Temperament Table 音律表



Temperament (調整、音律)

ピュタゴラス音律や純正律において、ある特定の音程に生じるシントニックコンマ(Syntonic comma)を複数の音程に分散させるアイディア。 それを用いて調律された音階自体も指す事もある。
ピュタゴラス音律や純正律はこのような分散の工夫がされていないので、Temperament(調整、音律) という概念とは厳密な意味においては外れるが、日本語で「音律」と云う場合はこれらも含めて考えるのが一般的である。

Relative name
相対音名。
Center tone=C
C=壱越を起点音におく。
Interval
音程関係や種類の名称
±mQ  ±nT
純正5度(Quintenzirkel)と純正3度(Terzbau)による表示。+は上行、-は下行。m,nは積重ねの回数。
Equal Temperament
等分平均律の表示。分数a/bは、b等分平均律(b-TET)に於ける、単位音程a個の意。音程比ではない。
TET
等分平均律の略記。12-TETは、12等分平均律 (12Tone Equal Temperament)の意。TETの他にEDO(Equal Division of the Octave)と略記する方法もある。12-TET = 12-EDO。
Cent
セント値。
音程比の常用対数を、2の常用対数0.30102999566398で除して、2を底とする対数を得、これを1200倍してセント値を得る。

1200 log  Ratio /1200 log 2 = X Cent

Common-logarithms
常用対数
Ratio
音程比
Notes
備考欄

Temperament Table 音律表

Relative name
(center tone=C)
Interval ±mQ±nT Equal Temperament Cent Common-logarithms Ratio Notes
C,壱越 Unison, Perfect first(Per1st),Diminished second(dim2nd),
1st overtone

ユニゾン, 完全一度, 減二度, 第1倍音,
Das Tonwort; bi


0.000000000000 0.00000000000000 1.0000000000000 1/1 Harry Partch's 43tone scale

8192√100cent

0.0122070312500.000003062235471.00000705108268192√(12√2)Pitch Bend Sensitivity

4096√100cent

0.0244140625000.000006124470941.00001410221494096√(12√2)Pitch Bend Sensitivity

2048√100cent

0.0488281249990.000012248941881.00002820462872048√(12√2)Pitch Bend Sensitivity

1024√100cent

0.0976562499990.000020904860801.00004813637931024√(12√2)Pitch Bend Sensitivity




0.9998464321030.000250819805931.00057770075101732/1731The nearest whole number ratio for 1 cent

1cent
(1200 equal Temperament)
1200等分平均律

1/1200-TET1.0000000000000.000250858329721.00057778950661200√21200 log  Ratio 
/1200 log 2
= X Cent




1.0004242110620.000250964746511.00057803468201731/1730

1024 equal Temperament
1024等分平均律

1/1024-TET1.1718750000000.000293974605141.00067713069311024√2

millioctave (mO)
1000 equal Temperament
1000等分平均律

1/1000-TET1.2000000000000.000301029995661.00069338746261000√2

768 equal Temperament
768等分平均律

1/768-TET1.5625000000000.000391966140191.0009029427990768√2
His-1 Schisma スキスマ 8Q+1T
1.953720787943 0.00049010713360 1.0011291503906 32805/32768 Pythagoras comma
- Syntonic comma

12 equal Temperament comma
十二等分平均律コンマ


1.9550008653870.000490428251691.00112989062753/(12√524288)Pythagoras 5th
-12tET5th

2cent
2/1200-TET2.0000000000000.000501716659441.0011559128538(1200√2)^2

3cent
3/1200-TET3.0000000000000.000752574989161.0017343702347(1200√2)^3

Angle value 角度値
360 equal Temperament
360等分平均律

1/360-TET3.3333333333330.000836194432401.0019272636247360√2

441(Hz)/440(Hz)

3.9301584394330.000985912981651.0022727272727441/440

440(Hz)/439(Hz)

3.9391007871620.000988156244071.0022779043280440/439

Savart サヴァール,
300 Equal Temperament
4cent

1/300-TET; 4/1200-TET4.0000000000000.001003433318881.0023131618422(1200√2)^4

5cent
5/1200-TET5.0000000000000.001254291648601.0028922878694(1200√2)^5

6cent
6/1200-TET6.0000000000000.001505149978321.0034717485095(1200√2)^6

7cent
7/1200-TET7.0000000000000.001756008308041.0040515439559(1200√2)^7

442(Hz)/440(Hz)

7.8514150401260.001969592862901.0045454545455442/440

440(Hz)/438(Hz)

7.8871847081830.001978565982081.0045662100456440/438

8cent
8/1200-TET8.0000000000000.002006866637761.0046316744021(1200√2)^8
Hisis-1 Kleisma クライスマ -5Q+6T
8.107278862068 0.00203377843391 1.0046939300412 15625/15552

9cent
9/1200-TET9.0000000000000.002257724967481.0052121400415(1200√2)^9

10cent
10/1200-TET10.0000000000000.002508583297201.0057929410679(1200√2)^10

11cent
11/1200-TET11.0000000000000.002759441626921.0063740776750(1200√2)^11

443(Hz)/440(Hz)

11.7638100364300.002951049736881.0068181818182443/440

440(Hz)/437(Hz)

11.8442928288730.002971239515761.0068649885583440/437

1centi octave(100 equal Temperament)
1センチオクターブ, 100等分平均律,12cent

1/100-TET; 12/1200-TET12.0000000000000.003010299956641.0069555500567(1200√2)^12

13cent
13/1200-TET13.0000000000000.003261158286361.0075373584071(1200√2)^13

128/127comma

13.5783758734010.003406248691911.0078740157480128/127

14cent
14/1200-TET14.0000000000000.003512016616081.0081195029203(1200√2)^14

15cent
15/1200-TET15.0000000000000.003762874945801.0087019837904(1200√2)^15

16cent
16/1200-TET16.0000000000000.004013733275521.0092848012119(1200√2)^16

17cent
17/1200-TET17.0000000000000.004264591605241.0098679553791(1200√2)^17

18cent
18/1200-TET18.0000000000000.004515449934961.0104514464868(1200√2)^18

440(Hz)/435.4(Hz)

18.1945394685780.004564251781111.0105649977033440/435.4standard pich
diapason normal
標準調子
1859

19cent
19/1200-TET19.0000000000000.004766308264681.0110352747294(1200√2)^19
Deses+2 Diaschisma ディアシスマ -4Q-2T
19.552568808781 0.00490492475311 1.0113580246914 2048/2025 全音階的half tone
-大クローマ

20cent
20/1200-TET20.0000000000000.005017166594401.0116194403019(1200√2)^20

21cent
21/1200-TET21.0000000000000.005268024924121.0122039433992(1200√2)^21
C+1,Pramana Syntonic comma
シントニックコンマ,
Didymus
ディデュモスコンマ

4Q-1T


21.506289596715

0.00539503188671

1.0125000000000

81/80

Pythagoras長3rd
-純正長3rd,
Harry Partch's 43tone scale


22cent
22/1200-TET

22.000000000000

0.00551888325384

1.0127887842162

(1200√2)^22



53 equal Temperament,
53等分平均律,
トルコのcomma,
Das Tonwort;bo

1/53-TET 22.641509433962 0.00567981123894 1.0131641430249 53√2 純正率に近い等分平均律
[Inv] 2 [x^y]53

Arabisches comma(19milli octave)
19/1000-TET22.8000000000000.005719569917621.0132569001591(1000√2)^19

23cent
23/1200-TET23.0000000000000.005769741583561.0133739629480(1200√2)^23
His Pythagorean comma
ピタゴラスコンマ
12Q
23.460010384649 0.00588513902031 1.0136432647705 531441/524288 Schisma x12

approximation to ditonic comma

23.5545680987190.005908859610521.013698630137074/73

24cent
24/1200-TET24.0000000000000.006020599913281.0139594797900(1200√2)^24

25cent, One eighth, Semi-quarter tone 八分音
1/48-TET;
25/1200-TET
25.000000000000 0.00627145824300 1.0145453349375 (1200√2)^25

