47edo: Difference between revisions
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| Line 87: | Line 87: | ||
| style="text-align:right;" | 178.7234 | | style="text-align:right;" | 178.7234 | ||
|189.4468 | |189.4468 | ||
|228.766 (E4.C416 | |228.766 (E4.C416<sub>16</sub>) | ||
| style="text-align:center;" | major 2nd | | style="text-align:center;" | major 2nd | ||
| style="text-align:center;" | M2 | | style="text-align:center;" | M2 | ||
| Line 95: | Line 95: | ||
| style="text-align:right;" | 204.2553 | | style="text-align:right;" | 204.2553 | ||
|216.5106 | |216.5106 | ||
| | |261.4468 (105.7262<sub>16</sub>) | ||
| style="text-align:center;" | aug 2nd | | style="text-align:center;" | aug 2nd | ||
| style="text-align:center;" | A2 | | style="text-align:center;" | A2 | ||
| Line 103: | Line 103: | ||
| style="text-align:right;" | 229.7872 | | style="text-align:right;" | 229.7872 | ||
|243.5745 | |243.5745 | ||
| | |294.1277 (126.20AE<sub>16</sub>) | ||
| style="text-align:center;" | double-aug 2nd | | style="text-align:center;" | double-aug 2nd | ||
| style="text-align:center;" | AA2 | | style="text-align:center;" | AA2 | ||
| Line 111: | Line 111: | ||
| style="text-align:right;" | 255.31915 | | style="text-align:right;" | 255.31915 | ||
|270.6383 | |270.6383 | ||
| | |326.8085 (146.CEFB<sub>16</sub>) | ||
| style="text-align:center;" | triple-aug 2nd, triple-dim 3rd | | style="text-align:center;" | triple-aug 2nd, triple-dim 3rd | ||
| style="text-align:center;" | A<span style="font-size: 90%; vertical-align: super;">3</span>2, d<span style="font-size: 90%; vertical-align: super;">3</span>3 | | style="text-align:center;" | A<span style="font-size: 90%; vertical-align: super;">3</span>2, d<span style="font-size: 90%; vertical-align: super;">3</span>3 | ||
| Line 119: | Line 119: | ||
| style="text-align:right;" | 280.8511 | | style="text-align:right;" | 280.8511 | ||
|297.7021 | |297.7021 | ||
| | |359.4894 (167.7D47<sub>16</sub>) | ||
| style="text-align:center;" | double-dim 3rd | | style="text-align:center;" | double-dim 3rd | ||
| style="text-align:center;" | dd3 | | style="text-align:center;" | dd3 | ||
| Line 127: | Line 127: | ||
| style="text-align:right;" | 306.383 | | style="text-align:right;" | 306.383 | ||
|324.766 | |324.766 | ||
| | |392.1702 (188.2B93<sub>16</sub>) | ||
| style="text-align:center;" | dim 3rd | | style="text-align:center;" | dim 3rd | ||
| style="text-align:center;" | d3 | | style="text-align:center;" | d3 | ||
| Line 135: | Line 135: | ||
| style="text-align:right;" | 331.9149 | | style="text-align:right;" | 331.9149 | ||
|351.8298 | |351.8298 | ||
| | |424.8511 (1A8.D9DF<sub>16</sub>) | ||
| style="text-align:center;" | minor 3rd | | style="text-align:center;" | minor 3rd | ||
| style="text-align:center;" | m3 | | style="text-align:center;" | m3 | ||
| Line 143: | Line 143: | ||
| style="text-align:right;" | 357.4468 | | style="text-align:right;" | 357.4468 | ||
|378.8936 | |378.8936 | ||
| | |457.5319 (1C9.882C<sub>16</sub>) | ||
| style="text-align:center;" | major 3rd | | style="text-align:center;" | major 3rd | ||
| style="text-align:center;" | M3 | | style="text-align:center;" | M3 | ||
| Line 151: | Line 151: | ||
| style="text-align:right;" | 382.9787 | | style="text-align:right;" | 382.9787 | ||
