Music Theory Q & A

Current Answer Source: Jeff Evans

© 2006, 2007, 2008 Ars Nova Software, LLC

If you have a music theory or other music-related question please visit our question form. If I know the answer or can convincingly pretend to know the answer it will appear below. Questions will be edited according to my own whims and arbitrary judgements. Your name will not appear unless you really insist. Answers appearing below carry no warranty of any kind but may be useful in dinner conversation.

1: D# vs. Eb. Keywords: enharmonic
2: Cambiata in 3rd species. Keywords: Counterpoint
3: The Neapolitan chord. Keywords: harmony, altered chords
4 When to beam notes. Keywords: notation, beaming
5: Hearing the difference between 2/2 and 4/4, etc. Keywords: meter, beat
6: Slur combined with staccato?? Keywords: articulation
7: What's a tritone?? Keywords: intervals, counterpoint
8: Modulation vs. key change. Keywords: harmony
9: Why no B# or E# in the scale? Keywords: diatonic, chromatic
10: Are there any easier-to-learn forms of music notation? Keywords: staff, shape notes, solfege
11: Can you elaborate on the use of rhythm in Bartok's Mikrokosmos no. 148? Keywords: Bulgarian rhythm
12: What is a cadence? Keywords: harmony, phrase
13: What is cambiata? Keywords: counterpoint
14: A mysterious pair of notes - half notes beamed together? Keywords: bowed tremolo, notation
15: What does "plena voce" mean? Keywords: performance instructions
16: Please explain the circle of fifths... Keywords: intervals, key signature
17: Please explain "The Dominant Triads." Keywords: harmony
18: What is the difference between a parallel minor and a relative minor? Keywords: key signature
19: How do you recognize an interval? Keywords: ear training, notation
20: What is the difference between a chord in major and a chord in minor? Keywords: harmony, triad
21: What is a closed Chord? Keywords: chord voicing, chord position
22: Hand signs for solfege? Keywords: diatonic, scale
23: How do you tell which notes in a melody determine the chords? Keywords: harmonize, harmony
24: How to analyze the chord E D A B E? Keywords: harmonic analysis
25: Meaning of numbers 6/5, 4/3, 4/2, etc.? Keywords: figured bass, thoroughbass, harmonic analysis
26: Can you tell me how leading tones work? Keywords: counterpoint, harmony, scale
27: Please explain the terms "ostinato" and "drone" Keywords: composition
28: Should E# be played on the F# key if F# is in the key signature? Keywords: enharmonics, key signature, accidentals
29: Repeat bars within a measure Keywords: meter, pickup note, barline, repeat
30: Spelling a given scale in Sol-Fa Keywords: Solfege, scale, Fixed-Do, Moveable-Do
31: Why do most musical scales start on C?Keywords: Scale, Key
32: Should I take music theory? Why do orchestra parts keep changing clef? Why are the instruments in different keys? Keywords: Music Theory, Transposing instruments, Range, Clef
33: Could you please give me information about rests in music theory? Keywords: Rests, rhythm, notation
34: How would one play a piano chord with a book notation of G/B? Keywords: Chords, harmony, chord inversion
35: Where do the 5 tones with hand symbols in the movie "Close Encounters of the Third Kind" come from? Keywords: Solfege, Curwen, partial series, scale
36: How do you notate a 16th-8th-16th note combination on one beam? Keywords: Beaming, rhythm, meter, notation
37: What is a sixth chord? Keywords: harmony, sixth chord

1. Q: I still don't get why it matters whether I call the middle note "D#" or "Eb" when writing a C minor chord. Aren't these the same pitch in practice? - D.E.

A: They're the same pitch on a fixed-pitch "equal-tempered" instrument like the piano but not necessarily the same pitch on instruments with free intonation, like the violin. Perhaps more importantly, the two different notes have different implications for the harmony. If the reader is to understand that this is meant to state the c minor harmony then the middle note must be Eb because that creates a visual triad. A D# would imply that you are not actually intending a c minor harmony but are attempting to do something else, perhaps moving though some kind of modulation to a different key. The music becomes harder to understand and is also harder to read; it would be comparable to mispelling words arbitrarily when writing a story. Notes that sound the same on the piano but are "spelled differently" in notation are known as enharmonic equivalents. The only purpose of notation is to convey your meaning, and the choice of enharmonic is part of the meaning.

Melodically there are differences, too: because a leap from C to D# is an "augmented second" a player will instinctively think that this is being treated as leading to E natural. A violinist might raise the D# a little extra to enhance that. But a C to Eb doesn't carry that implication of upward movement, and there is no temptation to stretch the pitch. One would expect an Eb after a C to either to be stable or else move to D. These are subtle things, but worth observing because they enhance the meaning of the music.

2. Q: I'm afraid I'm not clear on the relationship between the bass and the use of the cambiata. You state that in 3rd species it wouldn't be possible to place a cambiata in that measure (see example). How can I tell (regarding the bass) when I can and cannot use a cambiata. -R.G.

A: The short answer is that in a 3rd species exercise (4 notes against 1 of the cantus) a cambiata must begin on an octave if it is written above the cantus, and it must begin at the interval of a 3rd (or 10th, etc.) if written below the cantus. This is because the classical cambiata consists of 4 notes in which the 1st, 3rd and 4th notes are consonant. If you try a few experiments you'll see that a cambiata above a given bass must start on the octave to meet those requirements. And when written below it must start with a third (or third plus octaves, i.e. 10ths: same thing really). The classical cambiata is a second down to a dissonant tone, then a downward leap of a third, followed by an upward second. The 4th note is like a delayed resolution of the dissonance in the second note.

In free counterpoint the possibilities multiply because the bass doesn't have to stay the same; it can move to a different pitch before the cambiata finishes. So in free counterpoint a cambiata can begin on any consonance.

Q: Is it OK to hold hands in the hallway? - L.P.

A: Certainly, if they're your own hands.

[Editor's note: this question got in here by accident. Won't happen again.]

3. Q: What's the difference between a Neapolitan chord and a major triad? They sure look like the same thing. - F.H.

A: There's no difference if you're just looking looking at the chord all by itself. But a Neapolitan chord is a major triad whose root is the lowered second degree of the key (e.g., in A major it would be a Bb major triad). It is used as a way of approaching the V chord - most commonly when in a minor key. And it's usually in first inversion. Main thing to remember in voicing the Neapolitan chord is that its root is the upper leading tone of the tonic note and it wants to go home. So whatever voice has that lowered second degree should be the one that moves to the tonic. With typical Neapolitans it often gets there by way of a temporary detour to the leading tone, like below (tonic is A in this example):

4.Q: Sometimes two eighth notes are beamed together, sometimes not, sometimes 3 are beamed together, or 4 - what difference does it make? There must be some logic to this.- M.E.

