Intervals INTERVALS

In music, an INTERVAL is the distance between two notes. A Melodic Interval is the distance between two notes which sound one after the other. A Harmonic Interval is the distance between two notes which sound at the same time.

We use terms like Major 3rd, minor 2nd, Perfect 4th, or diminished 5th– to describe how far apart 2 notes are. So each interval is given a name that includes a description of its Quality and its distance or Number.

The Quality of an interval will be described as one of these: Major, minor, Perfect, Augmented, or diminished. The Number of an interval is simply the number of letter names encompassed by the notes. Or if it seems easier, start with the bottom note and count lines and spaces until you’ve included the top note. (The names or positions of both notes forming the interval are counted: A-B-C-D = a 4th; line space line space line = a 5th.)

Melodic Intervals (by Number)

7 7 8 5 6 6 6 4 4 4 5 4 5 4 5 2 2 3 2 3 2 3 2 3 2 3 2 3 & 1 1 1 1 w 1 œ w 1 œ œ w 1 œ œ œ w 2ndw 3rdœ w œ4thœ w œ 5thœ œ œ œ6thœ œ œ7thœ œ œ Octavœ e w w w w w w w (8th) Harmonic Intervals (by Number)

4th 5th 6th 7th w Octave & Unison 2nd 3rd w w w ww ww w w w w w w * Note that a Unison (also known as Perfect Prime) is the interval formed by two identical notes.

P1 M2 M3 P4 P5 M6 M7 P8 MAJORPerfect AND Unison PERFECTMajor 2nd INTERVALSMajor 3rd Perfect 4th Perfect 5th Major 6th Major 7th Perfect Octave

7 7 8 Major and Perfect intervals are defined by the distances5 we see in a5 Major6 Scale. 5 6 5 6 3 3 4 3 4 3 4 3 4 3 4 1 2 1 2 1 2 1 2 1 2 1 2 w1 2 w (The& distance in semitones from the Tonicw note to eachw one of the wdegrees of thew Major wScale.) œ w & wUnisonw w1 whole wstep 2w wholew steps 2 1/w2 wholeœ w steps 3 1/w2 wholeœ stepsœ w 4 1/w2 whole stepsœ œ œ5 1/w2 whole steps œ6w wholeœ œ steps w2ndw w 3rdœ w w œ4thœ w œ 5thœ w œ œ6th w œ œ7th w œ œ Octave ThePERFECT intervals include the Unison (or Prime), the 4th (W-W-H above the tonic), the 5th (W-W-H-W(8th) above the tonic), and the Octave or 8th (the note of the same name 8 scale steps higher). These intervals are actually m2 M2 m3 M3 m6 M6 m7 M7 based onminor harmonic 2nd overtonesMajor 2nd naturallyminor 3rd producedMajor by 3rdthe Tonicminor note, 6th and areMajor considered 6th tominor be 7th*perfectly Majorconsonant 7th harmonic sounds. All the minor scales even contain the Unison (or P1), Perfect 4th, Perfect 5th and Octave (P8)! 5th 6th 7th Octave 2nd 3rd 4th w w & Unison w w w w w bw w The& remainingww Majorw Scale intervals,w bthew 2nd, w3rd, 6thw, and w7th arebw classifiedw asw MAJORw intervals. w w1 half stepbw 1w whole stepw 1 w1/2 whole steps 2w whole steps 4w whole steps 4 w1/2 whole steps w5 whole steps 5 w1/2 whole steps

P1 M2 M3 P4 P5 M6 M7 P8 Perfect Unison Major 2nd Major 3rd Perfect 4th Perfect 5th Major 6th Major 7th Perfect Octave dim. 2 dim. 3 dim. 4 dim. 5 dim. 6 dim. 7 dim. 8 w & w w w w bw w w 1/2 1/2 1/2 1/∫2 w & wUnisonw w1 whole step∫w 2w whole steps bw2 w whole steps b3 ww whole steps 4∫ ww whole steps 5 w whole steps 6w whole steps w Unison∫w w1 whole step w2 whole steps w3 whole steps 3w 1/2 whole steps 4w 1/2 whole steps 5w 1/2 whole steps

