Okay! It’s time to take a look at the last interval of the series!
8ths – a.k.a. octaves. These intervals are easily identified because both notes share the same letter name. When written in standard music notation, the upper note will occupy a space if the lower note is on a line and vice versa, notwithstanding any accidentals which may be attached to either note.
Several perfect octaves are illustrated in the graphics just below.
On the piano keyboard, both notes of a perfect octave share the same letter name and they are 8 major scale steps apart (up or down).
Play some octaves starting on as many keys as you can with this playable onscreen piano keyboard.
Major Scale Legend 1-8 = scale steps w = whole step (major 2nd) 1/2= half step (minor 2nd) 1w2w3 1/2 4 w5 w 6 w7 1/2 8
The most commonly used accidentals are shown in the lineup just below followed by examples of the most common occurrences of 8ths in the key of C.
Perfect 8th = C to C (The 8th note of a major scale remains unmodified) Augmented 8th = C to C♯ (The 8th note of a major scale is sharped once) Minor 8th *(N/A) *(Minor functionality isn’t allowed on any perfect interval.) Diminished 8th = C to C♭**(The 8th 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.
After working with the “open-book” drag-and-drop drill exercises in this section, move on and dive into some deeper waters with the staff and keyboard exercises just below.
Dive into “deeper waters” with these staff and keyboard exercises
The blue staff 2 or 8 opens a page where only numeric values are required in your answer.
Clicking the treble staff or keyboard icon opens a respective interval ID page where numeric and quality values are required.
Since each exercise utility is never-ending and presents questions indefinitely, you may want to set some type of completion benchmark for yourself such as, answering 25 up to 100 questions correctly or using the timer, located at the top of each utility, to set a time limit, such as 5 to 10 minutes.
In any case, keep working until you have a success rate that’s between 90% and 100%.
This post is a round-up and review of the intervals we’ve covered in the series up to this point. The things I intended to cover in this series, like interval ID and modification, were done earlier. For your convenience, I’ve included lots of links to each of the earlier posts in numerical order.
Knowing all of the intervals within an octave enhances your musicianship in lots of ways. Your voicing, ear training, transposition, and reading abilities are among the things it enhances.
Construction of Intervals (1sts thru 7ths) from the steps of a Major Scale
Start with #1 then select any other scale step. Extract both numbers and your interval is created!
Major Scale Legend (a.k.a Major Heptachord {since we stop at 7}) 1-7 = scale steps w = whole step (major 2nd) 1/2= half step (minor 2nd) 1w2w3 1/2 4 w5 w 6 w7
Play a major heptachord in as many keys as you can with this playable onscreen piano keyboard. Start with any key and follow the schematic’s instructions, step-by-step, (or 1/2 step where needed).
Construction of Generic Intervals 1sts – 7ths from the 7-Letter Music Alphabet
C D E F G A B
Simply choose any two letters and your generic interval is instantly created. If there’s only 1 letter in between the 2 you’ve chosen, you have a 3rd. If there are 2 letters in between, you have a 4th etc. *(All accidentals are excluded In generic intervals. Only letter names and staff position matter.)
When written in standard music notation, intervals from 1sts thru the 7ths look like this in C.
Keep the following points in mind:
1. The staff represents a piano’s white keys only. The 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) (One staff step = the distance from any staff line to the very next staff space or vice versa, up or down)
(The video below shows intervalic 7ths being played up and down an octave in the key of C.)
I recommend practicing rudiments of any type in “musical” contexts because it provides more avenues to make music with the rudiments before starting to apply and use them in songs.
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.
After working with the “open-book” drag-and-drop drill exercises in this section, move on and dive into some deeper waters with the staff and keyboard exercises just below.
Dive into “deeper waters” with these staff and keyboard exercises
The blue staff 2 or 7 opens a page where only numeric values are required in your answer.
Clicking the treble staff or keyboard icon opens a respective interval ID page where numeric and quality values are required.
Since each exercise utility is never-ending and presents questions indefinitely, you may want to set some type of completion benchmark for yourself such as, answering 25 up to 100 questions correctly or using the timer, located at the top of each utility, to set a time limit, such as 5 to 10 minutes.
In any case, keep working until you have a success rate that’s between 90% and 100%.