|405.95745 | |405.95745 | ||
| | |490.2128 (1EA.3678<sub>16</sub>) | ||
| style="text-align:center;" | aug 3rd | | style="text-align:center;" | aug 3rd | ||
| style="text-align:center;" | A3 | | style="text-align:center;" | A3 | ||
| Line 159: | Line 159: | ||
| style="text-align:right;" | 408.5106 | | style="text-align:right;" | 408.5106 | ||
|433.0213 | |433.0213 | ||
| | |522.8936 (20A.E4C4<sub>16</sub>) | ||
| style="text-align:center;" | double-aug 3rd | | style="text-align:center;" | double-aug 3rd | ||
| style="text-align:center;" | AA3 | | style="text-align:center;" | AA3 | ||
| Line 167: | Line 167: | ||
| style="text-align:right;" | 434.04255 | | style="text-align:right;" | 434.04255 | ||
|460.0851 | |460.0851 | ||
| | |555.5745 (22B.931<sub>16</sub>) | ||
| style="text-align:center;" | triple-aug 3rd, triple-dim 4th | | style="text-align:center;" | triple-aug 3rd, triple-dim 4th | ||
| style="text-align:center;" | A<span style="font-size: 90%; vertical-align: super;">3</span>3, d<span style="font-size: 90%; vertical-align: super;">3</span>4 | | style="text-align:center;" | A<span style="font-size: 90%; vertical-align: super;">3</span>3, d<span style="font-size: 90%; vertical-align: super;">3</span>4 | ||
| Line 175: | Line 175: | ||
| style="text-align:right;" | 459.5745 | | style="text-align:right;" | 459.5745 | ||
|487.1489 | |487.1489 | ||
| | |588.2553 (24C.415D<sub>16</sub>) | ||
| style="text-align:center;" | double-dim 4th | | style="text-align:center;" | double-dim 4th | ||
| style="text-align:center;" | dd4 | | style="text-align:center;" | dd4 | ||
| Line 183: | Line 183: | ||
| style="text-align:right;" | 485.1064 | | style="text-align:right;" | 485.1064 | ||
|514.2128 | |514.2128 | ||
| | |620.9362 (26C.EFA9<sub>16</sub>) | ||
| style="text-align:center;" | dim 4th | | style="text-align:center;" | dim 4th | ||
| style="text-align:center;" | d4 | | style="text-align:center;" | d4 | ||
| Line 191: | Line 191: | ||
| style="text-align:right;" | 510.6383 | | style="text-align:right;" | 510.6383 | ||
|541.2766 | |541.2766 | ||
| | |653.617 (28D.9DF5<sub>16</sub>) | ||
| style="text-align:center;" | perfect 4th | | style="text-align:center;" | perfect 4th | ||
| style="text-align:center;" | P4 | | style="text-align:center;" | P4 | ||
| Line 199: | Line 199: | ||
| style="text-align:right;" | 536.1702 | | style="text-align:right;" | 536.1702 | ||
|568.3404 | |568.3404 | ||
| | |686.2979 (2AE.4C41<sub>16</sub>) | ||
| style="text-align:center;" | aug 4th | | style="text-align:center;" | aug 4th | ||
| style="text-align:center;" | A4 | | style="text-align:center;" | A4 | ||
| Line 207: | Line 207: | ||
| style="text-align:right;" | 561.7021 | | style="text-align:right;" | 561.7021 | ||
|595.4043 | |595.4043 | ||
| | |718.9787 (2CE.FA8E<sub>16</sub>) | ||
| style="text-align:center;" | double-aug 4th | | style="text-align:center;" | double-aug 4th | ||
| style="text-align:center;" | AA4 | | style="text-align:center;" | AA4 | ||
| Line 215: | Line 215: | ||
| style="text-align:right;" | 587.2340 | | style="text-align:right;" | 587.2340 | ||
|622.4681 | |622.4681 | ||
| | |751.6595 (2EF.A8DA<sub>16</sub>) | ||
| style="text-align:center;" | triple-aug 4th | | style="text-align:center;" | triple-aug 4th | ||