* A sound M2 which is stable m2 and does not M3 present an urgency m3 to resolve M6 is called a m6 consonance . MajorM7 and minor m7 thirds and sixthsMajor are 2nd imperfectminor consonances 2nd Major, and 3rd in certainminor cases3rd the MajorPerfect 6th Fourthminor may 6th also functionMajor 7th as a dissonanceminor 7th . Aug. 1 Aug. 2 Aug. 3 Aug. 4 Aug. 5 Aug. 6 Aug. 7 Aug. 8 w bw w bw & w bw w bw #w #w #w & 1w whole step w1 half step 2w whole# stepsw 1 w1/2 whole#w steps 4 w1/2 whole#w steps 4w whole steps 5 w1/2 whole steps w5 whole steps w1 half# stepw 1 1/w2 whole#w steps 2-w1/2 whole steps 3w whole steps 4w whole steps 5w whole steps 6w whole steps 6 1/w2 whole steps

dim. 2 dim. 3 dim. 4 dim. 5 dim. 6 dim. 7 dim. 8 P1 m2 M2 m3 M3 P4 Aug. 4 dim. 5 P5 m6 M6 m7 M7 P8 ∫w bw & ∫w bw bw ∫w bw w w w Unison∫w w1 whole step w2 whole steps w3 whole steps 3w 1/2 whole bstepsw 4ww 1/2 whole steps 5w 1/2 whole steps & ww bww ww bw w w #w bw w w w w w w

Aug. 1 Aug. 2 Aug. 3 Aug. 4 Aug. 5 Aug. 6 Aug. 7 Aug. 8 #w & #w #w #w #w #w w1 half# stepw 1 1/w2 whole#w steps 2-1/w2 whole steps 3w whole steps 4w whole steps 5w whole steps 6w whole steps 6 1/w2 whole steps

P1 m2 M2 m3 M3 P4 Aug. 4 dim. 5 P5 m6 M6 m7 M7 P8 bw w bw w w & ww bww ww bw w w #w bw w w w w w w 7 7 8 5 5 6 5 6 6 4 4 4 4 4 5 2 2 3 2 3 2 3 2 3 2 3 2 3 & 1 1 1 1 w 1 œ w 1 œ œ w 1 œ œ œ w 2ndw 3rdœ w œ4thœ w œ 5thœ œ œ œ6thœ œ œ7thœ œ œ Octavœ e w w w w w w w (8th) MINOR AND DIMINISHED INTERVALS

