What is meant by perfect, imperfect consonance and dissonance?

Question

I'm assuming that perfect consonance to imperfect consonance to dissonance, would be the measurement of consonance to dissonance within an octave? Or is there more than meets the eye within this concept?

Also, would my labeling of perfect/imperfect/dissonance be correct? If not could ye' correct it in your answers? and why is the minor sixth which has a high ratio of 8/5, considered imperfect consonance?

• Unison = 1/1 Perfect Consonance (1st note of an octave)
• Octave = 2/1 Perfect Consonance (13th note of an octave)
• Perfect Fifth = 3/2 Perfect Consonance (8th note of an octave)
• Perfect Fourth = 4/3 Imperfect Consonance/Dissonant when the bass note (6th note of an octave)
• Major Sixth = 5/3 Imperfect Consonance (10th note of an octave)
• Major Third = 5/4 Imperfect Consonance (5th note of an octave)
• Minor Third = 6/5 Imperfect Consonance (4th note of an octave)
• Minor Seventh = 7/4 Dissonant (11th note of an octave)
• Tritone = 7/5 Dissonant (7th note of an octave)
• Minor Sixth = 8/5 Imperfect Consonance (9th note of an octave)
• Major Second = 9/8 Dissonant (3rd note of an octave)
• Major Seventh = 11/6 Dissonant (12th note of an octave)
• Minor Second = 12/11 Dissonant (2nd note of an octave)

Kind regards!

Answer 1

I think you need to read an overview about musical intervals. You can get that from a harmony textbook or this Wikipedia page about intervals. It seems like you are inventing your own naming system, but there is a very, very well established nomenclature.

Perfect/imperfect are terms applied only to the unison, octave, fourth, and fifth.

Major/minor are terms applied to the second, third, sixth, and seventh.

What is meant by perfect, imperfect consonace and dissonance?

Perfect means: a unison or 0 semi-tones, fourth of 5 semi-tones, fifth of 7 semi-tones, or an octave of 12 semi-tones. Any one of those intervals that differs in the semi-tone size could be called imperfect but normally is called augmented if it is bigger, or diminished if it is smaller.

The sense of dissonance is a bit tricky. The perfect intervals are consonances... except the perfect fourth is considered dissonant in some styles/contexts. The imperfect intervals may or may not be dissonant. For example, an augmented fourth is a dissonance. But a diminished fourth is enharmonically equal to a major third, a consonance. Similarly an augmented fifth is enharmonically equal to a minor sixth, a consonance. But when an augmented fifth is used in an augmented triad, the chord is considered - at least by some/most - as dissonant.

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EDIT

My original answer misunderstood the question. I thought the question was why are some intervals called perfect? My original answer is below. Maybe it will be helpful.

If we think of intervals in relation to a tonic, then the perfect/imperfect intervals are about the relationships between the tonal degrees of the scale the tonic, subdominant, and dominant (numerically ^1, ^4, and ^5.)

You can think of perfect/imperfect being descriptors only applied to the intervals between the tonic and tonal degrees, and the tonic to itself for the unison and the octave.

The other degrees above the tonic - ^2, ^3, ^6, and ^7 are the modal degrees (sometimes ^2 is described as both a tonal or modal degree) - and the intervals between the tonic and those degrees are described as major/minor.

This seems to be the association of the interval descriptors to the various interval numbers. The associations originate from intervals relative to the tonic.

Those associations are then maintained to the intervals in any scale position or even outside of any scale or tonal context.

So, the fifth from a tonic to a dominant is a perfect fifth and is 7 semi-tones in size. Any other fifth of 7 semi-tones in size is also called a perfect fifth.

I don't know if that is the historic origin of the terminology, but it is how I make sense of it.

Answer 2

Your table is mostly OK. However when using numbers divisible by 5, the major seventh and minor second are taken to be 15/8 and 16/15 respectively. Neither 11 nor 7 is used. The minor seventh is a compound fourth or 16/9 (the inverse of 9/8 reduced to be between 1 and 2 by octave equivalence.

Note that each interval and its inversion have the same consonance or dissonance rating. Also, the inversion of each interval corresponds to the other's reciprocal. Everything is transposed by octave to have a ration between 1 and 2.

The minor sixth has the same (or at least equivalent) consonance as the major third. It's the 5, not the 8 that matters.

You could also construct a scale using only powers of 2 and 3. "Just" intonation uses powers of 3 5 and 7. https://en.wikipedia.org/wiki/Just_intonation

There are other possibilities. None allow for transposition of the base note (modulation) so some sort of tempering is used.

Answer 3

I'm assuming that perfect consonance to imperfect consonance to dissonance, would be the measurement of consonance to dissonance within an octave?

The grading of intervals as consonant (pleasing to the ear) to dissonant (unpleasant) is not restricted to the octave (if that's what you were asking) but is true for compound intervals as well.

why is the minor sixth which has a high ratio of 8/5, considered imperfect consonance?

While smaller integer ratios are used as a guide to what should sound pleasant versus unpleasant, it is the ear that determined how the intervals were classified.

1. Perfect intervals are those that are the least full, or empty sounding.

2. Imperfect intervals, thirds and sixths, since the 1300's, are felt to be richer, but still pleasant. The minor 6th, regardless of the ratio, sounds much fuller than an octave, fourth or fifth.

3. Dissonant intervals don't sound pleasant and minor seconds and major sevenths have a sharp biting quality.

4. Augmented 4ths/Diminished 5ths have been described as unstable and/or dissonant, depending upon the writer. Certainly Western ears find it satisfying for this interval to resolve into a third or sixth.

I would like to point out that there is confusion about the perfect fourth being a dissonance. In organum, it was common for singers to sing in parallel octaves, fifths or fourths. The first reference that I am aware of where the fourth is termed dissonant is in Fux, but at that time the distinction between dissonant and unstable was not made. Unfortunately, many authors since then have repeated Fux, perpetuating this claim. The bottom line is that the perfect fourth can be unstable such that the ear would like it resolved into a third, but it is not dissonant.