Sevenths are among the first intervals I bring to the attention of my students who are are interested in studying chord voicings. The use of 7ths, as they relate to jazz, may be heard by listening to the left hand of pianists like “Bud” Powell and Sonny Clark during their solos.
Sevenths come directly out of the major scale and although it’s a common practice to think of the major scale as an 8-note scale, the note we think of as 8 is only an octave-repetition of scale step 1. Scale step 8 is really scale step 1 of the major scale, starting in a different octave. So in reality, major scales are 7-note scales and there’s a term for 7-note scales. Heptachords! Ta! Da!
Heptachords are 7-note scales and perhaps the MAJOR heptachord is the most well-known of all heptachords because it actually IS the major scale upon which our music system is based.
Now I don’t know about you but saying “major scale” rolls off of my tongue a lot easier than saying “major heptachord”! I have to be careful to not bite my tongue when I say it! I use these kinds of terms in class as a way to provide a historical perspective. It’s good to know this kind of stuff but don’t get hung-up on names! They’re only words that are part of the historical record. Don’t over-analyze because too much analysis breeds paralysis! 😈 So, with that said, on we go!
Construction of Major 7ths from the 1st and 7th notes of major heptachords
Major 7th intervals are made by extracting the first and last note of a major heptachord. Just select and extract the 1st and 7th scale steps only and the interval is ready to be deployed.
Major Heptachord Legend (a.k.a Major Scale) 1-7 = scale steps w = whole step (major 2nd) 1/2= half step (minor 2nd) 1/2= half step (minor 2nd) 1 w2 w3 1/2 4 w5 w 6 w7
Start with C and follow the schematic’s instructions, step-by-step, the C major heptachord will reveal itself on your piano’s white keys. Play the heptachord in the keys of G, D, A and E too.
Construction of Generic 7ths from the 7-Letter Musical Alphabet
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 5 scale steps. (In doing that you skip over scale steps 2, 3, 4, 5, and 6 because your mission is to make a 7th.)
3. Having skipped over scale steps 2, 3, 4, 5, and 6, select the very next letter in the sequence. (In doing that, you’ve selected scale step “7” as the interval’s upper note and then you extract scale steps 1 and 6.)
That’s it! You’ve constructed a 7th… a generic 7th*. *(All accidentals are excluded In generic intervals. Only letter names and staff position matters.)
7ths – These intervals may be identified by their letter names because both letter names are the 1st and 7th letters of an alphabetically sequenced 7-letter string (heptachord).
When written in standard music notation, 7ths will have exactly 5 unoccupied staff steps in between the interval’s lower and upper notes–a space/line/space/line/space, OR, a line/space/line/space/line. Also, five alphabetically sequenced letters will be skipped over.
Keep the following points in mind:
1. The staff represents a piano’s white keys only. The 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) (One staff step = the distance from any staff line to the very next staff space or vice versa, up or down)
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 5 consecutive staff steps are skipped over, 5 correlating piano keys are also skipped over! (This “skip-over/fly-over” concept and analogy is illustrated in the key of C in the photos just below.) (Your eyes skip-over the 5 staff steps while your fingers “fly-over” the 5 correlating piano keys.)
(The video below shows LH 7ths being used in a practice exercise on blues chord changes.) In jazz and pop music chord symbol notation, 7ths, as in X7th, are played as minor 7ths or b7s. The only time a major 7th is played is when a specific instruction calls for it like (EbMaj7).
Major 7th = C to B (The major 7th is unmodified) Augmented 7th = C to B♯(The major 7th is sharped once) Minor 7th = C to B♭(The major 7th is flatted once) Diminished 7th = C to B♭♭(The major 7th 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.
Sixths are consonant intervals that add stability to many situations where stability is desired. They’re beautiful sounding intervals that add richness to the music in which they are used. Things like block chords, melodic passages, and improvisations are enhanced with their use.
Hopefully, the mechanics of transforming major intervals into their other states of modification is “old hat” to you by now. With that said, we’ll quickly move through this post and the rest of this series starting from here. If you have any questions, just sign-up for a few lessons.
Construction of Major 6ths from the numerical scale steps of Hexachords
Hexachords are 6-note scales. The Major Hexachord is a major scale subgroup that’s comprised of major scale notes 1 thru 6. Extracting the 1st and 6th notes make a major 6th.
