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More Intervals

Major Third

There are several interesting intervals back down at the low end of the Native American flute range that we'll cover. The first is a major third above the fundamental.

The major third has a frequency ratio of 5:4. Playing a 375 Hz note over a 300 Hz note gives you an interval of a major third.

The major third is a central note of the diatonic major scale, and the primary note that distinguishes the feel of "major" from "minor".

Since the minor third interval is a span of three semitones, you can probably guess that an interval of a major third is a span of four semitones.

The first two notes of "(Oh) When the Saints Come Marching In" are an ascending major third interval, and the first two notes of "Summertime" as well as "Here Come the Sun" form a descending major third.

Major Third interval written in Nakai Tab NotationThere is one interval of a major third in the pentatonic minor scale, between the notes Finger diagram closed closed closed closed closed open and Finger diagram closed closed closed open open open on six-hole flutes (Five hole finger diagram closed closed closed closed open and Five hole finger diagram closed closed open open open for five hole flutes). If you try the notes Finger diagram closed closed closed closed closed open Finger diagram closed closed closed open open open Finger diagram closed closed open closed open open Finger diagram closed open closed open open open, you'll probably recognize the start of "(Oh) When the Saints Come Marching In". The notes Finger diagram closed closed closed open open open Finger diagram closed closed closed closed closed open Finger diagram closed closed closed closed open open Finger diagram closed closed closed open open openFinger diagram closed closed closed open open open Finger diagram closed closed closed closed open open Finger diagram closed closed closed closed closed open Finger diagram closed closed closed closed closed closed Finger diagram closed closed closed closed closed open Finger diagram closed closed closed closed open open Finger diagram closed closed closed closed closed open Finger diagram closed closed closed closed closed closed also work for "Here Comes the Sun" (before we run out of notes). See the sheet music for Summertime, if you're interested in that melody, but it actually starts up much higher on the Native American flute range so you can play all the notes.

Root
Note
Major
Third
Finger diagram closed closed closed closed closed closed Finger diagram closed closed closed closed open closed
A C# (Db)
Bb (A#) D
B Eb (D#)
C E
C# (Db) F
D F# (Gb)
Eb (D#) G
E G# (Ab)
F A
F# (Gb) Bb (A#)
G B
G# (Ab) C

The table on the right shows the pairs of notes that are a major third apart

Major Third interval written in Nakai Tab NotationGetting a major third interval from the fundamental note on contemporary Native American flutes can be somewhat hit-or-miss. The only fingerings that works to get this interval from the fundamental (without using half-hole techniques) are Finger diagram closed closed closed closed closed closed Finger diagram closed closed closed closed open closed on six-hole flutes and Five hole finger diagram closed closed closed closed closed Five hole finger diagram closed closed closed open closed on five-hole flutes. The reason that these fingerings are problematic is that some flutes produce an interval of a major third, and on others the upper note is noticeably flat or sharp of a major third interval. However, we will get into issues of relative tuning in the next section.

Here is the sound of a well-tuned major third interval on a Native American flute:

Major Third Interval

Clint Goss. E minor flute of Spalted Maple by Barry Higgins. E minor flute of Spalted Maple by Barry Higgins

On a keyboard, you can locate the major third by going up four keys (and hence, four semitones):

Major Third  interval on a piano

Relative Tuning

A big question for any Native American flute is: "Is the flute in tune with itself?" What that question means has to do with all the

It's one of those rabbit-hole questions.

What's the pitch standard? Equal temperament? Just intoned? Pythagorean?

Major Sixth

The major sixth is another interval that opens up new scales and playing possibilities.

The major sixth has a frequency ratio of 5:3. Playing a 500 Hz note over a 300 Hz note gives you an interval of a major sixth.

The first two notes of the NBC theme and "My Bonnie Lies Over the Ocean" are an ascending major sixth.

Root
Note
Major
Sixth
Finger diagram closed closed closed closed closed closed Finger diagram closed open closed closed open open
A F# (Gb)
Bb (A#) G
B G# (Ab)
C A
C# (Db) Bb (A#)
D B
Eb (D#) C
E C# (Db)
F D
F# (Gb) Eb (D#)
G E
G# (Ab) F

The table on the right shows the pairs of notes that are a major sixth apart.