We can decrease or contract the distance of an interval by lowering the top note or raising the bottom note using accidentals– flats, sharps or natural signs. The Number of the interval continues to be determined by counting 4th 5th 6th 7th Octave Unison 2nd 3rd w w w staff& wpositionsw or letterww names, butw the Qualityw of the intervalw is modified.w w w • Decreasing any of the Major intervals (M2, M3, M6, M7) by 1/2 step results in a minor interval. • Decreasing any of the Perfect intervals (P4, P5, P8) by 1/2 step results in a diminished interval. P1 M2 M3 P4 P5 M6 M7 P8 Perfect m Unison2 Major 2ndm3 Major 3rddim. 4 Perfect 4thdim. 5 Perfect 5th m6 Major 6th m7Major 7th Perfectdim. Octave8 minor 2nd minor 3rd minor 6th minor 7th m2 m3 dim. 4 dim. 5 m6 m7 dim. 8 minor 2nd minor 3rd minor 6th minor 7th w & w w w w bw w w 1/2 1/2 1/2 1/2bw & wUnisonbww w1 whole stepbw 2w whole steps bw2 w whole steps b3 ww whole steps 4 bww whole steps 5 w whole steps 6w whole steps w1 half step 1w 1/2 whole steps w2 whole steps w3 whole steps w4 whole steps w5 wholeb stepsw 5w 1/2 wholebw steps & bw bw bw bw bw In addition,w 1 halfM2 stepif we go farther 1 w m1/22 whole steps M3w2 whole steps m3 w3 whole steps M6 w4 whole steps m6 w5 whole stepsM7 5w 1/2 whole m7 steps • Decreasing Major m2 2nd any ofminor thedim. 2ndminor 2 intervals Major m3 3rd by an additionalminordim. 3rd 3 1/2Major step m6 ALSO6th resultsminordim. in6th6 a diminished Major m7 7th interval.minordim. 7th 7 minor 2nd minor 3rd minor 6th minor 7th m2 dim. 2 m3 dim. 3 m6 dim. 6 m7 dim. 7 minor 2nd minor 3rd minor 6thw bw minor 7thw bw & w bw w bw bw ∫w bw ∫w & 1w whole step w1 half step 2w wholeb stepsw 1 w1/2 whole∫w steps 4 w1/2 whole steps 4w whole steps 5 w1/2 whole steps w5 whole steps w1 halfb stepw wUnison∫w 1 1/w2 whole steps w1 whole step 4w whole steps 3 1/w2 whole steps 5w whole steps 4 1/w2 whole steps & bw ∫w bw ∫w bw ∫w w1 halfb stepw wUnison∫w 1 1/w2 whole steps w1 whole step 4w whole steps 3 1/w2 whole steps 5w whole steps 4 1/w2 whole steps dim. 2 dim. 3 dim. 4 dim. 5 dim. 6 dim. 7 dim. 8 So, going from a PerfectSame to aSound diminished intervalSame only Sound takes a decrease ofSame 1 semitone Sound (1/2 step) but going from a Major to diminished intervalSame Sound takes a decreaseSame of 2 Soundsemitones (1 whole step).Same Major Sound → minor∫w → diminishedbw . & bw ∫w bw bw ∫w∫ww ∫ w Unison∫w w1 whole step# w w2 whole steps w3 whole steps w3w 1/2 whole steps 4w 1/2 whole steps 5w 1/2 whole steps AUGMENTED &INTERVALSw w #w bw w w bmw3 Aug.# w 2 M3 dim. 4 M6w ∫wdim.w 7 dbl.∫# wdim. 8 An Augmented &intervalminorw 3rd is createdw by expandingMajor#w 3rd eitherb wa Perfect Majorinterval 6th or a Major interval by 1/2 step. m3 Aug. 2 M3 dim. 4 M6w dim.w 7 dbl.# wdim. 8 Aug. 1 minorAug. 3rd 2 Aug. 3 Major 3rdAug. 4 Aug.Major 5 6th Aug. 6 Aug. 7 Aug. 8 #w & #w #w #w #w #w w1 half# stepw 1 1/w2 whole#w steps 2-1/w2 whole steps 3w whole steps 4w whole steps 5w whole steps 6w whole steps 6 1/w2 whole steps

IDENTIFYING INTERVALS

• First,P1 count them2 letterM2 namesm (or3 linesM3 and spaces)P4 Aug. to determine 4 dim. 5 theP5 interval’sm6 numberM6 . m7 M7 P8 • Next, think of the low note of your interval as the temporary starting note of a Major Scale. • & Count upward the same number of scale stepsw and# wcomparebw your notew againstbw thew Major bScalew step.w w • Determineww b whetherww w yourw topbw note matchesw w exactly wwith thew Major wScale (andw is Majorw or Perfectw ),w or hasw been contracted (to minor or diminished), or expanded (to Augmented) to identify the interval’s Quality.

