REPINO: LESSON PLAN

AP THEORY / 4th PERIOD 11:56 – 12:43

OVERVIEW

Mr. Dominguez has seen fit to formalize the students’ knowledge of major/minor scale construction by introducing the Circle of Fifths and key signatures. The Circle of Fifths is a visual construct which demonstrates the coordination between a key’s tonic (major or minor) and its key signature. I have had difficulty writing an adequate accompanying material for this lesson, as the students have already demonstrated difficulty grasping the use of flats/sharps, and the theoretical concept of ‘key’ is not independent from aural skills. Nevertheless, despite the exacting nature of the terminologies ‘key’, ‘key signature’, ‘major’, ‘minor’, ‘mode’, ‘whole-step’ and ‘half-step’, all the diatonic functions, ‘scale’ and the proper labeling thereof, and much else, the introduction of a definitive referential graphic may help to tie some of these concepts together, or at least provide an aid to memorization until such time as the students have thoroughly experienced these concepts in theoretical practice. They may then bring them to practical use.

OUTCOMES

1. Students will demonstrate an understanding of tonic by notating the tonic appropriately on the second page of the given packet.

2. Students will be able to name the Orders of Sharps and Flats.3. Students will identify the major and relative minor keys from key signatures. 4. Students will identify the relative minor key of an indicated major key (without key signature).

In consideration of the students’ current abilities, no outcome requires the written or notated construction of a scale, or the notated construction of a key signature. This will be done soon after a majority-passing assessment of the present material.

TEKS (Music Studies) (Level 1) (Level 2)

3. (Foundations: music literacy) B, C, E

MATERIALS

Students: Writing utensil, accompanying packet, staff paper (if desired), ‘paper piano’ graphic (previously distributed)

Teacher: Lesson Plan; demonstrative writing surface; digital piano (also if necessary, for demonstrations on student query)

STUDENT PRIOR KNOWLEDGE

Effect of key signatures on written music Construction of major and minor keys Expression of pitch on bass and treble staves Aural familiarity with varied tonalities and modes; passing familiarity with keywords and

concepts herein (tonic, var. interval – jargon (distance and quality), &c.)

PREPARATION

The packets have already been printed and are ready for distribution. The following is already drawn on the whiteboard:

Circle of Fifths, as it appears in the packet, excepting the key signatures need not be drawn with staves.

A long staff whereon the treble clef appears at the beginning, and the bass clef appears in the middle. Or, two staves of one each.

Space left for the Order of Sharps and the Order of Flats, consecutively, including accidentals, such that a mnemonic can be written under each of them.

Space left for the following: the intervallic patterns for constructing major and minor scales, written as Ws and Hs, also including carrots and brackets as appropriate.

PROCEEDURE (Questions taken also at end of each section.) (The procedure roughly follows the ordered content of the packet.)

Throughout: Students are selected from class to come to keyboard and construct scales from given key signatures. Class querried as to the identity of specific pitches according to what was played (ex: “If that was F# Major, what was the fourth note played?” – thereafter the specific scale is constructed on the whiteboard).

BEGIN 11:56

Introduction.

Teacher acknowledges the difficulty of late regarding major and minor scale construction using note names. Assures students that today’s activities should both aid in their continued efforts to learn this skill, as well as tie in some more practical skills of notation. Questions relevant to the topic at hand are encouraged as they arise. Objectives as listed in Lesson Plan are shared with students. Teacher explains, albeit dense, the packet is made for their continued study, reviews most of what’s covered in the lesson, and that the most crucial part is the Circle of Fifths diagram.

Instructions given:

Ready Materials (Students)o Rip first page from packet.

Students correct the following errata in packet:o Pg. 3 > Components > ¶2 : Strike last sentence. (Resources section was removed due to

time constraints; will be distributed at a later date)o Pg. 6 > 1st Q > Chart:

Blot sharp from C Mixolydian. (Error produced by entry into Excel) Add flat to C[ ] Lydian (Error produced by entry into Excel)

o Pg. 6 > 4th Q: Strike “relative”. (Misleading superfluous word)

12:00

Review of Major/Minor scale construction.

Teacher queries students on the intervallic pattern corresponding to maj/min scales, which is written on the board according to MATERIALS. Cmaj/aMin written on staves as examples. Teacher

queries, “And, remember, these patterns are used to construct any scale.” Process of writing scale as note names is covered with more difficult scale:

Select tonic Write out consecutive note names Add accidentals where appropriate, according to pattern, in conjunction with keyboard layout.

Teacher queries: “And, what if we wanted to write a G-Major scale? (Writes G Mixolydian). Is this G-Major? (No.) Why? (Answers.) (Adds F#, &c.) “Check this against our Circle of Fifths.” (Scales played throughout to give students an aural sense of the key quality).

