This is called the harmonic series The harmonic series is an array of pitches produced whenever any note is played on any acoustic instrument. This array of pitches is a natural consequence of acoustic physics. In the harmonic series, the strongest overtones are on the bottom. The first and strongest overtone excluding the root and octaves is the perfect fifth.
This means that whenever you play any note, the note a perfect fifth above is also audible in the overtones of the first note. Because of this strong relationship between a root and its fifth, the overtones of each note will also match closely.
In other words, they imply very strongly related or consonant A note that is consonant with another will seem to agree and fit well when played together with the first. The fifth is one of the easiest intervals for humans to learn to sing, meaning it is a strong and easily-learned musical interval that most people can learn to hear relatively quickly. This system posits that all harmony is based on fifths and that the Lydian mode is the ideal structure.
Re-arrange them and they form the Lydian scale. Hub Guitar. In a diatonic scale , the dominant note is a perfect fifth above the tonic note.
The perfect fifth is more consonant , or stable, than any other interval except the unison and the octave. It occurs above the root of all major and minor chords triads and their extensions. Up until the late 19th century it was often referred to by its Greek name, diapente , [ 1 ] and abbreviated P5. Its inversion is the perfect fourth.
The term perfect identifies the perfect fifth as belonging to the group of perfect intervals including the unison , perfect fourth and octave , so called because of their simple pitch relationships and their high degree of consonance. In fact, when an instrument is tuned using Pythagorean tuning or meantone temperament , one of the twelve fifths the wolf fifth sounds severely dissonant and can hardly be qualified as "perfect", if this term is interpreted as "highly consonant".
Perfect intervals are also defined as those natural intervals whose inversions are also perfect, where natural, as opposed to altered, designates those intervals between a base note and the major diatonic scale starting at that note for example, the intervals from C to C, D, E, F, G, A, B, C, with no sharps or flats ; this definition leads to the perfect intervals being only the unison , fourth , fifth, and octave , without appealing to degrees of consonance.
The term perfect has also been used as a synonym of just , to distinguish intervals tuned to ratios of small integers from those that are "tempered" or "imperfect" in various other tuning systems, such as equal temperament. Within this definition, other intervals may also be called perfect, for example a perfect third [ 6 ] or a perfect major sixth In addition to perfect, there are two other kinds, or qualities, of fifths: the diminished fifth, which is one chromatic semitone smaller, and the augmented fifth , which is one chromatic semitone larger.
In terms of semitones, these are equivalent to the tritone or augmented fourth , and the minor sixth , respectively. The idealized pitch ratio of a perfect fifth is , meaning that the upper note makes three vibrations in the same amount of time that the lower note makes two.
Something close to the idealized perfect fifth can be heard when a violin is tuned: if adjacent strings are adjusted to the exact ratio of , the result is a smooth and consonant sound, and the violin is felt to be "in tune". Idealized perfect fifths are employed in just intonation. Kepler explored musical tuning in terms of integer ratios, and defined a "lower imperfect fifth" as a pitch ratio, and a "greater imperfect fifth" as a pitch ratio.
Helmholtz uses the ratio cents as an example of an imperfect fifth; he contrasts the ratio of a fifth in equal temperament cents with a "perfect fifth" , and discusses the audibility of the beats that result from such an "imperfect" tuning. In keyboard instruments such as the piano , a slightly different version of the perfect fifth is normally used: in accordance with the principle of equal temperament , the perfect fifth is slightly narrowed to exactly cents seven semitones.
The narrowing is necessary to enable the instrument to play in all keys. The term " Perfect Fifth " is used to define an interval between two notes in a diatonic scale in Western Music. There are two parts to the phrase " perfect fifth " and each part is a descriptor of the interval between two notes.
Let me define each part separately. It will be easier to explain if we start with the number. The number in this case 5 defines the number of staff positions a particular interval occupies inclusive of the bass note and the higher note on a musical staff.
For example - in the key of C major - the interval between E and B is described as a Fifth because if you put a E and B on a musical staff and count the lines each note is on and the line and two spaces between them - that interval controls 5 staff positions thus is a "Fifth" interval.
An easier way to think of it is the interval number is equal to the number of notes in the particular key using only the 7 notes of the diatonic scale in that key that are occupied from the bass note to the higher note inclusive.
So that's what makes the interval a "Fifth". Now let's talk about what makes it "perfect". Setting aside all arguments about quantification to achieve even temperament so an instrument such as a piano can play in all keys and almost be in tune and how that makes almost every ratio technically imperfect - in common practice the term " perfect " as used in " Perfect Fifth " means that the higher note of the interval is exactly 7 semitones above the bass note.
One semitone is represented by one white or black key on the piano or one fret on the guitar on the same string. There are 12 semitones in a chromatic scale but only 7 notes in a diatonic scale key of C has 7 notes, Key of D has 7 notes etc. There are perfect fifths and there are diminished fifths.
Almost all fifths are perfect because if you play the bass note and the high note of a 5th interval ie: C and G and you count the number of white keys and black keys on a piano semitones from the C to the G starting with C and ending on G there are 7. Every Fifth Interval with 7 semitones between the bass note and high note is referred to as a " perfect " fifth.
