No, they are not considered consonant in all music cultures. The perception of consonance and dissonance can be different among cultures. The same interval can be perceived (and labeled) differently by different cultures. This is influenced by many factors (and the harmonic series is not the only one!)
For example, in medieval times major thirds were considered dissonances unusable in a stable final sonority. (from wikipedia)
A very interesting text is A History of 'Consonance' and 'Dissonance' by James Tenney. He goes through many eras to analyze what was going on with dissonances and consonances.
There he quotes Paul Hindemith:
The two concepts have never been completely explained, and
for a thousand years the definitions have varied. At first thirds
were dissonant; later they became consonant. A distinction
was made between perfect and imperfect consonances. The
wide use of seventh-chords has made the major second and
the minor seventh almost consonant to our ears. The situation
of the fourth has never been cleared up. Theorists, basing
their reasoning on acoustical phenomena, have repeatedly
come to conclusions wholly at variance with those of practical musician.
The whole text answers your question, so I really recommend you to give it a read. Some examples:
In most pre-9th-century theoretical sources, the cognates of consonance and
dissonance-or of related words like concord and discord, symphony and
diaphony, and even our more general term harmony-refer neither to the
sonorous qualities of simultaneous tones nor to their functional characteristics
in a musical context but rather to some more abstract (and yet perhaps more
basic) sense of relatedness between sounds which-though it might determine
in certain ways their effects in a piece of music-is logically antecedent to
The contrapuntal and figured-bass periods, ca. 1300-1700:
The new system of interval-classification which emerged in theoretical
writings sometime during the 14th century differs from those of the 13th century in several ways, but the most striking of these differences is that the number
of consonance/dissonance categories has been reduced from five or six to just
three- "perfect consonances," "imperfect consonances," and "dissonances."
Both the major and the minor sixth (as well as the thirds) are now accepted
as consonances (albeit "imperfect" ones), the fifth has been elevated from
an intermediate to a perfect consonance whereas the fourth has become a special
kind of dissonance (or rather, a hlghly qualified consonance). All of the other
intervals-if allowed at all in the music-are simply called "dissonances."
Norman Cazden dives into this subject in many occasions, including the text Musical Consonance and Dissonance: A Cultural Criterion, The Journal of Aesthetics and Art Criticism Vol. 4, No. 1, pp. 3-11. (paywall, but you can read online for free if you register)
In the musical system of ancient Greece, there were no "imperfect" consonances. Major and minor thirds and sixths were considered dissonant. The fourth was the basic consonance for the formation of modes and systems of tetrachords.
(...) Resolution is a criterion that has no application to the pentatonic scales. That is one reason why, to our perceptions, Chinese music sounds so inconclusive, so lacking in tendency and definition. The acoustically "perfect" consonances are the rule in some musics, but are not inevitable foundations, for nothing close to the ratio 3:2 is found in certain Javanese and Siamese scales. Intervals which bear no resemblance to any in our diatonic system form melodies which to their users seem "instinctive" and self-evidently natural. (…) In the Icelandic "Tvisöngvar" the third appears to be treated as dissonance.
He proposes that the perception of dissonance and consonance is not entirely based in ratios, harmonics, acoustics, etc; the perception can be trained, influenced.
The natural phenomena of vibratory wave-motions and their reception by the ear may be seen as limiting, rather than as a determining, factor in the perception of consonance and dissonance.
Studies of the psychology of musical perception have produced important negative results regarding consonance and dissonance. The naive view that by some occult process mathematical ratios are consciously transferred to musical perception has been rejected. Fusion, or "unitariness of tonal impression" has been found to produce no fixed order of preference for intervals, with the remarkable exception of the octave. It has been discovered that individual judgments of consonance can be enormously modified by training. Perceptions of consonance by adult standards do not seem generally valid for children bellow the age of twelve or thirteen, a strong indication that they are learned responses.
He suggests that the social factor is much more important.
In musical harmony the critical determinant of consonance or dissonance is the expectation of movement. This is defined as the relation of resolution. A consonant interval is one which sounds stable and complete in itself, which does not produce a feeling of necessary movement to other tones. A dissonant interval causes a restless expectation, or movement or movement to a consonant interval. Pleasantness or disagreeableness of the interval is not directly involved. The context is the determining factor.
For the resolution of intervals does not have a natural basis; it is a common response acquired by all individuals within a culture-area. It becomes evident that the science of music is not primarily a natural science. It is a social science devoted to the properties of a musical system or language belonging to a specific culture-area and a certain stage of historical development.
Due to the tonality relation, probably the most powerful systemic structure in our musical culture of the past few centuries, the most familiar consonant harmonies may act as dissonances. The C major triad is a dissonance in the key of F; as the dominant harmony, it requires resolution to the tonic. The requirement is a psychological imperative resulting from our conditioning; it has no basis on the nature of tone.
The origin of the minor mode and the minor triad in the overtone series has puzzled theorists for centuries. The ratios involved are, to say the least, rather more complicated than those of many "dissonances". (…) The minor harmony is accepted as frankly consonant, and as fundamentally so as the major.
The tempered major third, which is acoustically most badly out of tune, functions as the basic consonance in our system harmony. Where untempered intervals are possible (..) the skillful musician will produce thirds still more out of tune, in order to emphasize the major-minor contrast.
Perception and preference changes, varies.
During the 11th century, apparently, the preference for the fourth gave way to an increasing and almost exclusive use of fifths and octaves. In the period when our modern musical system came into existence, with its dependence on tonality and the major and minor modes, thirds and sixths became consonances and fourths dissonances, the full triad replaced the empty neutrals, and the functional value of resolution crystalized.
He has some interesting things to say about octaves, fifths, and fourths.
Octave and perfect fifth are noncommittal in respect to resolution tendencies, they are not in reality consonances within the meaning of harmonic relations.
Another "perfect consonance", the fourth, is actually a dissonance in musical practice; and what is worse, not consistently so.
More on this:
Moran, H., & Pratt, C.C. (1926). Variability of judgments of musical intervals. Journal of Experimental Psychology, Vol. 9, pp. 492-500.
Lundin, R.W. (1947). Toward a cultural theory of consonance. Journal of Psychology, Vol. 23, pp. 45-49.
Guernsey, M. (1928). The role of consonance and dissonance in music. American Journal of Psychology, Vol. 40, pp. 173-204.
Cazden, N. (1960). Sensory theories of musical consonance. Journal of Aesthetics and Art Criticism, Vol. 20, No. 3, pp. 301-319.
Consonance and Dissonance - Effect of Culture, Ohio State University
School of Music
Musical chord preference: cultural or universal? Data from a native Amazonian society.
The basis of musical consonance as revealed by congenital amusia.