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250:, in order to avoid confusing them with the more familiar, mathematically simple integer harmonics; both are often relevant in the same sentence. Partials measured in the sounds produced by real musical instruments almost always have a slightly higher pitch than the corresponding idealized harmonic, with the discrepancy being less important for high-pitched instruments (above
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must match, makes it necessary to widen every interval very slightly. Generally, it's more than sufficient to sharpen only whole octaves slightly, rather than separately modifying all intervals that reach individual pitches in the upper octaves
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are never tuned 2:1, but instead are stretched or compressed in a consistent manner throughout the range of each individual gamelan, due to the physical characteristics of their instruments. Another example is the tritave
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344:(hence making a single piano better able to be perceived over the volume of an entire orchestra) and giving them longer sustain than similar, smaller instruments.
141:, but is perceived or treated as equivalent to this ratio, and whose pitches are considered equivalent to each other as with octave equivalency.
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Octave stretching is less apparent on large pianos which have longer strings and hence less curvature for a given
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when played with lower notes whose overtones are themselves naturally stretched by an equivalent amount.
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The practical consequence of the discrepancy between the sharpened pitches in a
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411:"The Paradoxes of Octave Identities", p.213. Author(s): Jenő Keuler. Source:
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320:; that is one reason why orchestras go to the expense of using very long
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415:, T. 40, Fasc. 1/3, (1999), pp. 211–224. Published by: Akadémiai Kiadó.
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is not 2:1 (2.3:1 or 1.9:1, for example), that of the
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263:whose high-level overtones fall above the range of
340:than can short strings, making larger instruments
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390:"Interview with Max Mathews", p.21. Author(s):
205:causes small differences between the string's
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201:to how far it was bent or stretched. That
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209:frequencies and the mathematically ideal
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369:piano acoustics § Railsback curve
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97:Problems playing this file? See
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52:Problems playing this file? See
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224:is that rather than the simple
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1:
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220:The effect of strings' small
7:
1018:septimal chromatic semitone
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10:
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1024:septimal diatonic semitone
812:(Numbers in brackets refer
211:simple harmonic oscillator
171:pitch difference), sounds
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814:to fractional semitones.)
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1402:List of pitch intervals
1140:Subminor and supermajor
1079:minor diatonic semitone
989:refer to pitch ratios.)
175:when played with ideal
1200:Undecimal quarter tone
400:Computer Music Journal
111:
68:
23:
1195:Septimal quarter tone
1006:septimal quarter tone
274:overtone series that
230:fundamental frequency
110:Pseudo-octave (2.1:1)
109:
67:
22:
1382:Incomposite interval
1135:Pythagorean interval
987:(Numbers in brackets
495:(Numbers in brackets
322:concert grand pianos
238:inharmonic overtones
213:'s integer multiple
1165:Pythagorean apotome
1012:septimal third tone
311:Bohlen–Pierce scale
1278:Septimal semicomma
222:inelastic response
124:paradoxical octave
112:
69:
24:
1421:Intervals (music)
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1220:Pythagorean comma
1160:Pythagorean limma
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1054:supermajor fourth
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497:are the number of
303:play on clarinets
199:out of proportion
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39:
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1399:
1290:Septimal kleisma
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1060:subminor seventh
1042:supermajor third
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429:"Octave Types"
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423:External links
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89:Perfect Octave
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75:Perfect Octave
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243:partial tones
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207:real overtone
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203:non-linearity
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195:elastic limit
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167:(an 8.6
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116:pseudo-octave
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44:Pseudo Octave
31:
30:Pseudo Octave
1353:
1320:
1306:(0.72 cents)
1300:(1.95 cents)
1280:(13.8 cents)
1274:(10.1 cents)
1268:(19.5 cents)
1260:(35.7 cents)
1254:(62.6 cents)
1248:(41.1 cents)
1240:(27.3 cents)
1234:(22.6 cents)
1228:(21.5 cents)
1222:(23.5 cents)
1209:
1190:Quarter tone
1180:
1179:
1150:
1149:
1129:
1106:
1071:Higher-limit
986:
980:
892:major fourth
836:quarter tone
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494:
432:
412:
407:
399:
318:displacement
315:
288:
280:
276:treble notes
269:
246:
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191:piano tuning
188:
183:
172:
163:rather than
156:
154:
123:
120:pseudooctave
119:
115:
113:
96:
51:
1339:Millioctave
1321:Measurement
1312:(0.4 cents)
1292:(7.7 cents)
1286:(8.1 cents)
1170:Major limma
912:minor fifth
396:Max Mathews
364:octave band
272:bass note's
173:out of tune
165:2 : 1
1372:Semiditone
1266:Diaschisma
1081:(17-limit)
772:(22 or 23)
770:fourteenth
766:(20 or 21)
764:thirteenth
760:(18 or 19)
754:(17 or 18)
748:(15 or 16)
742:(13 or 14)
677:Diminished
504:interval.)
