The Indian Bamboo Flute · Laws, Acoustics and Principles

The Physics of
Flute Sound

Laws, principles and acoustical properties of the Indian bamboo flute — drawn from classical musicological tradition.

1

The Seven Factors That Determine the Flute Note

Classical scholarship identifies a definitive list. "The principal factors that determine the pitch, intensity and quality of the flute-note are" the following seven — each acting upon the sound independently, while all others remain constant.

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1. Material
The nature of the wood or bamboo composing the flute. Must be properly seasoned before use.
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2. Thickness & Density
Of the composing substance. Greater thickness and density → deeper note; thinner and less dense → shriller note.
3. Uniformity of Bore
The cylindrical bore must be uniform. Its uniformity determines the uniformity of intensity across all notes.
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4. Cross-Section
The cross-section of the tube affects tonal character. "Flutes with a larger cross-section will have a thin tone."
5. Speaking Length
Distance between mukha randhra and tara randhra — the vibrating column of air from mouth-hole to first open finger-hole.
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6. Strength of Air
The strength of the air blown across the mouth-hole. More strength → greater intensity of note.
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7. Area of Mouth-Hole
The area of the mouth-hole left open for the reception of the air. Pitch varies directly with this area.
2

The Nine Laws of the Flute

As stated in classical tradition

Each law holds good provided all other factors remain constant. "Here and elsewhere the pitch of the flute means the pitch of the note, middle octave Sa of the flute."

Law 1
The pitch of the flute is inversely proportional to the distance between the mukha randhra (mouth-hole) and the tara randhra (first finger-hole).
Law 2 — Speaking Length
The pitch of the note produced varies inversely with the speaking-length of the air-column. The less the distance between the mouth-hole and the nearest open finger-hole, the higher the pitch.
Law 3 — Mouth-Hole Area
The pitch of a note varies directly as the area of the mouth-hole exposed for the reception of the air blown across.
Law 4 — Finger-Hole Area
The pitch of a note varies directly as the area of the nearest finger-hole left open for the exit of air.
Law 5 — Thickness & Density
The greater the thickness and density of the composing material, the deeper the note; conversely, the thinner and less dense, the shriller.
Law 6 — Material Does Not Affect Pitch
"The pitch of a flute is the same whether it is made of bamboo, ivory, ebony, cedar, wood, glass or metal. The quality of the notes will however differ."
Law 7 — Harmonics Explain Timbre
"The different composing materials do no more than give rise to different harmonics and thereby impart a different quality to the compound tone produced."
Law 8 — Intensity
The intensity of a note varies directly with the strength of the air blown across the mouth-hole.
Law 9 — Bore Uniformity & Intensity
"The uniformity in the intensity of the flute tone is dependent upon the uniformity of its cylindrical bore."
3

The Wave Formula — How Pitch Is Calculated

"The length of the vibrating column of air in the flute is equal to the length of the tube from the mukha randhra down to the first svara randhra or stop-hole from which the air can make its escape. This length is equal to one-fourth of the wave length of the note heard."

The classical calculation
f = v ÷ 4L
v = velocity of sound in air = 1,100 feet per second
L = speaking length of air column

"If the length of the vibrating column of air is 6 inches, the frequency of the note produced will be equal to 1100 ÷ 24 (i.e. 6 inches multiplied by four) = 550 vibrations per second. This is of course subject to certain end corrections."

How the speaking length changes: The classical texts are clear that it is not only the distance between the mouth-hole and the nearest open finger-hole that determines pitch — "but also the open or closed condition of the subsequent two finger-holes."

Overblowing: "By over-blowing, the octave of the whole series of notes is obtained." This is the mechanism by which a single flute achieves two and a half octaves — not by changing finger positions, but by adjusting breath pressure to excite higher harmonics.

Partial opening: "The frequency of a full note is heard when the svara randhra is fully open. When it is open three-quarters, the pitch is reduced by one shruthi; when the finger-hole is half open, there is a reduction by two shruthis; when quarter-open, a reduction by three shruthis."

This is the physical basis of the bansuri's capacity for infinite gradation — the microtonal language of Indian classical music.

4

How Sound Is Produced — The Edge Tone

"A flute-note is sounded by blowing a stream of air across the opposite edge of the mouth-hole. The air is not blown into the orifice; only a part of it enters the tube. The flat stream of air blown through the small aperture between the lips results in edge-tones."

"When all the finger-holes are closed, the lowest note is produced and the speaking length of the air column is from the mouth-hole to the open end. With the opening of each finger-hole from the open end, the speaking or the effective length of the tube is lessened and this results in a corresponding increase of pitch."

The flute-tone's purity: "The flute-tone, unlike the human voice and stringed instruments, is pure and simple and is accompanied by few and feeble upper-partials. The acoustic spectrum of the flute reveals this character of the instrument."