Major Hexachord Legend 1-6 = scale steps w = whole step (major 2nd) 1/2= half step (minor 2nd) 1 w2 w3 1/2 4 w5 w 6
If you start with C and follow the schematic’s instructions, step-by-step, the C major hexachord will reveal itself on your piano’s white keys. Play the hexachord in the keys of G, D, A and E too.
Construction of Generic 6ths from the 7-Letter Musical Alphabet
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 3 scale steps. (In doing that you’re skipping over scale steps 2, 3, 4, and 5 because your mission is to make a 6th.)
3. Having skipped over scale steps 2, 3, 4, and 5, select the very next letter in the sequence. (In doing that, you’ve selected scale step “6” as the interval’s upper note and then you extract scale steps 1 and 6.)
That’s it! You’ve constructed a 6th… a generic 6th*. *(All accidentals are excluded In generic intervals. Only letter names and staff position matters.)
6ths – These intervals may be identified by their letter names because both letter names are the 1st and 6th letters of an alphabetically sequenced 6-letter string (hexachord).
When written in standard music notation, 6ths will have exactly 4 unoccupied staff steps in between the interval’s lower and upper notes–a space/line/space/line, OR, a line/space/line/space. Also, four alphabetically sequenced letters will be skipped over.
Keep the following points in mind:
1. The staff represents a piano’s white keys only. The 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) (One staff step = the distance from any staff line to the very next staff space or vice versa, up or down)
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 4 consecutive staff steps are skipped over, 4 correlating piano keys are also skipped over! (This “skip-over/fly-over” concept and analogy is illustrated in the key of C in the photos just below.) (Your eyes skip-over the 4 staff steps while your fingers “fly-over” the 4 correlating piano keys.)
(The video below shows 6ths being used in block chords and descending scale passages.)
The most commonly used accidentals are shown in the lineup just below followed by examples of the most common occurrences of 6ths in the key of C.
Major 6th = C to A (The major 6th is unmodified) Augmented 6th = C to A♯(The major 6th is sharped once) Minor 6th = C to A♭(The major 6th is flatted once) Diminished 6th = C to A♭♭(The major 6th 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.
Of all the intervals we’re covering, perfect 5ths are among the strongest and most versatile!
The interval is so strong that, with only 2 notes, (almost like a triad having 1 of its 3 hands tied behind its back!), it can hold its own as a “power chord” and sonically cut-thru and even overshadow chords that have a much higher note density. The use of this interval on pianos, as an “anchoring” type of “power chord”, can be heard in the LH boogie-woogie stylings of pianists like James P. Johnson and Sammy Price, and also in the sheer power of either hand of Dorothy Donegan and in the LH bomb-dropping, sonic-booms of McCoy Tyner.
The interval’s versatility is shown by its chameleon-like ability to comfortably blend in with both major and minor tonalities. This special ability is due to the fact that “power chords” lack 3rds, which is one of the reasons that the perfect 5th is an ever-present tool of “top-40” poppers as well as slammin’ hard rockers! Its use and presence in playing situations is easily revealed to people with trained ears. Its use and presence are also evidenced on many of today’s pop music lead sheets and piano scores that are populated with chord symbols like C5, F5, and G5… musical shorthand that signals a perfect 5th is to be played where those chord symbols appear.
Now with all of that being said about perfect 5ths and “power chords”, I want to make sure I say a few words about the following:
Is the “power chord” really a chord?
“It takes a minimum of 3 notes to make a chord” is a point that’s taught in music theory classes.
In many instances, in its role as a “power chord”, the perfect 5th is further strengthened by doubling its root note with an octave(see *2 – just below). This reinforcement adds a third note which bolsters and gives credence to the notion of referring to these intervals as chords. However, even with an added 3rd note, “power chords” still remain classified as an interval! Why? Let’s consider the consistency and congruency of the following three scenarios.
1 – Consider middle C. Add 2 more Cs to it in ascending octaves. You’ve got 3 notes! Is it a triad?
If you said yes, you’ve got one of these coming your way with an invitation to stay after class! If you said no, you’ve got one of these coming your way with an invitation to skip class today! Three Cs spread over 3 consecutive octaves is not a triad. It’s a triple octave unison!