But if you look at a piano and count all the white and black keys between B and F a 5th interval there are only 6. Six semitones in a 5th interval makes it a "Diminished" Fifth instead of a perfect Fifth. The reason there is not a perfect 3rd only a major 3rd or a minor 3rd is because there is no consistent number of semitones between the two notes comprising a 3rd. Counting all the notes in the chromatic scale white keys and black keys starting with C and ending with E there are 4 which make that interval a " Major " 3rd.
But the next 3rd interval in the key of C is comprised of D and F which is a " Minor " 3rd because counting from D to F starting with D and ending on F there are only 3 semitones or 3 keys on the piano. The 3 semitones we count to determine if it's a minor 3rd or major 3rd is the number of keys between D and F starting on D NOT including D.
The thirds intervals alternate back and forth between major and minor 3 keys or 4 keys on the piano so there are no "perfect thirds". Most Fifth intervals are perfect but there is the occasional Diminished Fifth 6 keys vs 7. Most Fourths are perfect exactly 5 semitones - or keys on piano including black and white but there is the occasional "Augmented" 6 semitones Fourth.
Octaves are all perfect, sixths are either major or minor like thirds, second and seventh intervals are also either major or minor depending on the number of semitones or black and white keys on the piano that separate the bass note from the high note. A Semitone is the next physical adjacent note on a piano after a given pitch.
Semitones are also often called "half-steps". If you pick a note on the piano, and count seven half-steps higher or lower, it will result in a perfect-fifth. If you count each grouping separated by commas, you will see that there are seven groups.
A perfect-fifth is one of the Class 1 intervals: perfect-octave, perfect-unison, perfect-fifth, perfect-forth. They are described as perfect because their wavelengths perfectly coincide with the wavelength of the fundamental tone.
The frequency ratio which you describe refers to the correlation between crests and troughs in the amplitudes of each sound wave for each pitch. A ratio of describes one in which the top note of a perfect-fifth interval produces three crests for every two crests of the fundamental pitch.
The problem with the definitions you dug up is that they refer to different things. The usual meaning of "perfect fifth" is in contrast to a "tempered fifth". In relation to a guitar, a perfect fifth is the interval you get between the first harmonic over fret 12 and the second harmonic over fret 7. When tuning, the most pleasing interval between most strings is a perfect fourth. When you play empty strings tuned to a perfect fourth, you get a single sound without beating.
Unfortunately, stacking one perfect fourth after the other which you can do by comparing 3rd harmonic over fret 5 on one string and 2nd harmonic on the next does not work. So instead one uses tempered intervals. These days, equal temper is almost universally used which makes all semitones equally wide.
With regard to frequency inversely proportional to string length given the same string and idealizing a bit , a perfect fifth has the frequency relation compared to the base note. The difference is quite small, but there is a slight bit of well-defined beating if you talk about instruments with fixed tuning and clear sound, like tubular bells or an organ or accordion fresh from a good tuner. With a guitar, the difference is small. Basically you want to stop tuning a fourth preferedly when you are slightly sharp rather than slightly flat as compared to the perfect fourth.
So much for the one "perfect fifth". Now the other use case talks about "perfect fifth" in comparison to "augmented" or "diminuished" fifth.
I would strongly discourage using "perfect" in this context since it really is reserved for consonant intervals with a "perfect" rather than "tempered" frequency ratio. I'd have called this a "proper fifth" or "plain fifth" instead because "perfect" has different connotations. Interval quality naming conventions have been around for centuries so it stands to reason that their are subtle changes in meaning.
While trained musicians generally know the conventions, they often don't understand the particular reasoning, whether Church-based, or based on Helmholz and other researchers. Perfect intervals are the set of intervals which were determined to be consonant by religious authorities until roughly the 15 century this is fuzzy, and obviously most people were unaware of the controversy, and I imagine there were outliers. This set of Perfect intervals includes unisons 1 , fourths 4 , fifths 5 , and the octave 8 plus their octave transpositions.
A simple way of defining this set is the unison, the fifth, plus all inversions and octave tranpositions. Think of it this way, in the first place these Perfect intervals, when sounded simultaneously and tuned justly, beat very little. Psychoacoustically we hear pitches relative to the harmonic series see the "case of the missing fundamental" , so one can imagine that we might subconsciously be evaluating the tonal qualities of pitches relative to their octave-reduced position within the harmonic series anyway.
As you can see the Perfect intervals come first, followed by the consonant ones. Next are the dissonant intervals. Imperfect intervals are intervals that don't sound quite as harmonious and introduce a little bit more of an interesting spin to the pendulum between P4th, root, and P5th as the perfect intervals. I am not a musician, so my answer might be completely wrong, but So, the first answer you showed from you research was actually not bad In the 12 tone system of Western Musical Notation, a fifth is pretty close to exact.
C4 is about Hope I got it right! In order to understand the definition you wrote, you must first understand half step and whole step. A half step is the musical distance from any key to the very next key up or down.
For example, C and C are half step away from each other, as are C and Cb. A whole step is equal to 2 half steps. For example in piano, keys which are whole step away have one key in between.
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