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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)

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 #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,

AC #33 Guest Speaker’s Tips on Reading and Sight-reading (part two)

Today, I turn again to Ms. Margaret Fabrizio for part two of “Guest Speaker’s Tips on Reading and Sight-reading”. (Part one appears in AC #30). Among many other things, Ms. Fabrizio is a master harpsichordist and a very well respected music educator.

In today’s post, she continues to share her opinions and give you valuable tips on various things that pertain to beginner and intermediate piano students. She gives hints and makes suggestions as to what you should be doing and how you might be “thinking” about certain things that are pertinent to your musical development, progress, and growth. Spend the next 5-minutes with her and check out more of what she has to say.

Of all the tips and things she briefly discusses in this video, I’d like to single-out and draw your attention to the tip she offers in the form of a question at the point of the video where she asks, “Do you know intervals?” (2:25) After elaborating a little she gives you a few examples of how intervalic information is applied to piano. I’ll focus on intervals a little more in the next post.

In addition to the entertainment value of watching her play, there are things you can actually learn from simply observing her hand positions and finger movements as she negotiates her way a piece like the one I’ve linked here.

I’ll close here and say practice daily, practice well, and be patient.

See you next post.

AC #30 Guest Speaker’s Tips on Reading and Sight-reading

I reached out to a very special person who is going to speak to you in this post via one of her videos. Please allow me to preface her appearance with a few thoughts and words of my own.

Two practice activities that are very often mistakenly regarded as being synonymous:

1. The practice of learning to read and sight-read music.
2. The practice of learning to play songs using a “sight-enhanced playing-by-ear” approach.

1. “LEARNING TO READ AND SIGHT-READ MUSIC”

After learning the names of the piano keys, teaching beginner students to focus on note reading in 5-finger positions, starting with the “C Position“, is and has been a widely-accepted practice for years. It’s how I was brought-up and many of today’s nationally recognized traditional method books use still this methodology. I wholeheartedly believe in the efficacy of this method and I use it with my beginner students. I also use it with some of my intermediate and advanced students who wish to go back to fine-tune or brush-up their music reading skills.

Did I say advanced students? Yes! That’s right! Some of the world’s most well-known and formidable musicians are/were not good “readers-of-music”. From Irving Berlin to Billy Joel. From Glenn Gould to Erroll Garner. From Bela Fleck to Sir Paul McCartney. There are loads of musicians who’ve been up-front and very honest about their music reading abilities which, by their own words, range from not-so-good to not-at-all.

As evidenced by their very successful careers, it’s easy to see that the ability to read music is in no way THE determinative factor as to whether or not you’re going to become an excellent player/musician or have a successful career.

Nevertheless, there are many musicians who, in their heart-of-hearts, later come to know and realize the importance of what they’re missing. Hopefully, many of them will also know and realize that it is never too late to go back and get any of the things which they may have missed during their formative years. Just go back and get it! It’s as simple as that! Put it on a “Bucket List”, then find someone to help get it done! If you’re just starting out, then get it done right now so that you don’t have to go back and do it later.

So, whatever the reason, if learning to read music is a high priority item on your list of objectives, then I recommend that you find a teacher/coach like me, my guest speaker, or someone you may know to guide you through the maze of activities that lie ahead of you. Don’t go it alone! It is difficult to do this alone!

2. LEARNING REPERTOIRE USING A “SIGHT-ENHANCED PLAYING-BY-EAR” APPROACH

The core component of “sight-enhanced playing-by-ear” lies in the key phrase, Playing-by-ear. Playing-by-ear happens when you use only your ears to recreate the sounds (melodies, chords, rhythms) you hear. It’s a wonderful skill to have and I encourage you to develop it to the best of your ability. Later on, playing by ear is often enhanced by other things that you may learn in music theory such as intervals and “note reading”. With this method, you’ll frequently find yourself working on small sections and segments of songs… perhaps 2, 4, or 8 measures at a time. As long as your objective is to “learn to play the piece”, this approach is very good! Using written notes to assist you with your playing by ear activities is what sight-enhanced playing-by-ear is all about.

However, learning to play songs that way is NOT at the center of what learning to read and sight-read music is all about.

Guest Speaker Video

Watch this video and spend the next 10-minutes with my guest speaker. Listen to her share some of her thoughts and tips on how to improve your reading and sight-reading music skills. She spells out her reasoning as to why you, and piano students in general, should slowly work your way through level-appropriate music. Everyone who is serious about either learning or brushing-up sight-reading skills should check out what she has to say. She is a real treasure!

Of all the tips and points that Margaret makes in this video, I’d like to emphasize the fact that consistent, daily work in this area is what will move you along. Practice well and be patient.

See you next post.