26cent
26/1200-TET26.0000000000000.006522316572721.0151315285860(1200√2)^26

27cent
27/1200-TET27.0000000000000.006773174902441.0157180609310(1200√2)^27

第7次comma(i~B)
七のコンマ


27.2640918001000.006839424530311.015873015873064/63Pythagorasmin.7th
-第7倍音

63/62comma

27.7003357356500.006948859955331.016129032258163/62

43 equal Temperament
43等分平均律

1/43-TET27.9069767441860.007000697573581.016250325193643√2

28cent
28/1200-TET28.0000000000000.007024033232161.0163049321682(1200√2)^28

62/61comma

28.1507673887870.007061854487491.016393442623062/61

61/60comma

28.6160903452410.007178584627121.016666666666761/60

29cent
29/1200-TET29.0000000000000.007274891561881.0168921424935(1200√2)^29

60/59comma

29.0970554960130.007299238741501.016949152542460/59

41 equal Temperament
41等分平均律

1/41-TET29.2682926829270.007342195016191.017049744443641√2

59/58comma

29.5944650811230.007424018079211.017241379310359/58

30cent
30/1200-TET30.0000000000000.007525749891601.0174796921027(1200√2)^30

58/57comma

30.1091771553970.007553137890451.017543859649158/57

57/56comma

30.6421105285650.007686828666291.017857142857157/56

31cent
31/1200-TET31.0000000000000.007776608221321.0180675811919(1200√2)^31

56/55comma

31.1942502395330.007825337511961.018181818181856/55

55/54comma

31.7666536334290.007968929671281.018518518518555/54

32cent
32/1200-TET32.0000000000000.008027466551041.0186558099573(1200√2)^32

54/53comma

32.3604571203230.008117890222181.018867924528354/53

53/52comma

32.9768837065280.008272525965991.019230769230853/52

33cent
33/1200-TET33.0000000000000.008278324880761.0192443785951(1200√2)^33

52/51comma

33.6172514035160.008433167536861.019607843137352/51

34cent
34/1200-TET34.0000000000000.008529183210481.0198332873016(1200√2)^34

51/50quarter Tone

34.2829826361250.008600171761921.020000000000051/50

50/49quarter Tone
七の第6音


34.9756147914200.008773924307511.020408163265350/49

35cent
35/1200-TET35.0000000000000.008780041540201.0204225362735(1200√2)^35

49/48quarter Tone
七のディエシス


35.6968120728620.008954842652931.020833333333349/48

36cent
36/1200-TET36.0000000000000.009030899869921.0210121257072(1200√2)^36

48/47quarter Tone

36.4483788522230.009143379439871.021276595744748/47

37cent
37/1200-TET37.0000000000000.009281758199641.0216020557995(1200√2)^37

47/46quarter Tone

37.2322747447490.009340026254141.021739130434847/46

38cent
38/1200-TET38.0000000000000.009532616529361.0221923267472(1200√2)^38

46/45quarter Tone

38.0506316728060.009545317906231.022222222222246/45

31 equal Temperament
31等分平均律

1/31-TET38.7096774193550.009710645021421.022611435601331√2Meantoneに近い

45/44quarter Tone

38.9057732308530.009759837289161.022727272727345/44

39cent
39/1200-TET39.0000000000000.009783474859081.0227829387473(1200√2)^39

40cent
40/1200-TET40.0000000000000.010034333188801.0233738919968(1200√2)^40

41cent
41/1200-TET41.0000000000000.010285191518521.0239651866929(1200√2)^41
Deses+3 diesis ディエシス,
minor diesis
-3T
41.058858405496 0.01029995663981 1.0240000000000 128/125 純正長3rd *3

42cent
42/1200-TET42.0000000000000.010536049848241.0245568230328(1200√2)^42

43cent
43/1200-TET43.0000000000000.010786908177961.0251488012140(1200√2)^43

40/39quarter Tone

43.8310512301370.010995384301461.025641025641040/39

44cent
44/1200-TET44.0000000000000.011037766507681.0257411214340(1200√2)^44

39/38quarter Tone

44.9696465023950.011281010409691.026315789473739/38

45cent
45/1200-TET45.0000000000000.011288624837401.0263337838904(1200√2)^45

Das Tonwort;bu
2/53-TET45.2830188679250.011359622477891.0265015807114(53√2)^2([Inv] 2 [x^y] 53)
→[x^y]2

46cent
46/1200-TET46.0000000000000.011539483167121.0269267887810(1200√2)^46

38/37quarter Tone

46.1689773775630.011581872549821.027027027027038/37

47cent
47/1200-TET47.0000000000000.011790341496841.0275201363035(1200√2)^47

37/36quarter Tone

47.4340370239650.011899223299711.027777777777837/36

48cent
48/1200-TET48.0000000000000.012041199826561.0281138266561(1200√2)^48

452.5(Hz)/440(Hz)

48.4971221350900.012165907055031.0284090909091452.5/440フィルハーモニック・ピッチ
1846

septimal quarter tone, 36/35quarter Tone

48.7703813968150.012234456417011.028571428571436/35

49cent
49/1200-TET49.0000000000000.012292058156281.0287078600367(1200√2)^49
Cis-3
-5Q+3T
49.1661372675670.012333735073731.0288065843621250/243

quarter tone , 四分音,
24 equal Temperament,
24等分平均律, 50cent,

1/24-TET; 50/1200-TET 50.000000000000 0.01254291648600 1.0293022366435 24√2

35/34quarter Tone

50.1842108335530.012589127308021.029411764705935/34

51cent
51/1200-TET51.0000000000000.012793774815721.0298969566749(1200√2)^51

34/33quarter Tone

51.6824662702630.012964977164371.030303030303034/33

52cent
52/1200-TET52.0000000000000.013044633145441.0304920203293(1200√2)^52

53cent
53/1200-TET53.0000000000000.013295491475161.0310874278052(1200√2)^53

undecimal comma,
33/32quarter Tone


53.2729432301440.013363961557981.031250000000033/32Harry Partch's 43tone scale

54cent
54/1200-TET54.0000000000000.013546349804881.0316831793014(1200√2)^54

22 equal Temperament
二十二等分平均律

1/22-TET54.5454545454550.013683181621091.032008279734222√2

32/31quarter Tone

54.9644275357500.013788284485631.032258064516132/31

55cent
55/1200-TET55.0000000000000.013797208134601.0322792750165(1200√2)^55

56cent
56/1200-TET56.0000000000000.014048066464321.0328757151494(1200√2)^56

31/30quarter Tone

56.7668577340280.014240439114611.033333333333331/30

57cent
57/1200-TET57.0000000000000.014298924794041.0334724998992(1200√2)^57

58cent
58/1200-TET58.0000000000000.014549783123761.0340696294649(1200√2)^58



2/41-TET58.5365853658540.014684390032391.0343901826729(41√2)^2

30/29quarter Tone

58.6915205771360.014723256820711.034482758620730/29

59cent
59/1200-TET59.0000000000000.014800641453481.0346671040459(1200√2)^59

60cent
60/1200-TET60.0000000000000.015051499783201.0352649238414(1200√2)^60

29/28quarter Tone

60.7512876839620.015239966556741.035714285714329/28

61cent
61/1200-TET61.0000000000000.015302358112921.0358630890509(1200√2)^61

62cent
62/1200-TET62.0000000000000.015553216442641.0364615998740(1200√2)^62
Deses+4Great Diesis4Q-4T
62.5651480022100.015694988526521.0368000000000648/625純正min.3rd *4

