Enharmonia

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What’s going on everyone! You’ve been out there cutting your teeth on some intense analysis, and I think you earn a treat! So today, we are briefly going to discuss enharmonic equivalents. Big words, simple concept. So sit right back and you’ll hear a tale, about two notes being one, its all about how you spell that stuff, now let’s go have some fun (Gilligans’ Island was a fun show).

So enharmonic equivalents are two notes with different names that share the same pitch. Pretty cut and dry, right? Good lesson everyone! Peace!

No. I won’t leave you like that. Lets listen to the pitch B (the note right below C). Grab an instrument, play the note, listen to the note, now internalize it in your ear brain… aaaaaaaand good! Ok, now I want you to play a C-flat… You hear that right? The same pitch, just spelled differently! “But Kyle! What’s the point!?” It’s to make music playing difficult, as it should be!!! No… No, that’s not the point. I would say that enharmonic spellings come most in handy when wanting to modulate to a key that’s not closely related to the one you are in. Let’s look at one of my favorite uses of enharmonic spelling, which is the German augmented 6th chord (Ger+6 for short).

A Ger+6 chord is spelled using these scale degrees: 1-b3-#4-b6. It Looks like this in C-major.
ee-1

Typically, a Ger+6 chord acts as a predominant chord (precedes the V chord in a progression) if you are staying within a key. This offers a different option for voice leading, which we’ll save for a different visit on my corner. As I said earlier, they work well as modulatory devices too.

ee-2

A Ger+6 chord in the key of D-minor (1 flat) is spelled D-F-G#-Bb. Now here is where the enharmonic spelling comes into play. If we were to resolve to V and use the predominant function of a Ger+6 chord, the resolution would look like the above example. Instead of that, let’s enharmonically spell one of the notes, specifically G#, which I’m choosing because in this scenario, it is a true accidental. The rest of the notes can be found naturally in the key of D-minor. So a G# can be enharmonically spelled to an Ab, which changes the game! So now we have D-F-Bb, and now Ab. Hopefully I have taught you well, and you recognize that as a dominant-seventh chord in first inversion.
ee-3

Which reminds me that I haven’t discussed how dominant chords of chords that are not the tonic do exist simply put, you can have a V of V marked V/V in roman numeral analysis, which in the key of C would be a D major chord since D is the V to G, which is the V to C, get it? No? Ok, next time then.

Where was I!? Oh yeah! If you did not recognize that, then you could restack the notes to a more recognizable chord.

ee-4

Bb-D-F-Ab is the root position of the chord, which is a Bb7 chord, or a V7 in the key of Eb (get it know? No? ok.). So this Ger+6 can be used to modulate to the key of Eb-major (3 flats which is fairly distant) or Eb-minor (6 flats which is really distant). Pretty wild stuff, huh?

Man! There is so much more to talk about. We touched on a couple things I have discussed, as mentioned earlier, but we will go deeper into those topics another time. You should take a moment and sign up for our e-mail list. I am doing some reviews of bands that I am listening that get put on the e-mail list, so if you wanna read that, then sign up! Of course I welcome you unload your music theory burden at my door. Comment, like, and share this with all your music friends, and as always, thanks for turning on my corner!

Puttin’ it All Together

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Long time no see my theory enthusiasts! I think it is time we put our knowledge so far to some use. From the get go I am hoping that you had a basic understanding of music fundamentals (note values, key signatures, time signatures, lines and spaces, etc…) so that the topics to come were easier to grasp. Well here is where the rubber meets the road, because we are going to do a harmonic analysis of Mozart’s Piano Sonata in B-flat, K.333, measures 1-10. This was the first sonata I analyzed at UTA, so thank you Dr. Hunt!

So first thing you should do is listen to what you are analyzing. Click here to listen to the portion we are going to discuss, which ends at the :20 mark. After listening, you want to have the sheet music, unless you are up for the challenge of doing it all by ear. The best website for public domain sheet music is the Petrucci Music Library. So we have listened, and we have the music. Basics are done. Let’s get into the real deal.

The first step you should take is addressing what key the piece is in. Luckily, a lot of classical pieces were simply titled, “sonata in X-major/minor”, which makes it easy, to an extent. But if there are no titular indicators, what do?

