787:
69:
371:
1995:
38:
58:
272:(on a piano for example) three major thirds in a row equal an octave, but three justly-tuned major thirds fall quite a bit narrow of an octave, and the diesis describes the amount by which they are short. For instance, an octave (2:1) spans from C to C′, and three justly tuned major thirds (5:4) span from C to B
447:
most commonly refers to the diminished second in quarter-comma meantone temperament. Less frequently and less strictly, the same term is also used to refer to a diminished second of any size. In third-comma meantone, the diminished second is typically denoted as a
409:
756:
708:
45:
455:
In quarter-comma meantone, since major thirds are justly tuned, the width of the diminished second coincides with the above-mentioned value of 128:125. Notice that 128:125 is larger than a
1716:
677:
125:128) as a "minor diesis" and 243:250 as a "major diesis", explaining that the latter may be derived through multiplication of the former by the ratio
86:
1059:
811:, where pitch is raised a small amount by slightly raising the finger on the lowest closed hole, letting a small amount of air "escape".
465:. In other tuning systems, the diminished second has different widths, and may be smaller than a unison (e.g. C′ may be flatter than B
87:
982:
887:
220:
172:
429:
In any tuning system, the deviation of an octave from three major thirds, however large that is, is typically referred to as a
1508:
1488:
858:
786:
1614:
910:
977:. Gossett, Philip: translator, introduction, notes (English ed.). New York, NY: Dover Publications. p. 30.
1620:
1403:
647:
has also been used to describe several distinct intervals, of varying sizes, but typically around 50 cents.
434:
269:
915:
2017:
1998:
1736:
1675:
1052:
78:
31:
1796:
375:
1791:
1602:
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1731:
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1632:
1218:
1017:
1007:
968:
934:
780:
769:
571:
541:
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352:
370:
1761:
1626:
1608:
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938:
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237:
1816:
1756:
1317:
1293:
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1262:
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1886:
1711:
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1448:
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1305:
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1226:
1068:
1020:(translator / editor) author of substantial appendicies (2nd English ed.). p. 453.
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191:
143:
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1238:
1181:
1144:
829:
741:
257:
133:
129:
853:
296:(125:64) is the diesis (128:125). Notice that this coincides with the interval between B
1834:
1828:
1822:
1594:
1121:
824:
344:
337:
253:
351:, equal to 648:625 or about 62.57 cents (almost one 63.16 cent step-size in
336:
for the difference between an octave and four justly tuned minor thirds (tuned in the
2011:
1958:
1807:
1726:
1721:
1667:
1528:
1468:
1354:
1342:
1207:
1170:
1127:
658:
340:
310:
261:
241:
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1973:
1930:
1925:
1786:
1432:
1189:
1152:
633:
265:
85:
17:
1935:
1766:
1201:
1195:
1164:
1158:
947:] (in French). Paris, FR: Jean-Baptiste-Christophe Ballard. pp. 26–27.
1968:
1862:
1360:
1273:
518:
390:
120:
1868:
1372:
693:. Other theorists have used it as a name for various other small intervals.
648:
661:) minus two whole tones (9:8), equal to 256:243 or about 90.22 cents.
636:
above unison, so it closely resembles the 1:1 unison ratio of twelve-tone
1900:
1348:
1096:
1028:
37:
1906:
1894:
1880:
1299:
1244:
745:
548:
348:
1963:
1940:
1133:
1115:
834:
779:
is equal to 45:44 or about 38.91 cents, closely approximated by
662:
456:
249:
1336:
808:
673:
653:
369:
57:
56:
36:
1041:
667:
1037:
616:
In eleventh-comma meantone, the diminished second is within
67:
209:
203:
200:
155:
152:
459:(1:1). This means that, for instance, C′ is sharper than B
93:
The octave C-C′, the three justly tuned major thirds C-E-G
313:, the above-mentioned 128:125 ratio is also known as the
161:
433:. The diminished second is an interval between pairs of
945:
Treatise on
Harmony distilled to its natural principles
914:(4th ed.). Cambridge, MA: Belknap Press. p.
