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contexts: everything from a blacksmith's hammer to a clock bell will naturally produce these intervals. The waveform of such a tone (as pictured on an oscilloscope) is characterized by a shape that is complex compared to a simple (sine) waveform, but remains periodic. When two tones depart from exact integer ratios, the shape waveform becomes erratic—a phenomenon that may be described as destabilization. As the composite waveform becomes more erratic, the consonance of the interval also changes. Furthermore, every interval created by two sustained tones creates a third tone, called a differential (or resultant) tone. This third tone is equal to the lower pitch subtracted from the higher pitch. This third tone then creates intervals with the original two tones, and the difference between these is called a second differential. Differentials are soft and difficult for the untrained ear to detect. Nevertheless, these relationships between differentials play a large role in determining which tunings create consonant sound.
285:, allowing intervals varying from the highest consonance to highly dissonant. For instance, 660 Hz / 440 Hz (a ratio of 3:2) constitutes a fifth, and 880 Hz / 440 Hz (2:1) an octave. Such intervals (termed "just") have a stability, or purity to their sound, when played simultaneously (assuming they are played using timbres with harmonic partials) because pure intervals do not waver or beat regularly.; the proportions of their frequencies can be expressed as whole numbers. If one of those pitches is adjusted slightly to deviate from the just interval, a trained ear can detect this change by the presence of
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291:, which are periodical oscillations in the note's intensity. If, for example, two sound signals with frequencies that vary just by 0.5 Hz are played simultaneously, both signals are out of phase by a very small margin, creating the periodical oscillations in the intensity of the final sound (caused by the superposition of both signals) with a repetition period of 2 seconds (following the equation
36:
234:, in which the frequency ratio between each pair of adjacent notes on the keyboard was made equal. In other words, the ratio between two notes that were one octave apart was kept pure, and the twelve notes in between the octave were equally spaced from one another. This allowed music to be transposed between keys without changing the relationship between notes.
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the interval of a perfect fifth slightly flatter than in just intonation, and then proceed much like
Pythagorean tuning, but using tempered fifths instead of the just fifths. With the correct amount of tempering, the syntonic comma is reduced to a unison, bringing the major and minor thirds closer to
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When a musical instrument with harmonic overtones is played, the ear hears a composite waveform that includes a fundamental frequency (e.g., 440 Hz) and those overtones (880 Hz, 1320 Hz, 1760 Hz, etc.)—a series of just intervals. These just intervals, due to their acoustic nature, are present in many
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Temperament, in music, the accommodation or adjustment of the imperfect sounds by transferring a part of their defects to the more perfect ones, in order to remedy, in some degree, the false intervals of those instruments, the sounds of which are fixed; as the organ, harpsichord, piano-forte,
320:
Tempering an interval involves the deliberate use of such minor adjustments (accepting the related destabilization) to enable musical possibilities that are impractical using just intonation. The most widely known example of this is the use of equal temperament to address problems of older
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is the name given to a variety of different systems of temperament that were employed to solve this problem, in which some keys are more in tune than others, but all can be used. This phenomenon gives rise to infinite shades of key-colors, which are lost in the modern standard version:
366:, which musicians of the time found annoying. A comma (in musical parlance) is the distance between two tones that are close enough that they share the same name but that are precisely calculated via different proportional spacing, creating a small difference in their exact pitches.
493:, thirds and fifths, to be fairly close to their just counterparts (the fifths almost imperceptibly beating, the thirds a little milder than the syntonic beating of Pythagorean tuning), while permitting the freedom to modulate to any key and by various means (e.g.
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refers to the various tuning systems for the subdivision of the octave," the four principal tuning systems being
Pythagorean tuning, just intonation, mean-tone temperament, and equal temperament. In
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being the difference in frequencies between both signals), because the amplitude of the signals is only in phase, and therefore has a maximum superposition value, once every period of repetition.
230:) were avoided, the sizes of intervals were still not consistent between keys, and so each key still had its own character. This variation led in the 18th century to an increase in the use of
412:, which makes that tonal area of the system more or less unusable. In meantone temperament, this effect is even more pronounced (the fifth over the break in the circle is known as the
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is the process of altering the size of an interval by making it narrower or wider than pure. "Any plan that describes the adjustments to the sizes of some or all of the twelve
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of music) without discarding many of the tones used in the previous key, thus for every key to which the musician wishes to modulate, the instrument must provide a few more
819:"A new study of six- and six-four chords [Based on just intonation rather than equal temperament, and the ratios of the intervals. Analytic musical examples]"
209:(1908), an anomalous chord is a "chord containing an interval" that "has been made very sharp or flat in tempering the scale for instruments of fixed pitches".
