Monthly Archives: February 2014

AC #37 Intervalics 101 (4ths)

Intro / Op-Ed

As the parenthesized number in the title suggests, 4ths are the main focus of this post. However, before we take a look at them, I want to say a few words about major scales. The scope of my comments is limited to the 1-octave span of the scale (major scale steps 1-8 only).

If you’re unsure about what you’re doing when you’re writing or playing major scales, you might try working from a “blueprint” that details a system for placing the scale’s notes in their proper sequential order. This helps minimize or eliminate mistakes in construction and/or execution. The “blueprint” I suggest you use contains numeric and intervalic information about the scale.

The numeric information gives you an outlined overview of the scale steps. Counting each step, as you move along (1-2-3-4-5-6-7-8), helps with keeping you aware of exactly where you are at each step of the construction process.

The intervalic information places the notes in order by measuring intervals: whole, whole, half, whole, whole, whole, half. This tells you the exact spacing required between each scale step.

The bone structure of a major scale is a string of major and minor 2nds, mostly whole steps between each note with the exceptions of steps 3 to 4, and 7 to 8.
The construction crew discusses the major scale specifications

Legend
1-8 = scale steps
w = whole step (major 2nd)
_1/2= half step (minor 2nd)
1 _w 2 _w 3 _1/24 _w 5 _w 6_w 7 _1/28

If you start with C and follow the schematic’s instructions, step-by-step, the C major scale will reveal itself on the white keys of your piano. Play the scale in the keys of G, D, A and E also.
Use this onscreen piano keyboard to play the scale in these 5 keys or go for all 12 if you like!

Constructing 4ths

Our musical alphabet uses only the 1st seven letters of our Arabic alphabet, A B C D E F G. However, for the reasons I mentioned in AC #10, I’ll use the same letter sequence but I’ll have the string start with C.

Now, to make a 4th, simply follow theses steps.

C D E F G A B

1. Select any letter from the 7-letter sequence.
(In doing that you’ve established the interval’s letter name and root… think of it as scale step “1”.)

2. Skip over the next 2 scale steps.
(In doing that you’re skipping over scale steps 2 and 3 because your mission is to make a 4th.)

3. Now, having skipped over scale steps 2 and 3, select the very next letter in the sequence.
(In doing that, you’ve selected scale step “4” as the interval’s upper note and then you extract scales steps 1 and 4.)

That’s it! You’ve constructed a 4th… a generic 4th*.
*(All accidentals are omitted or ignored In generic intervals. Only staff position matters.)

4ths – These intervals may be identified by their letter names because both letter names are the 1st and 4th letters of an alphabetically sequenced 4-letter string.

When written in standard music notation, 4ths will have exactly 2 unoccupied staff steps in between the interval’s lower and upper notes–a line and a space, OR, a space and a line–two alphabetically sequenced letters.

Keep the following points in mind:

1. The staff, by itself, represents a piano’s white keys only. Black keys are notated by accidentals. (Staff steps, unmodified by accidentals, are whole steps, except for the half steps at E to F and B to C)

2. Every staff line and every staff space correlates to a specific white key on the piano.
(This point applies to all ledger lines and ledger spaces.)

3. If two consecutive staff steps are skipped over, both correlating piano keys are also skipped! (One staff step = the distance from any staff line to the very next space or vice versa–up or down)

Perfect 4ths are formed by extracting the 1st and 4th notes of any major scale.

Perfect Intervals

What are they? Why are they called “perfect”?

Part of the answer to both questions has to do with the overtones and harmonics that only this particular class of intervals produce. Many piano tuners rely on perfect intervals in their craft. However, since the details that explain overtones and harmonics go far beyond the scope of this post, I’ll simply tell you which intervals are “perfect” and I’ll mention a distinguishing and affirming “key” characteristic of perfect intervals, (“Key” pun intended).

Which intervals are perfect?

There are only 4 of ’em! They come directly out of the major scale. Memorize ’em!

1-1 Perfect 1st or Perfect Unison
1-4 Perfect 4th
1-5 Perfect 5th
1-8 Perfect 8th or Perfect Octave

Here’s an optional verification process you can use to confirm an interval’s “perfect” status.

Perfect Interval Evaluative Characteristics Affirmation Test (P.I.E.C.A.T.) 😆
(OK! I just made-up this tongue-in-cheek acronym but here’s how the test works…)

A perfect interval is affirmed when the upper note of any given interval is also found in the major scale that begins on that interval’s lower note, AND, the lower note of that interval is also found in the major scale that begins on that interval’s upper note. Here’s another way to say it…

If your interval’s top note is present in its bottom note’s major scale, AND, its bottom note is present in its top note’s major scale, voilà! You’ve affirmed a perfect interval via “P.I.E.C.A.T.“!