651:
used it to describe the interval now usually called a
359:
while the 128:125 diesis (41.06 cents) was termed the
961:
959:
940:
Traité de l'harmonie réduite à ses principes naturels
807:
The Greek name Based on the technique of playing the
221:
212:
206:
173:
164:
158:
1031:. Tonalsoft Encyclopedia of Microtonal Music Theory.
197:
149:
1949:
1916:
1805:
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1576:
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1401:
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1272:
1217:
1180:
1143:
1108:
1090:
1075:
194:
146:
30:This article is about music. For other uses, see
437:notes; for instance the interval between E and F
248:, usually defined as the difference between an
1053:
929:
927:
925:
389:41.1 cents), or an interval between two
8:
951:English edition Rameau & Gossett (1971).
355:). Being larger, this diesis was termed the
290:). The difference between C-C′ (2:1) and C-B
1994:
1699:
1590:
1415:
1398:
1105:
1087:
1060:
1046:
1038:
657:, that of a justly tuned perfect fourth (
873:
871:
869:
473:
264:), equal to 128:125 or about 41.06
845:
800:
764:, which is the difference between the
118:
772:. It is about 35.70 cents wide.
7:
328:Many acoustics texts use the term
61:Diesis as three just major thirds.
25:
260:major thirds (tuned in the ratio
1993:
785:
665:(1722) names 125:148 ( [
236:"leak" or "escape" is either an
190:
142:
119:Problems playing this file? See
83:
783:'s 38.71 cent half-sharp (
443:. As mentioned above, the term
365:
880:Music: A mathematical offering
732:or approximately 29.61 cents.
105:and the descending diesis C′-B
79:Diesis (128:125) demonstration
27:An interval in classical music
1:
965:Ratio corrected to 125:128 in
862:– via ahdictionary.com.
736:Septimal and undecimal diesis
991:translation of Rameau (1722)
859:American Heritage Dictionary
1615:septimal chromatic semitone
911:Harvard Dictionary of Music
903:A. B. (2003). "Diesis". In
343:), which is equal to three
278:(namely, from C, to E, to G
2034:
1621:septimal diatonic semitone
1409:(Numbers in brackets refer
601:
569:
539:
507:
29:
1991:
1411:to fractional semitones.)
1404:24-tone equal temperament
1013:On the Sensations of Tone
435:enharmonically equivalent
391:enharmonically equivalent
270:12-tone equal temperament
111:are played (see example).
752:with the ratio of 49:48
1999:List of pitch intervals
1737:Subminor and supermajor
1676:minor diatonic semitone
1586:refer to pitch ratios.)
425:Alternative definitions
32:Diesis (disambiguation)
1797:Undecimal quarter tone
1024:as quoted and cited in
605:and interval budgeting
417:
376:quarter-comma meantone
302:and C', also called a
72:
62:
54:
1792:Septimal quarter tone
1603:septimal quarter tone
878:Benson, Dave (2006).
373:
71:
60:
40:
1979:Incomposite interval
1732:Pythagorean interval
1584:(Numbers in brackets
1092:(Numbers in brackets
781:31 equal temperament
770:septimal minor third
353:19 equal temperament
228:, or "difference";
1762:Pythagorean apotome
1609:septimal third tone
974:Treatise on Harmony
766:septimal whole tone
607:in descriptions of
595: 524 288
589: 531 441
244:), or a very small
1875:Septimal semicomma
603:Pythagorean tuning
563: 32 768
557: 32 805
513:(discussed below)
418:
374:Diesis defined in
73:
63:
55:
2005:
2004:
1987:
1986:
1817:Pythagorean comma
1757:Pythagorean limma
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1688:
1685:
1684:
1651:supermajor fourth
1627:supermajor second
1572:
1571:
1386:
1385:
1382:
1381:
1094:are the number of
638:equal temperament
614:
613:
609:well temperaments
533: 2 025
527: 2 048
431:diminished second
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421:
380:diminished second
304:diminished second
182:enharmonic diesis
88:
18:Enharmonic diesis
16:(Redirected from
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1997:
1996:
1887:Septimal kleisma
1700:
1657:subminor seventh
1639:supermajor third
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1579:Just intonations
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334:diminished comma
319:enharmonic comma
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2008:
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1983:
1945:
1912:
1855:Septimal diesis
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882:. p. 171.
