Theories {music theory} can be about tone, melody, rhythm, and scales.
Note sequences {melody} can rise, fall, or stay the same. Line or phrase notes typically go up, go down, pause, and build to climax. Melody typically repeats phrases. Melody can have small interval between adjacent notes {conjunction, notes} or large interval {disjunction, notes}. Humans can recognize melody from several notes. People perceive melodies more easily at higher frequencies.
Larger pitch changes are typically between longer-duration notes, and smaller pitch changes are typically between shorter-duration notes {Fitts' law} {Fitts law} {leap lengthening}. Large pitch changes are typically upward [Fitts, 1954].
Melody typically goes down after large rise and goes up after large fall {post-skip reversal}, because it reaches range end.
Regular musical beats {rhythm, music} can vary by slightly altering note times and by changing middle beats.
Music can have pauses {rest, music}. Rest can be for whole beat {whole rest}, half beat {half rest}, quarter beat {quarter rest}, eighth beat {eighth rest}, or sixteenth beat {sixteenth rest}.
In written music, one note {upbeat} can be before first measure.
Beats have groups {measure, music}. Measures have same number of beats. Measure type determines rhythm. First beat usually has stress. Recurrent and non-recurrent rhythm patterns over several measures can make stresses, which are the same as, complementary to, or opposite from meter.
Measures can have 1, 2, 3, 4, 5, 6, or 9 beats and have same stressed and unstressed beats {meter, music} {time signature}: 2/4 time, 2/2 time, 3/4 time, 3/8 time, or 4/4 time.
Measures can have two quarter notes {duple time} {2/4 time}.
Measures can have two half notes {alla breve}.
Measures can have three quarter notes {3/4 time} or three eighth notes {3/8 time} {triple time}.
Measures can have four quarter notes {quadruple time} {common time} {4/4 time}.
Measures can have two or more duple or triple meters {compound measure} {compound time}. In compound time, first-duple or first-triple first beat has stress, and second-duple or second-triple first beat has slightly less stress. Compound-meter measures can have six quarter notes {6/4 time}, six eighth notes {6/8 time}, nine eighth notes {9/8 time}, or twelve eighth notes {12/8 time}.
Rather than using one second as time unit, music has its own time unit {beat, rhythm}. Beats {whole note} can divide into half beats {half note}, quarter beats {quarter note}, eighth beats {eighth note}, or sixteenth beats {sixteenth note}. Notes can sound for any number of beats or beat fractions. Notes can have 1.5 beats {dotted note, beat}, 0.75 beats {dotted half note}, 0.375 beats {dotted quarter note}, and 0.1875 beats {dotted eighth note}.
In late 12th century, besides long notes, chants began to use short notes {brevis}. Brevis had one beat. Long had two beats. One long equaled two brevis. As in poetry, brevis and long can make two-syllable, three-syllable, or four-syllable meters: pyrrhic, iamb, trochee, spondee, tribrach, anapest, dactyl, and dispondee.
Later, chants began to use notes that combined long and brevis to make "longshort" three-beat notes. Then, trochee was long-short. Dactyl was long-short-short or longshort-short-long. Anapest was long-long-longshort. Spondee was longshort-longshort. Tribrach was short-short-short.
European time units {tempus} equal to brevis began [1300 to 1400]. Tempus had two or three parts {semibreve}, each of which had two or three parts {semibreve minimae} {minimae}. Time types were three semibreves {perfect time} or two semibreves {imperfect time}, to make four time signatures {prolation}. 2/4 time had two semibreves with two minimae. 6/8 time had two semibreves with three minimae. 3/4 time had three semibreves with two minimae. 9/8 time had three semibreves with three minimae.
Rhythm can use up {levatio} hand motions. Last phrase tone can end on levatio {metric rhythm}.
Rhythm can use down {positio} hand motions. Musical phrases can end with rest as long as positio.
A second note {accented note} can quickly play after a note.
Notes {dashed note} can be longer in time than normal beat, as indicated by a dash over or under note.
Notes {dotted note, note} can be shorter in time than normal beat, as indicated by a dot over or under note.
Two different-pitch notes can slide from one to the other {slur, music}.
Two same-pitch or different-pitch notes can link {tie, music}.
Musicians can play smoothly {legato}.
Musicians can play short sharp crisp notes {staccato}.
Musicians can increase tempo {accelerando}.
Musicians can play slow {ritardando}.
Musicians can use any tempo {rubato}.
short-short {pyrrhic, music}.
short-long {iamb, music}.
long-short {trochee, music}.
long-long or longshort-longshort {spondee, music}.
short-short-short {tribrach}.
short-short-long or long-long-longshort {anapest, music}.
long-short-short or longshort-short-long {dactyl, music}.
long-long-long-long {dispondee}.
Beats have speed {tempo}|.
extremely fast {presto}.
very fast {vivace}.
fast {allegro, tempo}.
moderately fast {allegretto}.
moderate {moderato}.
moderately slow {andante}.
slow {lento}.
very slow {adagio, tempo}.
very slow and broad {largo}.