First thing is to look at your key signature. That will bring it to two options, the major key, or the relative minor. Let’s assume there isn’t a title to this piece. The key signature is two flats, which means we are in B-flat major, or G minor. The first chord is going to be the determining factor of the key. In this case, the first measure of music is arpeggiating a Bb major chord, and a G minor chord in first inversion. The first chord in a piece typically denotes the what key the piece is in.

screen-shot-2016-09-19-at-5-10-45-pm

 

One thing that may present a challenge for first time analysts is that this isn’t a chordal texture. One more feature that could slip you up is that Mozart starts the bass voice in the treble clef, which could lead to a misanalysis of the first chord being a I^5, which isn’t bad, but isn’t right. The second measure the bass is arpeggiating a C-minor chord (ii), and is ended by switching back to the bass clef. The third measure of this phrase is the first time the bass doesn’t arpeggiate the full chord. The bass is fulfilling the root, fifth, and seventh of the V7 chord. Lucky for us, the melody of this piece provides the third to complete the chord.

There aren’t many other chords in this first section, but what a full, and rich portion of music Mozart has provided with only a handful of chords. As I have said in the past, the tendency of music is to return home, and if you listened to the music, you will hear that this section rests at the 0:20 mark where there is a V-I cadence. These demarcations in the overall piece are what help us figure out the form of a piece.

If you have kept up with me this far, then I’m guessing you are in for the long haul. I will continue to introduce new concepts as we go forward, and hope that you contact me with any questions if something doesn’t make sense. If you haven’t signed up for Lindby’s e-mail list, go to our homepage and scroll to the bottom. I have a segment that is coming out that I am pretty excited about. Could be a one-time thing, but who knows! Comment below, and thanks for turning on my corner.

Johnny 5 is Alive!!!

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MCTC #5: Chord Circuit

 

Johnny Five is Alive!!! This is technically the 5th installment of my theory corner, not counting the introduction, hence the Short Circuit reference! What’s goin’ on theory enthusiasts! I hope your respective seasons have treated you well (for all my Southern Hemisphere readers). We are making quite a trail so far in this music theory forest, but there is much more to explore. So let’s punch some trees, make some paper, and get to some theory!

We talked about inversions last time, but if you didn’t join us, then hop in your TARDIS and correct that (or just read it, but if you know the Doctor, hit me up). So we can stack all these chords, we know how to invert them, and we even have a method for categorizing the chord qualities and what they are in the key, but these chords all play a role as well. A couple posts back I reference a song by Stewie from Family Guy, and talked about how he referenced a chord as being his home. We are going to start with a chord that is typically the first and last chord you hear in a piece of music, or song. This is the I (roman numeral) chord, or, a more forgiving name in the written medium, the tonic.

Yes, the tonic you don’t mix with your gin, if you’re of age. If you’re under 21, MCTC® does not condone the consumption of alcohol; go read a book about music theory.

Sorry. Ok, but the tonic is just a starting place. To preface, what I am about to present to you is merely the tendency of composers studied by theorists, and in no way is a strict set of rules for how to compose your music. This is for the composition of tonal music, but learning new things never hurt. So don’t fight it. Let’s go ahead and pick a key!

The dice roll video posted on Lindby’s instagram last week was to help us decide the key (wanna know how that works, hit me up), which it looks like we are going with the key of D-major. Two Sharps (pound sign/hashtag/tic-tac-toe board – ## <-those things) So the tonic chord is a D-major chord. Pretty straight forward like that. The beauty of the tonic chord is its’ ability to go to any chord without an unsettling amount of dissonance. A tonal partner to the tonic is the dominant chord, or the V chord. In the key of D-major, that would be an A-major chord. Before continuing further I have included the tonal chords in D-major to help with the discussion.

mctc5.1

One aspect about the dominant (V) chord in a key is that you will typically see the seventh of the chord being used as well. This is important because adding the seventh will create a sound of tension between the 3rd and 7th of the chord (C#-G in an A7 chord). This is interval, as we know, is a diminished fifth, or tritone. The tension naturally wants to resolve itself inwards, with C# ascending to D, and G descending to F#. So the tritone in a dominant-seventh chord wants resolve to the root and third of the tonic. As far as the roll of the dominant within the key, it is the chord that is most likely to appear before the tonic, again because of the tritone resolution that happens. There are plenty of instances where the chord following a dominant chord is not the tonic, but we are just covering basic tendencies. Here is an example of a V65 – I progression so you can see the motion I mentioned.