Archytas half tone,
アルキタスの半音,
28/27 semitone


62.9609038729630.015794267183231.037037037037028/27クリ音-大全音

63cent
63/1200-TET63.0000000000000.015804074772361.0370604565103(1200√2)^63

19 equal Temperament
十九等分平均律

1/19-TET63.1578947368420.015843683982311.037155044446219√2

440(Hz)/424.2(Hz;プレトリウスのオルガン)

63.3106834577600.015882012305641.0372465818010440/424.2Year 1619

64cent
64/1200-TET64.0000000000000.016054933102081.0376596591598(1200√2)^64

65cent
65/1200-TET65.0000000000000.016305791431801.0382592080222(1200√2)^65

27/26quarter Tone

65.3373408268520.016390416188171.038461538461527/26

66cent
66/1200-TET66.0000000000000.016556649761521.0388591032977(1200√2)^66

67cent
67/1200-TET67.0000000000000.016807508091241.0394593451863(1200√2)^67

26/25quarter Tone

67.9002340396410.017033339298781.040000000000026/25

Das Tonwort;re
3/53-TET67.9245283018870.017039433716831.0400145943352(53√2)^3

68cent
68/1200-TET68.0000000000000.017058366420961.0400599338885(1200√2)^68

69cent
69/1200-TET69.0000000000000.017309224750681.0406608696045(1200√2)^69

70cent
70/1200-TET70.0000000000000.017560083080401.0412621525348(1200√2)^70

440(Hz)/422.5(Hz;ヘンデルの音叉)

70.2626188261360.017625963200481.0414201183432440/422.5Year 1751

17 equal Temperament
十七等分平均律

1/17-TET70.5882352941180.017707646803761.041616010650617√2
Cis-2 純正率半音階的小半音(小クローマ),(小)増1st(Ees+1~E-1),25/24half tone -1Q+2T
70.672426864282 0.01772876696043 1.0416666666667 25/24 小全音-
diatonic half tone

71cent
71/1200-TET71.0000000000000.017810941410121.0418637828801(1200√2)^71

72cent
72/1200-TET72.0000000000000.018061799739841.0424657608411(1200√2)^72

73cent
73/1200-TET73.0000000000000.018312658069561.0430680866187(1200√2)^73

approximation to meantone chromatic semitone, 24/23half tone

73.6806535969720.018483405694011.043478260869624/23

74cent
74/1200-TET74.0000000000000.018563516399281.0436707604138(1200√2)^74

75cent
75/1200-TET75.0000000000000.018814374729001.0442737824274(1200√2)^75

76cent
76/1200-TET76.0000000000000.019065233058721.0448771528609(1200√2)^76
(Cis-7/4) Meantone半音階的 half tone(増1st)

76.048999263461 0.01907752493211 1.0449067265257 (4√78125)/16

23/22half tone

76.9564049036590.019305155195391.045454545454623/22

77cent
77/1200-TET77.0000000000000.019316091388441.0454808719154(1200√2)^77



2/31-TET77.4193548387100.019421290042841.0457341482225(31√2)^2

78cent
78/1200-TET78.0000000000000.019566949718161.0460849397925(1200√2)^78

79cent
79/1200-TET79.0000000000000.019817808047881.0466893566937(1200√2)^79

15 equal Temperament
十五等分平均律,
80cent

1/15-TET;
80/1200-TET
80.0000000000000.020068666377601.047294122820615√2

22/21half tone

80.5370350302440.020203386088291.047619047619122/21

81cent
81/1200-TET81.0000000000000.020319524707321.0478992383751(1200√2)^81

82cent
82/1200-TET82.0000000000000.020570383037041.0485047035589(1200√2)^82

83cent
83/1200-TET83.0000000000000.020821241366761.0491105185742(1200√2)^83

84cent
84/1200-TET84.0000000000000.021072099696481.0497166836231(1200√2)^84

minor semitone,
21/20 semitone


84.4671934696780.021189299069941.050000000000021/20Harry Partch's 43tone scale

85cent
85/1200-TET85.0000000000000.021322958026201.0503231989077(1200√2)^85

86cent
86/1200-TET86.0000000000000.021573816355921.0509300646305(1200√2)^86

87cent
87/1200-TET87.0000000000000.021824674685641.0515372809940(1200√2)^87



3/41-TET87.8048780487810.022026585048581.0520262709424(41√2)^3

88cent
88/1200-TET88.0000000000000.022075533015361.0521448482007(1200√2)^88

20/19half tone,malcolm(dis~e)

88.8006977325320.022276394711151.052631578947420/19

89cent
89/1200-TET89.0000000000000.022326391345081.0527527664534(1200√2)^89

90cent
90/1200-TET90.0000000000000.022577249674801.0533610359548(1200√2)^90
Des, 断金 Pythagoras limma(min.2nd), 古代half tone -5Q
90.224995673063 0.02263369171354 1.0534979423868 256/243 小全音-大クローマ

Das Tonwort;ri,(バキーイェ)
4/53-TET90.5660377358490.022719244955771.0537054952030(53√2)^4

91cent
91/1200-TET91.0000000000000.022828108004521.0539696569080(1200√2)^91

92cent
92/1200-TET92.0000000000000.023078966334241.0545786295160(1200√2)^92
Cis-1 純正率半音階的大半音(大クローマ),小limma,(大)増1st(F0~Fis-1) 3Q+1T
92.178716460997 0.02312379884714 1.0546875000000 135/128 大全音-
diatonic half tone

93cent
93/1200-TET93.0000000000000.023329824663961.0551879539820(1200√2)^93

19/18half tone,malcolm(d~dis)

93.6030144015280.023481095849521.055555555555619/18

94cent
94/1200-TET94.0000000000000.023580682993681.0557976305092(1200√2)^94

95cent
95/1200-TET95.0000000000000.023831541323401.0564076593012(1200√2)^95

96cent
96/1200-TET96.0000000000000.024082399653121.0570180405614(1200√2)^96

Neidhardt 小min.2nd

96.0899982692250.024104976468611.0570729911135(4√8192)/9

97cent
97/1200-TET97.0000000000000.024333257982841.0576287744935(1200√2)^97

98cent
98/1200-TET98.0000000000000.024584116312561.0582398613012(1200√2)^98

Galilei'half tone, approximation to semitone of equal temperament

98.9545922303680.024823583725031.058823529411818/17

99cent
99/1200-TET99.0000000000000.024834974642281.0588513011885(1200√2)^99

(100cent Approximation
近似値)


99.9066043792230.025062403902561.0594059405940107/101
Cis,Des 12-TET Semitone, half step, Minor second(min2nd), augmented prime(aug1st), Augmented unison
十二等分平均律 半音(増一度, 短二度, 重減三度) ,100cent

1/12-TET;
2/24-TET;
100/1200-TET
100.000000000000 0.02508583297200 1.0594630943593 12√2 Pythagoras comma/12

(12tET half tone Approximation
近似値)


100.0992098251650.025110720583031.059523809523889/84

キルンベンガー第2のmin.2nd

100.9781404714200.025331207656891.060061855999964/27・√5

Neidhardt 大min.2nd

101.9550008653870.025576261223691.06066017177983/√8

17th overtone,
第17倍音


104.9554095004070.026328938722351.062500000000017/16

ヴァロッティのmin.2nd

105.8650025961620.026557117727081.063058385848827/3√16384
Des+1 minor diatonic semitone, just, 純正率全音階的half tone, (小)min.2nd, 1/15 overtone -1Q-1T
111.731285269778 0.02802872360024 1.0666666666667 16/15 Harry Partch's 43tone scale

Das Tonwort;ro
(キュチュク・ミュジュンネプ)

5/53-TET

113.207547169811

0.02839905619472

1.0675766250480

(53√2)^5


Cis Pythagoras・アポドメー(増1st),古代嬰half tone 7Q
113.685006057712 0.02851883073384 1.0678710937500 2187/2048 大全音-
Pythagoras・limma



