Why perfect intervals

Minors become majors, majors become minors, augmenteds become diminisheds, etc. The exceptions are the octaves, 4ths and 5ths. Unison doesn't count! Those do not change their identities. It hasn't changed. Since this has come up in comments, I feel like maybe it's different enough information to write a separate answer for those interested in the history of the actual term "perfect" consonance.

While SyntonicC's answer rightly points out the root of this distinction arising partly from Pythagorean theory, the history is a little more complicated. To the Pythagoreans, consonance was thought of melodically rather than as simultaneous pitches. The symphoniai thus included the ratios perfect octave , perfect fifth , perfect fourth , perfect twelfth , and double octave.

There were all sorts of mathematical and mystical reasons they gave as justifications for treating these numbers as special. I would note that the "perfect" eleventh is notably absent here, despite being simply composed of a perfect fourth and an octave, a point of contention over the millennia both in ancient Greece and in medieval Europe. A lot of these ideas were inherited by medieval Europe, translated imperfectly no pun intended by Boethius and others.

And there were lots of classifications on intervals, but the first use of term "perfect" Latin perfectus came in the early 13th century, where intervals were generally classified into three categories:. As for why the term perfectus was chosen, it likely had to do with the fact that unisons obviously enjoy a special status, and octave equivalence had become commonly accepted in the 11th and 12th centuries to the point that notes in different octaves were referenced with the same letter.

This is not an obvious development -- the original letter systems for pitches often began with A and just kept going through the alphabet in different octaves. Hence, by around , all notes we call "A" would have been thought of as equivalent in some respects, thus any unisons or octaves created by them would be "perfect" intervals. Over the 13th and 14th centuries, the fifth was gradually elevated to the perfectus category, while the fourth became sometimes perfectus and sometimes a dissonance in practical counterpoint, which is still generally its status in modern music theory.

It's likely that the elevation of the fifth and fourth to the perfectus category had something to do with the traditional Greek list of symphoniai intervals. This two-fold classification of perfectus vs. Ultimately, the definition is somewhat arbitrary -- for the Greeks it had to do with the integers up to 4 the tetractys and their mystical appreciation of the number For medieval folks, as they were trying to shuffle the fifth into the "perfect" category, they hedged about the fourth, as it already was causing counterpoint problems and being treated as dissonant sometimes.

And then they started dealing with the practicalities that thirds and sixths sounded pretty good too, which led to more debates. For a more detailed introduction to the historical issues, I might suggest starting with James Tenney's A History of Consonance and Dissonance.

All the rest have answered in terms of high-level music theory concepts, but I think it can be interesting to look at the intervals as raw coefficients instead.

Harmonic intervals between notes are the intervals that can be expressed with simple rational numbers, where a "simple" rational number is one with a small amount of small prime factors. As our ear detects two tones that only differ by an octave as the "same" tone, multiplying or dividing by 2 an arbitrary number of times doesn't make intervals less simple.

This makes 3 the simplest "significant" prime number. I like Dan04's answer re. I want to add a more straight forward answer:. The distinction is based on how the interval classes relate to the tonal center. Keep in mind notation and enharmonic spellings make a difference.

A minor seventh and augmented sixth are the same distance, but they are "spelled" differently in notation and those enharmonic spellings are used to make the harmony clear in a score. Tritone is an alternative term for augmented fourth or diminished fifth.

Do not use it if you want your enharmonic spelling to be clear. I mostly agree with the answers given here and elsewhere on the site, and in particular, the answer here correctly states that:. The minor intervals are not minor because they are found in the minor scale and the same goes for major intervals.

The intervals are In other words: when Western music theory decides that there's two versions of the same note, the sharp one is called "major" and the flat one is called "minor.

In more detail: the chromatic scale is traditionally broken up into adjacent notes that are called "minor something" and "major something" respectively. The pattern breaks down at the middle, and this is where the perfect notes are found. In particular, we have:. However, these are historical comments. From a future-oriented perspective, the question is really whether we ought to introduce the notion of a perfect second for example.

Under tone equal temperament, both these notes are given the same pitch - namely, they're both treated as being exactly 2 semitones above the tonic. However, you can add sweetness and sophistication to your music by ensuring they're treated differently. The question then arises of how to distinguish these notes terminologically. More generally, my position is roughly that "perfect" ought to mean Pythagorean , which means a note whose ratio only involves the prime numbers 2 and 3.

The most important examples are:. This doesn't quite accord with the historical meaning of the words "major" and "minor"; nonetheless, I think it significantly clarifies the underlying theory. For these reasons, if you're interested in microtonal music or just intonation, my position is that it's best to declare that "perfect" roughly means "pythagorean. My understanding, and I don't remember where I learned this, is that the early Catholic church at first forbade harmony of any kind, then finally allowed only limited harmony with intervals that the church fathers considered "perfect" in the eyes ears?

This is why organum uses only perfect intervals. The name "perfect" may be a reference to a numerical coincidence, which makes the interval of 7 semitones very close to the ratio of frequencies. The fifth divides the octave with a fourth remaining above.

The fourth divides the octave with a fifth remaining above. That is to complete the octave. Playing Perfect intervals that suggest no harmonic content and adding harmonic content is a'sound' approach to discovering the answer to the perfect interval question. All answers have certain validity. I think the best approach is the practice itself, which of course is music and musical instruments and listening.

Perfect intervals aren't simply there because they are the most consonant or stable or whatever. They are there because they have to be for it to even work in the first place and their presence helps define a lot of the music theory that we know today.