“Did somebody say pie cat? Yummy! Mmmm! Got Milk?

The most commonly used accidentals are shown in the lineup just below followed by examples of the most common occurrences of 4ths in the key of C.

♮ = natural
♯ = sharp
X = double sharp
♭ = flat
♭♭ = double flat

Perfect 4th = C to F (The 4th note of a major scale remains unmodified)
Augmented 4th = C to F^♯ (The 4th note of a major scale is sharped once)
Minor 1st *(N/A)
*(Minor functionality isn’t allowed on any perfect interval.)
Diminished 4th = C to F^♭ **(The 4th note of a major scale is flatted once)
**(Perfect intervals become diminished with only one flat)

This link will open an Acrobat/Adobe flash type of applet where you’ll be asked to correctly match ten intervals via a drag-n-drop process. Doing the exercise at least 4 or 5 times will give you an introductory workout on identifying and matching the intervals in C and other keys.

Study well and have fun,

See you next post,

AC #36 Intervalics 101 (3rds)

Intro / Op-Ed

Since 3rds are made from scales and chords are made of couplings of various kinds of 3rds, I’ll start this post by saying a few words about scales and chords.

Scales, at their basic level, are formed by stringing and connecting a series of 2nds together and each note in the string may or may not have a modifying accidental attached to it. In the case of most traditional scales, like the major scale, every scale step and its letter name must be arranged in numerical and alphabetical order. Also, consecutive sequencing of the same letter name is not allowed (using the same letter name twice in a row is not allowed). At the root of all scales, you’ll find intervals.

Chords, at their most basic level, are formed by extracting every other note of any given scale which creates a series of connected 3rds and each note in a chord may or may not have a modifying accidental attached to it. At the root of all chords, you’ll find intervals.

Thirds

Thirds are very important intervals to understand because our system of harmony, tertian harmony, is based on them. Our musical alphabet uses only the 1st seven letters of our Arabic alphabet, A B C D E F G. However, for the reasons I mentioned in AC #10, I’ll use the same letter sequence but I’ll have the string start with C.

Now, to make a 3rd, simply follow theses 3 steps.

C D E F G A B

1. Select any letter from the 7-letter sequence.
(In doing that you’ve established the interval’s name and root… think of it as scale step “1”.)

2. Skip over “scale step 1’s” next-door-neighbor.
(In doing that you’re skipping over scale step 2 because your mission is to make a 3rd.)

3. Now, having skipped over scale step 2, select the very next letter in the sequence.
(In doing that, you’ve selected scale step “3” as the interval’s upper note and then you extract scales steps 1 and 3.)

That’s it! You’ve constructed a 3rd… a generic 3rd*.
*(All accidentals are omitted or ignored In generic intervals. Only staff position matters.)

When 3rds are stacked on top of each other in a totem-pole-like fashion, they form chords, and in order to understand chords, it’s critical that you understand 3rds in general and major 3rds in particular.

Understanding major 3rds.

Major 3rds are particularly significant because they are the intervals by which the basic major and minor tonality and functionality of chords and scales are distinguished or determined.

Major 3rds are formed by extracting the 1st and 3rd notes of any major scale. Even when you’re dealing with non-major 3rds, (like augmented, diminished, or minor 3rds etc.), you’re still dealing, with the same letter names of the 1st and 3rd notes of a major scale. The specific major scale with which you’re dealing is determined by the name of the 3rd’s lowest note. The interval’s functionality (major/minor etc.) is determined by the name of the 3rd’s upper or top note, and in the case of major 3rds, the top note is unmodified (diatonic–which means only scale tones are allowed). Further analysis of the major 3rd reveals that it is an extraction of the 1st and 3rd notes of a subset of major scale notes which I call the major trichord (major scale steps 1, 2, and 3)–not to be confused with the major triad (major scale steps 1,3, and 5).

For example: If you were to play the first 3 notes of the C major scale (C-D-E), you would have played scale steps 1-2-3, you would have covered the distance of two full whole steps, and you would have simultaneously played the C major trichord. When you extract only the 1st and 3rd notes of any major trichord, and/or any major scale, you’ve extracted a major 3rd.

When building major 3rds on a piano, either point below will help guide your construction.