3/31-TET116.1290322580650.029131935064261.0693796985711(31√2)^3



4/41-TET117.0731707317070.029368780064781.0699630500100(41√2)^4
(Des+5/4) Meantone全音階的half tone(min.2nd, Cis~D)

117.107857668956 0.02937748157192 1.0699844879623 8/(4√3125) (5^-5/4)*(2^3)

approximation to meantone diatonic semitone, 15/14 semitone

119.4428082610970.029963223377441.071428571428615/14

10 equal Temperament
十等分平均律

1/10-TET120.0000000000000.030102999566401.071773462536310√2



2/19-TET126.3157894736840.031687367964631.0756905862202(19√2)~2

14/13half tone

128.2982446998140.032184683371401.076923076923114/13
Des+2 大limma(min.3rd-小全音), 和声的嬰half tone 3Q-2T
133.237574866493 0.03342375548695 1.0800000000000 27/25 大全音-小クロマ

9 equal Temperament
九等分平均律

1/9-TET133.3333333333330.033447777296001.08005973889239√2

Das Tonwort;ru
6/53-TET135.8490566037740.034078867433661.0816303564302(53√2)^6

13/12half tone

138.5726609039230.034762106259211.083333333333313/12



5/41-TET146.3414634146340.036710975080971.0882056465768(41√2)^5

150cent
3/24-TET; 150/1200-TET150.0000000000000.037628749458001.0905077326653(24√2)^3

lesser undecimal,
undecimal neutral second, 3/4-tone, トランペット3/4音(k~G),
12/11half tone


150.6370585006310.037788560889401.090909090909112/11perfect5th
-第11倍音
Harry Partch's 43tone scale



4/31-TET154.8387096774190.038842580085681.0935599087586(31√2)^4

Das Tonwort;te,
7/53-TET158.4905660377360.039758678672601.0958690931423(53√2)^7
D-2
-6Q+2T
160.8974225373450.040362458673971.0973936899863800/729
Cisis-3純正率2重増1st2Q+3T
162.8511433252790.040852565807571.09863281250001125/1024

greater undecimal,
11/10half tone, 4/5-tone


165.0042284999220.041392685158231.100000000000011/10Harry Partch's 43tone scale

7 equal Temperament
七等分平均律

1/7-TET171.4285714285710.043004285094851.10408951367387√2タイの音律に近い



6/41-TET175.6097560975610.044053170097171.1067592747530(41√2)^6
EsesPythagoras減3rd-10Q
180.4499913461260.045267383427071.109857914613365536/59049

Das Tonwort;ti
(ビュユク・ミュジェンネプ)

8/53-TET181.1320754716980.045438489911541.1102952706211(53√2)^8
D-1 minor whole tone, 小全音, 純正率長2nd(D~E-1),第9倍音~第10倍音 -2Q+1T
182.403712134060 0.04575749056068 1.1111111111111 10/9 純正率長3rd
-大全音
Harry Partch's 43tone scale



3/19-TET189.4736842105260.047531051946941.1156579177615(19√2)~3

Malcolm(cis~dis)

192.5576066318950.048304679574561.117647058823519/17
(D-1/2) 中全音(Meantone長2nd)

193.156856932417 0.04845500650403 1.1180339887499 √5/2



5/31-TET193.5483870967740.048553225107091.1182868682116(31√2)^5




193.7561072329400.048605333433501.118421052631685/76

ヴァロッティの長2nd

196.0899982692250.049190809440611.11992982212883√1024/9
D,Cisis,Eses 12-TET Whole tone, Major second(Maj2nd), Diminished third(dim3rd),
十二等分平均律 全音(長二度, 減三度), 200cent

1/6-TET;
2/12-TET;
4/24-TET;
200/1200-TET
200.000000000000 0.05017166594400 1.1224620483094 (12√2)^2

(12tET Whole tone Approximation)

200.0585339597070.050186349675361.1225000000000449/400




200.5319830023100.050305118311401.122807017543964/57

Das Tonwort;to
(タニーニー)

9/53-TET203.7735849056600.051118301150491.1249113563634(53√2)^9
D,平調major whole tone, 大全音, Pythagoras Major second,トノス, 9th overtone,
第9倍音
2Q
203.9100017307750.051152522447381.12500000000009/8Pythagoras limma*2
+Pythagoras comma
Harry Partch's 43tone scale



7/41-TET204.8780487804880.051395365113361.1256292375482(41√2)^7




210.6858775001450.052852307325281.129411764705996/85




216.6866947701850.054357662322591.133333333333317/15
Eses+2純正率減3rd-2Q-2T
223.4625705395560.056057447200491.1377777777778256/225
D+1
6Q-1T
225.4162913274900.056547554334091.1390625000000729/640

Das Tonwort;tu
10/53-TET226.4150943396230.056798112389431.1397198503489(53√2)^10

septimal whole tone,
1/7 overtone, SuperSecond


231.1740935308750.057991946977691.14285714285718/7({1/7}/{1/4}),
Harry Partch's 43tone scale



6/31-TET232.2580645161290.058263870128511.1435729397160(31√2)^6



8/41-TET234.1463414634150.058737560129561.1448209283866(41√2)^8

5 equal Temperament
五等分平均律

1/5-TET;
2/10-TET;
240/1200-TET
240.0000000000000.060205999132801.14869835499705√2
Eses+3
2Q-3T
244.9688601362700.061452479087191.1520000000000144/125

tridecimal minor third

247.7410529609120.062147906748841.153846153846215/13

Das Tonwort;ta
11/53-TET249.0566037735850.062477923628371.1547232854672(53√2)^11

250cent
5/24-TET; 250/1200-TET250.0000000000000.062714582430001.1553526968723(24√2)^5



4/19-TET252.6315789473680.063374735929261.1571102372827(19√2)~4
Dis-3SubminorThird-3Q+3T
253.0761389983420.063486257521111.1574074074074125/108



9/41-TET263.4146341463410.066079755145751.1643398326493(41√2)^9



2/9-TET266.6666666666670.066895554592001.1665290395761(9√2)^2

septimal minor third,
第7次min.3rd(G~i),クリ音


266.8709056037380.066946789630611.16666666666677/6Harry Partch's 43tone scale
(Dis-9/4)Meantone増2nd

269.2058561958780.067532531436141.1682412353291(4√1953125)/32{(4√3125)/4}
÷(8/5)



7/31-TET270.9677419354840.067974515149931.1694307655977(31√2)^7

Das Tonwort;mi
(アルテゥク・イキリ)

12/53-TET271.6981132075470.068157734867321.1699242279513(53√2)^12
Dis-2純正率増2nd1Q+2T
274.5824285950570.068881289407811.171875000000075/64




281.3583043644280.070581074285711.176470588235320/17




287.3591216344670.072086429283021.180555555555685/72




289.2097194045540.072550667148611.181818181818213/11



10/41-TET292.6829268292680.073421950161951.1841915292415(41√2)^10




292.7106994633070.073428917158531.184210526315845/38
Es,勝絶Pythagorean minor third-3Q
294.1349974038380.073786214160921.185185185185232/27Harry Partch's 43tone scale

Das Tonwort;mo
13/53-TET294.3396226415090.073837546106261.1853252778164(53√2)^13
Dis-1
5Q+1T
296.0887181917720.074276321294521.18652343750001215/1024

19th overtone,
第19倍音


297.5130161323030.074633618296901.187500000000019/16

(12tETmin.3rd Approximation
近似値)


299.9739036100170.075250952419191.189189189189244/37
Dis,Es 12-TET Minor third(min3rd), Augmented second(aug2nd),
十二等分平均律 短三度(増二度), 300cent

1/4-TET;
3/12-TET;
6/24-TET;
300/1200-TET

300.000000000000 0.07525749891600 1.1892071150027 (12√2)^3

ペルシアの3rd

302.8645939611420.075976106172411.191176470588281/68

Kirnberger第2のmin.3rd

304.8881422021950.076483730104271.19256958799998/3・√5




305.4873925027170.076634057033741.192982456140468/57

ヴァロッティのmin.3rd

305.8650025961620.076728783671071.193242693252327/6√134217728



8/31-TET309.6774193548390.077685160171351.1958732740441(31√2)^8
(Es+3/4)Meantonemin.3rd