A: In music it is not a sure thing that logic will be involved. But for beaming notes some logic is available, though you'll still sometimes find notes beamed capriciously. First there's the kind of beaming traditionally used for vocal music: notes sung to the same syllable are beamed together if they are eighth notes or less. But separate syllables are not beamed, as below:

Then there is instrumental practice, which is what you'll see most often. I like the instrumental practice even for vocal music, though tastes differ. In music for instruments the usual thing is to beam in such a way that the beat groups are clear. If two eighths are on the same beat then they are beamed together. In 2/2 time, where the beat has the value of 4 eighth notes, you'd beam 4 of them together. Here enters a matter of personal taste: even in 4/4, where one beat is worth 2 eighth notes, you'll often see 4 eighths beamed together. And that's good - if they are either the first or the last half of the measure (i.e., not crossing the center of the measure). That way the basic nature of the meter is reflected in the beaming: a 4/4 measure divides naturally at its middle with the start of the 3rd beat, the second-most important beat in a 4/4 measure. But if the meter is a compound 6/8 (beat equals a dotted quarter, equal to 3 eighth notes) then you'd beam in threes so that the beat is easy to see. Good notation is all about communication: the point is to make it easy to read and to understand the composer's intentions.

There's a discussion of this with more examples on pages 16-17 of Exploring Theory.

5. Q: When listening, how can you tell the difference between 2/2 and 4/4? Or 3/4 and 6/8? - P.C.

A: Often you can't tell the difference between 2/2 and 4/4, and sometimes it may appear that the composer made the choice for no other reason than simplicity in notation (writing fast eighth notes instead of sixteenths, perhaps). However, here are some principles that would help in making a guess: 4/4 implies, of course, 4 beats per measure, and this will tend to mean more "events" in the measure. Measures in 2/2 will most often tend to divide clearly in two parts - producing a feeling of two beats. This can relate to harmonic rhythm (speed of chord changes) or to melodic accents. In this 2/2 excerpt from Mozart, for example, six of the first eight measures have two chord changes per bar, with each measure dividing nicely in half:

Most of the time the melodic accents are also only on the first and third quarter notes of each bar - if you tap your foot with this music it feels natural to tap twice per bar.

This 4/4 example from the same composer has only one chord change in each bar, but the melodic accents produced by leaps and/or dissonances produce a feeling of four events in each bar. In particular you'll notice that there's often a melodic accent on fourth quarter of the measure, as in the first full measure and the measure following - that would not be typical of 2/2.

Similarly, two measures of a fast 3/4 might be confused with one measure of a slow 6/8. But a 3/4 is more likely to have a chord change or other emphasis on the third quarter - whereas a normal fast 6/8 will rarely have a chord change on the third eighth of three. The beat in 6/8 is two to a bar, counted by the dotted quarter note.

6. Q: What does it mean when you see notes that are slurred together and also have staccato dots? Seems kind of contradictory. - M.M.

A: A mark like that is most appropriate for string instruments, which will then play those notes all on the same bowstroke but separated. You may see a similar indication in piano music, and the intention then is to imitate what strings would do: join the notes but not completely. It's called portato and could be described as an effect midway between legato (smoothly joined) and staccato (completely separated).

7. Q: What's a tritone? I've heard this was considered dangerous music and banned by the church in the middle ages. - J.P.

A: Strictly speaking, it's an augmented fourth (such as C up to F#), and is called that because it's three whole scale tones in succession (for example, C-D, D-E, E-F#). But a diminished fifth (such as F# up to C) is just a tritone turned upside-down (inverted) and is treated in traditional music with the same care as the tritone. The tritone was in traditional counterpoint studies known as "the devil in music," and was avoided as a difficult-to-sing-in-tune awkward melodic interval. You may read stories at unreliable internet sources about this interval being "banned by the Catholic Church" but really it just presented a technical problem in composition and performance, and so the style "rules" studied by budding musicians advised that one should not use it. Nonetheless, it was used on occasion, and some theorists thought it useful when handled well.

Leonard Bernstein made a little joke out of this in West Side Story - in particular with his song "Maria," whose melody begins with a tritone, Eb-A, that is lovingly repeated.

If you're not sure how to identify an augmented fourth (or any other interval) remember that Practica Musica will identify any interval for you if you just play the notes on the screen piano when in Practice mode. Or enter the notes on the staff (same thing works for chords). If you need to choose specific flats or sharps you might find it easiest to use the "enharmonic keyboard" in which each key is divided up into sharps and flats.

More history, whether you want it or not: a line used to remember the tritone rule was "Mi contra Fa, Diabolus in Musica." That's the origin of the "devil in music" story; this has nothing to do with the church. The Mi and Fa don't refer to the third and fourth notes of a modern major scale (as in Do, Re, Mi, Fa), either: the reference goes back to medieval use of overlapping hexachords (six note scales) as an organizing principle for the gamut of tones that make up music. The Mi of any particular hexachord forms a tritone with the Fa of the next following hexachord. For example, the hexachord on G is followed by the hexachord on C, and the Mi of the G hexachord (B) forms a tritone with the Fa of the C hexachord (F). Similarly, the Mi of the C hexachord (E) forms a tritone with the Fa (Bb)of the next hexachord, which begins on F. There's an excellent article on the Tritone at Wikipedia that will provide as much detail as anyone could desire.

8. Q: What's the difference between a modulation and a key change? - S.P.

A: Sometimes people use these terms interchangeably, but I think it's better to reserve the term "modulation" for a prepared key change, as opposed to an abrupt switch to a new key. Typically the modulation will involve a pivot chord that is found in both keys. For example, in C major one could write I, IV, V, I, ii, V, then alter the ii to a major triad or a major triad with a seventh. The new II7 chord now sounds like a V7 in the key of G, and the I that preceded it now seems like a IV in the new key - the I/IV is the pivot. Another method of modulation is to change the function of a diminished seventh chord: changing the names (but not the actual pitches) of some notes so that, for example, what was a vii dim 7 in the key of C becomes a vii dim 7 in a different key - the vii dim 7 is very flexible this way.

An abrupt key change is a device sometimes found in popular song, in which a verse might be repeated but with melody and harmony all moved up a step. The key changes, but it's not really a modulation. Think of this as being like rectangles and squares: not all rectangles are squares, but every square is a rectangle. Not all key changes involve modulation, but every modulation is a key change. Finally, not every change of key requires a change of key signature. A key signature is a convenience for reading since it cuts down on the number of accidentals, but many pieces change key without any change of signature.

9. Q: Why is there no B# or E# in the musical scale? - M.L.B.

A: Scales are patterns of steps, not specific pitches. A major scale, for example, consists of these steps: whole, whole, half, whole, whole, whole. If you begin on C it's a "C major scale" and you're in the "key of C." Depending on the pitch you choose to start the pattern with, any pitch is a possible member of the scale. But people are often curious about pitches like B# and E# (and Cb and Fb) because the only way to play them on the piano is to use a white key: C for B# and so on. So the question arises: why do we bother with pitches like that anyway?

Most familiar melodies are based on the pattern of whole and half steps found in the major scale. That pattern is represented by the white keys of the piano and also by the natural notes on the staff. If you start on the right pitch you can play many melodies on the white keys only: start on E to play the famous choral theme from Beethoven's 9th Symphony, or on C to play the Beatles' "She loves you," or on G for "Home on the Range." (If you're learning to improvise tunes, try playing just on the white keys for a start).