485:(post-Bach
398:. Source:
375:References
326:baby grand
99:media help
54:media help
1334:Centitone
1272:Semicomma
1151:Semitones
1115:Microtone
1099:intervals
776:fifteenth
622:Augmented
500:semitones
472:Intervals
359:mel scale
226:harmonics
215:harmonics
180:overtones
132:frequency
1415:Category
1304:Breedsma
752:eleventh
732:Compound
487:Western)
482:semitone
392:C. Roads
348:See also
294:gamelans
291:Balinese
247:partials
177:harmonic
128:interval
1310:Ragisma
1298:Schisma
1284:Kleisma
1120:5-limit
1026:(15:14)
1020:(21:20)
1014:(28:27)
1008:(36:35)
998:7-limit
963:⁄
952:seventh
943:⁄
923:⁄
903:⁄
883:⁄
863:⁄
843:⁄
825:Neutral
798:systems
758:twelfth
715:seventh
666:seventh
611:seventh
574:seventh
512:Perfect
480:Twelve-
330:upright
313:(3:1).
309:of the
184:in tune
1367:Ditone
1354:Others
1344:Savart
1211:Commas
1107:Groups
1056:(10:7)
852:second
796:tuning
721:octave
697:fourth
685:second
648:fourth
636:second
630:unison
593:second
556:second
537:octave
525:fourth
519:unison
502:in the
342:louder
338:energy
234:timbre
232:, the
182:, but
139:octave
130:whose
1377:Secor
1125:Comma
1097:Other
1062:(7:4)
1050:(7:5)
1044:(9:7)
1038:(7:6)
1032:(8:7)
932:sixth
872:third
794:Other
746:tenth
740:ninth
709:sixth
703:fifth
691:third
660:sixth
654:fifth
642:third
605:sixth
599:third
585:Minor
568:sixth
562:third
548:Major
531:fifth
332:, or
135:ratio
122:, or
1362:Wolf
1329:Cent
778:(24)
723:(11)
668:(12)
662:(10)
613:(10)
576:(11)
539:(12)
394:and
169:cent
155:The
717:(9)
711:(7)
705:(6)
699:(4)
693:(2)
687:(0)
656:(8)
650:(6)
644:(5)
638:(3)
632:(1)
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595:(1)
570:(9)
564:(4)
558:(2)
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527:(5)
521:(0)
286:).
281:see
255:000
245:or
189:In
1417::
956:10
431:,
383:^
328:,
267:.
259:Hz
217:.
118:,
114:A
968:)
965:2
961:1
958:+
954:(
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945:2
941:1
938:+
936:8
934:(
928:)
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908:)
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896:5
894:(
888:)
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881:1
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876:3
874:(
868:)
865:2
861:1
858:+
856:1
854:(
848:)
845:2
841:1
838:(
464:e
457:t
450:v
437:.
279:(
261:)
253:5
101:.
56:.
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