1 – Place your fingers on the first 3 scale steps of any major scale you chose, then play the 1st and 3rd notes… (the outer “book-end” notes).

2 – Place your fingers on only 2 whole steps of any major scale you chose, then extract the 1st and 3rd notes… (the outer “book-end” notes).

Either process should lead you to a successful construction of a major 3rd.

More review, extra emphasis, a few cautious tips, and another hypothetical

3rds – These intervals are easily identified because of the contiguous way in which both letter names are alphabetically sequenced. With 3rds, the letter names of both notes will be alphabetically adjacent to exactly one letter in between them (the “skip-over” process mentioned just a few paragraphs above).

When written in standard music notation, both notes will be written in consecutive spaces or on consecutive lines, notwithstanding any accidentals which may be attached to either note.

Don’t let yourself be fooled by the sound or the physical spacing of your fingers on the piano keys when certain accidentals are used! Read your instrument panel and fly by the instruments!

On the piano keyboard, things can get a little trickier, as I illustrated with the hypothetical example in AC #35. Here’s another example. Look at the photo. What interval does that look like? Click the player… What interval does it sound like? Can you ID it beyond a shadow of a doubt?

The interval denies your assertion and cries, “Not guilty! Mistaken ID”! Can you be 100% certain of your ID?

I think NOT! You need more information! With the info you’ve been given, you just can’t be sure!

What looks like C might in fact be a B^♯ or a D^♭♭ and what looks like E could easily be D^Xor F^♭. We could argue probability all day long and, in many cases, probability will get you by just fine! However, probability and certainty are two different things. I’ll probably agree with you as to what it looks, sounds, and feels like, but our deductions would only be guesses. Without some other type of corroborating evidence, we can’t be certain that the interval we see is even a 3rd!

Here’s what I think would happen to both of us if we were in some special type of people’s court trying to prove our interval ID case and our courtroom transcripts read something like this… “Judge it looks like such-and-such, and it sounds like so-and-so, and it feels like it might be a…

The Honorable Judge Umust B. Wright and bailiff Orville Tossit Outler BAM!!! The Judge stops our case mid-sentence during my argument and says…!

BAM!!! “Case dismissed!” Click the player to hear the judge order his bailiff to show us the way out before calling me back for a sidebar. We were lucky to escape without being fined for wasting the court’s time! Now of course I’m just kidding around here but we really needed more information because our piano-scenario-only evidence was too inconclusive to prove anything. The Judge made the correct ruling!

In this particular hypothetical, you’ve been presented with both notes of an unknown interval on the piano keyboard without being told the note name of either piano key or anything about type of interval for which you’re looking. Also, you haven’t been given any other relevant, supportive information like a key signature, a sheet music representation, or replica of the interval. Under these circumstances, the interval might be a unison/1st or a 2nd, it could be a 3rd, it may be a 4th, and so on. You just don’t have enough info to definitively identify the interval pictured in the piano photo. In order to correctly identify the interval in this particular hypothetical, beyond the shadow of a doubt, you need to have the letter names of both notes of the interval.

Hopefully that’s all clear now and after a few more post-closing words, it’ll be time to take either the end-of-the-post-easy-quiz or a couple of aspirin! (:-)

Major 3rds occupy the 1st and 3rd notes of any given major scale. They occupy the outermost notes of 2 full whole steps. Once you’re able to clearly see and understand how to construct and analyze the major 3rd, analyzing, constructing, or identifying 3rds in any of their modified states should become a much easier task because each of the modifying accidentals that may be applied to the major 3rd is self-explanatory in terms of what it does to achieve its modification. Now that was a mouthful but trust me! This stuff is not difficult at all if you proceed on a step-by-step basis and don’t get ahead of yourself… or your teacher!

Let me ask you a question that’s unrelated to music. Once you learned your “ABCs”, how many times have you had to go back to re-study and re-learn the alphabet because you’d forgotten it? For most of you the answer is, “Not once”, because you studied and learned it thoroughly, and you use it in some form, every day of your life! The same thing applies to the language of music!

Thoroughly studying and learning the 15 major scales and their major intervals, by spelling them and writing them out, is what I recommend for you to do as a multi-week or multi-month project, once you’ve completed your study of intervals in this particular series of posts. There’s no rush or speed contest here! Just take your time, move systematically, and study thoroughly!

The most commonly used accidentals are shown in the lineup just below followed by examples of the most common occurrences of 3rds in the key of C.