321:
temperaments, allowing for consistent tuning of keyboard and fretted instruments and enabling musical composition in, and modulation among, the various keys.
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slightly, this beating effect on the fifths is only one quarter as strong as the beating effect on the thirds of
Pythagorean tuning in the case of
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186:." Temperament is especially important for keyboard instruments, which typically allow a player to play only the pitches assigned to the various
226:
takes full advantage of this breakthrough, with pieces written in all 24 major and minor keys. However, while unpleasant intervals (such as the
254:, because it is founded on temperature; that is, on the diminution of some intervals and augmentation of others, by which it partakes of the
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meant that such instruments could sound "in tune" in one key, or some keys, but would then have more dissonance in other keys.
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Pythagorean tuning also had a second problem, which non-extended meantone temperaments do not solve, which is the problem of
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408:. A series of 12 just fifths as in Pythagorean tuning does not return to the original pitch, but rather differs by a
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343:. Pythagorean tuning was a system of just intonation that tuned every note in a scale from a progression of pure
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The organ viewed from within : a practical handbook on the mechanism of the organ, with a chapter on tuning
68:
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508:). This freedom of modulation also allowed substantial use of more distant harmonic relationships, such as the
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Comparison of perfect fifths, major thirds, and minor thirds in various meantone tunings with just intonation
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Regulation and Repair of Piano and Player
Mechanism, Together with Tuning as Science and Art (1909)
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Elements of musical composition: comprehending the rules of thorough bass and the theory of tuning
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470:, or holes for him or her to use. When building an instrument, this can be very impractical.
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Essay on musical intervals, harmonics, and the temperament of the musical scale, &c
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allowed fixed-pitch instruments to play reasonably well in all of the keys. The famous
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to meet other requirements. Most modern
Western musical instruments are tuned in the
485:, which alters the fifth to "temper out" the syntonic comma, 12-TET tempers out the
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796:"Analogy of the Laws of Musical Temperament to the Natural Dissonance of Creation"
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Hubbard, William Lines (1908). The
American History and Encyclopedia of Music:
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of
Pythagorean tuning differed from a just major third by an amount known as
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their ratios in just intonation. While all fifths in this tuning system now
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915:(mathematical perspective with two chapters on temperament) by Dave Benson
347:. This was quite suitable for much of the harmonic practice until then (
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354:), but in the Renaissance, musicians wished to make much more use of
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is a tuning system that slightly compromises the pure intervals of
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Comparison of notes derived from, or near, twelve perfect fifths (B
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in the early 16th century, was a series of tunings referred to as
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The Wolf at Our Heels: The centuries-old struggle to play in tune
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Most just intonation tunings have the problem that they cannot
29:
706:
John Mason Good, Olinthus
Gregory, Newton Bosworth (1813).
400:
846:
The
Effects of Non-Equal Temperament on Chopin's Mazurkas.
771:
Temperament: The idea that solved music's greatest riddle
1003:
Construction, Tuning and Care of the Piano-forte (1887)
991:
Piano Tuning: A Simple and Accurate Method for Amateurs
416:, as its intense beating was likened to a "howling").
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Before Meantone temperament became widely used in the
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Harmonics, or The philosophy of musical sounds (1759)
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Rosetta Revisited: Bach's Very Ordinary Temperament
424:is used nowadays to extend quarter-comma meantone.
60:. Unsourced material may be challenged and removed.
458:(a very common means of expression throughout the
420:provides an extension of Pythagorean tuning, and
849:PhD diss., University of Houston, October 2001.
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891:18th century quotes on J.S. Bach's temperament
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1125:List of intervals in 5-limit just intonation
985:Modern organ tuning : the how and why?
339:, the most commonly used tuning system was
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1043:
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1015:Modern piano tuning and allied arts (1917)
920:Tuning And Temperament A Historical Survey
773:. New York: Random House. pp. 64–65.
