PHYS341/2024/Project14
Project Summary
The saxophone, with its diverse range of sizes and complex construction, is a fascinating subject of study within the realm of music and physics. This project delves into the construction nuances of the saxophone, paying particular attention to the variances in size among its main members – the soprano, alto, tenor, and baritone saxophones – and their consequential effects on sound production. Central to this study is an exploration of how the physical dimensions of each saxophone size influence its fundamental frequencies and harmonic content. Additionally, this research endeavours to conduct a comprehensive sound analysis by comparing authentic saxophone sounds produced through traditional means with digitally generated saxophone sounds. This study explores the interplay between saxophone design and sound production methods by studying the features and the distinctions between actual and digital saxophone performances. Through such an examination, we seek to deepen our understanding of the physics governing saxophone acoustics and its implications for both musicians and instrument designers alike.
Saxophone
The saxophone is a woodwind instrument typically made of brass and has a distinctive curved shape. Adolphe Sax invented it in the 1840s, and has since become widely used in various genres of music, including classical, jazz, and pop.
The Saxophone Family:
The size of a saxophone directly influences the length of its tubing, which in turn affects its fundamental frequency. As sound waves travel through the saxophone's tubing, they bounce off the inner walls and resonate at frequencies determined by the length and shape of the tube. Longer tubes allow for the formation of longer wavelength sound waves, resulting in lower frequencies, while shorter tubes generate shorter wavelength sound waves and higher frequencies. The size and shape of the saxophone's bore further influence the resonance and harmonic content of the instrument, with wider bores favouring lower frequencies and narrower bores favouring higher frequencies. Therefore, understanding these principles is essential for saxophone design and players seeking to manipulate the instrument's sound.
Main Four Sizes of Saxophone:
Soprano Saxophone:
The soprano saxophone is the smallest member of the main four, characterized by its straight design. Due to its short tubing, it has the highest pitch range. Since the overall size of a wind instrument most directly affects the lowest note it can play, the lowest achievable note on a soprano saxophone is B♭3. At the same time, the highest pitch can extend well into the altissimo range, reaching as high as F♯6 or higher with advanced techniques.
Alto Saxophone:
The alto saxophone is slightly larger than the soprano and has a slightly lower pitch range. With longer tubing, the alto saxophone can produce lower pitches than the soprano, with the lowest pitch being B♭2. The highest typically reaches E♭6 or F6, or even higher with advanced techniques.
Tenor Saxophone:
The tenor saxophone is larger than the alto and soprano and has a lower pitch range. Its longer tubing allows it to produce lower pitches than both the soprano and alto saxophone and the lowest achievable note on a soprano saxophone is B♭1. It can usually go up to A♭5 or B♭5, with altissimo notes achievable with practice.
Baritone Saxophone:
The baritone saxophone is the largest and lowest-pitched member of the main four, featuring significantly longer tubing than the other saxophones. Due to its extended tubing, the baritone saxophone produces the lowest standard pitch among saxophones, typically reaching down to A♭1 or B♭1. Its highest pitch generally extends to around D5 or E♭5, though altissimo notes are possible for proficient players.
The B♭ family and the E♭ family:
The saxophone family is divided into two main groups based on its fundamental pitch: the B♭ family and the E♭ family. This division refers to the key that the saxophone is pitched in, which has implications for the instrument's size, construction, and sound production.
The fundamental frequency of a saxophone is the lowest pitch it can produce when all tone holes are closed. Saxophones in the B♭ family are pitched in the key of B♭, meaning that when all tone holes are closed, the fundamental frequency produced is a B♭ note. Similarly, saxophones in the E♭ family are pitched in the key of E♭, producing an E♭ note as their fundamental frequency when all tone holes are closed.
Saxophones in the B♭ family include the tenor and baritone saxophones, which are larger and produce lower pitches suitable for supporting harmony and bass lines in ensembles.
Construction:
Mouthpiece and Reed
The mouthpiece of a saxophone is where the player blows air to produce sound. It consists of a chamber and a facing, which is the part where the reed is attached. When the player blows air into the mouthpiece, it creates a pressure difference between the inside and outside of the chamber. The reed is a thin piece of cane attached to the mouthpiece. It vibrates when air is blown through it, producing sound waves. The vibration of the reed is initiated by the flow of air from the player's breath. As the air passes between the reed and the mouthpiece, it causes the reed to oscillate. When the player blows air into the mouthpiece, it creates a pressure difference. This pressure forces the reed to vibrate. As the pressure alternates due to the player's breath, the reed vibrates back and forth. The vibrating reed creates sound waves in the air. These waves travel through the saxophone's body, amplifying and resonating to produce the saxophone's characteristic sound.
