Flutopedia - an Encyclopedia for the Native American Flute

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Flutopedia Symposium

Smaller Intervals

So far we have looked at intervals that are a fairly large distance apart. Octave, perfect fifth, and perfect fourth are often called "leaps" because are often used in melodies to call attention, make a change in feeling, or herald the beginning of a song or new section of music. They are fairly rare in most melodies.

Minor Second (one Semitone, one Half-step)

Now we look at the other end of the spectrum: the smallest interval that we have in the Western Classical music tradition. The minor second (also called the "semitone" or "half-step") is the interval between any two adjacent notes in the chromatic scale. It occurs frequently in diatonic melodies, but is rare in the pentatonic melodies that are common on the Native American flute.

In Western classical music, the note that is a semitone or minor second above a 300 Hz note would have a frequency of 317.839 Hz. This gives a frequency ratio of very close to 18:17 (it's really 18.0109:17).

The first and second notes, as well as the second and third notes of "Ta Ra Ra Boom De Ay" are a minor second interval apart.

Here are some examples of minor second intervals on a Native American flute:

Audio Player disabled - visit Troubleshooting.

So what is the feeling of a minor second interval? Most people say this interval provides "high tension", "dissonance", or even a "mistake" or "out of tune".

Root
Note
Minor
Second
A Bb (A#)
Bb (A#) B
B C
C C# (Db)
C# (Db) D
D Eb (D#)
Eb (D#) D
E F
F F# (Gb)
F# (Gb) G
G G# (Ab)
G# (Ab) A

The table on the right shows the pairs of notes that are a minor second apart - you simply go up one note in the chromatic scale.

Because the primary scale of the Native American flute has no minor second intervals, you have to use cross-fingerings to get this interval. Most contemporary six-hole Native American flutes will get a minor second interval with the fingerings Finger diagram closed closed closed open open open Finger diagram closed closed open closed open open. Other pairs of minor second intervals can be played on almost any Native American flute, but you have to experiment to get the right fingering. For example, the note that is a minor second above Finger diagram closed closed closed closed open open might be fingered Finger diagram closed closed closed open closed open or it might be fingered Finger diagram closed closed closed open closed closed. The idea is to use your ear to recognize the fingering that works best (see Finding the Right Fingering below). Likewise, a minor second above Finger diagram closed open closed open open open might be fingered Finger diagram open closed closed open open open or Finger diagram open open closed closed open open or Finger diagram open open closed closed closed open.

On five-hole flutes, finding a minor second above any particular note also takes experimentation. The note a minor second above Five hole finger diagram closed closed open open open might be Five hole finger diagram closed open closed open open or Five hole finger diagram closed open closed closed open or Five hole finger diagram closed open closed open closed.

On a keyboard, play any note and then the next higher note … including all the white and black keys. Here's a minor second interval, based on the root note we've been using above:

Minor Second interval on a piano

 

Semitones

Even though the minor second is rarely used in Native American flute music, it's very important for building up scales. The minor second is the smallest interval in the Western classical music, and the frequency ratio of every other interval in the equal-tempered scale is a multiple of the minor second interval.

The minor second is so important for building up scales, that it is given a specific name for this use: the semitone (also called the “half-step”). All the intervals discussed above can be given in terms of the number of semitones:

  • An octave is 12 semitones.
  • A perfect fifth is 7 semitones.
  • A perfect fourth is 5 semitones.
  • A minor second is 1 semitone.

Finding the Right Fingering

Many of the cross-fingered notes on the Native American flute are best found by ear. For example, you know that the fingerings Finger diagram closed closed closed closed open open and Finger diagram closed closed closed open open open produce notes that are two semitones apart. Let's say you're looking for the right fingering for the note in between - one semitone above Finger diagram closed closed closed closed open open and one semitone below Finger diagram closed closed closed open open open. Unless you want to try to use half-holing, you basically have to flatten the Finger diagram closed closed closed open open open note by closing some combination of the bottom two holes. The fingering might be Finger diagram closed closed closed open closed open or Finger diagram closed closed closed open closed closed or even Finger diagram closed closed closed open open closed. You can tell the best fingering by playing the three notes in order and see which middle note sounds closes to half way between the end notes: Finger diagram closed closed closed closed open openFinger diagram closed closed closed open closed openFinger diagram closed closed closed open open open or Finger diagram closed closed closed closed open openFinger diagram closed closed closed open closed closedFinger diagram closed closed closed open open open or Finger diagram closed closed closed closed open openFinger diagram closed closed closed open open closedFinger diagram closed closed closed open open open.

Here is a sound sample of a sequence where the middle note is too sharp (it uses the Finger diagram closed closed closed closed open openFinger diagram closed closed closed open open closedFinger diagram closed closed closed open open open fingering sequence):

Audio Player disabled - visit Troubleshooting.