♮ = natural
♯ = sharp
X = double sharp
♭ = flat
♭♭ = double flat

Major 3rd = C to E (The major 3rd is unmodified)
Augmented 3rd = C to E^♯ (The major 3rd is sharped once)
Minor 3rd = C to E^♭ (The major 3rd is flatted once)
Diminished 3rd = C to E^♭♭ (The major 3rd is flatted twice)

Study well and have fun,

See you next post,

AC #35 Intervalics 101 (2nds)

Intro / Op-Ed

Moving into 2nds introduces minor intervals, so a preliminary discussion of major, augmented, minor, and diminished intervals is in order.

As I mentioned in AC #34, the major scale is the scale upon which our music system is based.

Question: When an interval is classified as a “major interval”, what does that mean?
Answer: Both notes of the interval are unmodified, unaltered notes of the major scale.

Question: When an interval is classified as a “minor interval”… it is “minor” compared to what?
Answer: Compared to its unmodified, unaltered major scale counterpart.

Question: When an interval is diminished or augmented… that’s in contrast to what?
Answer: In contrast to its unmodified, unaltered major scale counterpart.

Let me emphasize this major scale point once more! The major scale is the scale upon which our music system is based. It is the backdrop against which intervalic modifications like minor, augmented, and diminished are contrasted or compared.

We’ll have a cursory examination of the major scale in the AC #37 post, but for now, I’d like to keep your attention focused on 2nds because of the various types of 2nds that will appear in the drill exercises at the end of this post, which I hope you’ll do.

Let’s take a closer, analytical look at 2nds.

2nds – These intervals are very easy to identify because the letter names of both notes will be alphabetically adjacent to each other. An interval with letter names that display that kind of juxtaposition is a 2nd of some type, notwithstanding any accidental modifiers that may be attached to either letter. If the two letter names form a whole step, you have a clear signal that you’re dealing with the first and second notes of some given major scale because the first two notes of any major scale is a major 2nd and all major 2nds are whole steps. The specific major scale to which both notes belong is determined by the interval’s first or lowest note, with the stipulation that it’s and ascending interval being identified.

Generic Alphabetical Identification: This is easy in the case of 2nds because the letter names of both notes are alphabetically adjacent such as A is to B, and B is to C, and C is to D, etc. Whenever both note names of an interval have this kind of consecutive alphabetical adjacency, you have a 2nd of some type.

Standard Music Notation Identification: This is easy in the case of 2nds because when 2nds are written on a staff, one note is a line note, the other note is a space note, and both note heads will be in the closest line/space proximity of each other that is possible on a music staff. (The note heads of 2nds never share the same line or space on a music staff)

Piano Keyboard Identification: On the piano keyboard, 2nds are still easily identified by their core note names. However, depending on the accidentals attached to the notes, identifying 2nds, or any other interval, can get a little tricky if you’re not careful! I’ll explain what I mean.

Airline pilots can fly planes by relying mostly on the information coming to them from their instrument panel because visual conditions in the air and on the ground may be misleading. Similarly, regarding interval ID and music-reading, conditions in your ear and on the piano may also be misleading and unreliable from time to time, and in those cases, good reading abilities will allow you to rely on your own “instrument panel”… the musical staff!

The following is a hypothetical example of where conditions in your ear and on the piano might be misleading and unreliable. Using ascending notes within the same octave, do the following…

Play B–double flat and C double sharp on a piano. What does it look, feel, and sound like to you?

If you answer “4th” in my theory class, I’ll have to place one of these next to your answer!

Don’t be fooled by physical spacing of the keys or the sound of the interval!

Notwithstanding any of the accidentals which may be attached to either note of any interval, if the core note names have consecutive alphabetical adjacency, you have a 2nd of some type!

When you strip away or ignore the accidental modifications of both notes, you should see that the core note names are B and C, and B to C is a 2nd at the core! Now when you reapply the accidental modifiers to both notes, your analysis should reveal the specific type of 2nd it is.

Does anyone have the answer for this hypothetical? If so, I’d love to give you one of these!

Let’s continue with 2nds and move on to the drill section.

The most commonly used accidentals are shown in the lineup just below followed by examples of the most common occurrences of 2nds in the key of C.