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830:septimal diesis
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345:syntonic commas
323:augmented comma
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256:2:1) and three
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134:Western culture
130:classical music
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1852:
1849:Greater diesis
1846:
1839:
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1835:Septimal comma
1832:
1829:Holdrian comma
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1823:Syntonic comma
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748:diesis) is an
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734:
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489:
488:greater diesis
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450:greater diesis
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419:
387:117.1 − 76.0 ≈
330:greater diesis
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1778:Quarter tones
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1727:Pseudo-octave
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905:Randel, D. M.
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831:
828:
826:
823:
822:
818:
810:
804:
801:
794:
792:
788:
782:
778:
773:
771:
767:
760:
751:
747:
743:
735:
733:
712:
704:
696:
694:
688: 15 625
676:
675:
670:
669:
664:
660:
656:
655:
650:
646:
641:
639:
635:
632:(0.14%) of a
610:
604:
584:
582:
577:
576:
573:
552:
550:
547:
546:
543:
522:
520:
517:
516:
511:
490:
487:
486:
482:
479:
476:
475:
472:
458:
453:
452:(see below).
451:
446:
436:
432:
424:
413:
393:notes (from D
392:
381:
377:
372:
368:
367:
364:
362:
358:
354:
350:
346:
342:
339:
335:
331:
326:
324:
320:
316:
315:lesser diesis
312:
307:
305:
271:
267:
263:
259:
255:
251:
247:
243:
239:
231:
227:
226:
217:
187:
183:
179:
178:
169:
139:
135:
131:
124:
122:
80:
59:
49:
39:
33:
19:
1950:
1917:
1903:(0.72 cents)
1897:(1.95 cents)
1877:(13.8 cents)
1871:(10.1 cents)
1865:(19.5 cents)
1857:(35.7 cents)
1851:(62.6 cents)
1848:
1845:(41.1 cents)
1842:
1837:(27.3 cents)
1831:(22.6 cents)
1825:(21.5 cents)
1819:(23.5 cents)
1806:
1787:Quarter tone
1777:
1776:
1747:
1746:
1703:
1668:Higher-limit
1583:
1577:
1489:major fourth
1433:quarter tone
1408:
1402:
1091:
1012:
998:
973:
944:
939:
908:
898:
879:
857:
848:
803:
791:) interval.
776:
774:
739:
703:small diesis
702:
700:
697:Small diesis
682:15 552
672:
666:
652:
644:
642:
615:
540:sixth-comma
508:third-comma
483:Typical use
454:
449:
444:
428:
360:
356:
333:
329:
327:
322:
318:
314:
308:
258:justly tuned
185:
181:
137:
127:
41:Diesis on C
1936:Millioctave
1918:Measurement
1909:(0.4 cents)
1889:(7.7 cents)
1883:(8.1 cents)
1767:Major limma
1509:minor fifth
1018:Ellis, A.J.
1008:Ellis, A.J.
579:Pythagorean
1969:Semiditone
1863:Diaschisma
1678:(17-limit)
1369:(22 or 23)
1367:fourteenth
1363:(20 or 21)
1361:thirteenth
1357:(18 or 19)
1351:(17 or 18)
1345:(15 or 16)
1339:(13 or 14)
1274:Diminished
1101:interval.)
1082:(post-Bach
841:References
519:diaschisma
238:accidental
121:media help
1931:Centitone
1869:Semicomma
1748:Semitones
1712:Microtone
1696:intervals
1373:fifteenth
1219:Augmented
1097:semitones
1069:Intervals
971:(1971) .
795:Footnotes
649:Philolaus
643:The word
384:m2 − A1 ≈
357:"greater"
184:, plural
2012:Category
1901:Breedsma
1349:eleventh
1329:Compound
1084:Western)
1079:semitone
1029:"diesis"
1010:(1885).
937:(1722).
