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                    "description": "A modern keyboard hides its compromise. Every key is equally in tune, which also means every key is equally out of tune, and a major third in C major is exactly the same size as a major third in F…",
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            "dek": "A cent is one hundredth of an equal-tempered semitone. Here is the formula, what the common intervals measure in cents, and what a tuner is showing you.",
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            "dek": "Twelve equal semitones solve the problem pure intervals create. The cost is small in fifths, large in thirds, and paid by every fixed-pitch instrument.",
            "topic": "tuning",
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            "excerpt": "A piano cannot retune between two chords, so its tuning has to work for every key in advance. Equal temperament is the arrangement that does that, and it earns the ability by making every fifth slightly narrow and every major third noticeably wide. The…",
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            "title": "The Harmonic Series: Why Octaves, Fifths and Thirds Come First",
            "dek": "A vibrating string or air column sounds a fundamental and a set of partials at whole-number multiples of it. Here are the first sixteen, their cents, and where they differ from equal temperament.",
            "topic": "acoustics",
            "topic_name": "Acoustics & Sound",
            "tags": [
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                "partials",
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            "excerpt": "A string or air column that sounds a note produces a fundamental, and it also vibrates in parts. Those parts sound partials at whole-number multiples of the fundamental frequency: f, 2f, 3f, 4f and so on. The collection is the harmonic series. Its first…",
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            "topic": "tuning",
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            "topic": "counterpoint",
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            "topic": "acoustics",
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            "dek": "A playable range and a usable register are different facts. Transposition arithmetic, endurance, doubling, and the notes that are another instrument.",
            "topic": "orchestration",
            "topic_name": "Orchestration",
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            "topic": "tuning",
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