12:05

Order of Sharps and Flats

(Throughout, teacher directs students’ attention to appropriate ring on Circle of Fifths). Teacher draws attention to Circle of Fifths.

Teacher notes:

Correspondence between Scale and Key Correspondence between Key and Key Signature

With students, teacher writes out the orders according to MATERIALS by analyzing the graphics on the Circle of Fifths.

Teacher notes:

The orders are always this way. Gives explanation of its construction in consecutive fifths (see FAQ).

Mnemonics discussed and written. Time allotted for extra examples, questions.

DI: Class encouraged to formulate their own acronyms for the Order of Sharps and Flats, according to current events, favorite foods, &c.

Example: order of flats: FCGDAEB: Fat Cats Gulp Dario’s Amazing Egg Burritos

12:15

Understanding Key Signatures.

Teacher instructs class to guide him in the note-name construction of a random scale according to the stepwise intervallic construction method covered above. Students copy.

Teacher notes:

All these accidentals are taken from this, and put over here (on staves) according to the Order of [].

Drawing of the accidentals, reference previous packet material. The use of a key signature as opposed to writing keyless-ly.

12:21

Relative Maj/Min.

Teacher writes example key on stave(s). Queries as to what key it is.

Teacher notes:

Circle of Fifths and Packet “How to identify…” ¶1.

Teacher instructs on visual methods to identify keys, per packet.

DI: Select students pulled to Keyboard to demonstrate construction of scales may choose their own scale regardless of the number of accidentals therein. -OR- Students may participate by filling in a chart on-board according to their chosen scale; multiple students may be called to complete the chart of scales (one student may be assigned all-tonics; another all-natural notes; another all-accidental notes.)

12:28

Student Activity: Finding the Tonic

Teacher guides activity as given on Pg. 2 of packet with one example. 8 minutes allotted to the completion of the activity. Instructions given to finish at home.

Review conducted of lesson components. Questions taken for whole of class. Time allotted for extra class practice of any component.

END 12:42

RE: ASSESSMENTS

Submitted formal assessments may include brief activities where students provide a solution to each new concept given in the lesson, written and collected at end of class. Informal assessments taken by query at the end of each section, through other queries, and through inspection of the student activity. Teacher will watch for visual discomfort and hesitation, and for students not volunteering answers.

ASSIGNMENTS GIVEN

Due Tomorrow:o Inscribe all major and minor tonics on the diagram as the indicated noteheads on the first

page of the packet, on each staff.

MUSIC THEORY: THE ORDER OF SHARPS/FLATS; THE CIRCLE OF 5ths; KEY SIGNATURES

ASSIGNMENT: on this page, write the major tonic pitch as a WHOLE NOTE on each staff, and the minor tonic pitch as a BLACK NOTEHEAD.

What is the Circle of Fifths?Overview.

The Circle of Fifths (or Fourths) may be thought of as a graphic representation of where the tonic of a piece of music is in relation to the whole-step/half-step relationships we have seen comprise the Major / Minor scales. In other words, it tells us what accidentals to put in the key signature for a given major or minor key.

Remember that the tonic is the ‘functional’ name given to the note which is the ‘center’, ‘first’, or ‘home’ of a piece. For example: the tonic note of a C-Major scale is C, because it begins and ends with C, and C sounds like ‘home’. Likewise with C-Minor: the C-Minor scale both begins and ends with C, and when played, the scale seems to revolve around and/or lead to C. In both cases, C is the tonic. Only the whole-step/half-step patterns within the scale have changed to give them their characteristic sounds. That is to say, both C-Major and C-Minor are C-scales (therefore, if you’re ever asked “What scale is this?”, saying “[note name]” is only a partially-correct answer).

The C-Major scale requires no ♯s or s to play – it is played beginning on C, and thereafter uses ♭only the ‘white notes’ (or ♮ notes) of the piano keyboard. But what if we wanted to play a different major scale, one which did not begin on C? We cannot simply, for example, begin on G and play only the white notes thereafter, because the whole-step/half-step pattern created by doing this will have changed from W-W-H-W-W-W-H (major scale) to W-W-H-W-W-H-W (Mixolydian mode). We will therefore need to add an accidental somewhere to change W-W-H-W-W-H-W back into the major scale pattern of W-W-H-W-W-W-H.

Components.The Circle of Fifths is only a graphic aid to understanding tonics and key signatures, and the

relationships between them. If you ever see another Circle of Fifths diagram, it is probably just as correct as the one given you, but may be organized differently or show have more or less information. The one we’re working with is among the more complete variations.

Outside of the circle, we see arrows directing us either clockwise or counterclockwise around the circle by fifths. The fifth we’re talking about is the P5, or Perfect 5 th. Each consecutive tonic on either side of a given part of the circle is a P5 away. We also see that the graphic was created by MusicCrashCourses.com; one of the websites mentioned in the Helpful Resources for Practice and Study section.