♮ = natural (cancels 1 accidental)
♯ = sharp (raises a note by one 1/2 step)
X = double sharp (raises a note by two 1/2 steps)
♭ = flat (lowers a note by one 1/2 step)
♭♭ = double flat (lowers a note by two 1/2 steps)

Major 2nd = C to D (The major 2nd is unmodified)
Augmented 2nd = C to D^♯ (The major 2nd is sharped once)
Minor 2nd = C to D^♭ (The major 2nd is flatted once)
Diminished 2nd = C to D^♭♭ (The major 2nd is flatted twice)

Study well and have fun,

See you next post,

AC #34 Intervalics 101 (1sts)

Intro / Op-Ed

The first scale that beginner music students encounter is usually the “major scale” and in studying the major scale they are inevitably introduced to the core building blocks of our Western music system. What are those building blocks? Intervals!

Understanding Intervals.

A solid understanding of intervals is essential to understanding how to construct scales, chords, and voicings. Understanding intervals also helps your ability to read music, compose melodies, construct bass lines, and improvise. Intervals comprise the bedrock upon which our Western music system is built and understanding them will help you build a solid foundation for your musicianship.

Please note that only ascending intervals will be covered in all of the “Intervalics 101” posts. Descending intervals are excluded. However, I can be persuaded to address them in the future!

Since the scope of this examination ranges from 1sts to 8ths, I’ve divided the presentation of material into a short series of eight individual mini-posts. I may add one or two more posts toward the end of the series for the purpose of giving you additional drill and review exercises. This will depend on the feedback I get from you and my students who also monitor these posts.

During this series, we’ll be taking a look at how to identify and name these intervals. From the brief examinations, discussions, and easy follow-up drill exercises in each post, you should come to have a very clear understanding of intervals. By the time you’ve successfully completed the work in all eight mini-posts, you should have an easier time of using intervalics to assist you in things like constructing bass lines, chords, specialized/personalized chord voicings and chord scales.

Speaking of chord scales… Let me draw your attention to the major scale again. In addition to being a chord scale, it’s also the scale upon which we base all of our musical analysis.

To understand the major scale, you need to understand half steps and whole steps… and to understand half steps and whole steps, you need to understand major and minor… and to understand major and minor, you need to understand the major scale… and to understand the major scale, you need to understand intervals… and to understand intervals, you need to understand half steps, whole steps, major, minor, diminished, and augmented! Whew! I’ll stop there! (Smile!) Now all of that may sound like some kind of riddle or comedy routine like Abbot and Costello’s “Who’s on First” skit, but it’s all true! So let’s get started by defining interval.

What is an interval?

An Interval, defined as a musical term, is the measured distance between any two given musical notes. The unit of measure used to calculate the distances is usually calibrated in half steps, whole steps, or a combination of half and whole steps.

Should you study intervals? Are they a waste of you time?

Yes and no! Yes! You should study them! No! They are definitely NOT a waste of your time!

Studying intervals provides you with a way to analyze and systematically identify the precise distances between two notes. It gives you another tool to help improve and sharpen your note-spelling/music-writing skills, your transposition abilities, and your eye-to-hand coordination skills as applied to finger placement/spacing on the piano keyboard. Intervalic analysis may be equally applied to notes on the staff and keys on the piano keyboard.

The ways in which this particular area of concentration help you to elevate your skills of music-reading and music-analysis are numerous and tremendous! Whether you are a beginner or an advanced musician who could use some review on the subject, interval study is well worth your while!

Intro “wrap-up”

I hope all that was said, in the intro-op-ed,
got you fired-up and ready-to-go!
If the info that’s ahead, is something yet you haven’t read,
then learn it well to make yourself a pro!

Intro Wrap-up; Art Matthews
(Beat Box)!

Okay! It’s time to take a look at the first interval of the series…1sts!

1sts – a.k.a. unisons or prime intervals. These intervals are easily identified because both notes share the same letter name. When written in standard music notation, they share the same line or space on the staff, notwithstanding any accidentals which may be attached to either note. On the piano keyboard, they are either the same key or next door neighbors depending on the attached accidental. (Next door neighbors, In the case of 1sts, have zero keys in between.)

The most commonly used accidentals are shown in the lineup just below followed by examples of the most common occurrences of 1sts in the key of C.

♮ = natural
♯ = sharp
X = double sharp
♭ = flat
♭♭ = double flat

Perfect 1st = C to C (The 1st note of a major scale remains unmodified)
Augmented 1st = C to C^♯ (The 1st note of a major scale is sharped once)
Minor 1st *(N/A)
*(Minor functionality is not allowed on any perfect interval)
Diminished 1st = C to C^♭ **(The 1st note of a major scale is flatted once)
**(Perfect intervals become diminished with only one flat)

Study well and have fun,

See you next post,