Body
Soprano and sopranino saxophones are usually constructed with a straight tube with a flared bell at the end, although some are made in the curved shape of the other saxophones. Alto and larger saxophones have a detachable curved neck and a U-shaped bend (the bow) that directs the tubing upward as it approaches the bell. The body is usually comprised of a main tube with a bell at one end and a curved neck at the other. The keys and tone holes are mounted along the body and operated by the player's fingers. Each tone hole on the saxophone corresponds to a key mechanism controlled by the player's fingers. Pressing a key closes the corresponding tone hole, while releasing it opens the hole. Opening and closing tone holes effectively change the length of the vibrating air column inside the saxophone, which alters the pitch of the notes produced. The first open hole on a saxophone acts as an "end" for the vibrating air column, similar to the open end of a closed tube in physics. Opening additional holes shortens the effective length of the air column, raising the pitch. In addition to the main tone holes, saxophones also feature an octave key mechanism. When engaged, the octave key raises the pitch of the instrument by activating an additional vent that alters the airflow and resonance within the saxophone. This allows players to access higher registers with greater ease.
Sound Analysis
How do spectrograms and combined time graphs reveal the disparities between real saxophone sounds and those generated by a music app?
To analyse the differences between “Real saxophone Sounds” and those “Saxophone Sounds Generated by Music App”, spectrograms and time graphs serve as indispensable tools for visualizing and analyzing sound patterns. For this study, I recorded myself playing the note E5, corresponding to the alto saxophone's E flat. By subjecting these recordings to rigorous analysis through spectrograms and combined time graphs, we aim to uncover any discernible differences in waveform characteristics, frequency distribution, and harmonic content between the authentic saxophone sound and its digitally generated counterpart.
Time Graph:
Time Graph:
In the comparison of combined time graphs between “Real saxophone Sounds” and those “Saxophone Sounds Generated by Music App”, the presence of perfectly matching wavelengths and similar shapes suggests a striking resemblance in terms of pitch, amplitude, and harmonic content. Both sets of graphs exhibit precisely four oscillations within a 0.01 second timeframe, indicating a high degree of similarity in waveform characteristics. However, despite these visual parallels, further scrutiny may reveal subtle differences, such as variations in transient responses or amplitude envelopes, hinting at potential distinctions in sound quality or timbral nuances.
The Spectrum Graph:
The spectrograms offer a more detailed perspective by providing visual representations of the frequency content of the sounds over time. The observation of similar patterns spanning a frequency range from below 20 Hz to 8000 Hz indicates consistency in harmonic distribution and intensity between the two types of sounds. However, closer examination may reveal differences in harmonic structures or frequency modulations that could shed light on the mechanisms underlying saxophone sound production and the algorithms employed by the music app for sound synthesis.
Findings:
The findings of this analysis highlights the remarkable similarity between authentic saxophone sounds and those generated by the music app. Both the combined time graphs and spectrograms reveal striking resemblances in terms of frequency, pitch, amplitude, harmonic content, and timbral characteristics. The presence of perfectly matching wavelengths and similar shapes in the combined time graphs indicates a high degree of fidelity in waveform replication, while the consistency in harmonic distribution and intensity observed in spectrograms further reinforces this notion. These results suggest that the music app has successfully replicated the intricate nuances of saxophone sound production, effectively capturing the essence of the instrument's timbre.
Works CIted:
App used in Sound Analysis:
Beliaev, Denys. 3D Saxophone Fingering Chart, App Store, 1 Dec. 2018, apps.apple.com/ca/app/3d-saxophone-fingering-chart/id1442215658.
Images:
- Instrument Construction, Saxophonia, 2024, rajivssaxophonia.weebly.com/instrument-construction.html.
- Saxophone Reeds: Saxophone Players Guide.” Saxophone Players Guide , 30 Mar. 2020, www.saxophone-players-guide.com/saxophone-reeds.html.
- The Saxophone Family, Henri SELMER Paris, 2024, www.selmer.fr/en/blogs/infos/la-famille-des-saxophones.