| style="text-align:center;" | A<span style="font-size: 90%; vertical-align: super;">3</span>4 | | style="text-align:center;" | A<span style="font-size: 90%; vertical-align: super;">3</span>4 | ||
| Line 223: | Line 223: | ||
| style="text-align:right;" | 612.7660 | | style="text-align:right;" | 612.7660 | ||
|649.5319 | |649.5319 | ||
| | |784.3404 (310.5726<sub>16</sub>) | ||
| style="text-align:center;" | triple-dim 5th | | style="text-align:center;" | triple-dim 5th | ||
| style="text-align:center;" | d<span style="font-size: 90%; vertical-align: super;">3</span>5 | | style="text-align:center;" | d<span style="font-size: 90%; vertical-align: super;">3</span>5 | ||
| Line 231: | Line 231: | ||
| style="text-align:right;" | 638.2979 | | style="text-align:right;" | 638.2979 | ||
|676.5957 | |676.5957 | ||
| | |817.0213 (331.0572<sub>16</sub>) | ||
| style="text-align:center;" | double-dim 5th | | style="text-align:center;" | double-dim 5th | ||
| style="text-align:center;" | dd5 | | style="text-align:center;" | dd5 | ||
| Line 239: | Line 239: | ||
| style="text-align:right;" | 663.8298 | | style="text-align:right;" | 663.8298 | ||
|703.6596 | |703.6596 | ||
| | |849.7021 (351.B3BF<sub>16</sub>) | ||
| style="text-align:center;" | dim 5th | | style="text-align:center;" | dim 5th | ||
| style="text-align:center;" | d5 | | style="text-align:center;" | d5 | ||
| Line 247: | Line 247: | ||
| style="text-align:right;" | 689.3617 | | style="text-align:right;" | 689.3617 | ||
|730.7234 | |730.7234 | ||
| | |882.383 (372.620B<sub>16</sub>) | ||
| style="text-align:center;" | perfect 5th | | style="text-align:center;" | perfect 5th | ||
| style="text-align:center;" | P5 | | style="text-align:center;" | P5 | ||
| Line 255: | Line 255: | ||
| style="text-align:right;" | 714.8936 | | style="text-align:right;" | 714.8936 | ||
|757.7872 | |757.7872 | ||
| | |915.0638 (393.1057<sub>16</sub>) | ||
| style="text-align:center;" | aug 5th | | style="text-align:center;" | aug 5th | ||
| style="text-align:center;" | A5 | | style="text-align:center;" | A5 | ||
| Line 263: | Line 263: | ||
| style="text-align:right;" | 740.4255 | | style="text-align:right;" | 740.4255 | ||
|784.8511 | |784.8511 | ||
| | |947.7447 (3B3.BEA3<sub>16</sub>) | ||
| style="text-align:center;" | double-aug 5th | | style="text-align:center;" | double-aug 5th | ||
| style="text-align:center;" | AA5 | | style="text-align:center;" | AA5 | ||
| Line 271: | Line 271: | ||
| style="text-align:right;" | 765.95745 | | style="text-align:right;" | 765.95745 | ||
|811.9149 | |811.9149 | ||
| | |980.4255 (3D4.6CF<sub>16</sub>) | ||
| style="text-align:center;" | triple-aug 5th, triple-dim 6th | | style="text-align:center;" | triple-aug 5th, triple-dim 6th | ||
| style="text-align:center;" | A<span style="font-size: 90%; vertical-align: super;">3</span>5, d<span style="font-size: 90%; vertical-align: super;">3</span>6 | | style="text-align:center;" | A<span style="font-size: 90%; vertical-align: super;">3</span>5, d<span style="font-size: 90%; vertical-align: super;">3</span>6 | ||
| Line 279: | Line 279: | ||
| style="text-align:right;" | 791.4894 | | style="text-align:right;" | 791.4894 | ||
|838.9787 | |838.9787 | ||
| | |1013.1064 (3F5.1B3C<sub>16</sub>) | ||
| style="text-align:center;" | double-dim 6th | | style="text-align:center;" | double-dim 6th | ||