The pattern formed by those seven notes C, D, E, F, G, A, B is the major scale: whole step, whole step, half step, whole step, whole step, whole step. Start on A and you get the natural minor pattern, A, B, C, D, E, F, G. But suppose you want to play something using that same pattern of steps but starting higher or lower? If that's what you want, you'll need to add some in-between notes, which are represented by the black keys. To play the major pattern starting on F, for example, you'll need to add a Bb, a lower form of B, between the A and the B. To play it starting on G you'll need to use a higher F, F#. This is the origin of the black keys, which are now found between every pair of white keys that is separated by a whole step.

Between B and C and between E and F there is just a half step - no room there for a black key. But there is a reason to have a "B#" and an "E#." For just one example, if you have written a G# in your music and want to make it the root of a major harmony you'll need a major third above it. A third brings you to the third letter, B, but to be major (4 half steps wide) it has to be a raised B: B#. You can't write C as a substitute because that wouldn't be a major harmony; it would confuse the band. C would be a diminished fourth above G# and would have different musical implications.

Since there's no black key between B and C you'll be playing that B# on the same piano key used for C, but that's part of the compromise that makes the piano workable. There was a time when musicians tried making keyboards with separate keys for B# and C, Fb and E, F# and Gb, and all the others, each tuned slightly different - but such keyboards were expensive to make and difficult to use - some had 53 keys to the octave. Musicians compromised by tuning just 12 keys in such a way that C could pass for B#, and so on.

To sum up: B# and E# can indeed be part of a scale, depending on the tonic (starting note) of the scale.

10. Q: The way we write music is beautiful and ornate, but complex and hard for some of us to process mentally. Some of us who can play by ear do not arrive at sight-reading music after years of practice and exposure. Are there any ways of writing music that reveal the rhythm and pitch in a more graphical manner than the standard way we write music? A method of writing music that might connect with the way those who play by ear conceptualize music?- C.B.

A:This is kind of a long one. Good, though.

The current system of music notation is the result of a long evolutionary process, and it seems to me that, like the shape of a dolphin, it exists in its present form only because it was found to be efficient. There are alternative or at least supplementary systems, though, as I'll describe below.

There are basically two elements that one would need to record in keeping a record of music: pitch and rhythm. Pitch was originally notated roughly, just squiggles above written words to remind the singer where the melody rose and where it fell. Eventually these were made more precise with staff lines, and the innovations of the Ars Nova in the 14th century (see the connection?) added the ability to record rhythmic information as well. Since then we've had six more centuries of improvement, but the result follows the same principle as the earliest forms: musical tones are represented by graphical symbols whose vertical position tells their pitch and whose shape tells their rhythm.

One might complain that standard notation doesn't reveal all possible information: in actual performance musicians will stretch or contract the time here and there, and maybe even the pitch, but then the notation has the great advantage of being readable. The more information conveyed, the more difficult is the reading. Standard notation has apparently found a pretty good balance: it increases readability by assuming that the reader knows the basic scale steps represented by the staff and has a feeling for the beat (just imagine if it told the pitch in terms of frequency and the rhythm in terms of milliseconds!)

There are some alternatives, but the most successful tend to build on standard notation. Shape notes have the familiar staff lines and clefs and rhythmic system, but note heads come in triangles, squares, etc. to tell which scale tone is represented by that note. Shape notes have been shown to be useful in teaching children, and are traditionally used by adults in some churches, but shape notation is harder to write, especially by hand, and it has the disadvantage of being limited to music that stays in the major or minor scale. On the other hand, for simple music it can be written without staff lines. Even better, singers who know the solfege syllables can quickly learn to read the pitches, while those can read standard notation alone can ignore the shapes, so it has a real practical advantage in vocal music meant to be performed by untrained singers. Here's the start of Amazing Grace as presented in an old hymn book:

(We've added support for Shape Notes to Songworks with version 2.725. Songworks will automatically pick the correct shape for each note if you'd like to try printing music with shape notes - see the online user manual page on shape notes).

Tonic sol-fa is another alternative system with a considerable history, but it, too is less adaptable than standard notation. Tonic sol-fa can also be combined with standard notation, and uses only text symbols. The scale notes Do, Re, Mi, Fa, Sol, La, Ti are represented by their initials, while a system of colons, dashes, etc. tell the rhythm. This is of course less graphic than standard notation and I personally find it harder to read.

Though we have some useful additions to standard notation no one has come up with a system that works more efficiently, and I think this is another instance of organic evolutionary design winning over invention. It would take a real genius to come up with the shape and physiology of the dolphin, but nature accomplished this by trial and error. Current music notation was arrived at by a similar process of trial and error, and I think it's here to stay. From time to time improvements may appear, the innovations that work will be retained, and the system will continue to evolve as it always has, incrementally.

So the short version is no: I don't think there are other ways of writing music that work better to reveal pitch and rhythm. And if one were invented it would be very difficult to overcome the fact that millions of pages of music are written in the current system and millions of musicians know how to read them. But if one learns the basis of staff notation in a step-by-step manner, perhaps doing natural pitch first, then simple rhythm, then sharps and flats, more complex rhythm, etc., it is not so difficult a task as many imagine it to be.

UPDATE: an exchange on this topic with one of our readers.

11. Q: Can you elaborate on the use of rhythm in Bartok's Mikrokosmos no. 148? K.D.

A: You wouldn't be just pulling my chain, would you? I have a feeling you're handing me your assigned essay topic. Those would be Bartok's Six Dances in Bulgarian Rhythm - how about if I just talk a little about Bulgarian Rhythm, which may be of more general interest?

"Bulgarian rhythm" is the use of asymmetrical rhythm groups within measures, particularly in a fast tempo. In Bartok's own words, "'Bulgarian' rhythm comes about when very quick rhythmic values (MM 300-400 or more) are grouped asymmetrically thus, e.g. such as 4+2+3 (and not 3+3+3!)."

Bartok sometimes indicates the irregular grouping by using an "additive time signature" for example, 4+2+3 /16 instead of 9/16. But an additive signature is not essential to Bulgarian rhythm. For example, the meter signature could be 9/16 grouped as above, or 8/16 with the notes grouped as 3 + 3 + 2 instead of the expected two groups of 4 (see below for an example).

What is "very quick"? The typical meter for Bulgarian rhythm is based on 16ths, and it is the 16ths that Bartok is referring to as moving at a metronome speed of 300 to 400. He also likes 8ths as a basic unit, but if the meter signature is based on 16ths you could set the quarter note speed to between 90 and 100 in our software to get the 16ths speed he's recommending.

An old friend of mine is a Bulgarian and I am assured that though he is not personally asymmetrical, this rhythmic device is not misnamed; it really does derive from traditional music in that country. You hear it in popular tunes like Shto Mi E Milo, whose tune has the pattern 3 + 3 + 2 and could be notated like this:

It's a charming sound, jagged and surprising (double-click the image of the music to hear it).