All scale systems {scale, music} {musical scale} depend on notes in octaves. Octaves can have tones, halftones, and quartertones. In many cultures, non-harmonic frequency ratios between notes fit notes into octave. For example, music of India has twenty-two microtones in octave.
Octave can have 42 evenly spaced tones {42-tone scale}.
The twelve octave semitones can have equal frequency spacing {chromatic scale}| {modern scale}. Twelve major and twelve minor chromatic keys are available. Major keys use tone-tone-semitone-tone-tone-tone-semitone. Minor keys use tone-semitone-tone-tone-semitone-tone-tone. Chromatic keys start on different semitones. All major keys sound the same, and all minor keys sound the same.
Diatonic scales {concordant scale} can have correct intervals and not use octaves. Alternatively, octaves can have unequal intervals to fit into octave, but singers altered tones to make correct intervals.
In 16th century, concordant-scale note intervals changed to fit the twelve scale tones into octave, with almost equal intervals between semitones {tempering the scale} {discordant scale} {discordance}.
Scales {ecclesiastical scale} can use fewer than five tones.
Scales {enharmonic scale} can use octave tones and quartertones.
Octaves can have five whole tones {pentatonic scale} {five-tone scale} {Greek scale}.
Octaves can have 24 quartertones {quartertone scale}.
Octaves can have six whole tones {whole-tone scale} {six-tone scale}.
Octaves can have five whole notes and two halftones {diatonic scale}|. Diatonic scales used other note spacing in 1600s but now are only major or minor scales.
Diatonic scales {major scale}| can have intervals tone-tone-semitone-tone-tone-tone-semitone and sound lighter and brighter.
Diatonic scales {minor scale}| can have intervals tone-semitone-tone-tone-semitone-tone-tone and sound heavier and darker.
Equal temperament scales have no sharps or flats {open key} {C key} {key of C}, one sharp note, one flat note, and so on.
The twelve acoustically correct diatonic-scale intervals do not make exact octaves, missing by one quartertone {Pythagorean comma}. To fit intervals into octaves, different keys {mode, Greek music} use different interval series, with different spacing between tones and semitones, so keys sound different.
Diatonic scales can start on first note {fundamental, music} {tonic, tone} {key, diatonic}.
Major diatonic scales have tone {dominant tone}| a fifth above tonic, in frequency ratio 3:2.
Major diatonic scales have tone {subdominant tone}| a fourth above tonic, in frequency ratio 4:3.
Major diatonic scales have tone {leading tone}| seventh above tonic, in frequency ratio 9:5 or 15:8.
Ancient Greece used eight different scales {mode, scale}, named after different tribes. Notes and intervals are the same for all modes, but fundamental tone and central tone differ.
Modes have associated moods {ethos, music}.
Greek modes were descending scales, so top tone was fundamental tone. Modes had central tones {nese}.
Dorian-mode nese is central tone of interval from second F below middle C to F above middle C {greater perfect system}.
Notes {chroma, pitch}, such as A, B, C, D, E, F, or G, are in each octave. Pitch takes into account chroma and octave.
Two tones can sound the same {tonal fusion}. Unison, octave, perfect fifth, and perfect fourth tend to fuse.
In 19th century, spacing the 12 semitones equally in the octave allows all keys to transpose {equal temperament tuning}, though different instruments tune to different keys. In equal temperament, all keys sound the same.
19th-century music scales can have pure fifths and pure thirds {just temperament} {just intonation}, instead of only pure fifths.
As musical instruments improved in 16th century, scales used fixed and unequal intervals between notes {meantone}. To make pure third, each fifth added equal frequency ranges. However, this created quartertones in higher keys. In meantone, keys have different sounds.
In 16th century, meantone changed to allow instruments to play full chords in all keys {well-tempered}. In well-tempered scale, keys have different sounds.
Song forms {song forms} are aaab, aaba, and abab.
Sound has vibration frequency {note, music} {tone, music} {pitch, music}. Sounds with one frequency are pure tones. Letters or syllables represent whole tones: do C, re D, mi E, fa F, so G, la A, and ti B. Between two whole tones are two halftones or four quartertones.
shift between keys {modulation, music}.
Notes {microtone} can be at unequal and non-harmonic intervals in the octave. For example, music of India has twenty-two microtones {sruti, tone} in octave.
Two tones have a number of tones {interval, music} between them. Interval can be halftone {minor second} or whole tone {major second}.
Interval can be whole tone and halftone {minor third}, with frequency ratio 6:5, or two whole tones {major third}, with frequency ratio 5:4.
Interval can be whole tone and two halftones {diminished fourth, interval}, two whole tones and halftone {perfect fourth, interval}, or three whole tones {augmented fourth, interval}.
Interval can be two whole tones and two halftones {divided fifth}, three whole tones and one halftone {perfect fifth}, with frequency ratio 3:2, or four whole tones {augmented fifth}.