| style="text-align:center;" | dd6 | | style="text-align:center;" | dd6 | ||
| Line 287: | Line 287: | ||
| style="text-align:right;" | 817.0213 | | style="text-align:right;" | 817.0213 | ||
|866.04255 | |866.04255 | ||
| | |1045.7872 (415.C988<sub>16</sub>) | ||
| style="text-align:center;" | dim 6th | | style="text-align:center;" | dim 6th | ||
| style="text-align:center;" | d6 | | style="text-align:center;" | d6 | ||
| Line 295: | Line 295: | ||
| style="text-align:right;" | 842.5532 | | style="text-align:right;" | 842.5532 | ||
|893.1064 | |893.1064 | ||
| | |1078.4681 (436.77D4<sub>16</sub>) | ||
| style="text-align:center;" | minor 6th | | style="text-align:center;" | minor 6th | ||
| style="text-align:center;" | m6 | | style="text-align:center;" | m6 | ||
| Line 303: | Line 303: | ||
| style="text-align:right;" | 868.0851 | | style="text-align:right;" | 868.0851 | ||
|920.1702 | |920.1702 | ||
| | |1111.1489 (457.2621<sub>16</sub>) | ||
| style="text-align:center;" | major 6th | | style="text-align:center;" | major 6th | ||
| style="text-align:center;" | M6 | | style="text-align:center;" | M6 | ||
| Line 311: | Line 311: | ||
| style="text-align:right;" | 893.617 | | style="text-align:right;" | 893.617 | ||
|947.234 | |947.234 | ||
| | |1143.8298 (477.D46D<sub>16</sub>) | ||
| style="text-align:center;" | aug 6th | | style="text-align:center;" | aug 6th | ||
| style="text-align:center;" | A6 | | style="text-align:center;" | A6 | ||
| Line 319: | Line 319: | ||
| style="text-align:right;" | 919.1489 | | style="text-align:right;" | 919.1489 | ||
|974.2979 | |974.2979 | ||
| | |1176.5106 (498.82B9<sub>16</sub>) | ||
| style="text-align:center;" | double-aug 6th | | style="text-align:center;" | double-aug 6th | ||
| style="text-align:center;" | AA6 | | style="text-align:center;" | AA6 | ||
| Line 327: | Line 327: | ||
| style="text-align:right;" | 944.68085 | | style="text-align:right;" | 944.68085 | ||
|1001.3617 | |1001.3617 | ||
| | |1209.1915 (4B9.3105<sub>16</sub>) | ||
| style="text-align:center;" | triple-aug 6th, triple-dim 7th | | style="text-align:center;" | triple-aug 6th, triple-dim 7th | ||
| style="text-align:center;" | A<span style="font-size: 90%; vertical-align: super;">3</span>6, d<span style="font-size: 90%; vertical-align: super;">3</span>7 | | style="text-align:center;" | A<span style="font-size: 90%; vertical-align: super;">3</span>6, d<span style="font-size: 90%; vertical-align: super;">3</span>7 | ||
| Line 335: | Line 335: | ||
| style="text-align:right;" | 970.2128 | | style="text-align:right;" | 970.2128 | ||
|1028.4255 | |1028.4255 | ||
| | |1241.8723 (4D9.DF52<sub>16</sub>) | ||
| style="text-align:center;" | double-dim 7th | | style="text-align:center;" | double-dim 7th | ||
| style="text-align:center;" | dd7 | | style="text-align:center;" | dd7 | ||
| Line 343: | Line 343: | ||
| style="text-align:right;" | 995.7447 | | style="text-align:right;" | 995.7447 | ||
|1055.4894 | |1055.4894 | ||
| | |1274.5532 (4FA.8D9E<sub>16</sub>) | ||
| style="text-align:center;" | dim 7th | | style="text-align:center;" | dim 7th | ||
| style="text-align:center;" | d7 | | style="text-align:center;" | d7 | ||
| Line 351: | Line 351: | ||
| style="text-align:right;" | 1021.2766 | | style="text-align:right;" | 1021.2766 | ||
|1082.5532 | |1082.5532 | ||