12. Q: What is a cadence? A.S.

A:I can hardly improve on Willi Apel in his Harvard Dictionary of Music: a cadence is "A melodic or harmonic formula that occurs at the end of a composition, a section, or a phrase, conveying the impression of a momentary or permanent conclusion." The important part of Apel's definition is the reference to the "end of a composition... or phrase." Any piece of tonal music will have lots of places where the real or implied harmony would be a dominant chord (V) followed by a tonic chord (I or i) but that harmonic change is a cadence only if it's at the end of a musical phrase.

We'll need a few examples.

A very final sort of cadence is one that presents or at least implies in its melody the movement V-I or V-i (the chord built on the 5th or dominant degree of the scale, followed by the tonic chord). That's the authentic cadence. There's also the half cadence, which ends on the V chord and feels "unfinished." And there's the plagal cadence, also called the "amen" cadence, of IV - I. You could distinguish further subtypes of these, but mainly you need to be aware of the authentic, the half, and the plagal cadences. The following tune ought to be familiar (if not, it's in the traditional songs section of our Music Library). The first phrase ends with a half cadence:

And the next phrase has a more conclusive-sounding authentic cadence:

As for the plagal cadence, just think of "amen" - if you've ever been in a church you'll know that one. In the key of C you'd play the chord F (IV) and then I (C). The melody will usually move from F to E, the middle note of the C chord.

13. Q: What is cambiata? A.S.

A: This one is described in the manual for our Counterpointer program:

Cambiata

The "cambiata," also called "changing tone," is an exception to the usual rule that dissonance should not be approached or left by leap (appoggiatura is another). The cambiata has four notes with a small leap between notes two and three. Both the 2nd and 3rd notes can be dissonant.

From the manual: "The cambiata is a figure that usually begins with a downward second to an unaccented note, then a downward third followed by an upward second to another unaccented note, so that it ends a third away from its beginning. Both the second and third notes can be dissonant."

The cambiata can, less commonly, also be inverted (so that the leap goes the other direction).

14. Q: A flute student has an audition piece that has an unusual marking...there is a measure that has two half notes connected with a beam as if they were 8th notes. Additionally, just above the beam is another beam, but not touching the note stems. So although it may appear at first to be 16th notes connected by a beam, they clearly are not. Any help??

A: What you're describing sounds like what on the violin would be called a fingered tremolo; shorthand for a tremolo on those two pitches, lasting for the time of two half notes. Below I've illustrated that as if it's a measured tremolo in 32nds, but the fact that the second beam doesn't contact the stems suggests it's meant to be an unmeasured flutter. If you're lucky the composer will have chosen two notes that can be played by changing just one finger.

15. Q: What does "plena voce" mean? - S.B.

A: Literally it means "full voice." It can be taken to mean singing in the full "chest voice," i.e. not falsetto (a high part might in old music be sung in a light high tone by a man singing falsetto (think the Beach Boys) or the same pitches could be sung by a tenor singing in plena voce (think Pavarotti). The term doesn't just apply to voice but can be extended by analogy to other instruments: the full sound of which the instrument is capable.

16. Q:Please explain the circle of fifths, first in the order played, and then the first note of each that is played (triad or root or inverted? Are they all played within the same octave, and do they progress naturally? - T.S.

A: The circle of fifths is a pedagogical device that illustrates the order in which key signatures add flats or sharps. It could as easily be drawn in a straight line, actually. Starting with C major the key signature has no sharps or flats. Go up one perfect fifth to G and the key of G major has one sharp. For each fifth you ascend from C another sharp is added to the key signature: D major has 2 sharps, A has 3, etc. When you reach C#, though, you need to stop because you now have seven sharps and that's as far as we go. In the other direction, go down a fifth from C and the major key on that note, F, has one flat. Another perfect fifth downward brings you to Bb major, which has two flats, and so on as before: Eb has 3, Ab has 4, etc. The downward direction ends at Cb with 7 flats.

tonic note:    Cb Gb Db Ab Eb Bb F  C  G  D  A  E  B  F# C#
key signature: 7b 6b 5b 4b 3b 2b 1b    1# 2# 3# 4# 5# 6# 7#

If you bend that chart into a circle you can overlap the last few in each direction: Db, with 5 flats, is enharmonically equivalent to C#, with 7 sharps, for example (that is, the two notes are on the same piano key but have different names). Gb is equivalent to F# and Bb is equivalent to A#. If the keyboard were to be tuned unequally these would not really be equivalent, and then the circle would have to be more of a spiral. But with the octave tuned in 12 equal steps as it is on modern instruments, the "enharmonic equivalents" sound exactly the same.

To remember the key signature for the major key on any tonic, count the perfect fifths from C to that note, ascending or descending.

From that you can also tell the key signature for the minor key of the same name: every minor key uses the key signature for the major key one minor third up. So A minor uses the C major key signature; D minor uses the F major signature, and so on. On the circle (or line as above) you can count left three steps (3 fifths) and that gets you to the same place: B minor will use the same key signature as D major.

The circle is therefore a list of tonics - the starting notes of all possible major scales - and their appropriate key signatures. The tonic of each scale is of course the root tone of the tonic triad for that key. The octave doesn't matter; this principle holds true for all octaves. Here's what the circle looks like in Exploring Theory with Practica Musica, with the minor keys included in an inner circle:

17. Q: Please explain "The Dominant Triads". I'm working in my theory book on Triads and finding it difficult. Thank you, M.Q.

A: The "perfect fifth" is the strongest interval in music, next to the octave. Two chords whose roots are separated by a perfect fifth have a close relationship. The tonic note of every scale has two such closely related triads: the one a fifth above the tonic is the dominant triad, and the one a fifth below is the subdominant.

So every tonic tone is the center of a trio of strongly related chords, for example, F...C...G, where C is the tonic, G the dominant, F the subdominant.

A dominant chord must be major, so that its middle tone is a half step away from the root of its partner triad and can "lead" back to the tonic. It's the 'leading tone." In the key of C, the leading tone is B, which is the middle tone of the G major chord.

The subdominant is the reverse: the tonic chord is a fifth above the subdominant and if the tonic is major it has just the same relationship to the subdominant as the dominant has to the tonic.

The leading effect of a dominant can be further enhanced by adding a minor seventh to the major triad. That's like adding another leading tone, this one seeming like it wants to move to the middle tone of the tonic triad. For example, G-B-D-F sets up a strong sense of movement to C-E-F. That's called a "dominant seventh chord."

In every key there is just one dominant seventh chord that can be spelled using the notes naturally available in the scale. In major keys it's the chord built on the dominant tone, a fifth above the tonic. You can alter other chords, though, to make them sound like a dominant. In C major you could change the normal d minor chord to major and it will start to sound like the dominant of G, a fifth below D. Add a seventh, making D-F#-A-C, and the effect is even stronger. That's a "secondary dominant" - a dominant chord made by altering notes in a chord that is not ordinarily a dominant. This can be used to modulate to another key, or just to give a particularly strong sense of movement, as in the progression C major, a minor, D dom7, G dom7, C major.

