The music theory content can be found at Music Fundamentals on the Web.
This assignment is related to the topic of Modes.
Just as you can build a chord on every scale degree, you can also build a entirely new scale that starts on each scale degree. This system of scales are know as the 'modes' of the major scale. The modal scales goes back millenniums in music history. The names we use for the modes comes from ancient greek names for scales used during their time. Since there are two methods for working with modes I'll call this first method 'Relative Modes' The names are as follows:
You may think 'it's all greek to me' but actually two of them we have already studied (by different names). (1) Ionian is exactly the same structure as a Major scale and (2) Aeolian is exactly the structure as a Natural Minor scale. The way the modal system works is for any given major scale (Ionian) you can create the other modes by moving to a different scale degree and playing from that new starting note and use the same notes as the 'parent' major scale. Sometimes the term 'parent' major scale is used to identfy the starting scale for the modal system. I guess that makes the modes children? (I actually think of it as if they're all siblings and the major scale is the oldest sibling, but I digress). For example if you start on the second note of C major (second note is letter D) and play from D up an octave using the notes of C major, that is D dorian. If you started on E, you'd create E phrygian. Starting on F creates F lydian, and so on. This type of relationship to is referred to as 'relative modes', they are all related to the 'parent' major scale. One way to easily create a mode is to first write out the 'parent' major scale's seven note (don't include the upper octave). Then for which every mode you need you can highlight the first notes up to the starting of the mode you desire, cut/paste them at the end of the notes and you have the relative mode of the major scale. The following example shows the process for creating the relative phrygian to A major. (C# phrygian)
1. First write out A Major without the octave at the end:
\\relative c' { a4 b cis d e fis gis }
2. Phrygian is the 3rd mode so cut/paste the first two notes
(a4 b) and to move them to the end:
\\relative c' { cis d e fis gis a4 b }
3. Add the duration 4 to the first note:
\\relative c' { cis4 d e fis gis a4 b }
4. Add the last note (octave). Done.
\\relative c' { cis4 d e fis gis a4 b cis }
(you can delete the 4 from a4 if you want)
But what if you wanted 'A Phrygian' not the relative Phrygian of A major but the Phrygian scale that starts on A. There are two ways to arrive at the answer. One method still uses this relative method but you have to answer the question 'What major scale has letter A as its 3rd note?'. Well let me think... 'the third note of a major scale is the interval of a major 3rd so if I go DOWN a major third from A I'll be at the letter name of the scale I want'. An interval of a major 3rd below A is F. So we'll do the same process as above but start with F major.
1. First write out F Major without the octave at the end:
\\relative c' { f4 g a bes c d e }
2. Phrygian is the 3rd mode so cut/paste the first two notes
(f4 g) and to move them to the end:
\\relative c' { a bes c d e f4 g }
3. Add the duration 4 to the first note:
\\relative c' { a4 bes c d e f4 g }
4. Add the last note (octave). Done.
\\relative c' { a4 bes c d e f4 g a }
(you can delete the 4 from f4 if you want)
The other method to determine the notes of a mode is referred to as 'Parallel Modes'. They are all of the modes that start on the same note as a Major scale. You can describe the interval structure of a mode on how it differs from a parallel comparison to a major scale's structure. If you use the scale degrees 1 2 3 4 5 6 7 8 to decribe a major scale, the following list shows the interval structure for the modes using the parallel comparison (same starting note).
If we wanted to solve the two modes shown above (C# phrygian and A phrygian) using the parallel method, we first start with the major scale of the same name:
1. start with C# major (yikes! all 7 sharps)
\\relative c' { cis4 dis eis fis gis ais bis }
2. The parallel formula for phrygian is to lower the 2nd, 3rd, 6th and 6th.
The formula shows b's but it really means 'lower one half step' so in this case
we can just remove the sharps to make those scale degrees natural notes.
\\relative c' { cis d e fis gis a b }
3. Add the octave at the end. Done.
\\relative c' { cis4 d e fis gis a b cis }
-------------
1. start with A major
\\relative c' { a b cis d e fis gis }
2. The parallel formula for phrygian is to lower the 2nd, 3rd, 6th and 6th.
The formula shows b's but it really means 'lower one half step' so in this case
when that scale degree is a sharp, just remove the sharp to make those scale
degrees natural notes. For the note B we will flat it.
\\relative c' { a bes c d e f g }
3. Add the octave at the end. Done.
\\relative c' { a bes c d e f g a }
Notice that either method results in the same answer. However, sometimes the parallel method presents roadblocks. Consider the G# phrygian scale (I often use the term 'mode' and 'scale' interchangeably). For the parallel method you start with the major scale of the same starting note but we don't use G# as a starting note for major scales (too many sharps, it results in a scale with a F double-sharp! You could start there if you want but bring the Excedrin.). So for that mode your better path is to use the 'relative mode' method and start with the major scale that has G# as its 3rd note (E major).
My brain prefers the 'parallel mode' method but I'm comfortable with either method. I think of it as similar to knowing how to get to San Francisco from Santa Clara using either 101 or 280. Both will get me there and I know both ways but I prefer 280.
This assignment is to write out the modes of C major. It is already completed and the solution is listed in the lilypond note entry field. Each mode (including Ionian) is on a separate line. Either method could have been used. Scroll down, take a look at the note entry code. Notice the down octave mark (,) on the first note of all lines (except the first). Otherwise this would just keep going up, up up until it went beyond the range available. Click play to hear it and generate a lilypond score, copy/paste both the lilypond notes and the lilypond score into your course lilypond file. Use the lilypond score to create a pdf of assignment 18 using the usual method with lilypond.
This assignment is to write out all of the modes (ascending only) starting on the same note: letter D. Use which ever method works best for you. Every mode should start on the letter D. One suggested workflow that uses the 'parallel mode' method is to write out the D major scale (make sure you are correct) then copy/paste it 6 more times and to each line to make the adjustment to the scale degrees as per the mode formula of 'parallel mode' method. The workflow for the 'relative mode' method for this case means answering 7 questions "which major scale has letter D as it (1st, 2nd, 3rd, 4th, 5th, 6th, or 7th) scale degree?" The first question is obvious, D major. For the other answers write the notes of that scale but start on D. As you are working on the assignment (click stop then) play it occasionally to make sure there aren't any typos that cause an error. When finished, (click stop then) click play to hear it and generate a lilypond score, copy/paste both the lilypond notes and the lilypond score into your course lilypond file. Use the lilypond score to create a pdf of assignment 19 using the usual method with lilypond.
This assignment asks you to write out selected modes. Write each mode ascending and descending using quarter notes for all notes except on last note use a half note. Make it one long score. The first mode (D dorian) should look like this:
\\relative c' { d4 e f g a b c d c b a g f e d2
}
As you are working on the assignment (click stop then) play it occasionally to make sure there aren't any typos that cause an error. When finished, (click stop then) click play to hear it and generate a lilypond score, copy/paste both the lilypond notes and the lilypond score into your course lilypond file. Use the lilypond score to create a pdf of assignment 20 using the usual method with lilypond.