Expanded by 1 semitone Aug. 1 Aug. 2 Aug. 3 Aug. 4 Aug. 5 Aug. 6 Aug. 7 Aug. 8 (1/2 Step) (Augmented 1st) (Augmented 2nd) (Augmented 3rd) (Augmented 4th) (Augmented 5th) (Augmented 6th) (Augmented 7th) (Augmented 8th) Major Scale P1 M2 M3 P4 P5 M6 M7 P8 INTERVALS (Perfect Unison) (Major 2nd) (Major 3rd) (Perfect 4th) (Perfect 5th) (Major 6th) (Major 7th) (Octave) Contracted by 1 semitone m2 m3 dim. 4 dim. 5 m6 m7 dim. 8 (1/2 Step) (minor 2nd) (minor 3rd) (diminished 4th) (diminished 5th) (minor 6th) (minor 7th) (diminished 8th) Contracted by 2 semitones dim. 2 dim.3 dim. 6 dim. 7 (1 Whole Step) (diminished 2nd) (diminished 2nd) (diminished 6th) (diminished 7th) IMPORTANT! See Also: Identifying Intervals by Ear Let’s see if we can simplify this for an easier understanding…

Many times we will simply hear 2 pitches and don’t see how they are written. When talking about the distance between 2 sounding notes… there’s a formula that works.

There’s a simple logical progression in the intervals between notes. The order begins: P1 (or Unison–which is the same note), then – minor 2nd, Major 2nd, minor 3rd, Major 3rd, Perfect 4th, Tritone, Perfect 5th, minor 6th, Major 6th, minor 7th, Major 7th, P8 (or Octave).

Note: all intervals which follow the pattern of a Major Scale above the bottom note are either Major or Perfect. Any Major interval that is made smaller by 1 semitone is minor. The only exceptional case is the Tritone which falls between the Perfect 4th and Perfect 5th (it is either an Augmented 4th or diminished 5th – depending on whether the pitches are written 4 or 5 letter names apart!)

When talking about the distance between 2 written notes… the same first rule applies: Intervals which follow the pattern of a Major Scale above the bottom note are either Major or Perfect. But to determine other intervals we have to also count the distance between the letter names of the notes. Intervals can have enharmonic equivalents. For instance, C to G is 5 letter names apart (C D E F G) and C to A is 6 letter names apart (C D E F G A). While C to G and C to A will sound the same, and are the same number of semitones apart in distance, C to G is an Augmenteds 5th, butf C to A is a minor 6th. s f

P8 (Octave) - 12 Semitones P8 (or Octave) M7 - 11 Semitones M7 m7 - 10 Semitones m7 M6 - 9 Semitones M6 m6 - 8 Semitones m6 P5 - 7 Semitones P5 A4/d5 - 6 Semitones Tritone (Aug4 or dim5) P4 - 5 Semitones P4 M3 - 4 Semitones M3 m3 - 3 Semitones m3 M2 - 2 Semitones M2 m2 - 1 Semitone m2 P1 (Unison) - Same Note

C D E F G A B C 7 7 8 5 5 6 5 6 6 4 4 4 4 4 5 2 2 3 2 3 2 3 2 3 2 3 2 3 & 1 1 1 1 w 1 œ w 1 œ œ w 1 œ œ œ w 2ndw 3rdœ w œ4thœ w œ 5thœ œ œ œ6thœ œ œ7thœ œ œ Octavœ e w w w w w w w (8th)

4th 5th 6th 7th Octave Unison 2nd 3rd w w w & ww ww w w w w w w

P1 M2 M3 P4 P5 M6 M7 P8 Perfect Unison Major 2nd Major 3rd Perfect 4th Perfect 5th Major 6th Major 7th Perfect Octave

m2 m3 dim. 4 dim. 5 m6 m7 dim. 8 minor 2nd minor 3rd minor 6th minor 7th w & w w w w w wUnisonw w1 whole wstep 2w whole steps 2 1/w2 whole steps 3 1/w2 whole steps 4 1/w2 whole steps 5 1/w2 whole steps 6w whole steps bw & bw bw bw bw bw w1 half bstepw 1w 1/2 whole steps w2 whole steps w3 whole steps w4 whole steps w5 whole steps 5w 1/2 whole steps M2 m2 M3 m3 M6 m6 M7 m7 Major 2nd minor 2nd Major 3rd minor 3rd Major 6th minor 6th Major 7th minor 7th Enharmonic m2 dim. 2Intervals m3 anddim. 3the Tritone m6 dim. 6 m7 dim. 7 minor 2nd minor 3rd minor 6thw bw minor 7thw bw ENHARMONIC& INTERVALS w bw 1w whole stepw w1 half stepbw 2w whole steps 1 w1/2 whole steps 4 w1/2 whole steps 4w whole steps 5 w1/2 whole steps w5 whole steps bw ∫w bw ∫w Be& careful! bSeveralw intervals∫w have the possibilitybw of ∫alternatew enharmonic names. For instance, a minor 3rd might sound wthe1 half same step as anw UnisonAugmented1 1/w 2nd,2 whole but steps the twow1 whole are step written4w whole differently steps 3 1/wand2 whole it’s steps essential5w whole that steps you identify4 1/w2 whole stepsand write intervalsdim. 2 correctly.dim. Every 3 phase of dim.music 4 theory studydim. 5requires a correctdim. 6 understandingdim. 7 of intervals.dim. 8