18. Q: What is the difference between a parallel minor and a relative minor?- K.B.

A: If you play the notes of a major scale but start on the 6th tone instead of the first, you'll hear the pattern of steps that defines the "natural minor scale." For example, the notes of the D major scale are D,E,F#,G,A,B,C#,D. Begin on B and play those same notes, and what you hear is B natural minor. So we say that B is the "relative minor" of D; it uses the same notes as D major. It will therefore have the same key signature as D major.

But if I want to make a minor scale that starts on the same pitch as a major scale, I'd have to use different notes to get that pattern of steps. A natural minor scale beginning on D would be D,E,F,G,A,Bb,C,D. That one would be called the "parallel minor" of D major: a minor scale that start on the same tonic as the major key. The parallel minor will always have a different key signature.

(Remember that in practice we usually raise the 7th degree of a minor scale and sometimes the 6th degree, too, forming the harmonic minor scale and the melodic minor scale. Those alterations are not part of the key signature. The key signature tells you the pitches of the natural minor and its corresponding major key).

To sum up: you find the relative minor of a major scale by counting up 6 scale steps (or, more easily, down 3) and playing the same pitches starting from there. To form the parallel minor you start on the same tonic but play different pitches. Major keys and their relative minor keys share the same key signature. Major keys and their parallel minor keys have different key signatures.

19. Q: How do you recognize an interval?- J.W.

A: That's a tough one. Do you mean visually, or aurally (by ear)?

Visually is pretty easy given the way the staff system works: from any line or space to the next adjoining line or space is always going to be some kind of "second" - two note names. Each line or space stands for a change in note name: A, B, C, D, E, F, G. From any line to the next line, or from any space to the next space, is always a third of some flavor - covering three note names. And so on.

Then to get the quality of the interval (major, minor, perfect, augmented, diminished) you have to be aware of how many half steps are included, and that's a little harder. It helps to learn to recognize the quality of the natural intervals in each clef, and then adjust if one of the notes is sharped or flatted.

Aural recognition is more difficult. Some people like to use familiar tunes as guides, for example the first two notes of "My Bonnie Lies Over the Ocean" form a major sixth. I don't think that is ideal, because the context in which you hear the interval might not match that of the song. The song might begin on the tonic, for example, while the interval you're hearing does not. I think it's better to learn the sound of a major triad and relate everything to that. That major sixth at the beginning of "My Bonnie" then sounds like two of the notes in the major chord, for instance, G - E in the chord C-E-G, if you're singing the chord with G in the low position: G-C-E. Fill in the missing C in your head. And that means this is a major sixth because the triad you're comparing it with is a major triad.

If you imagine a minor triad that would relate well to a minor sixth (G,-Eb, heard as G-C-Eb). A perfect fifth is the outer notes of the triad in its original position (C-G), a perfect fourth is the same notes if you sing the G below the C (G-C). Sounds complicated, but it quickly becomes instinct. Once you hear the primary intervals of the major and minor triads (fifth, fourth, major and minor thirds, major and minor sixths, octave) then other intervals are recognizable by how they compare to the ones you know: an augmented fourth is *almost* a perfect fifth, a minor seventh is *almost* a major sixth, a major seventh is *almost* an octave, and so on.

In Practica Musica the "Course 1" activity set has two activities particularly good for starting intervals: 1.06 Interval Names and 1.07 Interval Qualities. These activities include some on-screen explanation and help. And for further study you can use the Visual Intervals or Custom Visual Intervals activities to practice identifying intervals by sight (see Activities by Topic: Interval Names). For identifying them by ear you can also try Interval Ear Training or Custom Interval Ear Training or Speed Intervals, (Activities by Topic: Interval Ear Training) and there are some others that deal with recognizing several intervals at once, etc. There's a good one in the AP Course section that displays several harmonic intervals, plays one, and asks you which one you heard. But those Course 1 activities are the place to start.

20. Q: What is the difference between a chord in major and a chord in minor?- T.B.

A: A major triad is a perfect fifth combined with a major third (4 halfsteps) above the lowest note. Example: C-E-G.

A minor triad is the same but the third is minor (3 halfsteps). Example: C-Eb-G.

Rearranging the notes doesn't change their basic nature: E-G-C is still a major triad but it's "inverted." Most of the music we listen to is basically major and minor triads in succession with various added tones like sevenths, plus decorations and connecting tones.

Either kind of triad could be found in both major and minor keys. In the key of A minor the chord built on the tonic note A is a minor triad (A-C-E), while the chord built on the third note of the scale is major (C-E-G). In the key of C major it's the major triad C-E-G that is built on the tonic note, while the triad built on the 6th note is minor (A-C-E).

When you hear a piece in A minor you hear music that centers on the A minor triad and probably makes use of the chords, A minor, D minor, E major... when you hear music in C major you're hearing music centered on C, with the main chords being C major, G major, D minor, F major... You won't hear very much music that uses only major or only minor chords, fortunately, though a short and simple major piece in C might get by with just C major, F major, and G major.

So, major triads are different from minor ones, but both are used in major keys, and both are used in minor keys. You can't get very far without having both.

21. Q: What is a closed chord? is there such a thing? - M.N.

A: You're probably thinking of a "close position" chord. Here's the gist of it:

If a chord is played with all its tones as close together as they can be, then it's in "close position." If the notes are spread out then it's in "open position." An open position chord has some "air" between one or more of its tones. For any particular chord in a particular inversion there is only one close position but there are lots of possible open ones. Chords are most commonly heard voiced in an open position.

People often mishear this as "closed" position because the meaning seems somehow logical, and you may by now even see it written that way in some sources. Sort of like "web sight," which turns up a lot.

22. Q: I need you to show me hand signs of music notes for my daughter to practice. - J.

A: That's a topic that may interest others of our readers. I've always liked the moveable Do solfege system as a means of learning to sight-sing; and the hand signs are a useful teaching aid. Moveable Do is the system in which the first note of a major scale is always called Do, regardless of the key.

There's a long history of relating the notes of the scale to the body - going back more than a thousand years to Guido of Arezzo and the "Guidonian hand" image that presented the musical scale on various joints of each finger. The signs you're probably thinking of are those devised by John Curwen in the 18th century, which today are associated with the Kodály method of teaching.

The hand signs cover an octave of a major scale, and each is performed in a different vertical position - the first Do is at waist level, then each of the following signs is higher as the scale rises in pitch, with the last Do coming at eye level.

There's really no way to avoid using a picture for these:

Additional signals have been devised for the altered tones - raised Do, flatted Re, etc., but I'm not sure that hand signs are as useful when they become that complex.

Practica Musica has an exercise in which the student labels notes with the appropriate moveable Do solfege symbol, but the most useful activity for this purpose might be the one called "Display Solfege," in which you can enter the notes of any melody in any key and the program will show you the appropriate solfege syllable for each note. That activity is found under the Scales/Key Signatures topic heading.

23. Q: Can you please explain what notes of a melody determine the chords? - D.A. [Note to readers: this is not the actual wording of the question, which I think was translated from an eastern language, but I think this is the gist of it.]

A: When we see a melody, how do we know which harmonies make an appropriate accompaniment? Being able to harmonize a tune this way is a useful skill. Very good at parties, if you ever chance to attend a party at which people stand by the piano and sing. Which is to say, a real party.

