The
Guqin
Scale of harmonics on the
Moodswinger
Scale of harmonics on C.
Play
ⓘ
The
scale of harmonics
is a
musical scale
based on the noded positions of the natural
harmonics
existing on a
string
.
[
citation needed
]
This musical scale is present on the
guqin
, regarded as one of the first
string instruments
with a musical scale.
[1]
Most
fret
positions appearing on Non-Western string instruments (
lutes
) are equal to positions of this scale. Unexpectedly, these fret positions are actually the corresponding
undertones
of the
overtones
from the
harmonic series
.
[
example needed
]
The distance from the
nut
to the fret is an integer number lower than the distance from the fret to the
bridge
(see:
superparticular number
).
Origin
[
edit
]
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
relation of the pressed string part with the open string, similar to the calculations
Pythagoras
did on his
monochord
. The guqin has one
anomaly
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 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
major
and
minor scale
or the major scale in the
Pythagorean tuning
.
Related
[
edit
]
Vietnamese scale of harmonics on c.
Play
ⓘ
A Vietnamese monochord, called the
đan b?u
, 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
of the first seven
overtones
(see
7-limit
). The dots are on the string lengths
1
⁄
2
,
1
⁄
3
,
1
⁄
4
,
1
⁄
5
,
1
⁄
6
,
1
⁄
7
of the whole string length. 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
to switch to
just intonation
and alternate tuning systems to create more consonant music than possible with the equal temperament.
[
citation needed
]
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
⁄
5
of the string length and
4
⁄
5
is the complement of
1
⁄
5
, the position of the fifth harmonic (and the fourth overtone).
The
Norwegian
composer
Eivind Groven
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.
[
citation needed
]
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
. 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
tuning but a regular
equal temperament
.
[
citation needed
]
See also
[
edit
]
References
[
edit
]
- ^
Yin, Wei.
Zhongguo Qinshi Yanyi
【中?琴史演?】 (Chinese). Pages 1-10.
Further reading
[
edit
]
External links
[
edit
]
- "3rd Bridge Helix"
,
PerfectSoundForever
. Article about the overtoning positions and their relation to musical scales.
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Other types
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Ethnic origin
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Non-octave
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