The scale of harmonics is a musical scale

Musical scale

In music, a scale is a sequence of musical notes in ascending and descending order. Most commonly, especially in the context of the common practice period, the notes of a scale will belong to a single key, thus providing material for or being used to conveniently represent part or all of a musical...

 based on the noded positions of the natural harmonics existing on a string

Strings (music)

A string is the vibrating element that produces sound in string instruments, such as the guitar, harp, piano, and members of the violin family. Strings are lengths of a flexible material kept under tension so that they may vibrate freely, but controllably. Strings may be "plain"...

. This musical scale is present on the guqin

Guqin

The guqin is the modern name for a plucked seven-string Chinese musical instrument of the zither family...

, regarded as one of the first string instrument

String instrument

A string instrument is a musical instrument that produces sound by means of vibrating strings. In the Hornbostel-Sachs scheme of musical instrument classification, used in organology, they are called chordophones...

s with a musical scale . Most fret positions appearing on Non-Western string instruments (lute

Lute

Lute can refer generally to any plucked string instrument with a neck and a deep round back, or more specifically to an instrument from the family of European lutes....

s) are equal to positions of this scale. Unexpectedly, these fret positions are actually the corresponding undertone

Undertone series

The undertone series is a sequence of notes that results from inverting the intervals of the overtone series. While overtones naturally occur with the physical production of music on instruments, undertones must be produced in unusual ways....

s of the overtone

Overtone

An overtone is any frequency higher than the fundamental frequency of a sound. The fundamental and the overtones together are called partials. Harmonics are partials whose frequencies are whole number multiples of the fundamental These overlapping terms are variously used when discussing the...

s from the harmonic series

Harmonic series (music)

Pitched musical instruments are often based on an approximate harmonic oscillator such as a string or a column of air, which oscillates at numerous frequencies simultaneously. At these resonant frequencies, waves travel in both directions along the string or air column, reinforcing and canceling...

. The distance from the nut to the fret is an integer number lower than the distance of the played area.

Origin

On the guqin, the left end of the dotted scale is a mirror image of the right end. The instrument is played with flageolet tones (harmonics) as well as pressing the strings on the wood. The flageolets appear on the harmonic positions of the overtone series, therefore these positions are marked as the musical scale of this instrument.

The flageolet positions also represent the harmonic consonant

Consonant

In articulatory phonetics, a consonant is a speech sound that is articulated with complete or partial closure of the vocal tract. Examples are , pronounced with the lips; , pronounced with the front of the tongue; , pronounced with the back of the tongue; , pronounced in the throat; and ,...

 relation of the pressed string part with the open string, similar to the calculations Pythagoras

Pythagoras

Pythagoras of Samos was an Ionian Greek philosopher, mathematician, and founder of the religious movement called Pythagoreanism. Most of the information about Pythagoras was written down centuries after he lived, so very little reliable information is known about him...

 did on his monochord

Monochord

A monochord is an ancient musical and scientific laboratory instrument. The word "monochord" comes from the Greek and means literally "one string." A misconception of the term lies within its name. Often a monochord has more than one string, most of the time two, one open string and a second string...

. The guqin has one anomaly

Anomaly

Anomaly may refer to:-Astronomy and celestial mechanics :* In astronomy, an anomaly is a quantity measured with respect to an apsis, usually the periapsis...

 in its scale. The guqin scale represents the first six harmonics and the eighth harmonic. The seventh harmonic is left out. However this tone is still consonant

Consonant

In articulatory phonetics, a consonant is a speech sound that is articulated with complete or partial closure of the vocal tract. Examples are , pronounced with the lips; , pronounced with the front of the tongue; , pronounced with the back of the tongue; , pronounced in the throat; and ,...

 related to the open string (otherwise it would not be a harmonic) and has a lesser consonant relation to all other harmonic positions. This is the main reason all the ratios of the sevenths family (7:1, 7:2, 7:3, 7:4, 7:5 and 7:6) also often are not present in other musical scales like for instance the just intoned

Just intonation

In music, just intonation is any musical tuning in which the frequencies of notes are related by ratios of small whole numbers. Any interval tuned in this way is called a just interval. The two notes in any just interval are members of the same harmonic series...

 major

Major scale

In music theory, the major scale or Ionian scale is one of the diatonic scales. It is made up of seven distinct notes, plus an eighth which duplicates the first an octave higher. In solfege these notes correspond to the syllables "Do, Re, Mi, Fa, Sol, La, Ti/Si, ", the "Do" in the parenthesis at...

 and minor scale

Minor scale

A minor scale in Western music theory includes any scale that contains, in its tonic triad, at least three essential scale degrees: 1) the tonic , 2) a minor-third, or an interval of a minor third above the tonic, and 3) a perfect-fifth, or an interval of a perfect fifth above the tonic, altogether...

 or the major scale in the Pythagorean tuning

Pythagorean tuning

Pythagorean tuning is a system of musical tuning in which the frequency relationships of all intervals are based on the ratio 3:2. This interval is chosen because it is one of the most consonant...