This is discussed in more detail in Chapter 10 of Exploring Theory with Practica Musica, but here's the basic idea: Harmony normally changes only on a beat, and most frequently on strong beats. And notes that come on rhythmically strong positions (for example, 1 and 3 in 4/4 time, or 1 in 3/4) are the most important for harmony and are most likely to be members of the prevailing harmony.

There are exceptions that come under the heading of "non-harmonic tones" in voice-leading. A note on a strong beat might move by second to a chord tone, for example. But if a note on a strong beat moves by leap it is almost certain to be moving between two notes of the implied chord.

So, if you see melody notes that move by leap from a strong beat, they are probably outlining part of the prevailing implied harmony, and if they move by step then usually the strong note is the harmony tone and the second one is an "in-between" or "passing" tone, but occasionally it will be the reverse, with the second tone being the chord tone. A passage consisting of a number of successive scale steps is almost always one in which the strong notes are in the chord and the weak notes are passing tones moving to another chord tone.

If you add to those very basic principles an understanding of which chords typically follow each other, e.g. I and V, I and IV, iii and vi, ii and V, etc., then it's not so difficult to come up with a believable chord accompaniment for almost any tonal melody.

24. Q:I am in rehearsal for a setting of "The Cloths of Heaven" in a 5 part choral texture which SEEMS to be in a fairly straightforward dorian mode, at least in the initial motives. As the piece progresses, the dissonance increased so that what you would consider the tonic chord ends up being some permutation of both a d minor and e minor chord at the some time. For instance one cadence figure prepares as (from the bass up) ADFBE, inverts this chord to AEFBD, allows the alto voice to move upward to G while the other voices hold, then "resolves" to EDABE. I notice that the lack of the F in the resolution removes both the half step and tritone dissonance, but it's still far from a major chord, but it certainly SOUNDS settled by this point in the progression. Help? The voice leading is really quite good and the individual parts all make sense, but how would you analyze something like this?

A: This could require a cup of coffee. Maybe the piece was not made to be analyzed, but I'd say the composer has written a quintal harmony: a final chord built on fifths instead of thirds: D - A - E - B. And it's in a quintal version of 2nd inversion. If you look at it that way, the penultimate chord is a quintal dominant, making a quintal translation of V - I: A-E-B-F (the upper fifth being diminished), then D-A-E-B.

I don't really believe in quintal harmony, though. That is, while I know some have thought that one might just substitute fifths for thirds as the basis of harmony, a substitution like that doesn't really work in the same way that triadic harmony does. Triadic harmony is not arbitrary; it was as much discovered as it was invented. Triadic harmony derives from the overtone series; we all have heard triadic harmony and tend to mentally fill in a missing third in a sounding fifth. What you end up with in quintal/quartal harmony is something that sounds like triadic harmony with unresolved suspensions.

Which can sound pretty good! But it can't sound resolved; it leaves you with a question. In this case, since the E is the bass of the final chord and "inversion" of a quintal chord really isn't going to work for the listener, I think it will be perceived as an E7 sus 4. Maybe that's what counts. And with A as the bass of the previous two chords, one could even see this conclusion as a sort of plagal cadence, an "amen" cadence of IV- I.

25. Q: In the inversion of seventh chords, why are the numbers 6/5 used for the 1st inversion, 4/3 for the 2nd inversion, and 4/2 for the 3rd inversion? - K.P.

A: The numbers come from the old practice of "figured bass" or "thoroughbass," which in the 18th century was a common shorthand for keyboard players. The keyboard part was written as a bass line with numbers that indicated the desired harmony; the keyboardist would improvise accompaniment based on those numbers. It was really a lot like the practice of modern jazz keyboardists in improvising from a "lead sheet" that indicates only the melody and chord symbols. Some performers like Bach were famous for their ability to improvise complex accompaniment that sounded as if it had been composed.

The numbers indicate the intervals required above the bass note. A "6" would mean that the harmony should include a sixth above the bass - without or without additional octaves; the octave doesn't matter.

The numbers are themselves abbreviated. If the bass were the root of a triad its proper numbers would be 5/3 (a fifth and a third are above the bass), but that's a common occurrence, so if the bass is the root then the numbers are skipped. Similarly, a triad with its middle note in the bass position would have the numbers 6/3, but this is shorted to "6" because the 3 seems obvious enough.

At this point you can probably figure out the meaning of the numbers you mention for seventh chords. For example, put a G7 chord in 3rd inversion and the notes will read, from the bottom up, F, G, B, D (the upper three notes can be in any order). Measuring intervals from the bass note F you can see that the three needed intervals are 6, 4, and 2. Since all the inversions of a seventh chord include 6, this is abbreviated to "4/2." Here are all four positions for a G7 chord: root position, first inversion, second inversion, third inversion. Remember that you can freely mix up those upper notes, moving them by octaves.

You can find a more thorough description of figured bass in pages 56 ff. and p. 64 of Exploring Theory with Practica Musica, together with suggested exercises in the software.

26. Q: Can you tell me how leading tones work? - C.D.

A: Usually the term "leading tone" is applied to the 7th degree in a major scale or the raised 7th degree in a minor scale. For example, B in the key of C, or G# in the key of A minor. That is, this is the note that is just a half step away from the tonic and can seem to "lead" back to it (in minor keys the 7th degree is raised whenever it needs to function as a leading tone; the "natural" minor scale has no leading tone at all).

But here's the part that can lead the unwary astray: a note one half step below the tonic is not always serving as a leading tone. In the key of C, for example, you might have a melody that descends from C and passes through B on the way down, either as a dissonant "passing tone" or as part of an e minor harmony, in which cases it isn't really a leading tone. You can tell a real leading tone by its harmony, either real harmony or that implied by the melody. A leading tone would be part of a dominant chord (the V or V7 chord, or the vii dim. chord that is almost the same thing). But to use that B example again, if it was part of an e minor chord it wouldn't be a leading tone because the e minor harmony is not dominant; it's not trying hard to go anywhere in particular and if it does move it is more likely to move to the a minor chord rather than the tonic C major.

When the leading tone is part of a dominant harmony traditional counterpoint practice advises that it move to the tonic note as expected, particularly if it's in a part that's easy to hear, like the upper or lower voice. Otherwise it can seem a little disappointing.

To sum up, a leading tone is (1) a half-step away from its destination and (2) part of a harmony that is headed to that destination. Such a harmony is generally either the V chord or some other chord that is acting like a V (for example, D7 in the key of C, which is "V7 of V." In that chord the F# is the leading tone to the note G, as if you were changing now to the key of G).

In a more general sense, any note that is a half step from its destination and is part of a harmony that is tending to that destination could be called a leading tone, even including "upper leading tones" that lead downward by halfstep. But it's the rising leading tone that gets the most attention.

27. Q: Please explain the terms "ostinato" and "drone." -S.J.

A: OK. Drone is the simplest - a tone or tones held while other parts play. Think of the drone pipes on a bagpipe: they sound one or two pitches continuously while the melody pipe handles the tune. This is an ancient device and a very effective one. Typically a drone will be on the tonic pitch - the first note of the scale, or perhaps the tonic plus the dominant (fifth note of the scale), sometimes combined with one or more octaves of those pitches. A drone in classical music is often used to suggest a rural scene with peasant dancing, etc.