Interval can be three whole tones and two halftones {minor sixth}, with frequency ratio 8:5, or four whole tones and one halftone {major sixth}, with frequency ratio 5:3.
Interval can be three whole tones and three halftones {divided seventh}, four whole tones and two halftones {minor seventh}, or five whole tones and one halftone {major seventh}.
Interval can be five whole tones and two halftones {octave, interval}, so one tone has twice the other's frequency.
First concert music used two simultaneous notes, with ratio 2:1 between frequencies {octave, music}.
Three-tone intervals {tritone} can be whole tone and two halftones {diminished fourth, tritone}, two whole tones and halftone {perfect fourth, tritone}, or three whole tones {augmented fourth, tritone}.
Two tones heard together can sound pleasing {consonance, music} {harmonics, music} or sound harsh {dissonance, music}. Humans experience tension in dissonance and repose in consonance.
musical intervals
Two musical notes have musical notes between them. Perfect first means one note with zero notes between. Perfect octave means notes are separate by eight notes. Second means notes are separate by two notes. Third means notes are separate by three notes, and so on for fourth, fifth, sixth, and seventh.
frequency ratio
Tones have vibration frequencies, and two tones have frequency ratio.
ratio pairs
Frequency ratio can be higher frequency to lower frequency or lower to higher. Example is 200/100 or 100/200. Because tones are the same, both ratios have same consonance or dissonance. Musical intervals therefore are ratio pairs, each other's inverse.
Perfect first has ratio 1/1, whose inverse is also 1/1.
Perfect octave has ratios 2/1 and 1/2. Interval 2:1 is the same as interval 1/2, with octave and fundamental exchanged. Fundamental has octave 2/1 and subfundamental 1/2. Octave is most pleasing {perfect consonance}.
Perfect fifth has ratio 3/2, and perfect fourth has ratio 4/3 = 1/((3/2) * (1/2)). They are very pleasing.
Major third has ratio 5/4, and minor sixth has ratio 8/5 = 1/((5/4) * (1/2)). Minor third has ratio 6/5, and major sixth has ratio 5/3 = 1/((6/5) * (1/2)). They are pleasing {imperfect consonance}.
Other ratio pairs are 7/4 and 8/7, 7/5 and 10/7, 9/5 and 10/9, 7/6 and 12/7, 11/6 and 12/11, 9/7 and 14/9, 11/7 and 14/11, 13/7 and 14/13, 9/8 and 16/9, 11/8 and 16/11, 13/8 and 16/13, and 15/8 and 16/15. They are inharmonious. Dissonance increases with distance from octave.
musical interval pairs
Musical-interval pairs add to nine notes: perfect first and perfect octave, perfect fifth and perfect fourth, major sixth and minor third, major third and minor sixth, major seventh and minor second, and major second and minor seventh.
overtones
Fundamental tones have overtones. First overtone has frequency two times fundamental frequency. First overtone is the octave.
Second overtone has frequency three times fundamental frequency. Because 3/1 * 1/2 = 3/2, second overtone is same tone as perfect fifth and perfect fourth but over two octaves.
Third overtone has frequency four times fundamental frequency. Because 4/1 * 1/2 = 2/1, third overtone is same tone as octave, but over two octaves. First three overtones sound harmonious, stable, and pleasing.
Fourth overtone has frequency five times fundamental frequency. Because 5/1 * 1/4 = 5/4, fourth overtone is same tone as major third and major sixth, but over three octaves. It is somewhat harmonious.
one tone {unison, music}.
Tone and octave-above or octave-below tone {diapason, music}| are harmonious. Pipe organs have a diapason stop to express tone and its octaves.
Symbols {sharp sign} added after letter or symbol can raise note one halftone.
Symbols {flat sign} added after letter or symbol can lower note one halftone.
Symbols {natural sign, music} added after letter or symbol can indicate to play tone with no sharp or flat, though key uses sharp or flat tone.
Sharp, flat, or natural symbol changes note {accidental note} from normal tone in key.
Two or more notes can sound simultaneously, by same or different instruments or voices {chord, music}. Related chords share tone.
Chords can have four tones {tetrachord}.
Tetrachord can divide intervals three ways {genera}: diatonic, chromatic, and enharmonic.
Intervals can have two whole tones and one halftone {diatonic interval}, such as C, D, E, and F.
Intervals can have one minor third and two halftones {chromatic interval}, such as C, D#, E, and F.
Intervals can have one major third and two quartertones {enharmonic interval}, such as C, E, E/F, and F.
Sound has intensity {loudness, music} {volume, sound}.
very loud {fortissimo}.
loud {forte, loudness}.
moderately loud {mezzoforte}.
moderately soft {mezzopiano}.
soft {piano, loudness}.
very soft {pianissimo}.
Music can increase loudness {crescendo}. If loudness increases too much, people do not perceive crescendo. People can perceive crescendo better than diminuendo. For example, Beethoven used gradual crescendo and abrupt diminuendo.
Music can decrease loudness {decrescendo}.
Music can diminish loudness {diminuendo}.
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Date Modified: 2022.0225