mctc5.2

The viio typically precedes the tonic chord, and that is because of the same tritone that you find in a V7 chord. The viio is also labeled as the leading tone, again because of its’ tendency to lead to the tonic. As you can see below, the viio chord is essentially a V7 chord, but the root of the V7 has been removed.

mctc5.3

There is another pair of notes that act similarly to each other. Those are going to be the chords you should expect to precede the V or viio chord. On occasion, the V-chord will progress to a vi chord, but that is used to deceive the ear from the intended V-I sound the listener expects. We will discuss this further when we talk about cadences, but to be brief, cadences are basically the period/punctuation to a musical sentence.

The ii-chord (supertonic) and IV-chord (predominant) are going to be the chords that you will hear before a V (dominant) or viio (leading-tone). If you have played any level of jazz music, you should be familiar with a ii-V-I turn around. Sometimes I feel like jazz songs are parks where people just litter ii-V-I progressions with reckless abandon, but I digress. Anyway, you will typically encounter the ii-chord in first inversion, which you can see why in the example below. These two chords will sometimes precede one another, depending on your needs, but they are both chords that aurally set up the dominant chord well.

mctc5.4

A ii6 chord is similar to a IV chord because of the shared notes between the two chords (similar to the V7 and viio relation). The IV-chord will also go to the I chord at cadential moments, mentioned earlier. Unfortunately, this is where those kind of relationships end. Granted, that does knock out 5 of the 7 chords we are going to talk about.

So the remaining chords are the vi-chord (submediant) and the iii-chord (mediant), which don’t get as much face-time as the rest, but still can offer great compositional possibilities! These chords also share notes, but they are not interchangeable in the sense of tonal music. The mediants (both chords) get some wicked use in 19th century composition when composers are writing more emotionally charge music, but we will talk about chromatic harmonies a little further down the road (or you can e-mail me). Here is a quick guide for harmonic progression in Major, and also in Minor.

Majormctc5.5

Minor

mctc5.6

I know I am not presenting a lot of things in minor keys, or discussing them a lot. I will be mixing things up in the future, but I want to make sure we have some solid ground before I start fracking around in minor. (frack fracking…) We have a lot of ground to cover still, and if there is anything specific you want me to focus on, I am more than happy to take some requests. Maybe you want me to talk about a specific song instead of just giving you this textbook style. By all means! Feel free to give me something to discuss. If it isn’t on a level that is ascertainable by all the readers, than maybe I can do a separate post about it. But yeah, let me know.

This post was brought to you by the sounds of The Butthole Surfers albums “Independent Worm Saloon”, and “Locust Abortion Technician”. Got an album I should listen to? Buy it for me and I might listen to it while making the next post and give a shout out about how you either changed my life, or shoved garbage in my ears! Thanks for turning on my corner.

 

N-version 664.765.4342

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Welcome back my theory enthusiasts! I hope all us ‘Muricans enjoyed Independence Day, and I sincerely hope our international readers’ day was just as good! Mine went quite well, hence the lateness of this post. Lucky me that you don’t pay for this! Or maybe not lucky me… You can pay me if you want, but for now, let’s call it good.

Last time we talked about chords, specifically the types of triads and seventh chords, which are made of intervals and…well, go back and read it, if you haven’t. Remember that in a chord there is the root, 3rd, 5th, and sometimes 7th. There are times in music when a chord will not be in, what is called, “root position”.

Picture1

If a chord is not in root position, then it is in an “inversion.” The process of inverting is pretty simple over all, but I’m going to step back to a two-note harmony to explain this.

The most blunt way of explaining inversion is, one note must cross one or more notes in movement to the next octave like so:

Picture2

The reason for doing this is because it changes the sonority of the two notes. The above image shows an inversion from C-E, an interval of a M3, to E-C, an interval of a m6. You can also invert the other way, E-C to C-E, a m6 inverted to a M3. Here are a few examples of inverting intervals (I will not use an arrow going forward, just to let ya know, mangs).

