Complete Chapter 3 Evaluation

This evaluation follows the format of the sakai forms, but many sections exceed 4000 characters. This is the complete version:

What practical skills were helped?

Table 3.12: Ratio of Beginning and Ending Frequencies in Intervals
This chart is very interesting, and it shows us the mathematical ratios behind what we consider to be "consonant" and "dissonant". I find the harmonic intervals to be very useful, because it helps us to understand the development of keyboard instruments and tuning. This information will help me understand how my tuners work, and also allow me to account for temperament in my digital music.

What concepts were well explained?

I found the technical definition in terms of frequency of how tone and timbre are created was very helpful, and written from an interesting perspective apart from my own. I did find one error, in the section dealing with overtones, in which percussion instruments are said to not have harmonic overtones. This is not entirely accurate, as many percussion instruments are pitched.

3.1.2 Tones and Notes
I did think that in this section the math associated with half steps on a keyboard was extremely interesting. Since this is something I use each and every day in my area, I liked understanding the basic underlying math that describes a chromatic scale.

The text also discusses the idea of consonance and dissonance. Saying that Western music is based upon consonance isn't completely fair- the middle ages were based much more on dissonance than consonance- but the explanation of tension and release is well said.
I found table 3.9 to be very helpful- this is a very useful tool for anyone working with chord progressions. The same is true of figure 3.35- both images are quite useful and well-laid out.

3.1.6.4 Chord Progressions
Using the Twinkle Twinkle melody to demonstrate chord progressions is useful- it would be good for students to try to play the melody on the piano. Using the supplements to play these progressions so students can hear the accompaniments is helpful in this section. I also really liked the section on cadences. I thought the information was clear, accurate, and concise, and made them fairly easy to identify theoretically and aurally. I think that the fact that Mozart wrote this melody should have been mentioned earlier, and I also think that if the text is going to call it a variation, it should define a Theme and Variation form.

*Engaging and interesting?

Reorganization?

The frequency relationship defined as an octave is a definition that will confuse your music students. While discovering the relationship between frequencies is interesting, I think that in order to start defining intervals, you should define whole and half steps first. An octave, by musical definition, is 8 notes of the scale, or 12 half steps. Also, when introducing sharps and flats, I wouldn't wait to explain that C-sharp raises the pitch a half step, and that a flat lowers the pitch. It might be that the whole section on accidentals belongs BEFORE the mention of any intervals- including the octave- because intervals are defined by whole and half steps (letter names are only one way to define intervals). That way enharmonics could be explained here as well.

3.1.2 Tones and Notes
Showing a piano keyboard without describing that each note has a corresponding key may not be helpful- I think this section should be reworked in terms of order.

3.2.1.5 Guitar Chord Grid
I don't understand why we are spending so much time dealing with guitar tab and other types of notation for guitar. Is the idea to be fairly standard with keyboard and guitar as the primary instruments for learning? Other musicians might find this frustrating, so I want to know exactly why the focus is on guitar.

3.3.2 Equal Tempered vs. Just Tempered Intervals
If the text is going to mention Temperament, it is imperative that Bach be mentioned at some point, as he was the first to write in all 12 keys for the "well-tempered clavier (keyboard instrument)." With that addition, I found this section to be REALLY cool- I've always wanted to better understand the math behind temperament, and it really helps with the understanding of tuning and keys to know how the frequencies behind it work. I also think that Table 3.11: Frequencies of Notes from C4 to C5 is very useful for digital media, because it would help musicians use the programs available to them more efficiently by knowing both the pitches they need and the frequencies necessary to make them.

Better job relating concepts, practice, science?

3.1.1 Context
I begin this section with a certain amount of trepidation as I hold a bachelor's in music performance, and am going into the field of music education. As such, I not only have high standards for the level of accuracy of music theory and history, but I also have high standards for how well it is presented to potential non-musicians.

First of all, the introduction of context is somewhat misleading. Western music tradition began long before Mozart, and started essentially with the development of Gregorian chant. Also, MOzart and Beethoven were part of two distinct musical eras, so it would be better perhaps to mention Bach instead. Secondly, considering Gregorian chant to be somehow different from Western music isn't exactly fair, as chant used church modes which are the foundation for the diatonic system we use today.