310.2647146013740.077832488075951.19627902497704(4√5)/5
Es+1 minor third 1Q-1T
315.641287000553 0.07918124604762 1.2000000000000 6/5 Harry Partch's 43tone scale



5/19-TET315.7894736842110.079218419911571.2001027195781(19√2)~5

Das Tonwort;mu
14/53-TET316.9811320754720.079517357345201.2009290693046(53√2)^14
DisPythagoras +2nd9Q
317.5950077884870.079671353181231.201354980468819683/16384



11/41-TET321.9512195121950.080764145178141.2043816921874(41√2)^11
Feses+3
-3Q-3T
335.1938558093330.084086170800731.21362962962964096/3375
Es+2
5Q-2T
337.1475765972670.084576277934331.2150000000000243/200

Das Tonwort;ma
15/53-TET339.6226415094340.085197168584151.2167382713357(53√2)^15



2/7-TET342.8571428571430.086008570189711.2190136542045(7√2)^2

undecimal neutral third,
Ptolemaios 3rd


347.4079406339820.087150175718901.222222222222211/9Harry Partch's 43tone scale



9/31-TET348.3870967741930.087395805192771.2229136855675(31√2)^9

350cent
7/24-TET; 350/1200-TET350.0000000000000.087800415401991.2240535433047(24√2)^7



12/41-TET351.2195121951220.088106340194341.2249160922518(41√2)^12

ザルザルの中立3rd(ザルザルの中指)

354.5470602314060.088941083336781.227272727272727/22

1/13 overtone

359.4723382306890.090176630349091.230769230769216/13(1/13)÷(1/8)



3/10-TET360.0000000000000.090308998699191.2311444133449(10√2)^3

Das Tonwort;gi
16/53-TET362.2641509433960.090876979823091.2327555879635(53√2)^16
E-2
-4Q+2T
364.8074242681200.091514981121351.2345679012346100/81




365.8254978341050.091770373355651.2352941176471105/85



6/19-TET378.9473684210530.095062103893891.2446925894640(19√2)~6

サリナスの長3rd

379.1449506659300.095111669045821.2448346518214(3√625)/(3√4)(3√81)



13/41-TET380.4878048780490.095448535210531.2458005985896(41√2)^13
Fesピュタゴタス減4th-8Q
384.3599930769010.096419905874461.24859015394008192/6561

Das Tonwort;go
17/53-TET384.9056603773590.096556791062031.2489837588382(53√2)^17
E-1 major third, Meantone長, 5th overtone,
第5倍音, アルキタスの3rd


386.313713864835 0.09691001300806 1.2500000000000 5/4 大全音+小全音,
Harry Partch's 43tone scale



10/31-TET387.0967741935480.097106450214191.2505655196146(31√2)^10




393.0895896342050.098609797885951.254901960784364/51




399.0904069042450.100115152883271.259259259259334/27
E,Disis,Fes 12-TET Major third(Maj3rd), Diminished fourth(dim4th),
十二等分平均律 長三度(減四度), 400cent

1/3-TET;
3/9-TET;
4/12-TET;
8/24-TET;
400/1200-TET
400.000000000000 0.10034333188799 1.2599210498949 (12√2)^4

(12tET長3rd Approximation
近似値)


400.1084804702300.100370545117561.260000000000063/50

ガナッシの長3rd

404.4419847330850.101457640758781.263157894736824/19
Fes+1(小)減4th-4Q-1T
405.8662826736160.101814937761161.2641975308642512/405

Das Tonwort;gu
18/53-TET407.5471698113210.102236602300981.2654255596753(53√2)^18
E,下無 Pythagoras長3rd,2全音,ディトヌス 4Q
407.820003461550 0.10230504489476 1.2656250000000 81/64




409.2443014020800.102662341897151.266666666666719/15



14/41-TET409.7560975609760.102790730226731.2670411804232(41√2)^14




417.5079641043680.104735350520011.272727272727314/11Harry Partch's 43tone scale

マルカムの長3rd

420.5966965009600.105510184769971.275000000000051/40



11/31-TET425.8064516129030.106817095235611.2788426013265(31√2)^11
Fes+2(大)減4th, 1/25 overtone-2T
427.3725722703300.107209969647871.280000000000032/25

Das Tonwort;ga
19/53-TET430.1886792452830.107916413539921.2820838027303(53√2)^19

septimal major third

435.0840952616500.109144469425071.28571428571439/7Harry Partch's 43tone scale



15/41-TET439.0243902439020.110132925242921.2886439087490(41√2)^15



7/19-TET442.1052631578950.110905787876201.2909391979474(19√2)~7
Fes+3
4Q-3T
448.8788618670450.112605001534581.2960000000000162/125

450cent
9/24-TET; 450/1200-TET450.0000000000000.112886248373991.2968395546510(24√2)^9

Das Tonwort;ge
20/53-TET452.8301886792450.113596224778861.2989613372793(53√2)^20

tridecimal major third

454.2139479044760.113943352306841.300000000000013/10
Eis-3(小)増3rd-1Q+3T
456.9861407291170.114638779968491.3020833333333125/96



12/31-TET464.5161290322580.116527740257031.3077590684506(31√2)^12



16/41-TET468.2926829268290.117475120259121.3106149580720(41√2)^16

narrow fourth,
21th overtone,
第21倍音


470.7809073345120.118099312078001.312500000000021/16Harry Partch's 43tone scale

Das Tonwort;so
21/53-TET475.4716981132080.119276036017801.3160610501071(53√2)^21
F-1狭い4th-5Q+1T
476.5387095378980.119543704721591.3168724279835320/243
Eis-2(大)増3rd3Q+2T
478.4924303258320.120033811855191.3183593750000675/512



2/5-TET; 4/10-TET; 480/1200-TET480.0000000000000.120411998265591.3195079107729(5√2)^2




485.2683060952020.121733596733091.323529411764745/34




491.2691233652420.123238951730411.328125000000085/64



17/41-TET497.5609756097560.124817315275311.3329606081711(41√2)^17
F Pythagorean interval perfect fourth, 1/3 overtone,
ピタゴラス音律 完全四度, 第1/3倍音
-1Q
498.044999134613 0.12493873660830 1.3333333333333 4/3 octave-
perfect5th,
Harry Partch's 43tone scale

Das Tonwort;su
22/53-TET498.1132075471700.124955847256751.3333858660003(53√2)^22

(12tET4th Approximation
近似値)


499.9505954184430.125416771309181.3348017621145303/227
F,Eis,Geses 12-TET Perfect fourth(Per4th), Augmented third(aug3rd),
十二等分平均律 完全四度(増三度), 500cent

5/12-TET;
10/24-TET;
500/1200-TET
500.000000000000 0.12542916485999 1.3348398541700 (12√2)^5



13/31-TET503.2258064516130.126238385278441.3373293784088(31√2)^13
(F+1/4)Meantoneperfect4th

503.4215715337910.126287494579981.33748060995282/(4√5)



8/19-TET505.2631578947370.126749471858521.3389041012245(19√2)~8




508.1988936324480.127485925622181.3411764705882114/85




509.3973942334920.127786579481131.342105263157951/38



3/7-TET514.2857142857140.129012855284561.3459001926324(7√2)^3
F+1acute fourth3Q-1T
519.5512887313270.130333768495011.350000000000027/20Harry Partch's 43tone scale

Das Tonwort;sa
23/53-TET520.7547169811320.130635658495691.3509387482477(53√2)^23
EisPythagoras増3rd11Q
521.5050095192620.130823875628611.3515243530273177147/131072