And here's one where the middle note is too flat (it uses the Finger diagram closed closed closed closed open openFinger diagram closed closed closed open closed closedFinger diagram closed closed closed open open open fingering sequence):

Audio Player disabled - visit Troubleshooting.

Finally, this one with the Finger diagram closed closed closed closed open openFinger diagram closed closed closed open closed openFinger diagram closed closed closed open open open fingering sequence is just right (if this is beginning to sound like the story of Goldilocks and the Three Bears, maybe we should name this the Goldilocks method):

Audio Player disabled - visit Troubleshooting.

Minor and Major

Where does the name “minor” come from in “minor second”?

In order to extend the names of the note positions in the seven-tone diatonic scale (Root, Second, Third, Fourth, Fifth, Sixth, Seventh) to get a twelve-tone chromatic scale, five new names were needed. So five of the positions, the Second, Third, Fourth, Sixth and Seventh, were divided into two notes, each a semitone apart:

Lower
Note
Upper
Note
Root
Minor Second Major Second
Minor Third Major Third
Perfect Fourth Augmented Fourth
Perfect Fifth
Minor Sixth Major Sixth
Minor Seventh Major Seventh
(Perfect) Octave

This division allows us to talk about many (but not all) the scales that exist in world music.

Note that most of the pairs are named "Minor / Major", except for the perfect fourth. It's counterpart is called the "augmented fourth".

Many of the systems for naming scale degrees described above have a way to handle these new notes:

Degree Names Roman Numerals1 Solfège2 Sargam3
Lower
Note
Upper
Note
Lower
Note
Upper
Note
Lower
Note
Upper
Note
Lower
Note
Upper
Note
Root I Do Sa
Minor
Second
Major
Second
ii II Ra Re Komal
Re
Re
Minor
Third
Major
Third
iii III Me Mi Komal
Ga
Ga
Perfect
Fourth
Augmented
Fourth
IV IV+ Fa Fi Ma Tivra
Ma
Perfect Fifth V So Pa
Minor
Sixth
Major
Sixth
vi VI Le La Komal
Dha
Dha
Minor
Seventh
Major
Seventh
vii VII Te Ti Komal
Ni
Ni
(Perfect) Octave VIII Do Sa

Notes:

  1. The system of roman numerals is most often used to represent complete chords in the context of jazz improvisation. Use of roman numerals for scale degrees is less common, and the two uses can be confused.
  2. The names for the solfège syllables shown on this chart are from an extended version of solfège called the Sato Method ([Sato 2001] Sato Method of Solfege Syllables).
  3. The Sargam system does not have individual syllables for the minor and augmented versions of the scale degrees, so I've entered the formal name in that box.

Scale Steps

So far, we've looked at pairs of notes. If we want to include more notes in a sequence, we have a “scale”. And since all the notes that we're going to be using can be divided nicely into semitones, we have a handy system for specifying any scale.

Let's say we want to have a scale that contains the root note, the perfect fourth from the root, the perfect fifth from the root, and the octave from the root. On most contemporary six-hole Native American flutes, that scale would be fingered Finger diagram closed closed closed closed closed closed Finger diagram closed closed closed closed open open Finger diagram closed closed closed open open open Finger diagram open open closed open open open and sound like this:

Audio Player disabled - visit Troubleshooting.

On a piano, the scale would contain the notes:

Scale with root, perfect fourth, perfect fifth, and octave notes

One of the easiest ways to talk about the notes in a scale is to give the number of semitones between each of the notes. Between the root note and the perfect fourth there are five semitones. You can see this on the piano example by counting all the white and black keys up from the root note till you get to the perfect fourth.

From the perfect fourth to the perfect fifth there are two semitones. You can get this by counting the piano keys from the fourth to the fifth, or you could subtract the perfect fourth interval from the root note (five semitones) from the perfect fifth intervals from the root (seven semitones).

Finally, from the perfect fifth to the octave note there are five semitones … count the keys or subtract the seven semitones for the perfect fifth from the twelve semitones for the octave note.

So we can easily name this scale by giving the “scale steps” of 5-2-5.

Many of the scales used in the Western classical music tradition have seven tones with no two tones separated by more than 2 semitones. These scales are called diatonic scales, with the most common being the diatonic major scale having scale steps of 2-2-1-2-2-2-1.

On many flutes, particularly Native American flutes and recorders, the entire octave's worth of notes can be played in the low register of the flute. However, other flutes such diatonic Irish whistles and East Indian bansuris need to go into the second register to get the last note in the sequence. On these flutes, the last interval of the scale steps is shown in red, such as this: 2-2-1-2-2-2-1.