854:"diesis"
819:See also
768:and the
750:interval
572:meantone
542:meantone
510:meantone
468:♯
462:♯
440:♭
402:♯
396:♭
361:"lesser"
347:minus a
299:♯
293:♯
287:♯
281:♯
275:♯
252:(in the
225:-ə-seez)
108:♯
102:♯
96:♯
1907:Ragisma
1895:Schisma
1881:Kleisma
1717:5-limit
1623:(15:14)
1617:(21:20)
1611:(28:27)
1605:(36:35)
1595:7-limit
1560:⁄
1549:seventh
1540:⁄
1520:⁄
1500:⁄
1480:⁄
1460:⁄
1440:⁄
1422:Neutral
1395:systems
1355:twelfth
1312:seventh
1263:seventh
1208:seventh
1171:seventh
1109:Perfect
1077:Twelve-
907:(ed.).
746:slendro
730:
718:
691:
679:
671:],
630:
618:
598:
586:
566:
554:
549:schisma
536:
524:
504:
492:
349:schisma
177:-ə-siss
1964:Ditone
1951:Others
1941:Savart
1808:Commas
1704:Groups
1653:(10:7)
1449:second
1393:tuning
1318:octave
1294:fourth
1282:second
1245:fourth
1233:second
1227:unison
1190:second
1153:second
1134:octave
1122:fourth
1116:unison
1099:in the
981:
886:
835:ditone
727:3 072
663:Rameau
645:diesis
457:unison
445:diesis
284:, to B
250:octave
234:δίεσις
186:dieses
138:diesis
1974:Secor
1722:Comma
1694:Other
1659:(7:4)
1647:(7:5)
1641:(9:7)
1635:(7:6)
1629:(8:7)
1529:sixth
1469:third
1391:Other
1343:tenth
1337:ninth
1306:sixth
1300:fifth
1288:third
1257:sixth
1251:fifth
1239:third
1202:sixth
1196:third
1182:Minor
1165:sixth
1159:third
1145:Major
1128:fifth
943:[
809:aulos
721:3 125
674:recte
654:limma
581:comma
480:Ratio
378:as a
338:ratio
321:, or
311:comma
309:As a
268:. In
266:cents
254:ratio
242:sharp
240:(see
230:Greek
132:from
1959:Wolf
1926:Cent
1375:(24)
1320:(11)
1265:(12)
1259:(10)
1210:(10)
1173:(11)
1136:(12)
979:ISBN
909:The
884:ISBN
775:The
758:play
744:(or
740:The
710:Play
701:The
634:cent
477:Name
411:Play
399:to C
136:, a
47:Play
1314:(9)
1308:(7)
1302:(6)
1296:(4)
1290:(2)
1284:(0)
1253:(8)
1247:(6)
1241:(5)
1235:(3)
1229:(1)
1204:(8)
1198:(3)
1192:(1)
1167:(9)
1161:(4)
1155:(2)
1130:(7)
1124:(5)
1118:(0)
916:241
716:is
668:sic
659:4:3
471:):
405:).
341:6:5
332:or
262:5:4
180:or
128:In
2014::
1553:10
1016:.
1006:;
958:^
924:^
868:^
856:.
640:.
363:.
325:.
317:,
306:.
232::
223:DY
201:aɪ
175:DY
153:aɪ
99:-B
1565:)
1562:2
1558:1
1555:+
1551:(
1545:)
1542:2
1538:1
1535:+
1533:8
1531:(
1525:)
1522:2
1518:1
1515:+
1513:6
1511:(
1505:)
1502:2
1498:1
1495:+
1493:5
1491:(
1485:)
1482:2
1478:1
1475:+
1473:3
1471:(
1465:)
1462:2
1458:1
1455:+
1453:1
1451:(
1445:)
1442:2
1438:1
1435:(
1061:e
1054:t
1047:v
987:.
918:.
892:.
724:/
685:/
624:/
621:1
592:/
560:/
530:/
498:/
382:(
216:/
213:z
210:i
207:s
204:ə
198:d
195:ˈ
192:/
188:(
168:/
165:s
162:ɪ
159:s
156:ə
150:d
147:ˈ
144:/
140:(
123:.
53:.
34:.
20:)
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