18/41-TET526.8292682926830.132159510291501.3556872458939(41√2)^18



4/9-TET533.3333333333330.133791109183991.3607900001744(9√2)^4




536.9507723654660.134698573897461.363636363636415/11
Geses+32重減5th-1Q-3T
539.1038575401080.135238693248111.3653333333333512/375



14/31-TET541.9354838709680.135949030299861.3675683155264(31√2)^14

Das Tonwort;se
24/53-TET543.3962264150940.136315469734631.3687226991475(53√2)^24
Fis-3
-6Q+3T
547.2111364021800.137272471682031.37174211248291000/729

550cent
11/24-TET; 550/1200-TET550.0000000000000.137972081345991.3739536474581(24√2)^11
Kmajor fourth,
harmonic augmented fourth, 11th overtone,
第11倍音, アルプホルン・ファ


551.3179423647570.138302698166281.375000000000011/8Harry Partch's 43tone scale



19/41-TET556.0975609756100.139501705307701.3788013669819(41√2)^19

Das Tonwort;po
25/53-TET566.0377358490570.141995280973581.3867407605205(53√2)^25



9/19-TET568.4210526315790.142593155840831.3886511426147(19√2)~9
Fis-2
-2Q+2T
568.7174259988950.142667503568731.388888888888925/18
(Fis-3/2)Meantone増4th

579.4705707972520.145365019512091.3975424859374(4√15625)/8{(4√125)/2}÷{4(4√5)}/5}



15/31-TET580.6451612903230.145659675321281.3984909984233(31√2)^15

lesser septimal tritone,
第7次5th(E-1~i),Subminor fifth


582.5121926042900.146128035678241.40000000000007/5Harry Partch's 43tone scale



20/41-TET585.3658536585370.146843900323891.4023095779274(41√2)^20




586.8456968671450.147215131319451.403508771929880/57
Fes,鳧鐘Pythagoras減5th-6Q
588.2699948076760.147572428321841.40466392318241024/729

Das Tonwort;pu
26/53-TET588.6792452830190.147675092212521.4049960142305(53√2)^26
Fis-1純正律増4th,3全音,トライトーン2Q+1T
590.2237155956100.148062535455441.406250000000045/32




591.6480135361400.148419832457821.407407407407438/27

ガナッシの減5th

596.9995913649800.149762320333331.411764705882424/17
Fis,Ges 12-TET Tritone, Augmented fourth(aug4th), Diminished fifth(dim5th)
十二等分平均律 三全音(増四度, 減五度), 600cent

1/2-TET;
5/10-TET;
6/12-TET;
12/24-TET;
600/1200-TET
600.000000000000 0.15051499783199 1.4142135623731 (12√2)^6




603.0004086350200.151267675330651.416666666666717/12




608.3519864638600.152610163206161.421052631579027/19
Ges+1純正律減5th-2Q-1T
609.7762844043900.152967460208541.422222222222264/45

Das Tonwort;pa
27/53-TET611.3207547169810.153354903451461.4234915827113(53√2)^27
FisPythagoras増4th(Pythagoras3全音)6Q
611.7300051923240.153457567342141.4238281250000729/512

マルカムの減5th

613.1543031328550.153814864344531.425000000000057/40



21/41-TET614.6341463414630.154186095340091.4262185978619(41√2)^21

Euler's tritone, 10/7増4th

617.4878073957100.154901959985741.428571428571410/7Harry Partch's 43tone scale



16/31-TET619.3548387096770.155370320342701.4301128875731(31√2)^16
(Ges+5/2)Meantone減5th

620.5294292027480.155664976151901.431083505599964/√125

23th overtone,
第23倍音


628.2743472684160.157607853361671.437500000000023/16
Ges+2
2Q-2T
631.2825740011050.158362492095251.440000000000036/25



10/19-TET631.5789473684210.158436839823151.4402465375388(19√2)~10

Das Tonwort;pe
28/53-TET633.9622641509430.159034714690411.4422306295008(53√2)^28

14/9減5th

636.6176600385360.159700842867511.444444444444413/9



22/41-TET643.9024390243900.161528290356281.4505352604762(41√2)^22

minor fifth, harmonic diminished fifth

648.6820576352430.162727297497701.454545454545516/11Harry Partch's 43tone scale

650cent
13/24-TET; 650/1200-TET650.0000000000000.163057914317991.4556531828422(24√2)^13
Ges+3
6Q-3T
652.7888635978200.163757523981961.4580000000000729/500

Das Tonwort;lo
29/53-TET656.6037735849060.164714525929351.4612163597825(53√2)^29



17/31-TET658.0645161290320.165080965364121.4624497930330(31√2)^17
Fisis-32重増4th1Q+3T
660.8961424598920.165791302415871.4648437500000375/256



5/9-TET666.6666666666670.167238886479991.4697344922756(9√2)^5



23/41-TET673.1707317073170.168870485372481.4752665159738(41√2)^23
AsesPythagoras減6th(ウルフの5th)-11Q
678.4949904807380.170206120035381.4798105528177262144/177147

Das Tonwort;lu
30/53-TET679.2452830188680.170394337168291.4804520209330(53√2)^30
G-1narrow fifth,
狭い五度
-3Q+1T
680.4487112686730.170696227168981.481481481481540/27Harry Partch's 43tone scale



4/7-TET685.7142857142860.172017140379421.4859942891370(7√2)^4




690.6026057665080.173243416182861.490196078431476/51




691.8011063675520.173544070041801.491228070175485/57

マールプルクの5th

694.1349974038380.174129546048911.4932397628384




11/19-TET694.7368421052630.174280523805461.4937589616545(19√2)~11

サリナスの5th

694.7862376664830.174292915093451.4938015821857(3√2)(3√5)/(3√3)
(G-1/4)Meantone5th

696.5784284662090.174742501084011.49534878122124√5Pythagoras 5th-(Syntonic comma/4)



18/31-TET696.7741935483870.174791610385541.4955178823482(31√2)^18

Neidhardt 5th

698.0449991346130.175110402552301.4966160644125(6√8192)/3

(12tET5th Approximation
近似値)


699.9570386712550.175590053596821.4982698961938433/289
G,Fisis,Ases 12-TET Perfect fifth(Per5th), Diminished sixth(dim6th),
十二等分平均律 完全五度(減六度), 700cent

7/12-TET;
14=24-TET;
700/1200-TET
700.000000000000 0.17560083080399 1.4983070768767 (12√2)^7

Das Tonwort;la
31/53-TET701.8867924528300.176074148407231.4999409030781(53√2)^31
G,黄鐘 Pythagorean interval perfect fifth, 3rd overtone, Hemiola,
ピタゴラス音律 完全五度, 第3倍音, ヘミオリア
1Q
701.955000865388 0.17609125905568 1.5000000000000 3/2 Harry Partch's 43tone scale



24/41-TET702.4390243902440.176212680388671.5004194330574(41√2)^24




708.7308766347580.177791043933581.5058823529412128/85




714.7316939047980.179296398930891.511111111111168/45



3/5-TET; 6/10-TET; 720/1200-TET720.0000000000000.180617997398391.5157165665104(5√2)^3
Ases+2(小)減6th-3Q-2T
721.5075696741680.180996183808791.51703703703701024/675
G+1広い5th5Q-1T
723.4612904621020.181486290942391.5187500000000243/160

Das Tonwort;le
32/53-TET724.5283018867930.181753959646181.5196863396552(53√2)^32
wide fifth


729.2190926654880.182930683585991.523809523809532/21Harry Partch's 43tone scale



25/41-TET731.7073170731710.183554875404871.5260012009493(41√2)^25



19/31-TET735.4838709677420.184502255406961.5293336886355(31√2)^19
(G+3/2)中全音率(大)5th

737.6372868717040.185042457723821.5312371519705128/(4√48828125
Ases+3(大)減6th1Q-3T
743.0138592708830.186391215695491.5360000000000192/125

