale degree 7 and natural scale degree 6 (EX: The Diminished 7th [C#-Bb] immediately points to D as tonic, for no other tonic can generate this particular interval) |
| What is the result of the Diminished 7th's Powers of Key-Definition? | The Diminished 7th often appears in Major as a consequence of MIXTURE |
| Describe the Augmented 5th and Diminished 4th | These intervals occur in the inflected forms of Minor= These intervals arise from the combination of scale degree 3 and raised scale degree 7 |
| Describe the Diminished 3rd and Augmented 6th | Is the product of chromaticism= These intervals normally come about as a consequence of raising scale degree 4 in Minor= The intervals between raised scale degree 4 and natural scale degree 6 are the Diminished 3rd and Augmented 6th (EX: Raised scale degree 4 functions as a Lower Neighbor to scale degree 5, or as a Chromatic Passing Tone leading from scale degree 4 to 5) |
| Describe the Diminished Octave and Augmented 3rd | (Is a result of Chromaticism) Are formed by melodic ornamentation in one of the parts= The intervals are mere by-products of this ornamentation |
| What does the use of Enharmonically Equivalent tones make possible? | Makes it possible to construct 2 intervals of different size and quality, but whose tones have the same pitch in tempered tuning |
| How many diminished 5ths and augmented 4ths are in major and natural minor? | There is only one diminished 5th and only one augmented 4th |
| Major: Diminished 5th and Augmented 4th | In major, the diminished 5th occurs between scale degrees 7 and 4= The Augmented 4th lies between scale degrees 4 and 7 |
| Major: Resolution of the Diminished 5th and Augmented 4th | (Scale degree 4 resolves to 3 and scale degree 7 resolves to 1) The d5 resolves by moving in to a 3rd= The A4 resolves by moving out to a 6th |
| Minor: Diminished 5th and Augmented 4th | In minor, the diminished 5th lies between s.d. 2 and 6= The augmented 4th lies between s.d. 6 and 2 |
| Minor: Resolution of the Diminished 5th and Augmented 4th | (Scale degree 2 resolves to 3 and scale degree 6 resolves to 5) The resolution of the d5 goes to a 3rd and the resolution of the A4 goes to a 6th |
