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.

There is one interval of a major third in the pentatonic minor scale, between the notes and on six-hole flutes ( and for five hole flutes). If you try the notes , you'll probably recognize the start of "(Oh) When the Saints Come Marching In". The notes … 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
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

Getting 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 on six-hole flutes and 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.

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

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
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.

Most 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 fundamental note are:, , , or even . On contemporary five-hole Native American flutes, the fingering of a major sixth interval from the fundamental note is likely to be or .

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.

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

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 and and . The equivalent fingerings on five-hole flutes are and and .

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

Getting 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: - 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.

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

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

Root Note	Major Second
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.

Most 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 fundamental note are:, , or even . On contemporary five-hole Native American flutes, the fingering of a tritone interval from the fundamental note is likely to be or .

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.

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

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

Root Note	Tritone
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.

Most 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 fundamental note are:, , or even . On contemporary five-hole Native American flutes, the fingering of a major seventh interval from the fundamental note is likely to be or .

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.

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

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

Root Note	Major Seventh
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:

• Byzantine - Extended Scale
• Blues - Seven-Note Scale