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4th scale degree is "perfect" and is found before Major 3rd in overtone series.

Then why is it considered "unstable"?

Sean
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3 Answers3

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Aesthetics. In ancient music, the fourth was considered stable (i.e., consonant), but as thirds became more and more prominent, the fourth became problematic as a dissonance against the third. Also as the leading tone came into use, the fourth formed a tritone with it. As a result, the fourth came to be regarded as consonant in some contexts but dissonant in others.

There are various posts on this site about this issue. For example:

Aaron
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    This answer would be better if it made a clearer distinction between scale degrees and intervals. And it should be pointed out that perceived chord roots and tonal centers are important in making a listener expect a resolution or not. For example in C, the interval G-C can be heard as a tonic chord that doesn't need to resolve anywhere. But if the listener has G as a tonal center, the C can be expected to move to B, Bb or D - given that the interval occurs in a certain place in a longer rhythmic structure. Same interval, different contexts. – piiperi Reinstate Monica Feb 29 '24 at 19:13
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You really need to put it into specific context.

The 4th scale degree, the subdominant scale degree, as one of the tonal scale degrees, provides stability and clarity to a sense of tonal center. When it is the bass and root of a triad it is stable in both the context of the chord and the larger context of the tonality/key.

If the 4th scale degree is part of another chord, the sense of stability changes. For example, when it is part of a V7 or viio chord, the tone is dissonant in the tritone against the leading tone, or in V7 against the chord root of the 5th scale degree.

With your mention of the overtone series you hint at not the 4th scale degree but generally to the interval of a perfect fourth (P4.) The idea that a perfect fourth is unstable comes from the counterpoint harmony practice.

The essential idea from that practice is a perfect fourth above a bass is a displacement of a third above the bass in a supposed root position triad. The root position major triad is considered the primary stable harmony, so displacing its third up to a fourth de-stabilizes the harmony.

Notice that the sense of instability of a perfect fourth (or its compound form of an eleventh) is specifically in relation to the bass of the harmony. If, for example, there is a perfect fourth between soprano and alto (or other combinations not involving the bass) the interval is not considered unstable.

Michael Curtis
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    +1, I don't get why this was downvoted. This answer clearly tries to separate scale degrees and intervals, and explains that a chord root note are important in creating expectations of resolving somewhere. Context. – piiperi Reinstate Monica Feb 29 '24 at 19:07
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My take on this is that the perfect fourth is a consonant interval, but the perfect eleventh (i.e. fourth plus octave) is dissonant, and it gets worse the more octaves you add. Why? Well, as usual it's a mixture of cultural expectation but also simple physics, frequency ratios. The perfect fourth has a nice simple ratio of 4:3, but the perfect eleventh is 8:3, perfect eighteenth 16:3, etc..

Contrast this with the (JI) major† third and fifth, which actually get simpler as you pad octaves in (5:4 vs 5:2, and 3:2 vs 3:1). So a fifth is consonant regardless of octave spacing (which justifies glossing over the octaves, as theory discussions usually do), but it doesn't really work for the fourth.

So, it's perfectly fine to have a fourth between two upper voices, but when we discuss "stability of a scale degree" then you should rather think about the intervals between a high melody voice and a much lower bass accompaniment playing predominantly root notes. Which means the "4th scale degree" isn't actually associated with the perfect fourth, it's much more associated with the perfect eleventh or eighteenth, and as per the above those are dissonant intervals.

†Interestingly, the minor third also gets more ratio-complex as you increase the octave spacing, yet a wide minor chord is usually still considered consonant. This is one thing frequency ratios can't explain very satisfyingly.
leftaroundabout
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    That is a bit of an esoteric reasoning. Octaves of perfect 5ths and double octaves of perfect 3rds are part of of the harmonic series, which makes them particularly consonant. This implies that ”more complex“ ratios are less consonant. This is not the case: consider the interval 20000:10001 — quite complex, but quite consonant. What is true is that due to the 4th being off by 1/3 from a perfect unison it will always be ±1/3 off from the next hole number. But this affects all intervals that are not octaves of harmonics. – Lazy Mar 01 '24 at 08:30
  • @Lazy 20000:10001 is consonant because it is to the ear indistinguishable from 2:1. Similar story for e.g. 12-edo thirds (which are actually noticeably off from the JI ratio, but still close). Approximation-of-simple-ratio is not the only aspect to consonance (as the answer makes quite clear), but it is a very important one. – leftaroundabout Mar 01 '24 at 08:34
  • The point is that ”it is not a simple ratio" is not a reasonable justification of why something should be considered consonant — as can be seen by approximating consonant intervals by really complex ratios. – Lazy Mar 01 '24 at 13:03
  • @Lazy you can always approximate any number by arbitrarily complex ratios, that's an irrelevant distraction. The thing that matters is that the consonant intervals of common-practice harmony are precisely those intervals that are/approximate a simple ratio, whereas the dissonant ones can only be approximated by complex ratios. If you want it in exact specification, a pair of pitches from the 12-edo tuning makes a consonant interval if and only if it is within 16 cents of a JI ratio in which both numerator and denominator are at most 8. – leftaroundabout Mar 01 '24 at 20:43
  • ...And yes, in the answer I wrote "8:3 is dissonant", which doesn't quite match this scheme. If you leave out the minor sixth, then you could strengthen the criterion to "at most 6". Or you could say that the perfect eleventh is just about still consonant, but the perfect eighteenth certainly isn't. In actuality there's little point in looking for a hard cutoff, but the rule of thumb that simple ratios sound more consonant than complex ratios absolutely does hold up. – leftaroundabout Mar 01 '24 at 20:50