Table 3.10 is bulky- the columns that say "chord type if the triad sequence comes from a major key" could be switched to say "major" or "minor".

What could be added?

In the section describing accidentals, it would help to add that accidentals raise or lower a note when it needs to be different from the key. That way the later section on keys would make more sense- now I think people would find it confusing... why have a key signature if you can just write accidentals (or vice versa)? Simply clarifying early might help clear that up.

When explaining the treble and bass clefs, it would be helpful to include that the treble clef covers a higher range of notes on its staff than does the bass clef. This would explain the difference and why one is on top of the other.

3.1.5.2 Notes and Their Duration
Table 3.3 doesn't make the most sense when trying to explain note duration. The best way is to break down things from the whole note down. This way, the relationship from one note to another is made clear from the longest duration down. A similar format would work for explaining dotted notes, with a dotted quarter note creating a set of three half notes (or one quarter and a half note) etc.

In figure 3.17, adding lyrics to Twinkle Twinkle would not only help with practicing reading pitches, but also will help students place each note value of the tune with a written note value. It is also unnecessary to say that this is the "right hand"- it's just the melody, and is technically composed by Mozart as a theme and variations.

3.1.5.4 Rests and their Duration
Table 3.5 has the same problem that the note duration had- if you began with a whole rest and worked DOWNWARD in the format of the chart above, the rests would be much clearer. It would also be helpful to show rests next to their corresponding note value- that way students would be able to more easily connect that a quarter note is the same value as a quarter rest, etc. Table 3.6 is fairly clear, but I still feel that there is room for practice. Rhythmic notation is crucial, so maybe if each student was given a note and asked how many 8th, 16th, or 32nd notes it is equivalent to, including dotted notes, they would be able to more easily understand that it is fairly simple math, and not something to be feared.

3.1.5.5.1 Key Signature

I would prefer that in this section the use of 2's and 1's be altered, but generally within this structure the meaning is fairly clear. Perhaps have students create scales by starting on one pitch and creating the 2212221 pattern. Then identify the sharps and flats necessary for each scale. It would also be helpful to mention the idea of "flat keys" and "sharp keys" so that students understand that a key signature contains ONLY sharps or flats.
When discussing a key signature, you MUST mention what this tells a performer. If I am reading a piece in the key of D-Major, the key signature tells me that throughout the piece, unless there is an accidental, I have to play F# and C#.

3.1.5.5.2 The Circle of Fifths
When discussing the circle of fifths, it is useful to show a piano image. This makes the "counting up" or "counting down" process much simpler, because students are able to visualize how many half steps they're moving. The idea of adding or subtracting sharps and flats is pretty good- but it might be hard for students to understand that you are actually adding sharps clockwise all the way around the circle, and adding flats counterclockwise. This is easy to see when on one half of a circle (all flats or all sharps), but this is much more difficult to understand when you make the switch from sharps to flats (or vice versa) at the bottom of the circle. This may take some explanation on the part of the professor- but should be gathered given what sharps and flats do.

I think the most important part of this chapter is providing basic reading skills and also allowing students to make the connection between written notation and what they hear. The more listening exercises you can include, the more comfortable non-musicians will become with the idea that notation is just a way of writing what they've been hearing for years.
Figure 3.26 would benefit from having the names of the intervals written beneath the notation- that way students don't have to count them or read for them in the paragraph- you will be able to see the interval written right below the interval notated. The same should be true of 3.27.
When I got to the explanation of not being able to make Perfect intervals minor, I realized that there hadn't yet been a clear definition of what makes a perfect interval different. I think this information needs to be given at the beginning of the section on intervals. A perfect interval is so named for its high levels of consonance, and also because its inversion is also perfect. The point about the high levels of consonance would be useful to mention for the purpose of the later section dealing with frequency and consonance.
Also- Form is entirely left out of this section. I'm not suggesting that we cover Sonata-Allegro form and discuss transpositions from the tonic to the dominant when composing a fugue... but I think some mention of how repeat, da capo, coda, segno, and 1st and 2nd ending signs work would be useful.