Major Sixth interval written in Nakai Tab NotationMost Native American flutes can play an interval of a major sixth from the fundamental note, but you might have to play around to find the right fingering. Some of the choices on contemporary six-hole Native American flutes from the Finger diagram closed closed closed closed closed closed fundamental note are:Finger diagram closed open closed closed open open, Finger diagram closed closed open open open open, Finger diagram closed open closed closed open closed, or even Finger diagram closed open closed closed closed open. On contemporary five-hole Native American flutes, the fingering of a major sixth interval from the Five hole finger diagram closed closed closed closed closed fundamental note is likely to be Five hole finger diagram closed open closed open open or Five hole finger diagram closed open closed open closed.

Here is the sound of a major sixth interval on a Native American flute:

Major Sixth Interval

Clint Goss. E minor flute of Spalted Maple by Barry Higgins. E minor flute of Spalted Maple by Barry Higgins

On a keyboard, you can locate the major sixth by going up an octave and coming down three keys:

Major Sixth interval on a piano

Scales

With the addition of the major sixth to our toolbox of intervals, many new scales become available. Rather than explore them here, visit these pages that make use of the intervals we've seen so far:

  • Mode Five Hexatonic Major scale (starting <xxx|xoo, <xxx|ooo, <xox|xoo, …
  • Northern (Dargan)
  • Bugle

Major Second

The major second is a key interval in the music of all cultures. It is two semitones or one whole tone and has a frequency ratio 9:8. Playing a 337.5 Hz note over a 300 Hz note gives you an interval of a major second.

The first interval of "Happy Birthday" is a major second, as well as "Doe a Deer" (both between "Doe" and "a" as well as between "a" and "Deer"). The first interval of "Eight Day a Week" ("You Know I need...") form a descending major second.

The major second occurs three times in the pentatonic minor scale. Here are the pairs of major second intervals on most contemporary six-hole Native American flutes Finger diagram closed closed closed closed closed open Finger diagram closed closed closed closed open open and Finger diagram closed closed closed closed open open Finger diagram closed closed closed open open open and Finger diagram closed open closed open open open Finger diagram open open closed open open open. The equivalent fingerings on five-hole flutes are Five hole finger diagram closed closed closed closed open Five hole finger diagram closed closed closed open open and Five hole finger diagram closed closed closed open open Five hole finger diagram closed closed open open open and Five hole finger diagram closed open open open open Five hole finger diagram open open open open open.

This is how these three intervals of a major second are written in Nakai Tablature:

Three Major Second intervals written in Nakai Tab notation

 

Major Second interval written in Nakai Tab NotationGetting a major second interval from the fundamental note on contemporary Native American flutes is problematic - it requires half-hole techniques. The finger diagram would look like this: Finger diagram closed closed closed closed closed half-closed - but if you try this fingering on an Native American flute as a long tone, you probably won't like the sound. …

Here is the sound of major second interval on a Native American flute:

Major Second Interval

Clint Goss. E minor flute of Spalted Maple by Barry Higgins. E minor flute of Spalted Maple by Barry Higgins

On a keyboard, you can locate the major second by going up two keys (and hence, two semitones):

Major Second  interval on a piano

In music terms, here are pairs of notes that are a major third apart:

Root
Note
Major
Second
Finger diagram closed closed closed closed closed closed Finger diagram closed closed closed closed closed half-closed
A B
Bb (A#) C
B C# (Db)
C D
C# (Db) Eb (D#)
D E
Eb (D#) F
E F# (Gb)
F G
F# (Gb) G# (Ab)
G A
G# (Ab) Bb (A#)

Tritone

We now come to a most controversial interval in our toolbox. It's been maligned by various churches, oulawed during the Middle Ages, overplayed by new jazz players, and beloved by fans of the blues. Here are some names for this restless and colorful interval:

  • The tritone, because it is composed of three major second whole tone intervals.
  • The flat fifth or flat five, because it is a semitone below a perfect fifth. This is often the term used in jazz.
  • The augmented fourth is a more traditionally classical term for this interval.
  • The devil's note is how this interval was often named from at least the early 1700's and possibly as early as the middle ages.
  • Finally, it's often called the blue note because of it's central place in jazz in general and the blues in particular.