On the outermost ring of the circle, we have key signatures on a grand staff. Each of these key signatures corresponds to the tonic that key can represent, major or minor, farther in on the circle. Notice that the same number of accidentals occur on both the treble and bass staves, and on the same notes (they only appear shifted because of the given clef).

On the next ring in, we see the major key’s tonic as a note name. On the furthest-in ring, we see the minor key’s tonic. Each of these tonics gives the key their name. The C-Major key has a tonic of C, just as the C-Major Scale does. The A-Minor key has a tonic of A, and so on.

What is the Order of Sharps/Flats?Overview.

The Order of Sharps and the Order of Flats are derived from the Circle of Fifths in consecutive clockwise or counterclockwise motion, respectively. They say which accidental is added to the key signature next, in order to move the tonic a P5 away.

The Order of Sharps.The Order of Sharps is:

F♯ – C♯ – G♯ – D♯ – A♯ – E♯ - B♯When building a key signature with sharps in it, you must always add these sharps in this order.

Notice that each consecutive sharp is a P5 away from the one before it.

You may find it helpful to use a mnemonic to remember the order. The most common one is: “Fat Cats Go Down Alleys Eating Birds”. You may come up with your own mnemonic, but if all else fails, just remember that F♯ is the first sharp, and that each next sharp is a P5 above the previous one.

The Order of Flats.The Order of Flats is:

B♭ – E♭ – A♭ – D♭ – G♭ – C♭ – F♭Again, each flat you add to the key signature must go in this order. Mnemonics for the Order of

Flats are, for some reason, harder to come by, but I like this one: “Better Eat A Darn Good Chicken Fajita!”. In any case, similarly to sharps, each next flat is always a P5 below the previous one.

Helpful ‘tricks’:Notice that the Orders of Sharps and Flats are reversals of each other:

F♯ C♯ G♯ D♯ A♯ E♯ B♯B♭ E♭ A♭ D♭ G♭ C♭ F♭

Draw for yourself whatever patterns you may find useful from this observation – it is a consequence of what is known as modular mathematics. Commonly, people may remember / write down only one order, and read it in reverse if they need to know the other.

What are Key Signatures?Overview.

Key signatures are notated representations of keys. Keys, key signatures, scales, and tonics all share a note name, which is the tonic itself. For example, a tonic of G may correspond to the key of G-Minor, which is represented by the G-Minor scale and/or the G-Minor key signature, which has two flats. On any conventional piece of music, on any staff, the key signature will appear after the clef.

Note that it is insufficient to say a key itself is “The key of x-flats” (or –sharps), just as it is insufficient to call a key “the key of X”. One must also name the quality of the key, which is either major or minor. This is because any given key signature can signify either a major key or a minor key. Said

another way, the key signature itself is just a number of accidentals which may signify either of those keys.

What key is this, exactly?We have said that a key signature may signify one of two keys, either a major or a minor one.

Out-of-context, that is, without any music following it, a key signature is both and neither.

The only way to determine whether a key signature is either for a major key or a minor key is to hear and/or read the music following, and determine by the way it sounds and behaves whether it is one or the other. The easiest and most reliable way to do this is to look at the very first and last notes, which are often the same, because most melodies tend to begin and end on the tonic. If, for example, a melody with a key signature of three sharps begins and ends on an F♯, you know that F♯ is likely the tonic, and so the key will be F♯ minor.

How to identify a key by its key signature, and how to identify relative major and minor keys:

Since a key signature may signify either a particular major or minor key, we call these two keys relatives. For example, C-Major is the relative major to A-Minor, and A-Minor the relative minor to C-Major. The minor’s tonic, the major’s tonic, and their key signatures all share slices on the Circle of Fifths.

To quickly identify the major key of a key signature with sharps visually: remember that the final sharp is one half-step below the tonic. For example, the final sharp in the key signature with six sharps is E♯, and one half step above that is F♯, so the key is F♯ Major.

To quickly identify the major key of a key signature with flats visually: the second-to-last flat is the name of the key. For example, the second-to-last flat in the key of C♭ Major is C♭.

Many people find it easier to memorize the major keys only, and then figure the relative minors from that. You can do this by knowing that the relative minor key’s tonic is the sixth note of the major key’s scale. For example, G♭ Major is spelled:

G♭- A♭- B♭- C♭ - D♭- E♭- F - G♭And so its relative minor would be E♭ minor. Likewise, the relative major of a minor key is two steps (that is, the third) note in the minor

scale.

Frequently Asked QuestionsWhy don’t the X-Major scale and X-Minor scale share the same key signature?

Because, if they did, the intervallic patterns that make that scale what it is would be violated. If you take an E-Major key signature and simply start somewhere else on the keyboard, you will most likely produce a mode of the tonic you’ve picked than either a major/minor scale.