Same Sound Same Sound Same Sound { { { bw & ∫w bw bw ∫w ∫w w Unison∫w w1 whole step w2 whole steps w3 whole steps 3w 1/2 whole steps 4w 1/2 whole steps 5w 1/2 whole steps bw ∫ww ∫ & w #ww #w bw w m3 Aug. 2 M3 dim. 4 M6w dim.w 7 dbl.# wdim. 8 Aug. 1 minorAug. 3rd 2 Aug. 3 Major 3rdAug. 4 Aug.Major 5 6th Aug. 6 Aug. 7 Aug. 8 It will help in the process of naming and writing enharmonic intervals to determine the Number of the interval first, before addressing whether the interval is Perfect, Major, minor, Augmented, or diminished. #w & #w #w #w #w #w w1 half# stepw 1 1/w2 whole#w steps 2-1/w2 whole steps 3w whole steps 4w whole steps 5w whole steps 6w whole steps 6 1/w2 whole steps Since we’ve learned how the intervals are classified by number and quality let’s look at the full Chromatic Series of intervals. (Not all of the possible augmented or diminished intervals are included in this example.)

P1 m2 M2 m3 M3 P4 Aug. 4 dim. 5 P5 m6 M6 m7 M7 P8

& ( b w ) w bw w bw w w b w w bw w w #wTRITONE ww w w w w w Enharmonicallyw similarw w w w w w w

TRITONE

You will note that ONE pair of enharmonic intervals is included in this series: an interval which encompasses 3 whole steps is either an Aug. 4 or dim. 5, depending upon how the interval is written. (Remember, we count the lines and spaces to determine the number of each interval.) This specific interval has its own name: TRITONE, and it possesses several distinctive qualities. The note which forms a Tritone interval is exactly half the distance between the tonic and its octave (3 whole steps above the tonic, 3 whole steps below the octave). The sound of this interval is particularly dissonant or harsh to hear– creating a sound of great restlessness or instability. It can serve as a very useful interval to precede a harmonic resolution in modern music because of this restless quality.

Historically, the TRITONE was completely avoided on religious grounds in medieval church music because of its dissonant sound. The first explicit prohibition of the Tritone seems to occur when Guido d’Arezzo (the father of modern musical notation) called it a ‘dangerous interval’ around the year 1000, and ecclesiastical musicians began to refer to such dissonance as Diabolus in Musica (literally, “the devil in music”).

TIP: If an interval is INVERTED, that is– if you switched the positions of the two notes, so that the bottom note appears above the original top note, a Perfect interval always remains Perfect (Ex.: C–F a P4, becomes F–C a P5); a Major interval will always become minor and vice versa (Ex.: E –C a M6, becomes C–E a m3); an Augmented interval will always become diminished and vice versa (Exf.: C–G a A5, becomes Gf –C a d4). s s Quick tip for recognizing Perfect intervals:

This is just a small observation, but I’m continually delighted when I notice the order and structure, the relationships that God has placed into His creation... and especially to music. I know that the world’s ‘wisdom’ writes these observations off as mathematics or coincidences based on the structure that we’ve assigned to musical properties, but I can’t help seeing that all things point gloriously to our loving Father who allows us to perceive and enjoy and to also participate in the creativity He’s placed in us, by creating us in His own image.

