Most historical/traditional western music is composed from a series of tones we call scales. Scales are defined by the number of notes they use, and the relative distance of those notes from their adjacent notes. For example, the major scale is defined by seven pitches, with each note either a half step or a whole step higher than the one before it. A minor scale is also defined by seven pitches, but the sequence of whole and half steps has been modified to create a different set of pitches and intervals (the distance between pitches) to work with.
To create melodies, a composer generally picks a scale and then uses the pitches in the scale to create her melody. To create harmony, a composer arranges the notes from the scale into vertical stacks called chords. The movement from one chord to another is what creates the effect of harmony, or harmonic progression.
The mystery of harmony, however, is that some chords sound naturally pleasing to the ear, while others sound unfinished, jarring, or otherwise unpleasant. Additionally, if the instrument or choir playing a chord is out of tune, the chord doesn't lock into place, and the harmony sounds wrong. Most people who've attended a junior high school choir concert or youth recital can tell the difference immediately: while the players may have nominally played all the right notes, their collective tuning could have been off just enough to make people notice that something wasn't quite right.
Most music lovers and players have at some point had the experience of learning to play or sing in tune. But what does it mean for the player and listener to be "in tune" or "out of tune", and why does it matter?
When humans hear a certain pitch, we aren't hearing just that single frequency. This is because when strings or air in pipes vibrate, they don't vibrate at a single frequency. Instead, they vibrate primarily at the frequency that equals the length of the string/pipe, but simultaneously, they also vibrate in a sine wave along each whole-integer division of the length of the string. Each of those vibrations creates its own pitch. The volume of these pitches corresponds to their intensity relative to the other pitches being played. Because the longest vibration on the string is usually the most intense, the lowest pitch is the loudest pitch. In fact, all of the other pitches are quiet enough that we hear the whole array of vibrations as one pitch. Any pitches other than the fundamental (lowest) note are called overtones. The practical consequence of their existence is that they give nuance to the sound quality of a pitch.
For example, if you play the A on the middle of a piano (or on any other instrument, you'll hear the conglomeration of the following notes:
* The fundamental pitch, which happens to be 440Hz. This is the only one you'll probably notice. Everything else will blend into the sound of this tone.
* The first overtone, at 880Hz (or, vibrating twice as fast as the fundamental tone). This creates the sound of A an octave higher.
* The second overtone, at 1320Hz. This creates the sound of an E.
* The third overtone, at 1760Hz, sounds like a high A (again).
* The fourth overtone, at 2200Hz, sounds like a C#.
Again, while all of these notes (and further) are playing at once, the overtones are so much higher and quieter that their sound blends into the fundamental pitch.
The trick about the overtone series comes in the construction of harmony. Harmonies are generally built out of chords, or, multiple notes played at the same time. In most western music, chords are built by stacking the notes from the overtone series of the bottom note of the chord. So, an A major chord consists of the notes, A, C#, and E. The reason these notes sound good together, is that they are all present in the note A. When the C# and E are played on the piano, they are amplifying the sounds that are already present when just the single note A is played. A chord sounds harmonious or 'in tune' when the frequencies of the notes in the chord match the frequency of the overtones in the bottom note. This causes the sound waves to come into phase with each other. When sounds waves come into phase, the sounds amplifies, creating both more volume, and more overtones. (Thus, the volume of the in-tune chord is measurably greater than the sum of the individual notes if they were played separately).
However, to create this effect the notes of the chord have to be perfectly in tune. If the instrument is out of tune, the notes won't match the overtone series, the sound waves don't come into phase, no sound is amplified, and the chord sounds wrong, or out of place.
The way in-tune harmonies create and amplify overtones is metaphorical of some of my experiences with revelation. When the notes move into phase with each other, the effect is that everything about the sound and our experience of it is amplified. Revelation does the same thing: it can amplify and clarify our experiences, make them easier to digest or understand, and introduce us to a higher plane of ideas, insight, or living. Though we can go through life making the same motions, or playing the same chords, making the effort to tune them properly for me introduces a more complete, enjoyable, comprehensible, and rewarding way of living.
There are a lot of ways to connect these concepts; this is one I have been thinking about for some time. If you are interested in the connection between music and heaven, you might be interested in is the Musica Universalis theory of Pythagoras. It's related to this overtone schpeel, because it was Pythagoras who discovered that the relationship between pitches matched mathematical proportions, and those same proportions compose the overtone series. (For example, a 2-foot string and a 1-foot string will play notes exactly an octave apart, given that they are under the same tension). He further theorized that the planets were organized according to these proportions, and that each of them had a pitch associated with them. Bringing the pitches of the planets into harmony was then part of what made the universe a more perfect place to live, or opened a clearer conduit between man and the universal creator. It's all more complicated than that of course, but Pythagoras is credited with the general idea that musical harmonies house certain knowledge or energies.