Incidentally, the Ionian and Aeolian modes share scales with the Major and Minor scales, respectively. They are, however, not identical in theoretical function.

See the below chart:

KEY SIGNATURE HAS:

Maj/Ionian

Dorian

Phrygian

Lydian

Mixolydian

min/Aeolian

F♯ C♯ G♯ D♯ A♯ E♯ B♯ C♯ D♯ E♯ F♯ G♯ A♯

F♯ C♯ G♯ D♯ A♯ E♯ F♯ G♯ A♯ B C♯ D♯F♯ C♯ G♯ D♯ A♯ B C♯ D♯ E F♯ G♯

F♯ C♯ G♯ D♯ E F♯ G♯ A B C♯F♯ C♯ G♯ A B C♯ D E F♯

F♯ C♯ D E F♯ G A BF♯ G A B C D E[♮] C D E F G AB♭ F G A B♭ C D

B♭ E♭ B♭ C D E♭ F G B♭ E♭ A♭ E♭ F G A♭ B♭ C

B♭ E♭ A♭ D♭ A♭ B♭ C D♭ E♭ F B♭ E♭ A♭ D♭ G♭ D♭ E♭ F G♭ A♭ B♭

B♭ E♭ A♭ D♭ G♭ C♭ G♭ A♭ B♭ C♭ D♭ E♭B♭ E♭ A♭ D♭ G♭ C♭

F♭ C♭ D♭ E♭ F♭ G♭ A♭

Why is the Circle arranged by Fifths, and not Fourths, Thirds, Chromatically, or some other interval?

The Circle of Fifths is, in fact, the Circle of Fourths as well, because going a P5 up will produce the same note as going a P4 down from a particular note. The arrows on our graphic show this. Going in either of these directions will successively add/remove flats/sharps, one at a time. If we were to use some other interval, the diagram would look very disordered, and would not be so useful.

Can you mix Sharps and Flats in a key signature?No. If you did, you’d produce something theoretically contradictory, or a very strange scale

outside the scope of the Western Common Practice theoretical idiom.

Can Modes be represented by the Circle of Fifths?Yes, see the above chart. However, modes are usually represented as their relative ‘tonal’

modes (major/minor), with the use of accidentals in the music, rather than as a key signature.

Can I keep going around the Circle of Fifths and use only flats, or use only sharps?

Yes, but if you do, you’re going to have a bad time.

Notice how the bottommost key signatures have enharmonic equivalents, for example, B and C♭ are in the same position on the circle. If you go outside the maximum number of flats/sharps, relative to

the number of note names we have to pair them with (seven), you’ll have to start using double-flats and double-sharps within the key signature. We can all agree it’s easier to read a key signature with four sharps than one with a double-flat and six more flats. This does, however, bring us to the fact that the Circle is really just a portion of an infinite spiral, with an arbitrary middle set at C / ‘no key signature’.

Does it matter which key is at the top/bottom of the Circle of Fifths?No. It is only easier from a visual perspective. For example, D-Major is always two clockwise

movements away from C-Major, no matter how the Circle is oriented.

I’m reading music in B-Major but I don’t like sharps. Can I just use the notes of C Flat-Major instead?

If it helps you to ‘translate’ a note to its enharmonic equivalent, you may do so. But whether that ‘help’ is worth the sacrifice of mental time it takes to translate is doubtful. You must also remember that enharmonic equivalents are not functional equivalents. There are no B-flats in the key of G Sharp-Major, and even if a piece of music were written so, the use of a B-flat would indicate some modification to tuning.

Is the Circle of Fifths the secret tool to harmony and music composition?

Not at all. Some compositional techniques utilize concepts related to the Circle of Fifths, but there is no secret sauce within.

In writing key signatures, can I deviate from the Order of Sharps/Flats?Same as “can I mix sharps/flats in the key signature”. You would not be writing a key signature

or key as we know it, but either an exotic mode, or a harmonic disaster. In any case, prefer always to write the most readable music – this may mean having no key signature and adding accidentals as necessary.

If a key isn’t listed on the Circle of Fifths, does it not exist?Since the Circle of Fifths is actually a continuum with [no key signature] at the center, you can

think up almost any theoretical key you could imagine. There is, for example, a C double flat-Major key, which has a key signature of seven double flats. There doesn’t seem to be much advantage to preferring this over the two flats of B flat-Major, though. Your performers won’t appreciate it.

In my music, I once saw a natural in a key signature. What does that mean?

This is an editor’s blessing. If you were, within a piece, to modulate from A major to D major, the editor often puts a natural sign where the G-sharp was to remind you that it must now be played as G-natural. It is a nice reminder, but functionally the same as simply redrawing the key signature to two sharps.