939:A supplement to Mr. Chambers's cyclopædia
889:Willem Kroesbergen, Andrew Cruickshank: "
120:Learn how and when to remove this message
520:Frequently used equal temperament scales
131:
866:. UMI Research Press, Ann Arbor, 1983.
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947:Theory and practice of just intonation
436:Well temperament and equal temperament
246:Temperament is what the Italians call
274:between two pitches corresponds to a
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975:(1835) by Wesley Stoker B. Woolhouse
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665:, p.103-4. Irving Squire: London. .
58:adding citations to reliable sources
299:being the period of repetition and
1017:by William Braid White (1878–1959)
856:Frog Music Press, UPC 883629638829
205:In the words of William Hubbard's
25:
806:(144): 277–279 – via EBSCO.
512:, which became very important to
1200:Ptolemy's intense diatonic scale
933:) by Prof. Fisher (Yale College)
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829:(4): 347–365 – via EBSCO.
516:composers in the 19th century.
45:needs additional citations for
1030:. Oliver Ditson & Company.
912:Music: a Mathematical Offering
854:The Temperamental Mr. Purcell.
640:A Guide to Musical Temperament
174:so that they accommodate pure
1:
885:, by Jan Swafford, 2010-04-20
755:(3): 24–31 – via EBSCO.
725:, p.16. Dodd, Mead & Co.
696:(3): 24–31 – via EBSCO.
615:Mathematics of musical scales
178:and produce certain sizes of
1163:Harry Partch's 43-tone scale
987:by Hermann Smith (1824–1910)
927:Essay on Musical Temperament
723:Perspectives in Music Theory
369:Their solution, laid out by
981:by Robert Smith (1689–1768)
951:by Thomas Perronet Thompson
923:(1951) by J. Murray Barbour
817:Norden, N. Lindsay (1949).
1573:
1130:List of meantone intervals
709:Pantologia: New Cyclopedia
673:HathiTrust Digital Library
600:List of meantone intervals
439:
328:
1120:List of musical intervals
1115:Consonance and dissonance
572:72 tone equal temperament
567:53 tone equal temperament
562:41 tone equal temperament
557:34 tone equal temperament
552:31 tone equal temperament
547:22 tone equal temperament
542:19 tone equal temperament
537:17 tone equal temperament
532:15 tone equal temperament
527:12 tone equal temperament
479:12-tone equal temperament
959:(1812) by William Crotch
794:Whittingham, A. (1867).
769:Isacoff, Stuart (2001).
638:Donahue, Thomas (2005).
1005:by Edward Quincy Norton
964:An essay on temperament
1011:by William Braid White
745:"Handel's Temperament"
743:Pykett, Colin (2019).
686:"Handel's Temperament"
684:Pykett, Colin (2019).
620:Schismatic temperament
460:common practice period
432:
388:quarter-comma meantone
260:
256:diatonic and chromatic
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1387:Temperament ordinaire
1022:Biddle, Horace Peters
993:by Jerry Cree Fischer
721:Cooper, Paul (1975).
430:
375:meantone temperaments
224:Johann Sebastian Bach
219:Well-Tempered Clavier
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69:"Musical temperament"
27:Musical tuning system
1557:Musical temperaments
1190:List of compositions
900:". Academia website.
896:Dominic Eckersley: "
800:The Musical Standard
610:Pythagorean interval
483:meantone temperament
422:31 equal temperament
418:53 equal temperament
331:Meantone temperament
325:Meantone temperament
316:Temperament in music
200:meantone temperament
54:improve this article
967:(1832) by J. Jousse
937:"Temperament" from
843:Miller, Willis G.
642:, p.19. Scarecrow.
595:Regular temperament
212:The development of
1424:Chinese musicology
1210:Scale of harmonics
1205:Pythagorean tuning
1153:Euler–Fokker genus
999:by John Broadhouse
662:Musical Dictionary
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341:Pythagorean tuning
207:Musical Dictionary
196:Pythagorean tuning
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1027:The Musical Scale
852:Pressler, James.
