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    "source_title": "Encyclopaedia Britannica (1911)",
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    "chunk_id": "1911:harmonia:fbd904a6ca93",
    "title": "HARMONIA",
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    "verified_text": "harmonia, in greek mythology, according to one account the daughter of ares and aphrodite, and wife of cadmus. when the government of thebes was bestowed upon cadmus by athena, zeus gave him harmonia to wife. all the gods honoured the wedding with their presence. cadmus (or one of the gods) presented the bride with a robe and necklace, the work of hephaestus. this necklace brought misfortune to all who possessed it. with it polyneices bribed eriphyle to persuade her husband amphiaraus to undertake the expedition against thebes. it led to the death of eriphyle, of alcmaeon, of phegeus and his sons. even after it had been deposited in the temple of athena pronoia at delphi, its baleful influence continued. phayllus, one of the phocian leaders in the sacred war (352 b.c.) carried it off and gave it to his mistress. after she had worn it for a time, her son was seized with madness and set fire to the house, and she perished in the flames. according to another account, harmonia belonged to samothrace and was the daughter of zeus and electra, her brother iasion being the founder of the mystic rites celebrated on the island (diod. sic. v. 48). finally, harmonia is rationalized as closely allied to aphrodite pandemos, the love that unites all people, the personification of order and civic unity, corresponding to the roman concordia. apollodorus iii. 4-7; diod. sic. iv. 65, 66; parthenius, _erotica_, 25; l. preller, _griech. mythol._; crusius in roscher's _lexikon_. harmonic. in acoustics, a harmonic is a secondary tone which accompanies the fundamental or primary tone of a vibrating string, reed, &c.; the more important are the 3rd, 5th, 7th, and octave (see sound; harmony). a harmonic proportion in arithmetic and algebra is such that the reciprocals of the proportionals are in arithmetical proportion; thus, if a, b, c be in harmonic proportion then 1/a, 1/b, 1/c are in arithmetical proportion; this leads to the relation 2/b = ac/(a + c). a harmonic progression or series consists of terms whose reciprocals form an arithmetical progression; the simplest example is: 1 + 1/2 + 1/3 + 1/4 + ... (see algebra and arithmetic). the occurrence of a similar proportion between segments of lines is the foundation of such phrases as harmonic section, harmonic ratio, harmonic conjugates, &c. (see geometry: ii. _projective_). the connexion between acoustical and mathematical harmonicals is most probably to be found in the pythagorean discovery that a vibrating string when stopped at 1/2 and 2/3 of its length yielded the octave and 5th of the original tone, the numbers, 1-2/3, 1/2 being said to be, probably first by archytas, in harmonic proportion. the mathematical investigation of the form of a vibrating string led to such phrases as harmonic curve, harmonic motion, harmonic function, harmonic analysis, &c. (see mechanics and spherical harmonics).",
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