An ostinato (derives from the Italian for "obstinate") is a short melody, perhaps one or two measures, that repeats over and over while other parts play. This is also an old device that goes back at least to the 13th century, and today is heard very frequently in popular music - there must be thousands of rock or blues songs that use ostinato. Let me pick an oldie: "Smokestack Lightning" by Howlin' Wolf:

There's a little more on ostinato and related terms chaconne and passacaglia in Chapter XII of Exploring Theory with Practica Musica.

28. Q: I'm playing a song which is in key of G, that is, all the Fs should be played with F#. But there is a note E#, my teacher said I should play F#(the black key next to F) because E# is F and F should be played with F#. ****Is this correct?**** - C.L.

A: Nope. Your teacher is mistaken. Even teachers make mistakes from time to time; someday I intend to try making one myself.

The composer has written E# deliberately, probably as a leading tone to F#. An E# would be played on the same key as F, just as you thought.

The # in the key signature really does only apply to notes named F - not to notes named E, regardless of what accidental is on the E.

29. Q: Page twenty of Exploring Theory with Practica Musica, sentence 2., states: "A repeat bar can occur within a measure." I haven't seen this occur in music, do you have an example I could look at? - G.A.

A: Sure - Just popping open something that happens to be at hand, here is an aria from Telemann (Six Partitas for Violin, No. I, Aria 6:)

That is, the double repeat bar interrupts a 3/8 measure after a quarter note. Between the double repeat and the next barline is an eighth note, completing the measure. Naturally the aria begins with an eighth note pickup so that the repeat carries us back to the pickup and the meter is not broken. This is the occasion for repeat bars within a measure: a piece that begins with an incomplete measure.

30. Q: - I have this very basic question. Assume that you are sol-faing! a melody in A written in treble clef!**How do you spell notes in Sol-Fa. Do you spell it as if it is written in Bass clef ( since A is C in F-Clef which is Do). Or you first find the degree of note in the scale say B in A major key is supertonic therefore should be spelled Re.****This is confusing for me because, i have learn to read the music with do-re-mi-etc. Not with A-B-C-D-E-F-G!**** I would really appreciate if you could clarify this for me. - C.S.

A: It all depends on whether you have learned sol-fa with the "Fixed Do" method or the "Moveable Do" method. In the United States and England at least, movable Do is the most popular. In Movable Do solfege, the tonic note of a major scale is always "Do," regardless of the key. So in the key of A the note A would Do, B would be Re, C# would be Mi, etc.

But in Fixed Do, as used in France and some other countries (including, I now know from your response letter, Iran!), Do is just another name for C. Re is always D. In the Fixed Do system, the first note of the A scale would be La, because A is La regardless of the key.

In both cases, though, the clef would have nothing to do with it. The notes would be named regardless of clef.

If you think in terms of Movable Do, which is really the most useful kind of solfege, the notes of the A major scale would be A, B, C#, D, E, F#, G#, and they would be named Do, Re, Mi, Fa, So (or Sol), La, Ti, just like every other major scale, which is what is so nice about Movable Do.

But if you were using the Fixed Do method, the notes A, B, C#, D, E, F#, G# would be named La, Si, Do#, Re, Mi, Fa#, Sol#. Aside from being more singable the fixed Do syllables don't really offer any advantage over the letter names.

31. Q: Why do most musical scales start on C? - G.K.

A: To start with, let's not mislead any impressionable readers that may be in the room: it isn't actually correct to say that most scales start on C. But I think I know where you're coming from here - "C" has a big and seemingly undeserved reputation among musical pitches. One might ask, "Why not A? If we've decided to name the notes A,B,C,D,E,F,G why is it that we hear so much about C??"

The answer is that that the most familiar melodies use the major scale: whole step, whole step, half step, whole step, whole step, whole step, half step. And that is the pattern of steps outlined by the white keys of the piano if you start on C. Naturally the C major scale is therefore the first one everyone learns. And "middle C" is the pitch exactly between the treble and bass clefs used in piano music. "C" is famous.

But the major scale can start on any note. By using the black keys placed there for just this purpose you can play that same pattern of whole and half steps beginning on C#, or Eb, or any other. So really, C major is just one of the many transpositions of the major scale, and its only real distinction is that it is played without using any of the piano's black keys. On the violin it has no special status at all.

32. Q: I am a high school student, and I will be a senior next year. I am not sure if I should take music theory class next year, but I have always thought about this idea. I do like music, but I am not sure what the class music theory would be like. I enjoy music but am afraid that music theory could be too technical, and therefore boring. But I like to learn about different things and also be exposed to different materials. Could you give me any information as regards to the music theory class? I also would like to know why all the instruments are written in different keys. I play trombone, and I also find it very annoying that composers sometimes like to randomly switch clefs on the trombone parts. Is this a joke? Why can't they make up their minds? Is there a reason for this? Your response and time are greatly appreciated, L.W.

A: Now we're getting somewhere - almost a real advice-column type of letter. When I was in Junior High School, around the time of the Lincoln administration, I wrote an advice column called "Ask Sadie Glotz" and I've never gotten over it.

But I digress.

First let me say that nothing is boring. When you are young you might imagine that some things can be boring, but that is simply the consequence of not knowing very much yet. When you look at things properly you'll find that the entire world is interesting when examined as it should be.

As an undergraduate I was a composition major, which meant studying theory. But "theory" in music is not quite like theory in particle physics. Most of what is meant by "music theory" is nothing more than learning how notation works, how chords and intervals are named, and so on. Later on you would study, if you're lucky, fascinating topics like the traditional art of counterpoint (which involves lots of technical 'recipes' for creating good effects). There actually is such a thing as a person who studies the theoretical aspects of musical experience and perception, but that's not what music theory courses are about, at least in the first couple of years. "Music Theory" courses are not rocket science, in short. What they teach you is really the language of music and how to communicate with others who know the lingo, so that you'll have a clue when someone refers to an augmented-sixth chord or to asymmetrical meter, or tells you that what is needed here is a secondary dominant.

As to composers randomly changing clefs in the middle of a piece, yes, this is their twisted idea of humor. No, scratch that. Composers, or transcribers, will change clefs from time to time because they feel it's easier to read in a different clef than to read lots of ledger lines. If the music moves out of the convenient range for one clef, the writer will frequently change to one that doesn't require as many ledgers. But most musicians don't need to know all the clefs. A viola player knows the alto clef and will sometimes see the treble clef, but there is no need for a viola player to know the bass clef. Cellos play in a wide range, so a cello player needs to know the bass clef as a beginner and later the tenor clef and on some occasions the treble clef. And so on.

Why are the parts for some instruments written in different keys? This goes to the acoustics of wind instruments: an instrument whose bore length is such that it naturally sounds Bb has a series of harmonics in the Bb series, beginning with the notes of the Bb major triad, so Bb major is the natural key of that instrument. The instrument is equipped with various holes or valves (or in the case of your trombone, a slide) to produce tones that are not part of its natural overtone series. Wind instruments traditionally were made in various sizes to play in different keys; the parts were transposed so that the sound would come out right.