To create melodies, a composer generally picks a scale and then uses the pitches in the scale to create her melody. To create harmony, a composer arranges the notes from the scale into vertical stacks called chords. The movement from one chord to another is what creates the effect of harmony, or harmonic progression.
The mystery of harmony, however, is that some chords sound naturally pleasing to the ear, while others sound unfinished, jarring, or otherwise unpleasant. Additionally, if the instrument or choir playing a chord is out of tune, the chord doesn't lock into place, and the harmony sounds wrong. Most people who've attended a junior high school choir concert or youth recital can tell the difference immediately: while the players may have nominally played all the right notes, their collective tuning could have been off just enough to make people notice that something wasn't quite right.
Most music lovers and players have at some point had the experience of learning to play or sing in tune. But what does it mean for the player and listener to be "in tune" or "out of tune", and why does it matter?
When humans hear a certain pitch, we aren't hearing just that single frequency. This is because when strings or air in pipes vibrate, they don't vibrate at a single frequency. Instead, they vibrate primarily at the frequency that equals the length of the string/pipe, but simultaneously, they also vibrate in a sine wave along each whole-integer division of the length of the string. Each of those vibrations creates its own pitch. The volume of these pitches corresponds to their intensity relative to the other pitches being played. Because the longest vibration on the string is usually the most intense, the lowest pitch is the loudest pitch. In fact, all of the other pitches are quiet enough that we hear the whole array of vibrations as one pitch. Any pitches other than the fundamental (lowest) note are called overtones. The practical consequence of their existence is that they give nuance to the sound quality of a pitch.
For example, if you play the A on the middle of a piano (or on any other instrument, you'll hear the conglomeration of the following notes:
* The fundamental pitch, which happens to be 440Hz. This is the only one you'll probably notice. Everything else will blend into the sound of this tone.
* The first overtone, at 880Hz (or, vibrating twice as fast as the fundamental tone). This creates the sound of A an octave higher.
* The second overtone, at 1320Hz. This creates the sound of an E.
* The third overtone, at 1760Hz, sounds like a high A (again).
* The fourth overtone, at 2200Hz, sounds like a C#.
Again, while all of these notes (and further) are playing at once, the overtones are so much higher and quieter that their sound blends into the fundamental pitch.
The trick about the overtone series comes in the construction of harmony. Harmonies are generally built out of chords, or, multiple notes played at the same time. In most western music, chords are built by stacking the notes from the overtone series of the bottom note of the chord. So, an A major chord consists of the notes, A, C#, and E. The reason these notes sound good together, is that they are all present in the note A. When the C# and E are played on the piano, they are amplifying the sounds that are already present when just the single note A is played. A chord sounds harmonious or 'in tune' when the frequencies of the notes in the chord match the frequency of the overtones in the bottom note. This causes the sound waves to come into phase with each other. When sounds waves come into phase, the sounds amplifies, creating both more volume, and more overtones. (Thus, the volume of the in-tune chord is measurably greater than the sum of the individual notes if they were played separately).
However, to create this effect the notes of the chord have to be perfectly in tune. If the instrument is out of tune, the notes won't match the overtone series, the sound waves don't come into phase, no sound is amplified, and the chord sounds wrong, or out of place.
The way in-tune harmonies create and amplify overtones is metaphorical of some of my experiences with revelation. When the notes move into phase with each other, the effect is that everything about the sound and our experience of it is amplified. Revelation does the same thing: it can amplify and clarify our experiences, make them easier to digest or understand, and introduce us to a higher plane of ideas, insight, or living. Though we can go through life making the same motions, or playing the same chords, making the effort to tune them properly for me introduces a more complete, enjoyable, comprehensible, and rewarding way of living.
There are a lot of ways to connect these concepts; this is one I have been thinking about for some time. If you are interested in the connection between music and heaven, you might be interested in is the Musica Universalis theory of Pythagoras. It's related to this overtone schpeel, because it was Pythagoras who discovered that the relationship between pitches matched mathematical proportions, and those same proportions compose the overtone series. (For example, a 2-foot string and a 1-foot string will play notes exactly an octave apart, given that they are under the same tension). He further theorized that the planets were organized according to these proportions, and that each of them had a pitch associated with them. Bringing the pitches of the planets into harmony was then part of what made the universe a more perfect place to live, or opened a clearer conduit between man and the universal creator. It's all more complicated than that of course, but Pythagoras is credited with the general idea that musical harmonies house certain knowledge or energies.
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