TUNING AND TEMPERAMENT调谐和气质.doc

3TUNING GLOSSARYCompiled by Peter Middleton August 2012BeatsA periodic rise and fall in strength (amplitude) heard as a change in loudness that occurs when two pitches of slightly different frequency are played together. If, for example, two instruments play A = 440 Hertz (Hz) and A = 442 Hz together, the listener will hear a tone of 441 Hz (the average) whose loudness fluctuates at 2 beats per second with a “wah-wah-wah” sound. (442 Hz 440 Hz = 2 Hz or beats per second)CentOne one-hundredth of a semitone in equal temperament. For example, the equally tempered half-step interval from C to C# is 100 cents. An octave contains 1200 cents (12 semitones x 100 cents each = 1200). Electronic tuners are almost always calibrated in cents.CommaThe discrepancy in cents between pitches arrived at by two different successions of perfect fifths, the “leftovers.” For example, when a succession of perfect beatless fifths starting on C (C-G-D-A, etc.) is continued so as to produce every pitch, the resulting final B# will not be the same pitch as C, but will be 23.5 cents higher. This is called the Pythagorean comma. There are several different types of commas.Difference toneTones that occur within the brain and whose frequency is usually equal to the difference in frequency of the two primary tones. For example, if 1400 Hz and 1000 Hz are sounded together, a difference tone of 400 Hz will result. Sometimes called resultant or subjective tones. Very useful for tuning just intervals.FrequencyThe number of repetitions per unit of time, usually seconds. “A 440” has a frequency of 440 repetitions, or complete cycles, per second. Musical frequencies are measured in Hertz (Hz).FundamentalThe lowest frequency component of a complex tone. A complex tone will contain harmonics or partials in addition to the fundamental. Notes are “named “ based on their fundamental frequency; when we play A in the staff, the fundamental has a frequency of 440 Hz (repetitions per second).HarmonicA component of a complex tone that is a whole number multiple of the fundamental frequency. The fundamental is called the first harmonic. For example, the third harmonic of A = 440 is 1320 Hz (E above the staff in just intonation), since 440 x 3 = 1320. A common harmonic exercise involves progressively overblowing middle C to produce C in the staff, then G on top of the staff, C above the staff, E, G, Bb, C. These are all harmonics, and members of what is called the harmonic series or harmonic spectrum. HertzA unit used to describe frequency, specifically repetitions per second. Abbreviated “Hz” as in A = 440 Hz.IntervalThe distance separating two pitches that corresponds to a unique frequency ratio. The interval of an octave has 2:1 frequency ratio.IntonationThe degree of adherence to correct pitch within a specific harmonic context; more generally refers to the variable and dynamic inflections of pitch that form an inherent part of performance.Just (pure) intervalsIntervals derived from the natural harmonic series that have simple whole number ratios: 2:1 (octave), 3:2 (fifth), 5:4 (major third), etc. Just intervals have no beats.OvertoneA component of a complex tone (See Fundamental) that has a pitch higher than the fundamental. Partials above the fundamental are sometimes called overtones. The first overtone is the same as the second partial, since the first partial is the same as the fundamental. The term is not in as wide usage as it once was, due to the different numbering system used to identify overtones as compared with harmonics or partials. PartialOne of a group of components of a complex tone (See Fundamental) that are not necessarily harmonically related to the fundamental, and may or may not be in exact whole number multiples of the fundamental. Bells, xylophones, chimes and many other percussion instruments produce harmonically unrelated partials, as does the piano. PitchThe name of a note on a scale from low to high; also the subjective psychological response to a particular frequency. Usually the same as frequency, but very high and very low pitches that are loud can sound respectively higher and lower than they actually are when measured.ResonanceConsider a child in a swing. The swing has a natural frequency that is determined by the length of its ropes. If the swing is given a small push at the right time in each cycle, it gradually goes higher and higher. This is an example of resonancethe swing receives only a small amount of energy during each push, but continues to go higher. A flute is resonant at a frequency determined by the length of the tube (which keys are closed), and the way it is blown.TemperamentLiterally means “adjustment” or “modification” and is used to describe intervals that have in some way been altered from their pure or just whole number ratios to facilitate modulation. Used particularly to help make the intonation of instruments with fixed pitch like the piano, harpsichord, and organ sound acceptable in various keys.TimbreTone color. A characteristic of a tone that distinguishes it from others of the same frequency and loudness. Describes why a trumpet and a cello playing the same pitch sound different. Tone color is determined primarily by three factors: 1) which harmonics are sounding, 2) the strength of the individual harmonics (or partials in some cases) that are sounding, and 3) the time or phase relationship among the harmonics sounding, which is related to the attack or onset. TuningThe process of adjusting an instrument to a particular pitch. Tuning systemA scale of tones created by use of a succession of pure or just intervals that have no beats. Applies to systems such as Just and Pythagorean in which all intervals are expressed as rat