Background Concepts for the Viewer
- The Electric Bass
- The Neck
- The Pickups
- Just-Noticeable Difference
- Pulse-Width Modulation
This webpage is intended as an introduction to some of the concepts that are covered in this study. The majority of the following information was provided by team member Cheyn Rushing, who has been playing bass guitar for eight years. Research is cited.
The Electric Bass
An electric bass guitar is made up of several different parts, as shown on the right.1 The major parts of an electric bass guitar are the body, the neck, and the head stock. The body is the largest part of the bass guitar, and holds the volume and tone knobs, the pickups, and the bridge. The neck connects the body to the head stock, and is comprised of frets that are inlaid on a fretboard, a hidden truss rod, and a wooden back. The head stock is where the major tuning occurs, as one end of each string connects to a tuning machine, or tuner.
The majority of the bass guitar’s neck involves the fretboard. The bassist applies pressure to a string against the fretboard; this changes the frequency of the string’s vibration. The fretboard may be contain frets (fretted) or not (fretless). Frets are small metal bars that divide the fretboard into discrete notes. A fretless fretboard provides a continuous spectrum of frequencies, and is typically more difficult to learn. A hidden truss rod inside the neck determines the amount of bend, or bow, in the neck. The bow in the neck affects the pitch at individual frets. This is due to the bass guitar being an equal-temperament instrument.
The equal-temperament nature of bass guitars effects differences in fretted frequencies across the fretboard. The picture on the right displays the standard design of a fretboard.2 Equal-temperament is the standard tuning system in which adjacent musical notes (for example, from B to C) have the same frequency ratio. If the neck is misaligned, fretted notes will not be in tune; this causes fretted notes that are the same as open notes on other strings to be different. Because of this, a bassist will often set a guitar to a desired tuning, then make adjustments to the open tuning to provide for cohesion through across all the strings. Thus, providing a fast tuning mechanism and allowing for manual adjustments is important.
Pickups (including bass guitar pickups) are made of a thin copper wire wound around permanent magnets (the “core”). Pickups work by utilizing magnetic induction. The figure on the right shows the standard bass pickup with copper windings.3 When the bass player, or bassist, plucks the strings, the strings vibrate; this vibration induces an electric current in the wires that are wound around the magnet. This current is sent from the guitar to any electronics the guitar may have, and then to the amplifier. The frequency at which the string vibrates over the magnet is identical to the frequency of the alternating current induced in the coil. Typical pickups on an electric bass guitar include multiple single coil pickups housed in the bass guitar’s body, as the figure above shows. The SMARTune system will be using special pickups called polyphonic pickups. These pickups are discussed on the design page.
Electric guitars have two main components that affect the way a tensioned string interacts with the guitar’s pickups: the tuners and the bridge. The focus of this feasibility study is on the tuners located on the headstock, as the tuners control the majority of a bass guitar’s tuning. The second component is the bridge. The bridge of an electric guitar is adjustable to provide changes in intonation and string height, but the changes made to the string’s tension are minimal compared to that of the tuners. This is shown on the right.4 The springs are adjustable, as well as the heights of the saddles. The saddles on the bass guitar’s bridge are nodes for the standing wave generated when the bassist plucks a string. Adjustments pertaining to the bridge are typically required to fix small inconsistencies in the bass guitar’s intonation. These adjustments are unique for every bassist and bass guitar, so automation of this portion of the tuning is impractical.
The tuners control most of the tension adjustments in the guitar’s strings. The tuning keys on the tuners each turn a worm gear. This mechanism is depicted on the right.5 The worm, which is connected to the tuning key, turns a worm gear attached to a capstan on the other side of it. The capstan holds one end of the string. The worm drive serves two purposes: it provides a mechanical advantage to make tuning easier for the user, and it also prevents the tension in the string from releasing.
Frequency is "the number of periods or regularly occurring events of any given kind in unit of time, usually in one second."6 A couple examples of this are shown on the right.7 In music, the "regularly occurring event" is often a complex wave that are, in reality, composed of multiple frequencies. An example of this is in the figure below. In this example, the frequency of 73.68 Hz is present, and is the dominant frequency. The frequencies that follow are called "harmonics."
The tuning of an instrument consists of a set of notes within an “octave” that are based off of a standard frequency. This standard frequency is 440 Hz, which is an “A.” The twelve notes (also called half steps, or semitones) in an octave, in order, are: A, A#, B, C, C#, D, D#, E, F, F#, G, and G#. These twelve notes repeat in this order from 0 Hz upward. The frequency of notes are related to each other exponentially. For example, the ratio from A to A# is the same as the ratio from A# to B. The next “A” note above the 440 Hz A is at 880 Hz. Two frequencies that have a ratio of 2 are an octave apart. So the "A" note is all of the frequencies 55 Hz, 110 Hz, 220 Hz, 440 Hz, 880 Hz, and so on.
It is easier to understand the relation between notes when they are expressed linearly instead of exponentially. Instead of using frequencies, differences in frequencies are usually expressed in “cents.” There are 100 cents between every semitone. This linearizes the frequency spectrum, as there are now 100 cents from A to A# and 100 cents from A# to B. For engineering applications, cents make sense.
The most common mathematical expression of a note is by its frequency. Frequency is a rate of the number of times a waveform repeats itself (or cycles) in one second. For example, the standard A has a frequency of 440 Hz, or 440 cycles per second. This involves the “just-noticeable difference,” or jnd. The average human is able to discern a difference of approximately five cents in pitch.8 Since musicians’ ears are trained to hear smaller differences in pitch, a musician's jnd is likely closer to two cents. The team is developing a product that will be able to tune within this two-cent just-noticeable difference.
Pulse-width modulation, or PWM, is a method of expressing an analog signal in a digital format. The figure on the right is an example of a PWM signal.9 The blue waveform is the digital signal that is actually being transmitted, and the red waveform is the analog interpretation of the blue waveform. This is useful for transmitting analog information when an analog output is not available.
- 1 Source: LearnBass.co.uk.
- 2 Source: Guitar Nerding Blog.
- 3 Source: http://medias.audiofanzine.com/images/normal/634765.jpg.
- 4 Source: The Bass Guitar Blog.
- 5 Adapted from: Dalymusic.
- 6 Definition 3a from Dictionary.com.
- 7 Source: Wikipedia article on frequency.
- 8 Source: Georgia State University.
- 9 Source: Wikipedia article on pulse-width modulation.