749:Organists' Review
690:Organists' Review
487:Pythagorean comma
481:(12-TET). Unlike
446:Equal temperament
410:Pythagorean comma
232:equal temperament
160:equal temperament
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18:Tempering (music)
16:(Redirected from
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1383:Well temperament
1369:Regular diatonic
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605:Whole-tone scale
510:Neapolitan chord
474:Well temperament
442:Well temperament
406:circle of fifths
307:Acoustic physics
252:system temperato
214:well temperament
172:circle of fifths
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351:Quartal harmony
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746:
739:
736:
732:
731:0-396-06752-2
728:
724:
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710:
703:
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687:
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648:9780810854383
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415:
414:Wolf interval
411:
407:
403:
402:
396:
391:
389:
385:
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372:
367:
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237:
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228:wolf interval
225:
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197:
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185:
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177:
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113:
102:
99:
95:
92:
88:
85:
81:
78:
74:
71: –
70:
66:
65:Find sources:
59:
55:
49:
48:
43:This article
41:
37:
32:
31:
19:
1535:Lambda scale
1442:Arabic maqam
1399:Werckmeister
1230:Temperaments
1229:
1026:
971:
963:
955:
946:
938:
919:
911:
882:
863:
853:
844:
826:
822:
812:
803:
799:
789:
770:
752:
748:
738:
722:
717:
707:
702:
693:
689:
679:
660:
655:
639:
634:
585:Piano tuning
502:
501:modulation,
498:
494:
472:
449:
398:
392:
378:
368:
348:
334:
319:
310:
300:
296:
292:
286:
276:whole number
267:
263:
261:
251:
247:
242:
217:
211:
206:
204:
183:
182:is called a
180:major thirds
163:
151:
145:
116:
107:
97:
90:
83:
76:
64:
52:Please help
47:verification
44:
1530:Delta scale
1525:Gamma scale
1515:Alpha scale
1417:non-Western
1415:Traditional
1110:Pitch class
1090:Millioctave
1073:Measurement
495:common-tone
371:Pietro Aron
360:major third
337:Renaissance
283:frequencies
264:Temperament
184:temperament
152:temperament
1520:Beta scale
1498:Non-octave
1489:Tetrachord
1391:Kirnberger
1354:Schismatic
823:Musicology
780:0375403558
626:References
505:modulation
499:enharmonic
395:modulation
238:Definition
80:newspapers
1510:A12 scale
1464:Octoechos
1429:Shí-èr-lǜ
1378:Irregular
1195:Otonality
1135:Microtone
164:Tempering
1551:Category
1395:Vallotti
1348:septimal
1340:Meantone
1100:Interval
1024:(1867).
876:Articles
579:See also
514:Romantic
452:modulate
377:, which
272:interval
270:, every
258:systems.
162:system.
139:♯
1484:Slendro
1434:Dastgah
1359:Miracle
1322:96-tone
1317:72-tone
1312:58-tone
1307:53-tone
1302:41-tone
1297:34-tone
1292:31-tone
1282:24-tone
1277:23-tone
1272:22-tone
1267:19-tone
1262:17-tone
1257:15-tone
1252:12-tone
1183:7-limit
1178:5-limit
671:at the
464:strings
293:Tr=1/Δf
176:octaves
170:in the
94:scholar
1452:Mugham
1438:Maqam
1332:Linear
1286:pieces
1247:6-tone
1168:Hexany
1095:Savart
949:(1850)
941:(1753)
931:part 2
777:
729:
646:
379:temper
358:. The
96:
89:
82:
75:
67:
1469:Pelog
1457:Muqam
1403:Young
1364:Magic
1239:Equal
1173:Limit
1080:Pitch
905:Books
590:Comma
468:frets
401:below
349:See:
288:beats
279:ratio
250:, or
101:JSTOR
87:books
1474:Raga
1085:Cent
775:ISBN
727:ISBN
668:Also
644:ISBN
503:see
497:and
444:and
399:see
384:beat
244:etc.
198:and
188:keys
150:, a
73:news
862:.
753:106
694:106
456:key
222:by
146:In
56:by
1553::
1401:,
1397:,
1393:,
1346:,
825:.
821:.
804:VI
802:.
798:.
761:^
751:.
747:.
692:.
688:.
466:,
301:Δf
297:Tr
295:,
194:,
142:).
1480:)
1476:(
1405:)
1389:(
1385:/
1350:)
1342:(
1288:)
1284:(
1058:e
1051:t
1044:v
929:(
893:"
827:2
783:.
733:.
650:.
397:(
262:"
123:)
117:(
112:)
108:(
98:·
91:·
84:·
77:·
50:.
20:)
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