The air-chamber: "The air-chamber between the node and the embouchure and where the end is artificially closed with a stopper, the stopper's size, position and form, play a part in giving the peculiar timbre to the flute."

Underblowing: "Underblowing will result in the production of notes an octave lower down." — the mechanism by which the Mandra (lower) octave is accessed.

Harmonics on the European flute: For comparison, "in the European flute, it is possible for a trained flutist to play notes up to the 5th harmonic, by mere adjustment in blowing and without the change of fingers" — producing: mandra shadja, madhya shadja, madhya panchama, tara shadja, and tara sthayi antara gandhara.

5

Shruthis, Gamakas and Acoustical Detail

"The flute is an ideal instrument for the analytical study of shruthis (quarter-tones) and gamakas (graces)."

Semitones and quarter-tones are produced on the Indian flute "by the partial opening or closing of the finger-holes." The Indian flute's direct finger-to-hole contact means "the problem of playing ragas which take consecutive shruthis does not arise."

The classical texts are precise about the acoustical consequence of shruthi deviation: "If during flute playing, there are a few moments when the shruthi (tonic note) is slightly departed from, it is not the fault of the player. It is a defect inherent in all wind instruments, including the human voice."

Finger-Hole Position → Shruthi
Fully open → full svara
¾ open → reduction by 1 shruthi
½ open → reduction by 2 shruthis
¼ open → reduction by 3 shruthis
Fully closed → next lower svara

"Intricate gamakas are produced through cross-fingerings. The kampita madhyama of Yadukulakambhoji raga and the kampita rendering of the kaisiki nishada are instances in point."

"The fingers reveal to the flutist the delicate nature and the frequency relationships of such subtle notes as the Saveri dhaivata and Kuranji nishada."

6

The Human Voice and the Flute Compared

"The human voice and the flute are alike in many respects. They possess the same compass, viz., 2½ octaves, and are both monophonous — i.e., capable of producing only one note at a time."

"In singing, the air from the lungs sets the vocal cords in vibration and produces music. In flute-playing, the air from the lungs first passes through the aperture between the vocal cords without setting them in vibration; this air after passing through the mouth, enters the flute through the mouth-hole and gives notes of different pitch."

Key similarities: Same compass (2½ octaves) · Both monophonous · Both capable of the subtlest gamakas · Both subject to shruthi drift inherent in all wind instruments

Key differences: "A very high degree of speed is possible on the flute, which is not ordinarily possible in the voice." Unlike stringed instruments with strings of gut and metal, "the flute, like the voice, has a constant tone-colour over the whole available compass."

The discovery of harmonics: "It was the flute that gave the idea of larger intervals to early man. When a note like shadja (C) was played with some force, the octave note was immediately heard." — the flute thus gave early man his first encounter with the harmonic series.

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Technical Terminology

Classical Sanskrit and Tamil terminology
Mukha randhraThe mouth-hole or blow-hole
Tara randhraThe finger-hole nearest the mouth-hole; gives the note of highest pitch
Svara randhraFinger-hole
Vayu randhraThe outlet or 8th hole, never stopped; air blown across the mouth-hole escapes through it
Garbha randhraThe bore of the flute; cross-section
DandiThe flute tube
SirasThe distance between the mukha randhra and the adjoining closed end
PrantaThe distance between the vayu randhra and the adjoining closed end (same as siras)
VamsangulaThe distance between the mouth-hole and the tara randhra; determines the pitch of the flute
ChidramSushira vadya — a wind/pipe instrument
Phutkara doshaFaults in blowing
Phutkara gunaMerits in blowing
KakiA harsh, crow-like sound — a vamsika gosha (flute fault)
KaphilaBlowing interrupted by phlegm — a fault in flute play
KampaThe process of flattening or sharpening a note by partial hole coverage
SkalitaAgitated, unsteady playing — to be avoided
8

The Flute's Acoustical Utility

The flute has played many roles as an acoustical instrument — not just a concert instrument:

  • Used to work out and verify musical laws and phenomena
  • Longer flutes "enabled the ancients to understand something of the harmonic series of notes"
  • Revealed the phenomenon of beats when two flutes of nearly equal pitch were played together
  • Served as an instrument of absolute pitch for tuning stringed instruments like the vina and yazh, in days before the tambura
  • Used as an acoustical meter to study the nature of gamakas and the lore underlying various musical phenomena
  • Used to work out the cycles of fifths and fourths (sa-pa and sa-ma series) to their logical conclusions
  • Helped to find new scales by the process of modal shift of tonic

"In the days when the tambura and the present acoustical devices were unknown and notes of absolute pitch could not be readily sounded, the flute served as an instrument of absolute pitch for tuning stringed instruments like the vina and the yazh."

"The flute served as an acoustical meter to study the nature of gamakas and the lore underlying various musical phenomena. It was of use in working out to their logical conclusions the cycles of fifths and fourths."