Definitions

"It is not merely that I want to tell you how it is with me, how I feel, in order to find sympathy or to be left alone, or for any other of the reasons for which one reveals one’s feelings. It’s rather that I want to tell you something I’ve seen, or heard, or realized, or come to understand, for the reasons for which such things are communicated because it is news, about a world we share, or could.  Only I find that I can’t tell you; and that makes it all the more urgent to tell you. I want to tell you because the knowledge, unshared, is a burden-not, perhaps, the way having a secret can be a burden, or being misunderstood; a little more like the way, perhaps, not being believed is a burden, or not being trusted. It matters that others know what I see, in a way it does not matter whether they know my tastes. It matters, there is a burden, because unless I can tell what I know, there is a suggestion and to myself as well! that I do not know. But I do-what I see is that pointing to the object! But for that to communicate, you have to see it too. Describing one’s experience of art is itself a form of art; the burden of describing it is like the burden of producing it." 

Cavell, Stanley, 1976, Must We Mean What We Say? Cambridge: Harvard University Press, pp. 192-93. See also Lewin, pp. 381-91 and Kramer, Jonathan D., The Time of Music. New York: Schirmer Books, 1988, p. 8.

For each definition there is a sound and or video example. The labeling system is related to the book page, paragraph number, and sequence of definitions.  Put your cursor over the highlighted number for a link related to the word and its definition.

 

For example:  5-1A  Page in the book is:   5   

                              Paragraph is:              1   

                              Sequence is:              

1         Acoustical Physics—The science of sound production and propagation.

5-1A    Cents—The logarithmic division of the octave into equal half-steps of 100 cents.

  5-1A  

 

5-1B    Overtone—A harmonic of a fundamental pitch (sine wave).

  5-1B 

  5-1B 

 

5-1C    Comma—The small frequency difference in cents in two pitches of the same name.

  5-1C  

 

5-1D    Fundamental—The first partial and generator of an identifiable pitch.

  5-1D      5-1D  

 

5-1E    Partials—The whole integer vibrations sounding above a fundamental.

  5-1E  

5-1F    Schisma— Small frequency difference between two pitches of approximately 2 cents.

  5-1F 

2         Pitch

 

5-2A    Musical—The specific vibratory frequency of a unit of sound, such as A=440. 

           

  5-2A 

 

5-2B    Perfect—The ability of an individual to discern the frequency of a pitch as different from other pitches and give the pitch a commonly held name, such as A is distinct from B. 

           

  5-2B  

 

5-2C     Absolute—The ability of an individual to discern the specific frequency of a pitch, such as A4 equals 440 or A4 equals 442.

           

  5-2C 

 

5-2D    Relative—The ability of an individual to distinguish between pitches after the establishment of a pitch, such as A is referenced and the movement of pitch to B is discerned by individual demonstration.

  5-1D 

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3         Tuning Systems

 

5-3A    Just Intonation—An intonation system derived from the overtones of a given fundamental.

 

 5-3A 

 

5-3B    Three-limit—An intonation system derived from the 2nd and 3rd partials of the overtones of a given fundamental and their multiples. Also called Pythagorean tuning.

 5-3B 

6-3C     Five-limit—An intonation system derived from the 2nd, 3rd, and 5th partials of the overtones of a given fundamental and their multiples.

 

 6-3C 

 

6-3D    Mean-tone temperament—An intonation system that tempers the fifths in order to preserve the pure resonances of the major 3rds.

 

 6-3D 

 

6-3E    Well-temperament—An intonation system where the entire chromatic scale of a particular fundamental were tempered so that all the major and minor keys could be played in one tuning, while preserving distinct coloristic features of each key.

 

 6-3E 

 

6-3F     Equal Temperament—An intonation system where the entire keyboard has been tempered into equal half-steps.

 6-3F 

Additional Sound Samples

Three-Limit

Ross Duffin compares the performance of the Hillier Ensemble and 3-Limit intonation.

3-Limit Harmonium

 

Hillier Ensemble

 

Equal Temperament

Score

 

 

 

Five-Limit

List of Five-Limit Intervals https://en.wikipedia.org/wiki/List_of_intervals_in_5-limit_just_intonation

Mean-Tone

Well-Temperament

 

 

 

Bach played in Equal Temperament                        Bach played in Werckmeister III, 

Well-Temperament

Equal Temperament

Additional sound files 

A_Major_Scale,_Triads,_and_Fifths_Equal.
A_Major_Scale,_Triads,_and_Fifths_Just (
Just_vs_equal.mp3
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Definitions

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