Screen Shot 2016-07-06 at 9.32.10 AM

Regarding the new interval, there is a pattern to inverting notes and knowing what the new interval is.  I picked up a trick from the Tonal Harmony 5th Ed. by Stefan Kostka and the late Dorothy Payne.  The constant value of 9 is the method you can use to find the interval.  Essentially, start with 9 and subtract the current interval.

9 9 9 9 9 9
-2 -3 -4 -5 -6 -7
=7 =6 =5 =4 =3 =2

 

Picture4

You may have noticed earlier that I changed the quality of the interval as well.  The major 3rd became a minor 6th upon inverting, which holds true when inverting a diminished interval.  They become augmented chords, and vice versa.  Perfect intervals are the exception.

Picture5

Old quality M m P + o
New quality m M P o +

 

So, them’s the basics of inverting intervals, which I feel we can talk about inverting triads and seventh chords now!

As I said earlier, inverting intervals changes the harmony, and this is used to create more interesting textures in compositions. Other than root position triads, there are also 1st, and 2nd inversion triads. Seventh chords are the same, but with a 3rd inversion, with the 7th acting as the root of the chord. If you want to, think of inverting a chord as moving a chord member, other than the root, to the bass position (lowest voice) of your composition.

Picture6

At the end of the last post, I started talking about Roman Numeral analysis. A quick guide to telling us what quality a chord is, and where it is in the key. To add to that, there are symbols that tell us what inversion the chord is in. Root position triads will have no marker. First inversion triads are marked with a 6, and second inversions are 6 over 4 (6/4). Check the Roman numeral markers in the image above. The marker 6 is in reference to the interval of a 6th between the 3rd of the chord and the root of the chord. The 2nd inversion triad has an interval of a 6th and a 4th above the acting root. For the seventh chords, I want to try something different. I want to see if any readers want to explain the markers for the seventh chords. Let’s omit the position for obvious reasons. If you already know this, I ask that you give those who don’t know a chance to mull it over. To help memorize the inversion symbols, I think of it as a phone number (665)-765-4342. I know we aren’t in an age of remembering phone numbers, but come on – you can do it!

As always, if you want to ask any questions, please leave a comment below, or e-mail me at the link below. Hit me up on Instagram (@boognishtheory) for anything music related! Know of a band I should hear? Then quit hording those tunes, and send them to me! Want to know the best beer for bratwurst? Then share this, and I’ll let you stuff my opinion down your face hole. Here is one last table giving you those inversion symbols, if you didn’t like my hand-drawn one.

Bass position Triad symbol Seventh chord symbol
Root position (none) 7
First inversion 6 6

5

Second inversion 6

4

4

3

Third inversion (none) 4

2   (or just 2)

As always, thanks for turning on my corner!

 

Plugging In The Chord

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Welcome back, you theory enthusiasts! This time around, we are going to be talking about chords. These delightful, little triads have dominated the practice of music composition for centuries, despite many composers’ attempts to break away from what is called “tonality.” Tonal music has a home, and one of the best explanations of this comes from a lad who is way ahead of his age in understanding. Please take a moment and watch this.

In that song, he started with a G chord, which was his home, and also made the key of the song G-major. We are going to delve into tonality and how chords are used in a specific key, but first, let’s talk about building chords.

Remember when we talked about melodic and harmonic intervals? Well, chords are multiple harmonic intervals combined. Every chord has a root, third, and fifth. In the image below, the root note is G, the third of the chord is B, and the fifth is D.

mctc1

This is a major chord; one of four triads we are going to cover. The image below shows the intervals used to make the four different triads. There are two ways you can look at these: as a stacking of two different intervals of a third, or a combination of an interval of a third starting from the root and an interval of a fifth from the root.

mctc2

So how do you prefer to think of a major chord? A, or B?

mctc3

At the end of the day, every chord has a root, third, and fifth. However, there are chords that have a seventh, which is either adding a note a third above the fifth, or a seventh above the root. Again, both are correct.

mctc4

mctc5

Wow! Look at all these new chords we have! Wait, you didn’t think you were just getting 4 different chord qualities, did you? Imagine if you added a third on top of the seventh… NO KYLE!!! They aren’t ready!! …Anyways, essentially what you have here are major, minor, or diminished triads, with either a major, or minor third stacked on the fifth of the chord. Building from the root of the triad, you are adding a M7, m7, or d7.

