Scale of harmonics

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Scale of harmonics

The scale of harmonics

Scale of harmonics

The scale of harmonics is a musical scale based on the noded positions of the natural harmonics existing on a string. This musical scale is present on the guqin, regarded as one of the first string instruments with a musical scale ....
is a musical scale

Musical scale

In music, a scale is a group of musical note collected in ascending and descending order that provides material for or is used to conveniently represent part or all of a musical work including melody and/or harmony....
based on the noded positions of the natural harmonics existing on a string. This musical scale is present on the guqin

Guqin

The is the modern name for a plucked seven-string List of traditional Chinese musical instruments of the zither family. It has been played since ancient times, and has traditionally been favored by scholars and literati as an instrument of great subtlety and refinement, as highlighted by the quote "a gentleman does not part with his qin'...
, 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 .

he guqin, the left end of the dotted scale is a mirror image of the right end.

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The scale of harmonics

Scale of harmonics

Musical scale

Guqin

String instrument

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 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 being the musical scale of this instrument. The flageolet positions also represent the harmonic consonant

Consonant

Pythagoras

Pythagoras of Samos was an Ionians Ancient Greeks mathematician and founder of the religious movement called Pythagoreanism. He is often revered as a great mathematician, mysticism and scientist; however some have questioned the scope of his contributions to mathematics and natural philosophy....
did on his monochord

Monochord

A monochord is an ancient Musical instrument and scientific laboratory instrument. The word "monochord" comes from the Greek language and means literally "one string." In the monochord, a single Strings is stretched over a sound box....
. The guqin has one anomaly

Anomaly

An anomaly is any occurrence or object that is strange, unusual, or unique. It can also mean a discrepancy or deviation from an established rule....
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 upper vocal tract, the upper vocal tract being defined as that part of the vocal tract that lies above the larynx....
related to the open string (otherwise it wouldn't be a harmonic) it 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

Major scale

In music theory, the major scale or Ionian mode scale is one of the diatonic scale Musical scales. It is made up of seven distinct notes, plus an eighth which duplicates the first an octave higher....
and minor scale

Minor scale

A minor scale in music theory is a diatonic scale with a third scale degree at an Interval of a minor third above the Tonic . While this definition encompasses Musical mode with the minor third, such as Dorian mode, the term may more usually refer only to the natural minor, harmonic minor, and melodic minor scales, descri...
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 interval are based on the ratio sesquialterum. Its name comes from medieval texts which attribute its discovery to Pythagoras, but its use has been documented as long ago as 3500 B.C....
.

A Vietnamese monochord, called the Ðàn b?u

Ðàn b?u

The d?n b?u is a Vietnamese monochord. While the earliest written records of the Dan Bau date its origin to 1770, many scholars estimate its age to be up to one thousand years older than that....
, 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 can refer to a variety of methods used to characterize the harmonies found in a piece of music, genre of music, or by extension, the harmonies that can be made with a particular scale or class of scales....
of the first seven overtone

Overtone

An overtone is a natural resonance of a system. Systems described by overtones are often sound systems, for example, blown pipes or plucked strings....
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

File:Harry Partch Institute-6.jpgHarry Partch was an United Statesn composer and musical instrument creator. He was one of the first twentieth-century composers to work extensively and systematically with microtonality scale s, writing much of his music for custom-made instruments that he built himself, tuned in 11-limit just intonation....
to switch to just intonation

Just intonation

In music, just intonation is any musical tuning in which the frequency of notes are related by ratios of whole numbers. Any interval tuned in this way is called a just interval; in other words, the two notes 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 scale is also present on the Moodswinger. Although this functions quiet differently than a Guqin, oddly enough the scale occurs on this instrument while it is not played in a just intonation

Just intonation

Equal temperament

Equal temperament is a musical temperament, or a system of Musical tuning in which every pair of adjacent notes has an identical frequency ratios....
.

Scale of harmonics

Origin

See also

Further reading