Anything not relevant or helpful?

On page 3, define the term "chromatic" as referencing notes that are a half step away from each other. Also, the term "semitone" is typically used in European English, and not generally heard in the US. While it is technically accurate, the "half-step" is a much more commonly used term. The same is true of "whole tones"- generally the accepted term is "whole step".

3.1.3 Music Versus Noise
Careful with the idea that music is easily distinguishable as noise. Your lovers of 20th century experimental music will take issue with that, so you might want to be prepared to defend Western traditions. Many very well trained musicians experimented with very unpleasant sounds in recent decades, and their pieces are still completely justified musical endeavors.

Once again, be careful with generalizing all percussion as being non-pitched. Many percussion instruments are, and your timpani players will be offended. They ARE transient, but wind instruments can create very percussive sounds as well.

3.1.4 Scales
Very rarely does anyone refer to types of scales as intonations. Generally your scales are called diatonic or they aren't, so this term isn't particularly useful. Also, the system of writing the scales as a series of 1's or 2's is extraordinarily uncommon and confusing. You are way more likely to hear musicians talking about scales in terms of whole and half steps, or abbreviating half steps as ^ and whole steps as arcs or upside down half-squares. You would be better off to show these scales on a keyboard or defining them as patterns of "whole" and "half"- this would be much clearer (even to math students, I believe, because the patters are easier to see than a whirlwind of 1s and 2s) than numbers.
Also in this section, it says that there are two types of diatonic scales. Be sure your students understand that there are two TYPES, not just two diatonic scales (of which there are 84). It is also important to know that there are other "major" scales (the other church modes) that are not in the 2212221 pattern. In addition, the "familiar" [do, re, mi, fa, sol, la, ti, do]: "Sol" has an l at the end in traditional solfège syllables (which is what these syllables are called in musical pedagogy).
In table 3.1 the vii is called the leading "note", which is more commonly referred to as the leading "tone". The section following regarding minor scales is completely unhelpful. The best way to learn minor scales is to HEAR them, and see what's being played on a keyboard. You need a visual here, with pitch names, a staff, and the ability to HEAR each different kind of minor scale. Most people will be able to tell that there is a difference, and the text will explain WHY they sounds different. While using a musical example is a good idea, Showboat won't be particularly well known for students now, and is a touch controversial, so perhaps another well known piece could show a minor key- think God Rest ye Merry Gentlemen, maybe. Again, the 1s and 2s (and now 3s) are very confusing, and table 3.2 is a wash of numbers and patterns that are hard to distinguish. How necessary is it to know some of this? How will the combination of whole and half steps creating scales (as opposed to just knowing the pitch names that are used in each scale) help students create digital media? I think most students will be wondering why this is included, and what good it will do them.

3.1.5.1 Score
The paragraph below figure 3.10 includes a sentence about whole notes shown in the table below- this is irrelevant, and will only confuse the students. They can figure out that the notes below are notes, and once you describe note duration, that will be explained without the disjointed introduction.

3.1.5.3 Rhythm, Tempo, and Meter
Rather than saying "placement of accents" in notes- perhaps change it to "emphasis", as accents are something distinct and having to do with articulation.
The explanation of time signature in this section is way more confusing than it needs to be. While I understand the idea of creating an "equation" of sorts, it would be better to set it up as an explanation rather than as variable. For example: # of beats per measure/what kind of note gets the beat. The top shows HOW MANY of the bottom note are in each measure. It would also be much clearer if there were a visual example of a measure included at the mention of a measure (this way students will be able to tell why it is also called a "bar").