Remember how, as we were learning to recognize Key Signatures, we had tips and trick to help us, but there was One essential thing we simply needed to notice and to memorize— that the Key of F contains 1 flat– B . It is the only ‘Flat’ key that doesn’t have ‘Flat’ as part of its name. Well, I’d like to point out something– which mightf be especially helpful if you’ve struggled with the builder this week to quickly recognize the Perfect intervals of a P4 and P5. Score PERFECT FIFTHS You can quickly recognize when an interval of a 5th is Perfect, because the accidentals (flat, sharp, or natural) for both notes will be exactly the same. (Both will be natural, or both will be flat, etc.) Except... for one thing you may notice and to memorize— when the pair of B and F both get involved in the interval... B and F make a Perfect 5th and B and F make a Perfect 5th. f Score s bw nw nw #w & nw #w bw nw #w bw nw #w nw bw nw #w bbw nnw b w n w b w n w n w # w b w n w # w b w n w # w n w b w n w # w U U U Same U U U Different f n s f n s PERFECT FOURTHS You can quickly recognize when an interval of a 4th is Perfect, because theb accidentalsw nw b (flat,w n wsharp,b wor natural)nw nw #w bw nw #w bw nw #w nw bbw nnw ##w b w n w b w n w nnw ##w for& bothn w notes# w willb wbe exactlyn w # thew bsamebw . n(Bothnw # will#w benn natural,w bw or nbothw will#w beb flat,w netc.)w Exceptbw ...n wfor bonew thingn w you& maynw notice#w andbw to memorize—nw #w when the pair of F and B both get involvedb w in nthew interval...b w n Fw and B make a Score b w n w # w b w n w # w n w b w n w # w Perfectn 4thw # andw F and B make a Perfect 4th! f s 14 w w bww nw #w bw nw bw nw nbw #wnw &1nww#w wbw nw #w bbw nnw ##w nnw b w n w # w#wb w n#ww b w n bw bw & n wP5w# w bP4 w n w # wM3w m6wwbm3w bM6w Aug.5w dim.4 dim.5w Aug.4 U U U Same U U U Different f n s f n s Curious, isn’t: it– how this relationship: between F and B :and the accidentals which: appear on those :pitches continue to provide us with something special to notice, anb exceptionw nw to# wthe rules,bw ornw somethingbw nw to thinknw about.#w —& Selah.nw #w bw nw #w bw nw #w nw b w n w # w b w n w b w n w b w n w & 14n w # w bww n w # w b wwn w # w n w ∑ w w w &1This wwas in ourw PDF notes, but it’s worth repeating here because it also points to the#w order and#w wcomplexity inb God’s design.bw P5w P4 M3w m6wwbm3w bM6w Aug.5w dim.4 dim.5w Aug.4 When an interval: is inverted: :bw nw #w nw:bw nw #w bw: nw bbw nnw nb:w #nw That& nis,nw if #you#w useb bthew samennw #two#w noteb wnames,n w but# wreversen w whichb w ofn thew #twow pitchesb w isn whigher, a Perfect interval will& always∑ remain∑ a ∑Perfect∑ interval.∑ A Major∑ interval∑ ∑always∑ becomes∑ minor.∑ A minor∑ interval∑ ∑ always∑ becomes∑ Major.& Augmented intervals always become diminished. Diminished∑ intervals always become Augmented. 4ths become 5ths and 5ths become 4ths. 3rds and 6ths invert in to each other. 2nds and 7ths do the same. 14 &1 w w w w #w #ww b bw P5w ∑P4 M3w m6ww∑ bm3w bM6w ∑ Aug.5w dim.4 dim.5w∑ Aug.4 & ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ : : : : : ∑ & ∑ ∑ ∑ ∑ & ∑ ∑ ∑ ∑

∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ & ∑ ∑ ∑ & ∑ ∑ ∑ ∑

& ∑ ∑ ∑ ∑ & ∑ ∑ ∑

& ∑ ∑ ∑ ∑

& ∑ ∑ ∑