| | |1307.234 (51B.3BEA<sub>16</sub>) | ||
| style="text-align:center;" | minor 7th | | style="text-align:center;" | minor 7th | ||
| style="text-align:center;" | m7 | | style="text-align:center;" | m7 | ||
| Line 359: | Line 359: | ||
| style="text-align:right;" | 1046.8085 | | style="text-align:right;" | 1046.8085 | ||
|1109.617 | |1109.617 | ||
| | |1339.9149 (53B.EA36<sub>16</sub>) | ||
| style="text-align:center;" | major 7th | | style="text-align:center;" | major 7th | ||
| style="text-align:center;" | M7 | | style="text-align:center;" | M7 | ||
| Line 367: | Line 367: | ||
| style="text-align:right;" | 1072.3404 | | style="text-align:right;" | 1072.3404 | ||
|1136.68085 | |1136.68085 | ||
| | |1372.5957 (55C.9883<sub>16</sub>) | ||
| style="text-align:center;" | aug 7th | | style="text-align:center;" | aug 7th | ||
| style="text-align:center;" | A7 | | style="text-align:center;" | A7 | ||
| Line 375: | Line 375: | ||
| style="text-align:right;" | 1097.8723 | | style="text-align:right;" | 1097.8723 | ||
|1163.7447 | |1163.7447 | ||
| | |1405.2766 (57D.46CF<sub>16</sub>) | ||
| style="text-align:center;" | double-aug 7th | | style="text-align:center;" | double-aug 7th | ||
| style="text-align:center;" | AA7 | | style="text-align:center;" | AA7 | ||
| Line 383: | Line 383: | ||
| style="text-align:right;" | 1123.4043 | | style="text-align:right;" | 1123.4043 | ||
|1190.8085 | |1190.8085 | ||
| | |1437.95745 (59D.F51B<sub>16</sub>) | ||
| style="text-align:center;" | triple-aug 7th, triple-dim 8ve | | style="text-align:center;" | triple-aug 7th, triple-dim 8ve | ||
| style="text-align:center;" | A<span style="font-size: 90%; vertical-align: super;">3</span>7, d<span style="font-size: 90%; vertical-align: super;">3</span>8 | | style="text-align:center;" | A<span style="font-size: 90%; vertical-align: super;">3</span>7, d<span style="font-size: 90%; vertical-align: super;">3</span>8 | ||
| Line 391: | Line 391: | ||
| style="text-align:right;" | 1148.9362 | | style="text-align:right;" | 1148.9362 | ||
|1217.8723 | |1217.8723 | ||
| | |1470.6383 (5BE.A3678<sub>16</sub>) | ||
| style="text-align:center;" | double-dim 8ve | | style="text-align:center;" | double-dim 8ve | ||
| style="text-align:center;" | dd8 | | style="text-align:center;" | dd8 | ||
| Line 399: | Line 399: | ||
| style="text-align:right;" | 1174.4681 | | style="text-align:right;" | 1174.4681 | ||
|1244.9362 | |1244.9362 | ||
| | |1503.31915 (5DF.51B4<sub>16</sub>) | ||
| style="text-align:center;" | dim 8ve | | style="text-align:center;" | dim 8ve | ||
| style="text-align:center;" | d8 | | style="text-align:center;" | d8 | ||
Revision as of 20:56, 3 April 2019
47 tone Equal Temperament
47-EDO divides the octave into 47 equal parts of 25.5319 cents each. It has a fifth which is 12.5933 cents flat, unless you use the alternative fifth which is 12.9386 cents sharp, similar to 35edo. It has therefore not aroused much interest, but its best approximation to 9/8 is actually quite good, one-third of a cent sharp. It does a good job of approximating the 2.9.5.7.33.13.17.57.69 23-limit 2*47 subgroup of the 23-limit, on which it tempers out the same commas as 94edo. It provides a good tuning for baldy and silver temperaments and relatives.
47edo is the 15th prime edo, following 43edo and preceding 53edo.
