Just intonation is a method of tuning musical instruments that involves using pure intervals, rather than the tempered intervals used in equal temperament. This results in a more harmonious and natural sound, as the frequencies of the notes are in a ratio that is more closely aligned with the harmonic series. In this article, we will explore the various instruments that use just intonation and the techniques used to tune them. From ancient instruments like the Greek aulos to modern innovations like the 8-note scale, we will delve into the fascinating world of just intonation and discover how it is transforming the way we think about music.
What is Just Intonation?
Definition and Principles
Just intonation is a tuning system that aims to produce a more harmonious and pure sound by adjusting the frequencies of notes to create smaller and more precise intervals between them. Unlike equal temperament, which divides the octave into 12 equally spaced semitones, just intonation strives to replicate the true ratios of natural harmonics found in nature.
In just intonation, each note is assigned a frequency that is a whole number ratio to the next note in the scale. For example, the frequency of the first note is 1, the second note is 2, the third note is 3, and so on. This creates a more accurate representation of the natural harmonic series, resulting in a more pure and harmonious sound.
The principles of just intonation can be seen in various ancient cultures, such as the ancient Greeks, who used the Pythagorean tuning system, which is based on the ratios of whole numbers. However, the widespread adoption of equal temperament in Western classical music has led to a decline in the use of just intonation.
Despite this, many contemporary musicians and instrument makers are reviving the art of just intonation, exploring new instruments and tuning techniques to create a more authentic and immersive musical experience.
History and Evolution
The concept of Just Intonation dates back to ancient civilizations such as the Greeks and Chinese, who were known to have developed musical systems based on the natural harmonic series. The natural harmonic series is a sequence of pitches produced by an idealized vibrating string or air column in which the frequencies of the lower notes are whole-number multiples of the frequency of the higher notes.
In Western music, the use of Just Intonation began to decline during the Middle Ages with the rise of equal temperament, a tuning system in which each note is separated from its neighbor by a consistent interval. Equal temperament became the standard tuning system for Western music due to the widespread use of keyboard instruments such as the piano, which are more easily tuned using equal temperament.
However, in the 20th century, there was a resurgence of interest in Just Intonation among musicians and music theorists. This was partly due to the work of composer Arnold Schoenberg, who developed a twelve-tone technique that relied heavily on Just Intonation.
Today, there is a growing community of musicians and instrument builders who are exploring the possibilities of Just Intonation and developing new instruments and tuning techniques to better capture its unique sound.
Instruments that Use Just Intonation
Acoustic Instruments
Just intonation is not limited to electronic instruments, as it can also be found in acoustic instruments. The following are some examples of acoustic instruments that use just intonation:
- Piano
The piano is an acoustic instrument that can be tuned to use just intonation. The piano’s strings can be adjusted to create intervals that are in tune with the natural harmonic series, resulting in a more harmonious and complex sound. This tuning method is known as “pure” or “natural” tuning and can produce a unique and beautiful sound. - Guitar
The guitar is another acoustic instrument that can be tuned to use just intonation. Similar to the piano, the guitar’s strings can be adjusted to create intervals that are in tune with the natural harmonic series. This tuning method is known as “just” tuning and can produce a more complex and richer sound. - Violin
The violin is an acoustic instrument that can also be tuned to use just intonation. The violin’s strings can be adjusted to create intervals that are in tune with the natural harmonic series, resulting in a more harmonious and complex sound. This tuning method is known as “just” tuning and can produce a more expressive and nuanced sound. - Cello
The cello is another acoustic instrument that can be tuned to use just intonation. The cello’s strings can be adjusted to create intervals that are in tune with the natural harmonic series, resulting in a more harmonious and complex sound. This tuning method is known as “just” tuning and can produce a more powerful and resonant sound.
These are just a few examples of acoustic instruments that can be tuned to use just intonation. Each instrument has its own unique sound and character, and just intonation can enhance these qualities, creating a more expressive and nuanced musical experience.