I'm going to take a different approach to explain this: proof by contradiction. Let's try to make a system of only diminished, minor, Major and Augmented intervals and see what we come up with. We start out with some issues from the start. K, whatever, let's press on. Ah, this makes sense. Woah, woah, hold on! I'm getting dizzy Examples 10 and 11 again demonstrate and summarize the relative size of intervals.

Each bracket in these examples is one half-step larger or smaller than the brackets to their right and left. Example 10 shows intervals with the top note altered by accidentals:. Example Relative size of intervals with top note altered. As you can see in Example 10 , intervals one half-step larger than perfect intervals are augmented, while intervals one half-step smaller than perfect intervals are diminished.

Likewise, in Example 10 , intervals one half-step larger than major intervals are augmented, while intervals one half-step smaller than major are minor and intervals one half-step smaller than minor are diminished. Example 11 shows intervals with the bottom note altered by accidentals:. Relative size of intervals with bottom note altered. Example 11 outlines the same qualities as Example 10 ; the only difference between the examples is which note is altered by accidentals.

In Example 10 it is the top note, while in Example 11 it is the bottom note. Intervals can be further contracted or expanded outside of the augmented and diminished qualities. An interval a half-step larger than an augmented interval is a doubly augmented interval , while an interval a half-step larger than a doubly augmented interval is a triply augmented interval. An interval a half-step smaller than a diminished interval is a doubly diminished interval , while an interval a half-step smaller than a doubly diminished interval is a triply diminished interval.

The intervals discussed above, from unison to octave, are simple intervals , which have a size an octave or smaller. Any interval larger than an octave is a compound interval. Example 12 shows the notes A and C, first as a simple interval and then as a compound interval:.

A simple and compound interval. The notes A to C form a minor third in the first pair of notes; in the second pair of notes, the C has been brought up an octave.

Quality remains the same for simple and compound intervals, which is why a minor third and minor tenth both have the same quality. These are the most common compound intervals that you will encounter in your music studies. Intervallic inversion. You might be wondering: why is this important? There are two reasons: first, because inverted pairs of notes share many interesting properties which are sometimes exploited by composers , and second, because inverting a pair of notes can help you to identify or write an interval when you do not want to work from the given bottom note.

First, the size of inverted pairs always add up to With that information you can now calculate the inversions of intervals without even looking at staff paper. For example; a major seventh inverts to a minor second; an augmented sixth inverts to a diminished third; and a perfect fourth inverts to a perfect fifth.

Now for the second point: sometimes you will come across an interval that you do not want to calculate or identify from the bottom note. Example 14 shows one such instance of this:. An interval in which the key of the bottom note is imaginary. So, if you were given this interval to identify you might consider inverting the interval, as shown in Example 15 :.

The interval from Example 14 has been inverted. That means this interval is a d5 diminished fifth. Now that we know the inversion of the first interval is a d5, we can calculate the original interval from this inversion. A diminished fifth inverts to an augmented fourth because diminished intervals invert to augmented intervals and because five plus four equals nine.

Thus, the first interval is an augmented fourth A4. Intervals are categorized as consonant or dissonant. Consonant intervals are intervals that are considered more stable, as if they do not need to resolve, while dissonant intervals are considered less stable, as if they do need to resolve. These categorizations have varied with milieu.

Example 16 shows a table of melodically consonant and dissonant intervals:. Perfect intervals sound "perfectly consonant. It sounds perfect or resolved. Whereas, a dissonant sound feels tense and in need of resolution. Non-perfect intervals have two basic forms. The second, third, sixth and seventh are non-perfect intervals; it can either be a major or minor interval.

Major intervals are from the major scale. Minor intervals are exactly a half-step lower than major intervals. Here is a handy table that will make it easier for you to determine intervals by counting the distance of one note to another note in half steps.

You need to count every line and space starting from the bottom note going to the top note. Remember to count the bottom note as your first note.

To understand the concept of size or distance of an interval, look at the C Major Scale. Interval qualities can be described as major, minor, harmonic , melodic , perfect, augmented, and diminished. When you lower a perfect interval by a half step it becomes diminished. When you raise it a half step it becomes augmented.

When you lower a major non-perfect interval a half step it becomes a minor interval. When you lower a minor interval by a half step it becomes diminished. They are ideal for choir, band, general music class, private lessons, and orchestra.

Learn to recognize intervals through both sight and sound. Learn music intervals in a fun and engaging way through these coloring pages. After identifying and coloring each interval, a unique geometric design appears.

Use these flash cards to practice learning and memorizing music intervals on the grand staff. It includes intervals of a 2nd through an octave. They are best for piano students.

This foldable 8x10 inch music theory cheat sheet is an excellent quick reference guide when you need to find the answer fast. The side 3-hole punch allows you to keep it in a 3-ring binder. It is sturdy and folds out featuring music theory and notation on the front and music history on the back.

A practical pocket-size music theory dictionary and music notation reference guide that is perfect for all musicians from beginner to professional. A convenient music theory book that is small enough to fit in your pocket, backpack, or instrument case. A great reference guide for all musicians at any level of music study. Thank you so much for such an informative little article. Thank you for a concise explanation of the perfect interval in your article. The topic came up in a piano lesson with a student.

The perfect octave of concert A Hz rings at Hz — exactly two vibrations for every one vibration of the root tone. The perfect fourth rings at very close to Hz — one and one third vibrations for every one of the root tone. And the perfect fifth rings at very close to Hz — one and one half vibrations for every one of the root tone.

I think when our ears hear these perfect intervals our brains neatly slot the faster vibrations in between the slower ones, tidily filling up the gaps, like completing a jigsaw. None of the other intervals have anywhere near such tidy ratios to the root tone, so they jar to some degree, like a jigsaw with missing or extra pieces.