Listen to the differences in the chords in this video. I play four chords: (1) a major triad, (2) a major seventh chord, (3) a major triad again, and (4) a major-minor seventh chord. The visual difference between a major seventh chord and a major-minor seventh chord is small, but the difference you hear is substantial.

The minor seventh chord stands alone as the only minor triad based seventh chord. If you are wondering why I haven’t listed a minor triad with a major seventh, it is because that would actually create and augmented triad between the third, fifth, and seventh of the chord, which I don’t feel aurally holds the quality of a minor chord. It does have that wicked, James Bond sound to it though!

The half-diminished and fully-diminished seventh are easy to differentiate. One way or the other, you have a diminished triad. As far as the seventh of the chord, if there is M3 between the fifth and the seventh, it is a half-diminished seventh chord. A m3 between the fifth and the seventh is a fully-diminished seventh chord.

We are going to discuss diatonic functions, which is how these chord qualities are used in a key, but first we are going to go back to the diagram of the C-major scale. As I said earlier, you aren’t going to see an augmented triad in a key without adding accidentals (either by raising the fifth of a major triad, or lowering the root of a minor triad).

mctc6

To wrap up, we are going to learn some super shorthand terms that are going to hopefully allow us to speak with some brevity. In the practice of music theory, we use Roman Numerals to define a chords place in a key, and it’s quality. Using numbers I-VII, we are able to account for the basic triads in a key. Uppercase Roman Numerals define major triads, and lower case defines minor triads. Augmented and diminished triads are marked with a +, or a º, respectively. Half-diminished seventh chords will have a ø rather than a º. So here it is, what we’ve been working towards.

mctc7

Hopefully we have some good groundwork going on to where we can discuss chords in this fashion, and if I need to clear things up, comment/e-mail all your questions! Until next time, and thanks for turning on my corner!

Interval-halla

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Welcome back everyone! This time we are going to cover simple intervals!  Now you may be thinking, “Intervals? Like high intensity interval training?” Lucky you! It is not that. Intervals are the distance between two notes. “Simple Intervals” are intervals that do not exceed an octave, and compound intervals are ones that do (but we won’t get into compound intervals for now).

When I discussed the major scale, I explained it as a series of half-steps, and whole-steps. These are intervals as well, and they can also be called a “minor 2nd” and “major 2nd”. On the piano, a minor 2nd would be any motion between C and C# (Db), and a major 2nd would be any motion between C to D. Feel free to reference the image I have included when needed. The #/b refers to the black keys being the respective sharp or flat of the neighboring keys.

keyboard

The main types of intervals are major (M), minor (m), perfect (P), diminished (d), and augmented (A). Each interval is going to receive a letter and number to classify what it is. Augmented intervals are a major or perfect interval that has been expanded a half-step, and diminished intervals are minor or perfect interval that has been decreased a half-step. Now this can cause confusion, because an A4 and a d5 are the exact same notes. The real difference between the two is the treatment of resolution, which we can talk about at a later time. So here are all the simple intervals:
staff

Wow! That’s a lot of intervals! Aren’t they amazing!? That’s the general idea of simple intervals, but now let’s talk about the different categories of intervals – maybe organize them out a little.

Let’s just clear up that there are melodic intervals, which is when two notes are played in succession, and harmonic intervals, when two notes are played simultaneously. Also, there are consonant and dissonant intervals. The sounds of these types of intervals are what classify them. Dissonant intervals have a lot of tension in their sound. You, the listener, usually like to hear this tension resolve, which is where consonant intervals come into play. The consonant intervals are: P1 (unison), P4, P5, P8, M3, m3, M6, m6. The dissonant intervals are: m2, M2, A4 (or d5), m7, M7.