Electronic Instruments
Electronic instruments are a popular choice for exploring just intonation due to their ability to generate and manipulate sound electronically. Some of the most commonly used electronic instruments for just intonation include:
- Synthesizers: Synthesizers are electronic musical instruments that generate audio signals that can be modified to produce a wide range of sounds. Many synthesizers have built-in just intonation tuning capabilities, allowing musicians to explore new sounds and harmonies.
- Digital Audio Workstations (DAWs): DAWs are software programs that allow musicians to create, record, and edit music on a computer. Many DAWs have built-in just intonation tuning algorithms, making it easy for musicians to experiment with different tunings and scales.
- Samplers: Samplers are electronic instruments that allow musicians to record and play back sounds from other instruments or sources. With just intonation tuning, samplers can be used to create new and unique sounds by sampling and manipulating the pitch of existing sounds.
- MIDI Controllers: MIDI controllers are devices that allow musicians to control digital musical instruments and software using physical controls such as knobs, buttons, and sliders. With just intonation tuning, MIDI controllers can be used to create new and interesting sounds by controlling the pitch and tuning of electronic instruments and software.
Overall, electronic instruments offer a wide range of possibilities for exploring just intonation and creating new and interesting sounds. By using these instruments and tuning techniques, musicians can push the boundaries of traditional music theory and create unique and innovative sounds that were previously impossible.
Tuning Techniques for Just Intonation
Pythagorean Tuning
Pythagorean tuning is a tuning technique used in just intonation that involves tuning each note to a specific ratio of small integers. This technique is based on the work of the ancient Greek philosopher and mathematician Pythagoras, who proposed that the perfect ratio of small integers is 1:2, 2:3, 3:4, and so on.
In Pythagorean tuning, each note is tuned to a specific ratio based on the small integers, such as 1:2, 2:3, 3:4, 4:5, and so on. This technique results in a harmonious and pleasing sound, with each note in harmony with the others.
One of the advantages of Pythagorean tuning is that it allows for a wide range of harmonies and chords to be played, resulting in a rich and complex sound. This technique is commonly used in classical music and is often used in combination with other tuning techniques, such as meantone tuning and equal temperament tuning.
Pythagorean tuning can be achieved using a variety of instruments, including the piano, guitar, and harp. The process of tuning an instrument to Pythagorean tuning involves adjusting the strings or keys to the correct ratio of small integers, using specialized tuning tools and software.
In summary, Pythagorean tuning is a tuning technique used in just intonation that involves tuning each note to a specific ratio of small integers. This technique results in a harmonious and pleasing sound, with each note in harmony with the others. Pythagorean tuning is commonly used in classical music and can be achieved using a variety of instruments.
Meantone Tuning
Meantone tuning is a system of tuning in which the intervals between notes are chosen based on a combination of ratios of small integers. This system is used to achieve a more accurate representation of the harmonic series, which is the sequence of frequencies produced by a vibrating string.
One of the main advantages of meantone tuning is that it allows for a more accurate representation of the major and minor thirds, which are the most commonly used intervals in Western music. This results in a more stable and pleasing sound when playing chords.
Meantone tuning is also used in the construction of the pipe organ, where the tuning system is used to create a range of distinct pitches that can be played together in a single instrument.
In addition to its use in the pipe organ, meantone tuning has also been used in the tuning of harpsichords, and is still used today by some musicians who are interested in historical performance practices.
It is important to note that while meantone tuning is an accurate representation of the harmonic series, it does not accurately represent the natural overtones produced by a vibrating string. This can result in a less natural and less pleasing sound when playing certain types of music.
Overall, meantone tuning is a versatile and accurate system of tuning that has been used in a variety of musical contexts, and is still used today by some musicians and instrument builders.