Since diatonic scales contain only 2s and 1s for scale steps, they are often written with Ss for "Semitones" and Ts for "Whole Tones". They are salso written at times using Hs for "half-steps" and Ws for "Whole Steps". The diatonic major scale would be written as T-T-S-T-T-T-S and W-W-H-W-W-W-H in these systems.

Minor Third

Sheet Music example of a Minor Third intervalWe now move on to an interval that is most responsible for distinguishing the primary scale of the Native American flute from the diatonic scale used in most Western classical music.

The minor third has a frequency ratio of 6:5 - a 360 Hz note is a minor third above a 300 Hz note.

The first two notes of the traditional melody “Greensleeves” are a minor third apart. So are the first two notes of “Hey Jude”, in descending order.

There are two minor third intervals in the primary scale of most contemporary six-hole Native American flutes: Finger diagram closed closed closed closed closed closed Finger diagram closed closed closed closed closed open and Finger diagram closed closed closed open open open Finger diagram closed open closed open open open. The equivalent fingerings on five-hole flutes are Five hole finger diagram closed closed closed closed closed Five hole finger diagram closed closed closed closed open and Five hole finger diagram closed closed open open open Five hole finger diagram closed open open open open.

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

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

Two Minor Third intervals in the Pentatonic Minor ScaleThe Nakai Tablature for these two minor third intervals is shown at the left.

The interval is called "minor" because it is the lower note of the pair of "third" notes called "minor third" and "major third". We'll explore the major third later in this series of web pages.

In the sargam system, this third musical degree is "Gandhara" (shortened to "Ga"; Sanskrit: गान्धारं). It originated from the goat and is related to the chakra of the solar plexus chakra (navel or belly chakra; Sanskrit: अनाहत, “maṇipūra”). Sargam has a concept of pairs of notes, calling their major notes "shuddha" ("natural" or "pure") and their minor notes "komal" ("flat" or "soft"), so the minor third is called "Komal Gandhara"

On a Native American flute, here are some minor third intervals in melody and harmony:

Audio Player disabled - visit Troubleshooting.

On a keyboard, minor third intervals are easy to locate:

Minor Third interval on a piano

In any group of two or three black keys, play the rightmost black key. Then add the next higher black key, which will be the leftmost black key in its group. That interval is a minor third.

The minor third interval represents three semitones - you'll see that there are two intervening (white) keys on the keyboard between the two black keys above.

So listening to the music samples, or playing them on a Native American flute or keyboard … what is the sound of this interval? Many people describe it as "sad" or "somber", others "mellow" or "meditative". As a musician on the Native American flute, working with this inteveral is an important part of the instrument, since it is central to distinguishing the primary Native American flute scale from the major scale that is so often used in Western music.

If we want to create a scale that contains the root note, the minor third, the perfect fourth from the root, the perfect fifth from the root, and the octave from the root, we could play it on most contemporary six-hole Native American flutes with the fingerings 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 open open open Finger diagram open open closed open open open and sound like this:

Audio Player disabled - visit Troubleshooting.

On a piano, the scale contains the notes:

Scale with root, minor third, perfect fourth, perfect fifth, and octave notes

... and it has the scale steps 3-2-2-5.

Minor Seventh

We began with intervals that are large leaps - octaves and fifths - and progressed to intervals that are smaller and smaller - fourths and minor thirds. Now we return to a leap that will let us complete the primary scale on the Native American flute.

The minor seventh has a frequency ratio of 16:9 - fairly complex to the year. Playing a 533.33 Hz note over a 300 Hz note gives you an interval of a minor seventh.

Since it's such a large leap, there aren't a lot of songs that begin with this interval. The original theme from Star Trek goes up a minor seventh and the jazz standard "Watermelon Man" descends a minor seventh.

Most contemporary Native American flutes get a minor seventh interval with the fingerings Finger diagram closed closed closed closed closed closed Finger diagram closed open closed open open open on six-hole flutes and Five hole finger diagram closed closed closed closed closedFive hole finger diagram closed open open open open on five-hole flutes.

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

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

Minor Seventh interval in Nakai Tab NotationThe Nakai Tablature for this minor seventh interval is shown at the left.

The interval is called "minor" because it is the lower note of the pair of "seventh" notes called "minor seventh" and "major seventh". We'll explore the major seventh on a later page.

In the sargam system, the seventh musical degree is "Nishada" (shortened to "Ni"; Sanskrit: निषादं). It originated from the elephant and is related to the crown chakra (Sanskrit: सहस्रार, “sahasrāra”). Since this is the minor seventh, it is called "Komal Nishada"

Here is the sound of the minor seventh interval and harmony on a Native American flute:

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On a keyboard, you can locate the minor seventh by going up an octave interval and then coming down two keys (or one black key, in this case):

Minor Seventh  interval on a piano

The minor seventh interval represents ten semitones.

 
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