Das Tonwort;li
33/53-TET747.1698113207550.187433770885121.5396917079834(53√2)^33

750cent
15/24-TET; 750/1200-TET750.0000000000000.188143747289991.5422108254079(24√2)^15
Gis-3
-4Q+3T
751.1211381329550.188424994129411.5432098765432125/81



12/19-TET757.8947368421050.190124207787781.5492596422667(19√2)~12



26/41-TET760.9756097560980.190897070421061.5520191314461(41√2)^26

subminor sixth,
septimal minor sixth
アルキュタスの減6th


764.9159047383500.191885526238911.555555555555614/9Harry Partch's 43tone scale

Das Tonwort;du
34/53-TET769.8113207547170.193113582124061.5599604298416(53√2)^34
Gis-2純正律(小)増5th,Meantone増5th, 25th overtone,
第25倍音
2T
772.6274277296700.193820026016111.562500000000025/16



20/31-TET774.1935483870970.194212900428381.5639141188489(31√2)^20




779.4033034990400.195519810894011.568627450980480/51

11/7(Ptolemaios 6th)

782.4920358956320.196294645143971.571428571428611/7Harry Partch's 43tone scale




785.4041207690800.197025165891321.574074074074185/54



27/41-TET790.2439024390250.198239265437261.5784806610089(41√2)^27




790.7556985979200.198367653766831.578947368421130/19
A,鸞鐘Pythagorasmin.6th-4Q
792.1799965384500.198724950769221.5802469135803128/81

Das Tonwort;da
35/53-TET792.4528301886790.198793393363011.5804959720532(53√2)^35
Gis-1純正律(大)増5th(F~Cis-1)4Q+1T
794.1337173263850.199215057902821.5820312500000405/256




795.5580152669150.199572354905201.583333333333319/12

(12tETmin.6th Approximation
近似値)


799.8915195297700.200659450546421.5873015873016100/63
Gis,As 12-TET Minor sixth(min6th), Augmented fifth(aug5th),
十二等分平均律 短六度(増五度), 800cent

6/9-TET;
8/12-TET;
16/24-TET;
800/1200-TET
800.000000000000 0.20068666377599 1.5874010519682 (12√2)^8




800.9095930957550.200914842780711.588235294117727/17




806.9104103657950.202420197778031.593750000000051/32



21/31-TET812.9032258064520.203923545449791.5992764622332(31√2)^21
As+1minor sixth, Just min6th, Meantone min6th, 第1/5倍音

813.6862861351650.204119982655931.60000000000008/5Harry Partch's 43tone scale

Das Tonwort;de
36/53-TET815.0943396226420.204473204601951.6013018470796(53√2)^36
Gis,AsPythagoras増5th8Q
815.6400069230990.204610089789531.60180664062506561/4096



28/41-TET819.5121951219510.205581460453451.6053933528883(41√2)^28



13/19-TET821.0526315789470.205967891770091.6068224531338(19√2)~13
As+2
4Q-2T
835.1925757318800.209515014542631.620000000000081/50

Das Tonwort;di
37/53-TET837.7358490566040.210153015840891.6223816136206(53√2)^37



7/10-TET840.0000000000000.210720996964791.6245047927125(10√2)^7

Thirteenth harmonic,
13th overtone,
第13倍音


840.5276617693110.210853365314891.625000000000013/8



29/41-TET848.7804878048780.212923655469651.6327648992866(41√2)^29

850cent
17/24-TET; 850/1200-TET850.0000000000000.213229580261991.6339154532411(24√2)^17



22/31-TET851.6129032258060.213634190471211.6354383989676(31√2)^22

undecimal neutral sixth,
ザルザルの中立6th


852.5920593660180.213879819945081.636363636363618/11Harry Partch's 43tone scale



5/7-TET857.1428571428570.215021425474271.6406707120153(7√2)^5

Das Tonwort;fu
38/53-TET860.3773584905660.215832827079841.6437388772233(53√2)^38
A-2
-5Q+2T
862.8524234027330.216453717729651.6460905349794400/243
Gisis-32重増5th3Q+3T
864.8061441906670.216943824863251.64794921875003375/2048



30/41-TET878.0487804878050.220265850485841.6606031235559(41√2)^30
HesesPythagoras減7th-9T
882.4049922115130.221358642482761.664786871919932768/19683

Das Tonwort;fa
39/53-TET883.0188679245280.221512638318781.6653772908987(53√2)^39



14/19-TET884.2105263157890.221811575752411.6665240127971(19√2)~14
A-1major sixth,
純正律長6th
-1Q+1T
884.3587129994480.221848749616361.66666666666675/3Harry Partch's 43tone scale
(A-3/4)Meantone長6th

889.7352853986260.223197507588031.6718507624411(4√125)/2



23/31-TET890.3225806451610.223344835492631.6724180090057(31√2)^23




894.5126074972830.224395938630241.676470588235357/34
A,Gisis,Heses 12-TET Major sixth(Maj6th), Diminished seventh(dim7th),
十二等分平均律 長六度(減七度), 900cent

9/12-TET;
18/24-TET;
900/1200-TET
900.000000000000 0.22577249674799 1.6817928305074 (12√2)^9

(12tET長6th Approximation
近似値)


900.0260963899830.225779043244791.681818181818237/22




902.4869838676970.226396377367081.684210526315832/19
Heses+1
-5Q-1T
903.9112818082280.226753674369461.68559670781892048/1215

Das Tonwort;fe
40/53-TET905.6603773584910.227192449557721.6873005557465(53√2)^40
A,盤渉Pythagorean major sixth, 27th overtone,
第27倍音
3Q
905.8650025961620.227243781503061.687500000000027/16Harry Partch's 43tone scale




907.2893005366930.227601078505451.688888888888976/45



31/41-TET907.3170731707320.227608045502041.6889159824349(41√2)^31

ガナッシの長6th

912.6408783655330.228943566380961.6941176470588144/85

マルカムの長6th

918.6416956355730.230448921378271.700000000000017/10
Heses+2純正律減7th-1Q-2T
925.4175714049430.232148706256171.7066666666667128/75

Das Tonwort;fi
41/53-TET928.3018867924530.232872260796671.7095124215884(53√2)^41



24/31-TET929.0322580645160.233055480514051.7102337811147(31√2)^24

supermajor sixth, septimal major sixth

933.1290943962620.234083206033371.714285714285712/7Harry Partch's 43tone scale



7/9-TET933.3333333333330.234134441071991.7144879657062(9√2)^7



32/41-TET936.5853658536590.234950240518231.7177115683221(41√2)^32
Heses+3
3Q-3T
946.9238610016580.237543738142881.7280000000000216/125



15/19-TET947.3684210526320.237655259734721.7284437865632(19√2)~15

950cent
19/24-TET; 950/1200-TET950.0000000000000.238315413233991.7310731220123(24√2)^19

Das Tonwort;fo
42/53-TET950.9433962264150.238552072035611.7320166876091(53√2)^42
Ais-3
-2Q+3T
955.0311398637300.239577516576791.7361111111111125/72



4/5-TET; 8/10-TET; 960/1200-TET960.0000000000000.240823996531191.7411011265923(5√2)^4



33/41-TET965.8536585365860.242292435534421.7469981115899(41√2)^33



25/31-TET967.7419354838710.242766125535471.7489046221195(31√2)^25
.i Harmonic seventh, SubminorSeventh,
自然(和声的)七度, 7th overtone,
第7倍音

968.825906469125 0.24303804868629 1.7500000000000 7/4 Harry Partch's 43tone scale

Das Tonwort;ka
43/53-TET973.5849056603770.244231883274551.7548172030063(53√2)^43
B-1
-6Q+1T
974.5837086725100.244482441329891.75582990397811280/729