These days wind instruments are more highly adapted to playing full chromatic scales, but the tradition of transposing their parts remains. And it's a good thing, too, for the instrumentalist. One instrument will be easier than the other one to play in a given key, so long as the part is transposed appropriately. Also, instruments with different fundamental pitch have different characters; so a composer might prefer one or the other. Transposing instruments are likely to remain with us, complicating your life and mine.

33. Q: Could you please give me information about rests in music theory. Thank you, D.A.

A: [D.A, if you are reading this: your email address doesn't work. That's why you didn't get a direct response to this question. This happens to us all the time; if any of you out there find that you are not being answered by Ars Nova (and maybe never get any mail at all!) check to see if you are giving people the correct email address].

Going right on: That's a pretty broad question, don't you think? But every note has a corresponding rest that takes up the same amount of time - except that of course a rest is the opposite of a note - it's a moment of silence.

Rests are important, though. You count them in your mind just like notes; the hidden rhythm of the music continues to beat right through them; they are as definite in time as notes are. They say time is nature's way of keeping everything from happening all at once; rests are how we measure time between note events.

Here's a chart showing the rests and their corresponding note values; a similar chart can be found on page 13 of Exploring Theory with Practica Musica:

34. Q: How would one play a piano chord with a book notation of G/B? - R.G

A: An understandable question. Chord notation in the form G/B could easily give you the idea that you have your choice of playing G, or alternatively B if it suits your mood. But actually this refers to a G major chord, and the B after the slash tells you that the B of the chord should be the bass.

In terms that would be understood in a music theory class, this is a first-inversion major triad, a triad with its third (the middle note) in the bass. The order of the upper notes doesn't matter, but the bass must be B, and the other pitches will be G and D.

35. Q: Where do the 5 tones d e c C G that are used with hand symbols in the movie "Close Encounters of the Third Kind" come from and what is their meaning?**I have heard that these came from some German scientist that had a theory that all music stems from these notes or variations of these notes. Can anyone elaborate or tell me more? Thanks! - H.

A: I'm always happy to discuss the nexus between alien visitations and music theory. The five musical tones in Close Encounters are, in solfege, Re, Mi, Do, Do, So, as below. The second Do is an octave below the first.

The five tones were chosen by composer John Williams after trying about 350 of the approximately 134,000 possible five-note combinations available in the 12-tone chromatic scale. He said the choice was arbitrary, but actually they are critical tones of the major scale (see below). I haven't watched this movie for a long while, but I believe the hand signals are the Curwen hand signs as illustrated for Question 22, above. Learn the signs for Do, Re, Mi, and So, perform the second Do lower, around waist level, and you can communicate with aliens yourself, should the need arise.

I think that the inhabitants of a distant galaxy would recognize and appreciate a melody formed of the major or minor scales, because they are both derived from universal acoustic principles: a vibrating string in another galaxy will have the same harmonic partials as it does here (partials you'll find discussed in the appendix of Exploring Theory with Practica Musica), and the first and most audible of those partials are Do, Do an octave higher, So, Mi, and Re - hey, those are the same ones John Williams chose! So maybe his choice wasn't as random as he implied in interviews. In that sense the German scientist would be on the right track, at least, in claiming all music to be derived from these. But it might be better to go a little farther and include the tones derived by filling in the scale with the above tones mirrored on the other side of the main note: the opposite of Mi is La, the opposite of So is Fa. That much I think you could trust the aliens to know, but I'll bet they'd like Mozart too.

What I would like to hear is their own Mozart. They must have one.

36. Q: How do you notate a 16th-8th-16th note combination on one beam? -B.R.

A: The normal thing is to join all the notes with what they have in common - in this case that's the single beam of the eighth note - and then add short beams for the 16ths. The short beams should be inward, as illustrated below. The nice thing about beaming, as opposed to just writing flagged notes, is that the reader can clearly see the beat groups. Makes reading errors less likely.

That's the way Practica Musica or Songworks or Counterpointer will automatically beam the above notes if you choose them as a group and press the beam button. In 4/4 time or 2/4 time the above would have the value of one beat, so the musicians reading this can play it easily.

Cases might arise where you have to decide which way short beams will go. Again software will help with this, but since you have the power to override those choices it's good to know what would be right. For example, suppose you have 3/8 meter with an eighth note, 2 sixteenths, then an eighth. The software acting on its own would do it with the sixteenths grouped together, which is correct because it displays the nature of the 3/8 grouping: here are three things for you, an eighth, a pair of sixteenths, then another eighth. If you grouped these the second way it would sound just the same on the computer but it would be harder for a musician to read because now it looks more like two groups: an eighth note with a sixteenth, then a sixteenth with an eighth. If your meter were 6/16 that would make sense, but in 3/8 it's just confusing.

So, clarity for the reader is always the first goal. That is not to say composers don't sometimes ignore it. Witness this excerpt from the orchestra's rhythm in the Sibelius Violin Concerto, third movement:

Probably Sibelius had his own reasons for notating that the way he did. In fact, I'm sure of it; he means for the fourth note to be emphasized as if it were the first of a group of 3 in 6/8. But he's going to get that effect anyway, having indicated two upbows on the previous pair of notes. Making 3/4 look like 6/8 could mix up the viola section - the conductor is probably beating in 3 - and those of us who are not Sibelius might have better luck with the band if we notate this the second way. You can find more discussion of this topic on pages 16-17 of Exploring Theory with Practica Musica.

37. Q: In chords what does it mean when for instance the c chord is described as a c major 6th - what does the 6th imply. thank you, K.R.

A: K.R., as in another previous case let me begin by telling you your email address is invalid. If you have noticed a certain lack of responses to your letters this is the reason; your correspondents do not mean to be unfriendly. Now, for sixth chords:

A "sixth chord," also called the "added sixth chord," in modern terms is a major triad with the interval of a sixth added (as measured from the root of the chord). You've got your root tone, then the third, then a fifth, and finally that extra topping of the sixth. This chord has a sort of jazzy sound and you often hear it as the final chord of a jazz number. The major sixth is the most common one: a major triad with a major sixth:

There's always some confusion of terminology here with regard to traditional music theory. I regard Wikipedia as mistaken in its description of "Sixth Chord." The author of the Wikipedia article says a sixth chord is "any chord or meaningful combination of notes that contains the interval of a sixth." But an ordinary triad in first inversion contains the interval of a sixth, and it is not a "sixth chord:"

In traditional music theory that could be referred to as a "six" chord, but only in the sense that the figured bass for a first inversion triad is "6." There are still only three pitch classes: the root, third, and fifth. Since the third is in the bass the interval of a sixth is created between the bass and the root. But a genuine guaranteed "sixth chord" is one that contains the interval of a sixth above its root.

Perhaps more confusingly, a minor seventh chord uses the same tones as the major sixth chord and if it's in first inversion it is identical with the modern sixth chord. But in classical theory there is really no such thing as a sixth chord, so if that combination of notes appears it's a minor seventh.