Equal Temperament Tuning
Equal Temperament Tuning is a method of tuning musical instruments that has become the standard in modern music. In this method, each note is tuned to a specific frequency based on a mathematical ratio. The ratio used is the twelfth root of 2, which is approximately 1.059463. This means that the frequency of the next note is very close to the previous note’s frequency plus a small increment. This method of tuning ensures that the distance between any two adjacent notes is the same, making it easier to play and transpose music.
One of the advantages of equal temperament tuning is that it allows for easy transposition. Since the distance between any two adjacent notes is the same, musicians can easily transpose a piece of music to a different key without having to adjust the tuning of their instruments. This makes it easier to play and perform music in different keys.
Equal temperament tuning is used in most modern musical instruments, including pianos, guitars, and orchestral instruments. It is also used in electronic music and music software, such as synthesizers and digital audio workstations.
However, equal temperament tuning has its drawbacks. One of the main drawbacks is that it can make some intervals sound slightly out of tune. For example, the third and fifth intervals may sound slightly off when played on an equal temperament tuned instrument. This is because the ratios of the frequencies of these intervals are not exact mathematical ratios.
Despite its drawbacks, equal temperament tuning remains the most widely used method of tuning musical instruments in modern music. Its advantages, such as ease of transposition and standardization, have made it the preferred method for most musicians and music educators.
Advantages and Disadvantages of Just Intonation
Aesthetic and Musical Benefits
One of the main advantages of just intonation is the increased range of musical expression it provides. By tuning instruments to the harmonic series, the musician has access to a greater variety of harmonies and dissonances, allowing for a more nuanced and sophisticated musical experience. The unique tuning of just intonation also allows for a more natural representation of the overtone series, creating a more organic and natural sound.
Furthermore, just intonation can also enhance the timbre of instruments, providing a more complex and varied tone color. This can result in a more immersive and engaging listening experience, as the listener is able to perceive a greater range of harmonics and overtones.
Another benefit of just intonation is that it can provide a more accurate representation of the natural harmonic series found in the world around us. This can result in a more authentic and realistic sound, allowing the listener to connect more deeply with the music.
However, it is important to note that just intonation is not without its challenges. The tuning of instruments can be more complex and time-consuming, requiring a greater level of skill and knowledge. Additionally, just intonation may not be as easily compatible with some genres of music, such as those that rely heavily on equal temperament tuning.
Despite these challenges, the aesthetic and musical benefits of just intonation are undeniable. By providing a greater range of harmonies and dissonances, enhancing timbre, and providing a more accurate representation of the natural world, just intonation offers a unique and immersive musical experience.
Practical Considerations and Limitations
- Inconsistent Pitch Standards: One of the main limitations of just intonation is the lack of a consistent pitch standard. This can make it difficult for musicians to transcribe and perform music written in just intonation, as they may need to adjust their tuning to match the composer’s intentions.
- Limited Availability of Instruments: Another limitation of just intonation is the limited availability of instruments that are properly tuned for this system. While some instruments, such as the piano and guitar, can be retuned to accommodate just intonation, other instruments, such as the violin, are not as easily adaptable.
- Increased Complexity: Just intonation requires a greater degree of accuracy and precision in tuning than equal temperament. This can make it more difficult for musicians to achieve and maintain the desired tuning, particularly in ensembles where multiple instruments are being played.
- Limited Flexibility: Because just intonation is based on the ratios of whole numbers, it can be difficult to achieve a wide range of chromatic intervals. This can limit the flexibility of the system and make it more challenging to compose and perform certain types of music.
- Audience Expectations: Finally, there is the issue of audience expectations. Many listeners are accustomed to the sound of equal temperament, and may find the sounds of just intonation unfamiliar or dissonant. This can make it more difficult for composers and performers to gain a receptive audience for their work.
Exploring Specific Instruments
Examples of Instruments Using Just Intonation
While the history of just intonation can be traced back to ancient civilizations, it was during the Baroque period that it found a resurgence in the form of equal temperament. This led to the development of a wide range of instruments that could take advantage of the unique properties of just intonation. Here are some examples of instruments that use just intonation:
- Harps: Harps are perhaps the most well-known instruments that use just intonation. They are stringed instruments that have a range of several octaves and can produce a variety of tones and overtones. The just intonation of harps allows for a more natural and accurate representation of harmonics, resulting in a richer and more nuanced sound.