.

Related

A Vietnamese monochord, called the Đàn bầu, also functions with the scale of harmonics. On this instrument only the right half (from the view of the musician) of the scale is present up to the limit

Limit (music)

In music theory, limit or harmonic limit is a way of characterizing the harmony found in a piece or genre of music, or the harmonies that can be made using a particular scale. The term was introduced by Harry Partch, who used it to give an upper bound on the complexity of harmony; hence the name...

 of the first seven overtone

Overtone

An overtone is any frequency higher than the fundamental frequency of a sound. The fundamental and the overtones together are called partials. Harmonics are partials whose frequencies are whole number multiples of the fundamental These overlapping terms are variously used when discussing the...

s. The dots are on the string lengths 1/2, 1/3, 1/4, 1/5, 1/6, 1/7 of the whole stringlength. The reason for this half scale is because the left half creates the same tones as the right half when played as a flageolet tone and therefore the extra dots on the left half are useless for how this instrument is played.

The scale of harmonics was, together with the book of Helmholtz an inspiration for Harry Partch

Harry Partch

Harry Partch was an American composer and instrument creator. He was one of the first twentieth-century composers to work extensively and systematically with microtonal scales, writing much of his music for custom-made instruments that he built himself, tuned in 11-limit just intonation.-Early...

 to switch to just intonation

Just intonation

In music, just intonation is any musical tuning in which the frequencies of notes are related by ratios of small whole numbers. Any interval tuned in this way is called a just interval. The two notes in any just interval are members of the same harmonic series...

 and alternate tuning systems to create more consonant music than possible with the equal temperament. Partch's tone selection otonality from his utonality and otonality concept are the complement pitches of the overtones. For instance: the frequency ratio 5:4 is equal to 4/5th of the string length and 4/5 is the complement of 1/5, the position of the fifth harmonic (and confusingly enough the fourth overtone!).

The Norwegian composer Eivind Groven

Eivind Groven

Eivind Groven was a Norwegian microtonal composer and music-theorist. He was from Telemark and had his background in the folk music of the area.- Biography :...

 also wrote a thesis on the scale of harmonics, claiming this to be the oldest usable scale, frequent in Norwegian folk music, and seemingly in other folk musical traditions as well. Groven used the seljefløyte as basis for his research. The flute uses only the upper harmonic scale.

The scale is also present on the Moodswinger

Moodswinger

The Moodswinger is a twelve string electric zither with an additional third bridge designed by Yuri Landman. The rod which functions as the third bridge divides the strings into two sections to cause an overtone multiphonic sound...

. Although this functions quite differently than a Guqin, oddly enough the scale occurs on this instrument while it is not played in a just intonation

Just intonation

In music, just intonation is any musical tuning in which the frequencies of notes are related by ratios of small whole numbers. Any interval tuned in this way is called a just interval. The two notes in any just interval are members of the same harmonic series...

 tuning but a regular equal temperament

Equal temperament

An equal temperament is a musical temperament, or a system of tuning, in which every pair of adjacent notes has an identical frequency ratio. As pitch is perceived roughly as the logarithm of frequency, this means that the perceived "distance" from every note to its nearest neighbor is the same for...

.

Further reading

• Partch, Harry (1979). Genesis Of A Music
  Genesis of a Music
  Genesis of a Music is a book first published in 1947 by American microtonal composer Harry Partch .Partch first presents a polemic against both equal temperament and the long history of stagnation in the teaching of music, then goes on to explain his tuning theory based on just intonation, the...
  
  : An Account Of A Creative Work, Its Roots, And Its Fulfillments (Second Edition). ISBN 030680106X.

External links

• "3rd Bridge Helix", PerfectSoundForever. Article about the overtoning positions and their relation to musical scales.