3.1.5.5 Keys
On page 16, (and tables 3.7 and 3.8) the discussion of how to determine the tonic from a key signature is MUCH harder than it needs to be. Finding sharp keys is done fairly well, but the easiest way to find a flat key is to look at the second to last flat in the key signature. If there are two flats, B-flat and E-Flat, the key is B-Flat. This works for all flat keys with the exception of F-major/D-minor, which only has one flat. If you can remember that ONE flat key, the rest of them are quite easy to find. There's no need to count down 5 half steps. Finding the minor key just requires going down a minor third from the major key (or three semitones in this context).
After reading this section I'm not wholly convinced that compound intervals are worth so much time- I think it would suffice to say that intervals bigger than an octave exist, and that you can essentially pull one of the pitches closer to the other by an octave to determine the compound interval.
3.1.6.3 Chords
I think the explanation for the minor triad is overcomplicated. The best way to explain chords other than major chords is to start with a major chord and alter it. For example: start with a major triad, flat the third, and you have a minor triad. If you start with major and flat the third and fifth, you have diminished, and if you start with a major tried and sharp the fifth you have an augmented triad. I find this explanation in relation to the major triad to be much easier to understand.
Trying to combine Twinkle Twinkle with Over the Rainbow isn't useful. The progression, flatly, isn't the same. The second chord really should be a IV for the progression to work. Is that what the text means by sounding a bit "off"? That is very unclear. There are plenty of other pieces with the same chord progressions. Try youtube remixes, (my favorite, http://www.youtube.com/watch?v=JdxkVQy7QLM). The progression I IV V I IV I V I is very common, and works for a number of folk songs such as This Land is Your Land, etc. Maybe this progression would be better to exemplify the flexibility of progressions.

Mistakes? Typos?

3.1.5 Musical Notation
3.1.5.1 Score
Page 9, 10- "There are scores of different types, depending on the instrument being played", SHOULD READ: instrument(s). Also the plural of staff in the next paragraph can also be "staves", but both are technically correct.

Firgure 3.18 has a few issues. First of all, it should be labeled as Mozart's Eine Kleine Nachtmusik. Also, this piece is NOT written in 6/8 time. The original version (and the most widely accepted transcriptions) was written in 4/4. Writing it in 6/8 creates groupings of notes that don't make sense given the melodic shape. The same is true of Tutorial 2.1.5.4: Music With Rests. Though it is true that the eight notes line up similarly, 6/8 time groups notes in triples, which isn't conducive to the structure of the melody. It is also written in such a key that you end up with a lot of ledger lines above the staff. Either take this melody down an octave or write it in a friendlier key so that more notes lie on the staff. It will be easier for students to identify the pitches that way.

Key Signatures:
To say that keys are no different except their higher or lower pitch is not entirely accurate. If that were true, we would all play in C major or A minor all the time unless we were dealing with singers. Composers write in certain keys because of varying tone colors- flat keys are often a smoother, darker sound while sharp keys tend to be brighter and more pronounced.

3.1.6 Musical Composition
3.1.6.1 Historical Context
Polyphony became more standardized in the Baroque period, but was most certainly used in the middle ages. It began primarily with decorations on Gregorian Chant, and developed into organum. Be sure not to say that polyphony wasn't used until the Baroque, because that is inaccurate.

3.1.6.2 Intervals
In the introduction to this section, the text reads "An understanding... composition begins intervals". It should read "begins with intervals".
On page 24, the text says that sharps or flats aren't significant when naming intervals. This is incorrect- F and D is a sixth, F and D# is an augmented sixth; they do not sound the same, so they are not named the same. This is explained in a later section, so it's better to just leave those sentences out and explain augmented intervals later.
On the figure 3.28, an octave is listed as a "perfect eighth". This is a term that isn't used in musical circles, so it would be better to call these intervals a perfect/diminished/augmented octave. This chart is labeled as "all intervals"- it should rather say "all intervals within the octave".
Page 26 says "compound augmented fifth", which should, according to the example, say compound augmented third.
Figure 3.34 is the wrong figure. According to the title it should be dominant 7th chords in 3 inversions. It would also be much easier to abbreviate the intervals:
M2 (Major second), m2 (minor second), P4 (Perfect fourth), P5 (Perfect fifth), d^o7 (diminished seventh), A⁺6 (augmented sixth), etc. This might help clean up the layout of some of the charts.
The lyrics to Over the Rainbow are incorrect. ... "way up high, There's a land that I've dreamed of... once in a lullaby".
3.2.1.3 Tablature
pg. 34 says that tablature uses "six lines like the regular musical staff". This is wrong- regular staff has 5 lines, not 6.