- Pianos: While most pianos are tuned using equal temperament, there are some instruments that use just intonation. One example is the “pianoforte” developed by the Italian instrument maker, PianoForte & C. This instrument uses a system of levers and pulleys to create a more accurate representation of just intonation, resulting in a more expressive and nuanced sound.
- Violins: Violins are another instrument that can benefit from just intonation. Some luthiers have experimented with creating violins that use a system of bridges and strings to produce a more accurate representation of just intonation. This results in a more resonant and harmonious sound, with a greater emphasis on the natural harmonics of the instrument.
- Chamber Music: Chamber music, such as string quartets and quintets, can also benefit from just intonation. By using instruments that are tuned to just intonation, the natural harmonics of the instruments can be better highlighted, resulting in a more expressive and nuanced sound. Additionally, the use of just intonation can help to create a more cohesive and integrated sound, with each instrument blending seamlessly with the others.
- Experimental Instruments: Finally, there are a number of experimental instruments that have been developed specifically to take advantage of just intonation. These include the “harmonic canon,” which uses a system of resonating tubes to produce a variety of justly tuned intervals, and the “stretched piano,” which uses a system of strings and resonators to produce a more accurate representation of just intonation.
In conclusion, just intonation is not limited to a single instrument or style of music. It can be found in a wide range of instruments, from harps and pianos to violins and chamber music. By using just intonation, these instruments can produce a more natural and nuanced sound, with a greater emphasis on the harmonics and overtones that give music its unique character.
How Just Intonation Enhances the Sound of Specific Instruments
When it comes to music, the quality of the sound produced by an instrument is of utmost importance. The way an instrument is tuned can have a significant impact on the final sound that is produced. Just intonation is a method of tuning that can greatly enhance the sound of specific instruments.
The Benefits of Just Intonation for String Instruments
String instruments such as the violin, cello, and double bass are typically tuned using a system of tuning pegs. In standard tuning, these instruments are tuned to a specific pitch, and the strings are stretched to maintain that pitch. However, in just intonation, the strings are tuned to specific frequencies that result in a more harmonious sound. This results in a richer, fuller sound that is more pleasing to the ear.
The Benefits of Just Intonation for Wind Instruments
Wind instruments such as the flute, clarinet, and saxophone are typically tuned using a system of keys. In standard tuning, these instruments are tuned to a specific pitch, and the keys are adjusted to maintain that pitch. However, in just intonation, the keys are adjusted to specific frequencies that result in a more harmonious sound. This results in a richer, fuller sound that is more pleasing to the ear.
The Benefits of Just Intonation for Keyboard Instruments
Keyboard instruments such as the piano and harpsichord are typically tuned using a system of tuning pins. In standard tuning, these instruments are tuned to a specific pitch, and the tuning pins are adjusted to maintain that pitch. However, in just intonation, the tuning pins are adjusted to specific frequencies that result in a more harmonious sound. This results in a richer, fuller sound that is more pleasing to the ear.
In conclusion, just intonation can greatly enhance the sound of specific instruments by tuning them to specific frequencies that result in a more harmonious sound. Whether you are a professional musician or a hobbyist, exploring the world of just intonation can open up new possibilities for your musical endeavors.
The Future of Just Intonation in Music
Innovations and Technological Advancements
The world of just intonation is constantly evolving, and the future of this tuning system is bright. Advancements in technology have allowed for new instruments and techniques to be developed, making it easier for musicians to explore the world of just intonation.
Digital Instruments
Digital instruments, such as digital pianos and synthesizers, have made it possible to easily produce just intonation on a wide range of instruments. These instruments can be programmed to produce any tuning system, including just intonation, and are capable of producing complex and intricate sounds that were previously impossible to achieve.
