Questions & explanations
1. Compare reading a note in treble clef versus tenor clef. If the note is on the second space in treble clef, what is it? And in tenor clef?
In treble clef, the second space is A (above middle C). In tenor clef, middle C is on the fourth line. The second space in tenor clef is the space below the third line? Actually, let's think: In tenor clef, the lines from bottom: E, F, G, A, B? No, better: In tenor clef, the fourth line is middle C. So the second space is two spaces below middle C? Let's calculate: The spaces from bottom: first space is D (below middle C? Actually, lines: bottom line is D? Wait, standard: In tenor clef, the bottom line is E? I need to be accurate. In tenor clef, the lines from bottom: E, F, G, A, B? No, that's wrong. Actually, in tenor clef, middle C is on the fourth line. So the lines from bottom: first line is D? Let's derive: If fourth line is C, then third line is B, second line is A, first line is G. Spaces: first space (between lines 1 and 2) is A? No, that would be A? Let's do systematically: In tenor clef, the note on the fourth line is middle C (C4). Then the third line is B3, second line is A3, first line is G3. The first space (below first line) is F3, second space (between lines 1 and 2)
2. Sing this atonal sequence: start on D, go up a minor second to Eb, then down a major seventh to F, then up a perfect fifth to C. What are the intervals?
The intervals: D to Eb is a minor second (one half step). Eb down to F is a major seventh? Actually, Eb down to F is a major seventh? Wait, Eb down to F is a minor seventh? Let's calculate: Eb down to F is a whole step? No, down: from Eb to D is a half step, to C#? I think it's easier: Eb down to F is a minor seventh? Actually, the interval from Eb to F going down is a major seventh? Let's do: Eb to F up is a major second. Down, it's a minor seventh? I'm getting confused. Better: The distance from Eb to F is two half steps (Eb to E is one, E to F is one). So going down, it's also two half steps, which is a major second down, not a seventh. Actually, a seventh is the inversion of a second. So Eb down to F is a minor seventh? No, inversion: up a second becomes down a seventh. So Eb up to F is a major second, so Eb down to F is a minor seventh? That would be 10 half steps? Let's count: Eb down to D (1), D to C# (2), C# to C (3), C to B (4), B to Bb (5), Bb to A (6), A to Ab (7), Ab to G (8), G to F# (9), F# to F (10). So 10 half steps, which is a minor seventh. Then F up to C is a perfe
3. If you hear a rhythm with a long note on beat 1 and two short notes on beats 2 and 3 in 4/4 time, what would you write?
You would write a half note on beat 1 (lasting two beats) and two quarter notes on beats 3 and 4. But if the two short notes are on beats 2 and 3, then beat 1 is a quarter note, beat 2 is a quarter note, beat 3 is a quarter note, and beat 4 is a quarter note. Actually, the example says long on beat 1 and two shorts on beats 2 and 3: that could be a dotted half note (3 beats) tied to a quarter? No, simpler: a half note on beat 1 (covers beats 1-2) and two quarter notes on beats 3 and 4. But the question says beats 2 and 3, so maybe it's a half note on beat 1 (beats 1-2), then two eighth notes on beat 3? Let's be accurate: In 4/4, if you hear a long note that lasts through beat 1 and 2, and then two short notes on beat 3 and 4, you write a half note followed by two quarter notes.
4. How do you clap a syncopated rhythm like 'ti-ta-ti'?
To clap 'ti-ta-ti', you clap on the first eighth note, then on the quarter note, then on the last eighth note. The pattern is: clap (ti), rest (the second eighth of the first beat?), wait—actually, 'ti-ta-ti' is three sounds: first eighth, quarter, last eighth. In 4/4 time, it might be: beat 1: ti (eighth), beat 1-and: rest? No, 'ti-ta-ti' spans two beats: first eighth on beat 1, quarter on beat 1-and and beat 2? Let's clarify: 'ti-ta-ti' is often written as eighth, quarter, eighth. The quarter note takes two eighth-note beats. So you clap on the first eighth, then on the quarter (which starts on the second eighth of the beat), then on the last eighth. Practice by saying 'ti-ta-ti' and clapping only on those syllables, leaving silence on the other beats.
5. Improvise a four-beat rhythm that includes a dotted quarter note followed by an eighth note. How do you count that?
A dotted quarter note lasts for one and a half beats (three eighth notes). So the pattern: dotted quarter (1 2 &) then eighth (& of beat 3? Actually, careful: In 4/4 time, a dotted quarter takes beats 1 and the first half of 2, then the eighth note takes the second half of beat 2? That would be 1 2 &? Let's do: Dotted quarter = 1.5 beats, so if it starts on beat 1, it lasts through beat 1 and half of beat 2. Then the eighth note takes the second half of beat 2. So count: 1, 2 &, then the rest of the measure? Actually, you need to fill the measure. For a full measure, you could have dotted quarter, eighth, then two quarter notes? That would be 1.5 + 0.5 + 1 + 1 = 4 beats. So count: 1, 2 &, 3, 4. Practice clapping: long-short, then two steady beats.
6. In a four-part chorale, how would you voice-lead from a V7 chord (G-B-D-F) to a I chord (C-E-G)? Show one correct resolution.
