User:Squib: Difference between revisions

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===Terms===

~~First, some terms.~~ Most of these are widely-used but I might be using them slightly differently ~~here~~.

Most of these terms are widely-used but I might be using them slightly differently than most people.

- Harmonic ~~series~~

- Interval

The set of ~~pitches with frequencies that~~ are ~~integer multiples~~ of the fundamental, including the fundamental itself. This is ~~called~~ the harmonic ~~series~~ of ~~that fundamental~~.

The frequency ratio between two notes. Can be a measurement of specific notes or just a ratio.

- Harmonic

An interval which is an integer ratio (including 1/1). Also, a note which is a harmonic interval above another note.

- Harmonic Series

The set of notes which are harmonics of the fundamental, including the fundamental itself.

- Overtone

A tone produced with the fundamental, forming the timbre of a single note.

===Explanation===

The simplest interval is the unison, 1/1. This is the interval between a note and itself. Stacking it multiple times doesn't do anything, which isn't very interesting, so let's consider the next simplest interval: the octave, 2/1. Although notes an octave apart are not considered equivalent, they do have a special relationship: the higher note is a harmonic of the lower. 3/1 is also a harmonic interval. Stacking these gives us intervals like 4/1, 6/1, and 8/1, which are also harmonics. Since only harmonics can be created, this does not allow for much progression, since every note only contains overtones from the root note. So we will now allow intervals to be subtracted from each other, creating nonharmonic intervals like 3/2 which have new overtones. Going up by harmonics removes some overtones and strengthens the remaining ones; going down by harmonics weakens existing overtones and adds new ones in the gaps. Combining these gives us nonharmonic intervals.

@@ Line 8: / Line 8: @@
 ===Terms===
-First, some terms. Most of these are widely-used but I might be using them slightly differently here.
+Most of these terms are widely-used but I might be using them slightly differently than most people.
-- Harmonic series
+- Interval
-The set of pitches with frequencies that are integer multiples of the fundamental, including the fundamental itself. This is called the harmonic series of that fundamental.
+The frequency ratio between two notes. Can be a measurement of specific notes or just a ratio.
+- Harmonic
+An interval which is an integer ratio (including 1/1). Also, a note which is a harmonic interval above another note.
+- Harmonic Series
+The set of notes which are harmonics of the fundamental, including the fundamental itself.
+- Overtone
+A tone produced with the fundamental, forming the timbre of a single note.
+===Explanation===
+The simplest interval is the unison, 1/1. This is the interval between a note and itself. Stacking it multiple times doesn't do anything, which isn't very interesting, so let's consider the next simplest interval: the octave, 2/1. Although notes an octave apart are not considered equivalent, they do have a special relationship: the higher note is a harmonic of the lower. 3/1 is also a harmonic interval. Stacking these gives us intervals like 4/1, 6/1, and 8/1, which are also harmonics. Since only harmonics can be created, this does not allow for much progression, since every note only contains overtones from the root note. So we will now allow intervals to be subtracted from each other, creating nonharmonic intervals like 3/2 which have new overtones. Going up by harmonics removes some overtones and strengthens the remaining ones; going down by harmonics weakens existing overtones and adds new ones in the gaps. Combining these gives us nonharmonic intervals.