I know that everything I have presented is only on a visual level, but there are tons of apps you can use to practice aural and visual recognition of these intervals. Personally, visual recognition of intervals is great for any musician, but is mostly used by the academic musician. On the other hand, both academic and non-academic musicians will benefit from aural practice of interval recognition. At UTA, the popular program was MacGamut. “MacDammit” was our name for it, but it got the job done. Another way of cementing some of these intervals into the old noodle is by associating them to musical pop culture. John Williams’ theme to “Jaws” is a easy way to memorize the sound of a m2. The video gamer in me relates a M3 to the pause sound from Super Mario Bros. 3. The opening two notes, “The Simp-”, of The Simpsons is how I learned to recognize A4/d5 (remember, they are the same thing). The list goes on. NBC Chimes are a M6 up, then a M3 down. So go! Go find your favorite music, and start making those relations people, because it will translate to your playing.

If you want to talk further about intervals with me, email or comment. Also, let me know what you use to remember intervals if you already know this stuff. Next time, we are going to be putting this interval knowledge to use by making chords out of 2-3 separate sets of intervals.

This entry brought to you by me watching my wife play Zelda, and as always, thanks for turning on my corner!

A Mode To New Scales

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Welcome back! Let’s dive in by readdressing the image I put up before:
MCTC-sacle-image
As is shown, two tetrachords are used to make a major scale. What is a tetrachord you say? Let’s flash back to Greece around 330 B.C.E. and meet one of the earliest theorists, Aristoxenus. Back in his time, there were 3 types of tetrachords: Diatonic, Chromatic, and Enharmonic.
mctc2.1
          Another theorist of the time, Cleonides, had used these to make his Species of Consonances, which state that the fourth, fifth, and octave are the most consonant sounding notes in a diatonic type of tetrachord. He had created our first full octave scales, and named them after different ethnic regions in Greece. Now flash-forward to the tenth century, which is where the current names for a handful of the modes we are going to discuss came from; all because some one messed up! Yeah, someone was translating Boethius, another Greek theorist, and just botched the labeling of the scales.
The modes that have kept their tenth century name are Dorian, Phrygian, Lydian, and Mixolydian. The remaining names, Ionian, Aeolian, and Locrian, are used in lieu of the Greek and Church mode names to eliminate confusion. Which if you really want me to post about those, just ask. So, onto putting some sense behind these names.
          Ionian is the name of the first mode, and this scale we all probably know pretty well considering it is a major scale. You probably caught this one early in your lessons, and now you have a new fancy name for it! Of course, if you take the intervallic pattern of the notes W-W-H-W-W-W-H (W=Whole step H=Half-step) and start them on any note, you will have a(n) major/Ionian scale based on that note. Below is C-Ionian:
mctc2.2
but if you wanted F-Ionian, you would start on F, and flat the fourth note of the scale (Bb). I feel like this is cut and dry, but please comment or e-mail if you would like to delve into this further.
          Next is Dorian, which if you are familiar with the natural minor scale, it is like that, but you raise the sixth note of the scale. Using the same notes from the C-major scale, we are going to start D. Check how we haven’t added any accidentals.
mctcdorian
We have a new scale, simply by maintaining the key signature of C-major and changing starting note. Each mode has it’s own characteristic sound to it, offering a variety of ways to change the tone of a song. A popular jazz tune written in Dorian is “So What”, written by Miles Davis.
          Next is the Phrygian Mode, which offers a significantly different color to the scale. Again, this mode also leans toward the natural minor scale, but with a flatted second.
mctcphrygian
This is a very Eastern, or gypsy, sounding mode, which has been used in many compositions. One you might be familiar with is Jefferson Airplane’s “White Rabbit.” I’m always looking for good examples of this in recent music, so if you know of any, please send them my way.
          As to not go on ad nauseam about a concept you might have grasped at this point, I will put the remaining modes at the bottom for you to look over. If you want to hear these, click here so that you can listen to the sound clips on the Wikipedia page for each mode. Specifically note that the Aeolian mode, is simply natural minor. So one major take away is that Ionian = major scale, and Aeolian = natural minor scale. But how will you use it? Certainly there are chords that these modes work over, right? Well, that is the exact case! In fact, the next installment is going to be about chords. We are going to look at how we can use these modes over chord changes in a key. We will also look at how chords are created, and what harmonic function they serve, specifically in a tonal sense. In the mean time, please comment/e-mail any questions you might have. I am glad to discuss this, and other topics you may be interested in, so please send any questions you have, and I will message back as soon as I am able.
mctclydian
mctcmixolydian
mctcaeolian
mctclocrian

Thanks turning on my corner!