Ais-2

純正律増6th2Q+2T
976.5374294604450.244972548463491.7578125000000225/128




989.3141224998550.248177688338711.770833333333385/48



34/41-TET995.1219512195120.249634630550621.7767839829360(41√2)^34
B,神仙Pythagorean minor seventh, 純正律min.7th(D~C), 1/9 overtone-2Q
996.0899982692250.249877473216601.777777777777816/9Harry Partch's 43tone scale

Das Tonwort;ke
44/53-TET996.2264150943400.249911694513491.7779178676492(53√2)^44
Ais,B 12-TET Minor seventh(min7th), Augmented sixth(aug6th),
十二等分平均律 短七度(増六度), 1000cent

10/12-TET;
20/24-TET;
1000/1200-TET
1000.000000000000 0.25085832971998 1.7817974362807 (12√2)^10

(12tETmin.7th Approximation
近似値)


1000.0201567086600.250863386198251.781818181818298/55




1006.2438927670600.252424662230481.7882352941177152/85



26/31-TET1006.4516129032300.252476770556891.7884498663553(31√2)^26
(B+1/2)Meantonemin.7th

1006.8431430675800.252574989159951.78885438199984/√5




1007.4423933681000.252725316089431.789473684210534/19



16/19-TET1010.5263157894700.253498943717041.7926641922757(19√2)~16
B+1just minor seventh, 純正律min.7th(E-1~D)2Q-1T
1017.5962878659400.255272505103311.80000000000009/5Harry Partch's 43tone scale

Das Tonwort;ki
45/53-TET1018.8679245283000.255591505752441.8013226327455(53√2)^45
AisPythagoras増6th10Q
1019.5500086538700.255762612236911.802032470703159049/32768



35/41-TET1024.3902439024400.256976825566811.8070776957766(41√2)^35



6/7-TET1028.5714285714300.258025710569131.8114473285278(7√2)^6

29th overtone,
第29倍音


1029.5771941530900.258278015243031.812500000000029/16




1034.9957715000800.259637310505761.818181818181820/11Harry Partch's 43tone scale
Ceses'+32重減8th-2Q-3T
1037.1488566747200.260177429856411.82044444444442048/1125
B+2
6Q-2T
1039.1025774626500.260667536990011.8225000000000729/400

Das Tonwort;ko
46/53-TET1041.5094339622600.261271316991381.8250355015170(53√2)^46



27/31-TET1045.1612903225800.262187415578311.8288892853345(31√2)^27

undecimal neutral seventh,
Ptolemaios 7th, 21/4-tone


1049.3629414993700.263241434774581.833333333333311/6Harry Partch's 43tone scale

1050cent
21/24-TET; 1050/1200-TET1050.0000000000000.263401246205981.8340080864093(24√2)^21



36/41-TET1053.6585365853700.264319020583011.8378879086793(41√2)^36

Das Tonwort;na
47/53-TET1064.1509433962300.266951128230321.8490605298845(53√2)^47



8/9-TET1066.6666666666700.267582218367981.8517494245746(9√2)^8
H-2(小)長7th-3Q+2T
1066.7624251335100.267606240177031.851851851851950/27

13/7長7th

1071.7017553001900.268845312292581.857142857142913/7



17/19-TET1073.6842105263200.269342627699351.8592707100168(19√2)~17



9/10-TET1080.0000000000000.270926996097581.8660659830736(10√2)^9
(H-5/4)Meantone長7th

1082.8921423310400.271652514092061.8691859765265(4√3125)/4



37/41-TET1082.9268292682900.271661215599201.8692234278384(41√2)^37



28/31-TET1083.8709677419400.271898060599731.8702430976317(31√2)^28
Ces',上無Pythagoras減8th-7Q
1086.3149939422900.272511164930141.87288523090994096/2187

Das Tonwort;ne
48/53-TET1086.7924528301900.272630939469271.8734018271616(53√2)^48
H-1classic major seventh, 純正律(大)長7th, 15th overtone,
第15倍音
1Q+1T
1088.2687147302200.273001272063741.875000000000015/8Harry Partch's 43tone scale




1095.0445904995900.274701056941631.882352941176532/17

(12tET長7th Approximation
近似値)


1099.9007901748400.275919275080951.8876404494382168/89
H,Aisis,Ces' 12-TET Major seventh(Maj7th),
Diminished octave(dim8th),
十二等分平均律 長七度(減八度), 1100cent

11/12-TET;
22/24-TET;
1100/1200-TET
1100.000000000000 0.27594416269198 1.8877486253634 (12√2)^11

17/9長7th

1101.0454077696300.276206411938951.888888888888917/9

ガナッシの長7th

1106.3969855984700.277548899814461.894736842105336/19
Ces'+1純正律(小)減8th(Cis-1~C)-3Q-1T
1107.8212835390000.277906196816841.8962962962963256/135

Das Tonwort;ni
49/53-TET1109.4339622641500.278310750708211.8980635567575(53√2)^49
HPythagoras長7th5Q
1109.7750043269400.278396303950441.8984375000000243/128

マルカムの長7th

1111.1993022674700.278753600952831.900000000000019/10



38/41-TET1112.1951219512200.279003410615401.9010932095910(41√2)^38




1115.5328065303200.279840696594041.904761904761940/21Harry Partch's 43tone scale



29/31-TET1122.5806451612900.281608705621141.9125319789925(31√2)^29
Ces'+2純正律(大)減8th(Cis-2~C)1Q-2T
1129.3275731357200.283301228703551.920000000000048/25

Das Tonwort;no
50/53-TET1132.0754716981100.283990561947151.9230499368891(53√2)^50



18/19-TET1136.8421052631600.285186311681671.9283519958850(19√2)~18



39/41-TET1141.4634146341500.286345605631591.9335063629781(41√2)^39

31th overtone,
第31倍音


1145.0355724642500.287241711178351.937500000000031/16




1146.7270567698600.287666034106001.939393939393964/33Harry Partch's 43tone scale

semidiminished octave, 1150cent
23/24-TET; 1150/1200-TET1150.0000000000000.288487079177981.9430638823072(24√2)^23
Ces'+3
5Q-3T
1150.8338627324300.288696260590261.9440000000000243/125

Das Tonwort;ba
51/53-TET1154.7169811320800.289670373186101.9483652413023(53√2)^51
His-3
3T
1158.9411415945000.290730039024171.9531250000000125/64



30/31-TET1161.2903225806500.291319350642561.9557770726709(31√2)^30



40/41-TET1170.7317073170700.293687800647791.9664721523470(41√2)^40
Deses' Pythagoras減9th-12Q
1176.5399896153500.295144856643681.97308073709031048576/531441

Das Tonwort;be
52/53-TET1177.3584905660400.295350184425041.9740138000036(53√2)^52
C'-1
-4Q+1T
1178.4937104032900.295634963777281.9753086419753160/81Harry Partch's 43tone scale
His-2
4Q+2T
1180.4474311912200.296125070910881.97753906250002025/1024
C',壱越 Octave, Perfect Eighth(Per8th),
Augmented seventh(aug7th),
2nd overtone
オクターヴ, 完全八度, 増七度, 第2倍音, 1200cent
0Q+0T
1200.000000000000 0.30102999566398 2.0000000000000 2/1 Harry Partch's 43tone scale

参考文献:
音楽大事典;音律表(平凡社)
音楽理論を考える/東川清一(音楽の友社)
ニューグローヴ世界音楽大事典(Macmillan)
ゼロビートの再発見―「平均律」への疑問と「古典音律」をめぐって/平島達司(ショパン/東京音楽社)
ゼロ・ビートの再発見 技法篇―「古典音律」の解釈と実践のテクニック/平島達司(ショパン/東京音楽社)
響きの考古学/藤枝守(音楽の友社)
古楽の音律/東川清一(春秋社)

明庵
DGBSTUDIO
wikipedia en; 音律
wikipedia en; ピタゴラス音律
wikipedia en; 純正律
wikipedia en; 中全音律
wikipedia en; 平均律

→参考文献