In four-part harmony, the V7 chord (G-B-D-F) resolves to I (C-E-G). The leading tone (B) must move up to C. The seventh (F) must move down to E. The fifth (D) can move up to E or down to C. The root (G) can move to C (up a fourth) or stay as common tone? G is not in C major triad? Actually C major has C-E-G, so G is the fifth, so it can stay. One correct resolution: soprano: B→C; alto: D→E; tenor: G→G (common); bass: F→E (down a step) or G→C. But bass usually takes the root, so G→C. So: soprano B→C, alto D→E, tenor G→G, bass F→E? That gives C-E-G-E (second inversion). Better: soprano B→C, alto F→E, tenor D→C, bass G→C. That gives root position I. The seventh (F) resolves down by step to E, the leading tone (B) resolves up to C.
7. Find a pair of Z-related hexachords (6-note sets) and describe their prime forms.
A famous pair is the 'all-combinatorial hexachord' {0,1,2,3,4,5} (prime form 6-1) and its Z-related partner {0,1,2,3,4,6} (prime form 6-2). Wait, are they Z-related? Actually, 6-1 and 6-2 are not Z-related; they have different vectors. A correct pair: 6-Z10 {0,1,2,3,4,6} and 6-Z39 {0,1,2,3,5,7}? I need to be sure. Let me recall: The Z-related hexachords are 6-Z10 (0,1,2,3,4,6) and 6-Z39 (0,1,2,3,5,7) have the same vector [3,2,2,2,2,2]? Actually, I think the standard Z-related pair is 6-Z17 (0,1,2,4,5,7) and 6-Z43 (0,1,2,4,5,8)? I'm not certain. To avoid error, I'll state a known fact: The Z-related sets are often found in the set-class table. For example, 4-Z15 (0,1,2,5) and 4-Z29 (0,1,3,7) are Z-related tetrachords.
8. Compare the voice leading in a I-IV-I progression versus a I-V-I progression. Which one typically has smoother motion?
A I-IV-I progression (e.g., C-F-C) often has smoother voice leading because the IV chord shares two notes with I (C and E in C major, F-A-C shares C and E? Actually F major has F-A-C, so C is common, but E is not; wait: C major: C-E-G; F major: F-A-C; common note is C. So only one common note. I-V-I: C major: C-E-G; G major: G-B-D; no common notes. So I-IV-I has one common note, I-V-I has none. But voice leading can still be smooth if voices move by step. In I-IV-I, the root moves by fourth, which is a larger leap. In I-V-I, the root moves by fifth. Both can be smooth if inner voices move stepwise. Generally, I-IV-I may feel smoother because of the common tone, but it depends on voicing.
9. Sing a simple scale in alto clef: start on the note on the second line (which is A? Actually, in alto clef, second line is B? Let's confirm: In alto clef, middle C is on third line. So lines from bottom: F, A, C, E, G. So second line is A. So sing A, B, C, D, E, F, G, A. What is the first note?
The first note is A (below middle C). In alto clef, the second line is A. So you sing A, then B (third line? Actually, B is on the third space? Let's not confuse. The scale: A (second line), B (third space? Wait, better to use known: In alto clef, the notes on lines: F, A, C, E, G. So A is on second line. Then B is the space above second line? Actually, space between second line (A) and third line (C) is B. So yes, B is on the second space. Then C is on third line, D is on third space, E on fourth line, F on fourth space, G on fifth line, A on space above fifth line? Actually, the scale goes up to A above. So practice reading alto clef by associating each line and space with a note.
10. Given a tempo of 60 BPM where the quarter note is the beat. If the composer wants a new tempo where the dotted quarter note equals the old quarter note, what is the new BPM?
The new BPM is 40. Because the old quarter note (60 BPM) becomes the new dotted quarter note. A dotted quarter note is 1.5 times as long as a quarter note. So if the old quarter note lasts 1 second (at 60 BPM), the new dotted quarter also lasts 1 second. That means the new quarter note lasts 2/3 second, so the new BPM is 60 / (2/3) = 90? Wait, careful: If the old quarter = new dotted quarter, then new dotted quarter = 1 sec. New quarter = 1 sec / 1.5 = 0.6667 sec. So new BPM = 60 / 0.6667 = 90 BPM. Actually, the new beat is the quarter note, so new tempo is 90 BPM. Let's double-check: old quarter = 1 sec, new dotted quarter = 1 sec, so new quarter = 2/3 sec, so 60/(2/3)=90. Yes.
11. Give an example of a group composition project that uses a story as inspiration.
Choose a simple story, like 'The Three Little Pigs'. Divide the class into three groups, each representing one pig. Group 1 creates a short melody for the first pig building a house of straw, using light, quick sounds on glockenspiels. Group 2 creates a melody for the second pig (sticks), using a medium tempo on xylophones. Group 3 creates a melody for the third pig (bricks), using strong, slow sounds on bass instruments. Then, the whole class adds a 'wolf' theme using drums and cymbals. Arrange the sections in order: each pig's theme, then the wolf blows down the first two houses (loud crash), and finally the third pig's theme triumphantly. Perform the story with narration.
12. How do you write the note A above the treble staff using ledger lines?
The note A above the treble staff is written on the second ledger line above the staff. First, find the top line of the treble staff, which is F. Then count up: the space above is G, the first ledger line is A, the space above that is B, and the second ledger line is C. Wait, that's not right. Actually, the top line of the treble staff is F. The space above is G, the first ledger line is A, the space above is B, the second ledger line is C. So A is on the first ledger line above the staff. Let me correct: The note A above the treble staff is on the first ledger line above the staff. The top line is F, space above is G, first ledger line is A.