47edo is a regular edo because its 5th falls between 4\7 = 686¢ and 3\5 = 720¢. (Its alternate 5th does as well.) 47edo is one of the most difficult regular edos to notate, because no other regular edo's 5th is as flat (see 42edo for the opposite extreme).
A notation using the best 5th has major and minor 2nds of 7 and 6 edosteps respectively, with the naturals creating a roughly 7edo-ish scale:
D * * * * * * E * * * * * F * * * * * * G * * * * * * A * * * * * * B * * * * * C * * * * * * D
D# is next to D. This notation requires triple, quadruple and in some keys, quintuple or more sharps and flats. For example, a 0-15-27-38 chord (an approximate 4:5:6:7) on the note three edosteps above D would be spelled either as D#3 - F#5 - A#3 - C# or as Eb4 - Gbb - Ab4 - Db6. This is an aug-three double-dim-seven chord, written D#3(A3)dd7 or Eb4(A3)dd7. It could also be called a sharp-three triple-flat-seven chord, written D#3(#3)b37 or Eb4(#3)b37.
Using the 2nd best 5th is even more awkward. The major 2nd is 9 edosteps and the minor is only one. The naturals create a roughly 5edo-ish scale, with two of the notes inflected by a comma-sized edostep:
D * * * * * * * * E F * * * * * * * * G * * * * * * * * A * * * * * * * * B C * * * * * * * * D
D# is next to E. This notation requires quadruple, quintuple, and even sextuple ups and downs, as well as single sharps and flats.
Intervals of 47edo
| Degree | Size (Cents) | pions | 7mus | relative notation | absolute notation | |
|---|---|---|---|---|---|---|
| 0 | 0.0000 | perfect unison | P1 | D | ||
| 1 | 25.5319 | 27.0638 | 32.68085 (20.AE4C16) | aug 1sn | A1 | D# |
| 2 | 51.0638 | 54.1277 | 65.3617 (41.5C98816) | double-aug 1sn | AA1 | Dx |
| 3 | 76.5957 | 81.1915 | 98.04255 (62.0AE516) | triple-aug 1sn, triple-dim 2nd | A31, d32 | D#3, Eb4 |
| 4 | 102.1277 | 108.2553 | 130.7234 (82.B93116) | double-dim 2nd | dd2 | Eb3 |
| 5 | 127.6596 | 135.31915 | 163.4043 (A3.677D16) | dim 2nd | d2 | Ebb |
| 6 | 153.1915 | 162.383 | 196.0851 (C4.15CA16) | minor 2nd | m2 | Eb |
| 7 | 178.7234 | 189.4468 | 228.766 (E4.C41616) | major 2nd | M2 | E |
| 8 | 204.2553 | 216.5106 | 261.4468 (105.726216) | aug 2nd | A2 | E# |
| 9 | 229.7872 | 243.5745 | 294.1277 (126.20AE16) | double-aug 2nd | AA2 | Ex |
| 10 | 255.31915 | 270.6383 | 326.8085 (146.CEFB16) | triple-aug 2nd, triple-dim 3rd | A32, d33 | E#3, Fb3 |
| 11 | 280.8511 | 297.7021 | 359.4894 (167.7D4716) | double-dim 3rd | dd3 | Fbb |
| 12 | 306.383 | 324.766 | 392.1702 (188.2B9316) | dim 3rd | d3 | Fb |
| 13 | 331.9149 | 351.8298 | 424.8511 (1A8.D9DF16) | minor 3rd | m3 | F |
| 14 | 357.4468 | 378.8936 | 457.5319 (1C9.882C16) | major 3rd | M3 | F# |
