Saturday, February 11, 2012

cello strings, harmonics & spectograms

thinking about how to set things up... things to consider for barrel gurdy...

cello strings

Strings on a cello have cores made out of gut (sheep or goat), metal, or synthetic materials, such as Perlon. Most modern strings used today are also wound with metallic materials like aluminum, titanium and chromium. Cellists may mix different types of strings on their instruments. The pitches of the open strings are C, G, D, and A (, unless alternative tuning (scordatura) is used. -

harmonics & spectograms

A vibrating string subdivides itself into many parts vibrating at the same time. Each part produces a pitch of its own, called a partial. A vibrating string has one fundamental and a series of partials. The most pure combination of two pitches is when one is double the frequency of the other.

A harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency, i.e. if the fundamental frequency is f, the harmonics have frequencies 2f, 3f, 4f, . . . etc. The harmonics have the property that they are all periodic at the fundamental frequency, therefore the sum of harmonics is also periodic at that frequency. Harmonic frequencies are equally spaced by the width of the fundamental frequency and can be found by repeatedly adding that frequency. For example, if the fundamental frequency is 25 Hz, the frequencies of the harmonics are: 50 Hz, 75 Hz, 100 Hz etc.

Spectogram of a D chord arpeggiated on the cello. Yellow bands at the same level indicate the same harmonics excited by the bowing of different notes. Notes played from left to right: D F# A F# D.

3D spectrum diagram of the overtones of a violin G string (foreground). Note that the pitch we hear is the peak around 200 Hz. - Violin - Wikipedia, the free encyclopedia

Many oscillators, including the human voice, a bowed violin string, or a Cepheid variable star, are more or less periodic, and so composed of harmonics.

Most passive oscillators, such as a plucked guitar string or a struck drum head or struck bell, naturally oscillate at not one, but several frequencies known as partials. When the oscillator is long and thin, such as a guitar string, or the column of air in a trumpet, many of the partials are integer multiples of the fundamental frequency; these are called harmonics. Sounds made by long, thin oscillators are for the most part arranged harmonically, and these sounds are generally considered to be musically pleasing. Partials whose frequencies are not integer multiples of the fundamental are referred to as inharmonic. Instruments such as cymbals, pianos, and strings plucked pizzicato create inharmonic sounds.

Spectrogram of dolphin vocalizations; chirps, clicks and harmonizing are visible as inverted Vs, vertical lines and horizontal striations respectively

The untrained human ear typically does not perceive harmonics as separate notes. Rather, a musical note composed of many harmonically related frequencies is perceived as one sound, the quality, or timbre of that sound being a result of the relative strengths of the individual harmonic frequencies. Bells have more clearly perceptible inharmonics than most instruments. Antique singing bowls are well known for their unique quality of producing multiple harmonic partials or multiphonics.

Harmonics and overtones

The tight relation between overtones and harmonics in music often leads to their being used synonymously in a strictly musical context, but they are counted differently leading to some possible confusion. This chart demonstrates how they are counted:

Frequency Order Name 1 Name 2
1 · f = 440 Hz n = 1 fundamental tone 1st harmonic
2 · f = 880 Hz n = 2 1st overtone 2nd harmonic
3 · f = 1320 Hz n = 3 2nd overtone 3rd harmonic
4 · f = 1760 Hz n = 4 3rd overtone 4th harmonic

Harmonics are not overtones, when it comes to counting. Even numbered harmonics are odd numbered overtones and vice versa.

In many musical instruments, it is possible to play the upper harmonics without the fundamental note being present. In a simple case (e.g., recorder) this has the effect of making the note go up in pitch by an octave; but in more complex cases many other pitch variations are obtained. In some cases it also changes the timbre of the note. This is part of the normal method of obtaining higher notes in wind instruments, where it is called overblowing. The extended technique of playing multiphonics also produces harmonics. On string instruments it is possible to produce very pure sounding notes, called harmonics or flageolets by string players, which have an eerie quality, as well as being high in pitch. Harmonics may be used to check at a unison the tuning of strings that are not tuned to the unison. For example, lightly fingering the node found half way down the highest string of a cello produces the same pitch as lightly fingering the node 1/3 of the way down the second highest string. For the human voice see Overtone singing, which uses harmonics.

While it is true that electronically produced periodic tones (e.g. square waves or other non-sinusoidal waves) have "harmonics" that are whole number multiples of the fundamental frequency, practical instruments do not all have this characteristic. For example higher "harmonics"' of piano notes are not true harmonics but are "overtones" and can be very sharp, i.e. a higher frequency than given by a pure harmonic series. This is especially true of instruments other than stringed or brass/woodwind ones, e.g., xylophone, drums, bells etc., where not all the overtones have a simple whole number ratio with the fundamental frequency.

Madness and Methods Page 2: The "Stello" (steel cello)

Cello strings attached to a steel drum via crafted wood parts. Tailpiece and tuning machines are from an electric bass.

Used contact mic on "bridge" and XY stereo about 6 feet back from cavity. Played on its side with a horsehair Cello bow.

Produces low resonant tones, quite musical, akin to a waterphone.

Was part of the design recordings done for Gary Rydstrom for AI Artificial Intelligence.

Apocalyptica at the 2009 Ilosaarirock festival. – Free Audio Engineering Software - Audio Experiments - visit pages for sound samples - Sound Of the Month Edition

One sine wave + high speed frequency modulation – Free Audio Engineering Software - SoME 2010 Aug: Harmonic Burst: 440 Hz harmonic modulated with speed: 0 -> 220 -> 0 [Hz] and amplitude: 0 -> 3 -> 0 [octave] – Free Audio Engineering Software � SoME 2010 Dec: Prime notes: This idea was on my mind long before starting the whole Falasol project. What kind of cacophony would it be if each note is assigned a prime number and played only on the number’s multiplication beats. Total chaos? Or would the mind be able to recognize some hidden patterns?

thinking about how to set up everything... things to consider for barrel gurdy...

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