The tritone has by far the most complex frequency ratio of the twelve intervals in the octave, and thus is the most dissonant interval in the set. In fact, you can use either of two frequency ratios for this interval: 45:32 or 64:45. To get a tritone above a 300 Hz note using these two ratios would give you frequencies of 421.875 Hz and 426.667 Hz.

The tritone is an interval of six semitones - one semitone up from a perfect fourth and one semitone below a perfect fifth. Six semitones is the same as three whole tones, hence the name "tritone".

There aren't a lot of songs that begin with a tritone, but the ones that do are distinctive: "Maria" from West Side Story and the theme from "The Simpsons" both begin with an ascending Tritone.

Tritone interval written in Nakai Tab NotationMost Native American flutes can play an interval of a tritone interval from the fundamental note, but you might have to play around to find the right fingering. Some of the choices on contemporary six-hole Native American flutes from the Finger diagram closed closed closed closed closed closed fundamental note are:Finger diagram closed closed closed open closed open, Finger diagram closed closed closed open closed closed, or even Finger diagram closed closed closed open open closed. On contemporary five-hole Native American flutes, the fingering of a tritone interval from the Five hole finger diagram closed closed closed closed closed fundamental note is likely to be Five hole finger diagram closed closed open closed open or Five hole finger diagram closed closed open closed closed.

Here is the sound of a tritone interval on a Native American flute:

Tritone Interval

Clint Goss. E minor flute of Spalted Maple by Barry Higgins. E minor flute of Spalted Maple by Barry Higgins

On a keyboard, you can locate the tritone by going up a perfect fifth and coming down one key:

Tritone interval on a piano

In music terms, here are pairs of notes that are a tritone apart:

Root
Note
Tritone
Finger diagram closed closed closed closed closed closed Finger diagram closed closed closed open closed open
A Eb (D#)
Bb (A#) E
B F
C F# (Gb)
C# (Db) G
D G# (Ab)
Eb (D#) A
E Bb (A#)
F B
F# (Gb) C
G C# (Db)
G# (Ab) D

The Blues

The use of this note in the blues will be familiar to everyones ear. Here's a Native American flute improvisation using the blue note added to the pentatonic minor scale:

Scales

With the addition of the blue note to our toolbox of intervals, many new scales become available. Rather than explore them here, visit these pages that make use of the intervals we've seen so far:

  • The Blues Scale

Major Seventh

The major seventh is the final interval in the octave that we have not yet looked at.

It is a semitone above the minor seventh and a semitone below the octave. and a frequency ratio of 15:8. Playing a 562.5 Hz note over a 300 Hz note gives you an interval of a major seventh.

The first and third notes of "Bali Hai" from South Pacific are a major seventh interval (the sequence goes root - octave - major seventh). The Cole Porter standard "I Love You" has a descending major seventh.

Major Seventh interval written in Nakai Tab NotationMost Native American flutes can play an interval of a major seventh from the fundamental note, but you might have to play around to find the right fingering. Some of the choices on contemporary six-hole Native American flutes from the Finger diagram closed closed closed closed closed closed fundamental note are:Finger diagram open closed closed open open open, Finger diagram open open closed closed open open, or even Finger diagram closed open open open open open. On contemporary five-hole Native American flutes, the fingering of a major seventh interval from the Five hole finger diagram closed closed closed closed closed fundamental note is likely to be Five hole finger diagram open closed open open open or Five hole finger diagram open open closed open open.

Here is the sound of a major seventh interval on a Native American flute:

Major Seventh Interval

Clint Goss. E minor flute of Spalted Maple by Barry Higgins. E minor flute of Spalted Maple by Barry Higgins

On a keyboard, you can locate the major seventh by going up an octave and coming down one key:

Major Seventh interval on a piano

In music terms, here are pairs of notes that are a major seventh apart:

Root
Note
Major
Seventh
Finger diagram closed closed closed closed closed closed Finger diagram open closed closed open open open
A G# (Ab)
Bb (A#) A
B Bb (A#)
C Eb (D#)
C# (Db) C
D C# (Db)
Eb (D#)  
E Eb (D#)
F E
F# (Gb) F
G F# (Gb)
G# (Ab) G

Scales

With the addition of the major seventh to our toolbox of intervals, some new scales become available. Rather than explore them here, visit these pages that make use of the intervals we've seen so far:

 

 
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