*2 – Consider C perfect 5th (C and G or 1 and 5). Add another C exactly 1-octave above the root.
You have 3 notes! Is it a triad? No! You have a Perfect 5th interval with a doubled root!
3 – Consider C major triad (root position, 1-3-5). Add another C exactly 1-octave above the root.
You’ve got 4 notes! Is it a 7th chord? No! It’s a triad with a doubled root, a 4-note triad if you will.
Octave-doubling any note(s) of an interval or a chord does not change the entity’s classification. The rule that says “it takes a minimum of 3 notes to make a chord” governs chord classification and the 3 notes must be 3 different notes, not an octave doubling of an original unit member.
So although perfect 5ths are also known as “power chords”, by definition, they are not chords. They are intervals, and it is my hope that that you’ll get to know these intervals a little better through the work you’re doing in this series.
Construction of Perfect 5ths from the scale steps of Pentachords/Pentascales
Pentachords and pentascales (synomous terms), are the first 5 notes of a diatonic scale. Major pentachords and/or major pentascales are comprised of major scale notes 1 thru 5. Extracting only the 1st and 5th notes of this major scale subgroup yields a perfect 5th interval.
If you start with C and follow the schematic’s instructions, step-by-step, the C major pentascale will reveal itself on your piano’s white keys. Play the pentascale in the keys of G, D, A and E too.
Construction of Generic 5ths from the 7-Letter Musical Alphabet
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 3 scale steps. (In doing that you’re skipping over scale steps 2, 3, and 4 because your mission is to make a 5th.)
3. Now, having skipped over scale steps 2, 3, and 4, select the very next letter in the sequence. (In doing that, you’ve selected scale step “5” as the interval’s upper note and then you extract scale steps 1 and 5.)
That’s it! You’ve constructed a 5th… a generic 5th*. *(All accidentals are excluded In generic intervals. Only letter names and staff position matters.)
5ths – These intervals may be identified by their letter names because both letter names are the 1st and 5th letters of an alphabetically sequenced 5-letter string (pentachord or pentascale).
When written in standard music notation, 5ths will have exactly 3 unoccupied staff steps in between the interval’s lower and upper notes–a space/line/space, OR, a line/space/line. Also, three alphabetically sequenced letters will be skipped over.
Keep the following points in mind:
1. The staff represents a piano’s white keys only. The 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) (One staff step = the distance from any staff line to the very next staff space or vice versa, up or down)
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 3 consecutive staff steps are skipped over, 3 correlating piano keys are also skipped over! (This “skip-over/fly-over” concept and analogy is illustrated in the key of C in the photos just below.) (Your eyes skip-over the 3 staff steps while your fingers “fly-over” the 3 correlating piano keys.)
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! (1-4-5-8)
1-1 Perfect 1st or Perfect Unison – (The 1st note of a major scale doubled directly upon itself) 1-4 Perfect 4th – (The 1st and 4th notes of a major scale) 1-5 Perfect 5th – (The 1st and 5th notes of a major scale) 1-8 Perfect 8th or Perfect Octave – (The 1st and 8th notes of a major scale)
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 confess! I just made-up this tongue-in-cheek acronym but many cats have been known to eat non-cat-like foods. I had a cat that loved vinegar potato chips! Anyway, here’s how the test works…)
A “purr-fect” 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 ID’d a “purr-fect” interval via “P.I.E.C.A.T.“!
Perfect 5th = C to G (The 5th note of a major scale remains unmodified) Augmented 5th = C to G♯ (The 5th note of a major scale is sharped once) Minor 1st *(N/A) *(Minor functionality isn’t allowed on any perfect interval.) Diminished 5th = C to G♭**(The 5th 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.
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.
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.“!
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.
Okay! It’s time to take a look at the last interval of the series! 
Clicking the treble staff or keyboard icon opens a respective interval ID page where numeric and quality values are required.
Clicking the 
to you by now. With that said, we’ll quickly move through this post and the rest of this series starting from here. If you have any questions, just 
coming your way with an invitation to stay after class! If you said no, you’ve got one of these 
coming your way with an invitation to skip class today! Three Cs spread over 3 consecutive octaves is not a triad. It’s a triple octave unison! 
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. 