Virtual Instruments
Virtual instruments, such as software synthesizers and digital audio workstations, have also made it easier for musicians to explore just intonation. These instruments allow musicians to create and manipulate sounds using a computer, and can be used to create virtual instruments that are specifically tuned to just intonation.
Alternate Tuning Systems
Advancements in technology have also allowed for the development of alternate tuning systems, such as the “stretched tuning” system developed by composer and theorist Ben Johnston. This system allows for a more flexible approach to just intonation, making it possible to play microtonal music on standard instruments.
Just Intonation Pedals and Effects
Pedals and effects units have also been developed to make it easier for musicians to explore just intonation. These devices can be used to change the tuning of an instrument in real-time, allowing musicians to seamlessly switch between different tuning systems during a performance.
Overall, the future of just intonation in music is exciting, and the innovations and technological advancements that have been made have opened up new possibilities for musicians to explore this unique tuning system.
The Evolving Role of Just Intonation in Modern Music
The world of music is constantly evolving, and the role of just intonation is no exception. In recent years, there has been a growing interest in just intonation among musicians, composers, and music theorists. This interest has been fueled by a desire to explore new sonic territories and to push the boundaries of traditional tuning systems.
One of the main drivers of this interest in just intonation has been the development of new musical technologies. With the advent of digital audio workstations (DAWs) and other music software, it has become easier than ever for musicians to experiment with alternative tuning systems. This has led to a surge of interest in just intonation, as well as other alternative tuning systems such as microtonal music and Xenharmonic music.
Another factor that has contributed to the growing interest in just intonation is the rise of experimental music. Experimental music is a broad category that encompasses a wide range of musical styles and approaches. One of the key features of experimental music is its willingness to challenge conventional norms and expectations. Just intonation is a natural fit for experimental music, as it offers a way to explore new sonic possibilities and to create music that is unlike anything that has come before.
In addition to its use in experimental music, just intonation is also being explored in other genres. For example, some classical composers are incorporating just intonation into their works, using it to create new and interesting harmonies and textures. Similarly, some jazz musicians are experimenting with just intonation, using it to create new sounds and to push the boundaries of traditional jazz harmony.
Overall, the evolving role of just intonation in modern music is a reflection of the ever-changing nature of the music industry. As technology continues to advance and as musicians continue to push the boundaries of what is possible, just intonation is likely to play an increasingly important role in the world of music.
FAQs
1. What is just intonation?
Just intonation is a method of tuning musical instruments in which the intervals between notes are determined by the harmonic ratios of the sound frequencies. This creates a more harmonious and natural sounding tuning system, as opposed to equal temperament, which is used in most modern instruments.
2. What instruments use just intonation?
Many early musical instruments, such as harpsichords, lutes, and viols, were tuned using just intonation. However, with the rise of equal temperament in the 18th century, just intonation fell out of favor and is now less commonly used. Today, some modern instruments, such as the violin family and some synthesizers, can be tuned using just intonation.
3. How is just intonation different from equal temperament?
In equal temperament, each note is tuned to a specific frequency, and the intervals between notes are equally spaced. In just intonation, the intervals between notes are determined by the harmonic ratios of the sound frequencies, which creates a more natural and harmonious sound. This means that the pitch of some notes may be slightly different in just intonation compared to equal temperament.
4. What are the benefits of using just intonation?
One benefit of using just intonation is that it creates a more natural and harmonious sound. It also allows for more accurate tuning of certain intervals, such as the perfect fifth, which can be difficult to tune accurately using equal temperament. Additionally, just intonation can make certain chords and melodies sound more harmonious and pleasing to the ear.
5. How is just intonation used in practice?
Just intonation can be used in a variety of ways in practice. Some musicians tune their instruments using just intonation for specific pieces or genres of music, while others use it as a reference when tuning their instruments using equal temperament. Additionally, some modern synthesizers and other electronic instruments allow for the use of just intonation as a tuning option.