| 15 | 382.9787 | 405.95745 | 490.2128 (1EA.367816) | aug 3rd | A3 | Fx |
| 16 | 408.5106 | 433.0213 | 522.8936 (20A.E4C416) | double-aug 3rd | AA3 | F#3 |
| 17 | 434.04255 | 460.0851 | 555.5745 (22B.93116) | triple-aug 3rd, triple-dim 4th | A33, d34 | F#4, Gb3 |
| 18 | 459.5745 | 487.1489 | 588.2553 (24C.415D16) | double-dim 4th | dd4 | Gbb |
| 19 | 485.1064 | 514.2128 | 620.9362 (26C.EFA916) | dim 4th | d4 | Gb |
| 20 | 510.6383 | 541.2766 | 653.617 (28D.9DF516) | perfect 4th | P4 | G |
| 21 | 536.1702 | 568.3404 | 686.2979 (2AE.4C4116) | aug 4th | A4 | G# |
| 22 | 561.7021 | 595.4043 | 718.9787 (2CE.FA8E16) | double-aug 4th | AA4 | Gx |
| 23 | 587.2340 | 622.4681 | 751.6595 (2EF.A8DA16) | triple-aug 4th | A34 | G#3 |
| 24 | 612.7660 | 649.5319 | 784.3404 (310.572616) | triple-dim 5th | d35 | Ab3 |
| 25 | 638.2979 | 676.5957 | 817.0213 (331.057216) | double-dim 5th | dd5 | Abb |
| 26 | 663.8298 | 703.6596 | 849.7021 (351.B3BF16) | dim 5th | d5 | Ab |
| 27 | 689.3617 | 730.7234 | 882.383 (372.620B16) | perfect 5th | P5 | A |
| 28 | 714.8936 | 757.7872 | 915.0638 (393.105716) | aug 5th | A5 | A# |
| 29 | 740.4255 | 784.8511 | 947.7447 (3B3.BEA316) | double-aug 5th | AA5 | Ax |
| 30 | 765.95745 | 811.9149 | 980.4255 (3D4.6CF16) | triple-aug 5th, triple-dim 6th | A35, d36 | A#3, Bb4 |
| 31 | 791.4894 | 838.9787 | 1013.1064 (3F5.1B3C16) | double-dim 6th | dd6 | Bb3 |
| 32 | 817.0213 | 866.04255 | 1045.7872 (415.C98816) | dim 6th | d6 | Bbb |
| 33 | 842.5532 | 893.1064 | 1078.4681 (436.77D416) | minor 6th | m6 | Bb |
| 34 | 868.0851 | 920.1702 | 1111.1489 (457.262116) | major 6th | M6 | B |
| 35 | 893.617 | 947.234 | 1143.8298 (477.D46D16) | aug 6th | A6 | B# |
| 36 | 919.1489 | 974.2979 | 1176.5106 (498.82B916) | double-aug 6th | AA6 | Bx |
| 37 | 944.68085 | 1001.3617 | 1209.1915 (4B9.310516) | triple-aug 6th, triple-dim 7th | A36, d37 | B#3, Cb3 |
| 38 | 970.2128 | 1028.4255 | 1241.8723 (4D9.DF5216) | double-dim 7th | dd7 | Cbb |
| 39 | 995.7447 | 1055.4894 | 1274.5532 (4FA.8D9E16) | dim 7th | d7 | Cb |
| 40 | 1021.2766 | 1082.5532 | 1307.234 (51B.3BEA16) | minor 7th | m7 | C |
| 41 | 1046.8085 | 1109.617 | 1339.9149 (53B.EA3616) | major 7th | M7 | C# |
| 42 | 1072.3404 | 1136.68085 | 1372.5957 (55C.988316) | aug 7th | A7 | Cx |
| 43 | 1097.8723 | 1163.7447 | 1405.2766 (57D.46CF16) | double-aug 7th | AA7 | C#3 |
| 44 | 1123.4043 | 1190.8085 | 1437.95745 (59D.F51B16) | triple-aug 7th, triple-dim 8ve | A37, d38 | C#4, Db3 |
| 45 | 1148.9362 | 1217.8723 | 1470.6383 (5BE.A367816) | double-dim 8ve | dd8 | Dbb |
| 46 | 1174.4681 | 1244.9362 | 1503.31915 (5DF.51B416) | dim 8ve | d8 | Db |
| 47 | 1200 | 1272 | 1536 (60016) | perfect 8ve | P8 | D |