User:Eufalesio/Holopyth and Hemipyth
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Pythagorean and Hemipythagorean systematic nomenclature. Open to suggestions.
Pythagorean may be used to talk about both the non-hemi and yes-hemi structures but this is ambiguous, so Holopythagorean (Holopyth) shall refer only to 2.3 NOT √2.√3 or √2.3 or 2.√3. Resumed:
- Holopyth 2.3
- Hemipyth √2.√3
- Ouranpyth 2.√3
- Demipyth √2.3
The nomenclature is called EPN and EHPN (Eufa's Pythagorean Nomenclature and Eufa's HemiPythagorean Nomenclature). It is based on some other musings I did.
Important is to distinguish the interchromatic nominals and interdiatonic nominals (interseptimals). The key distinguishing feature is that interchromatics have √2 AND √3, Interdiatonics have √2 OR √3. No augmented/diminished in here, better dodecatonic or icositetratonic system, less difficult and also I don't like them. Included also new nominals to make all even more compact but not strict necessity.
| Category | Name | Mapping or Action | Abbreviation | Pitches (Revo) | Pitches (Evo) | Frequency (Hz) | |
|---|---|---|---|---|---|---|---|
| Prime 2 | Prime 3 | ||||||
| Pythagorean diatonic nominals | unison | 0 | 0 | 1 | D4 | 293.3 | |
| fifth | -1 | 1 | 5 | A4 | 440 | ||
| fourth | 2 | -1 | 4 | G4 | 391.1 | ||
| major second | -3 | 2 | M2 | E4 | 330 | ||
| minor seventh | 4 | -2 | m2 | C4 | 521.481 | ||
| major sixth | -4 | 3 | M6 | B4 | 495 | ||
| minor third | 5 | -3 | m3 | F4 | ~347.654 | ||
| Pythagorean chromatic nominals | major third | -6 | 4 | M3 | P4 | F#4 | ~371.25 |
| minor sixth | 7 | -4 | m6 | O4 | Bb4 | ~463.539 | |
| major seventh | -7 | 5 | M7 | K4 | C#4 | 556.875 | |
| minor second | 8 | -5 | m2 | L4 | Eb4 | ~309.026 | |
| tritone | -9 | 6 | TT | T4 | G#4 | 417.65625 | |
| Hemipythagorean interchromatic nominals | mid third | -0.5 | 0.5 | N3 | φ4 | Ft4 | ~359.258 |
| mid sixth | 1.5 | -0.5 | N6 | θ4 | Bd4 | ~479.011 | |
| mid seventh | -1.5 | 1.5 | N7 | η4 | Ct4 | ~538.888 | |
| mid second | 2.5 | -1.5 | N2 | λ4 | Ed4 | ~319.341 | |
| trinterfourth | -3.5 | 2.5 | 4T | γ4 | Gt4 | ~404.166 | |
| trinterfifth | 4.5 | 2.5 | 5T | α4 | Ad4 | ~425.788 | |
| Hemipythagorean Interdiatonic nominals | ouranic | 0 | 0.5 | 67 | ω4 | Bzt4 / CZd4 | ~508.068 |
| chthonic | 1 | -0.5 | 23 | χ4 | Ezt4 / FZd4 | ~338.712 | |
| naiadic | -2 | 1.5 | 34 | δ4 | GZd4 | ~381.051 | |
| cocytic | 3 | -1.5 | 45 | κ4 | Azt4 | ~451.616 | |
| tartaric | -3 | 2.5 | 78 | τ4 | DZd5 | ~571.577 | |
| barbaric | 4 | -2.5 | 12 | β4 | Dzt4 | ~301.077 | |
| Modifiers | super- | -19 | 12 | S- | DS4 | ||
| sub- | 19 | -12 | s- | Ds4 | |||
| hyper- | -38 | 24 | H- | DH4 | |||
| hypo- | 38 | -24 | h- | Dh4 | |||
| semiper- | -9.5 | 6 | Z- | DZ4 | |||
| semisub- | 9.5 | -6 | z- | Dz4 | |||
| sesquiper- | -28.5 | 18 | Q- | DQ4 | |||
| sesquisub- | 28.5 | -18 | q- | Dq4 | |||
| semimerc- | -42 | 26.5 | v- | Dv4 | |||
| merc- | -84 | 53 | w- | Dw4 | |||
| semiqian- | -242.5 | 153 | σ- | Dσ4 | |||
| qian- | -485 | 306 | Σ- | DΣ4 | |||
| co- | 1 | 0 | c- | – | |||
| trans- | ± <-84 53];
fifthspan%53≥26:+ fifthspan%53≤26:- |
r- | Dr4 | ||||
| alter- | ± <-485 306];
fifthspan%53>153:+ fifthspan%53<153:- |
a- | Da4 | ||||
| cis- | explicit not trans- | k- | Dk4 | ||||
| ipso- | explicit not alter- | i- | Di4 | ||||
| den- | reverse direction | n- | |||||
| Evo pitch accidentals | -sharp | -11 | 7 | -# | |||
| -flat | 11 | -7 | -b | ||||
| -semisharp | -5.5 | 3.5 | -t | ||||
| -semiflat | 5.5 | -3.5 | -d | ||||
| -semisubsharp | 4 | -2.5 | -zt | ||||
| -semiperflat | -4 | 2.5 | -Zd | ||||
| Syntax | interval: (den)(co)(alter)(trans)([semi]qian)([semi]merc)(super/sub/hyper/hypo/semiper/semisub/sesquiper/sesquisub)nominal | ||||||
| pitch: (alter)(trans)pitch-class([semi]qian)([semi]merc)(super/sub/hyper/hypo/semiper/semisub/sesquiper/sesquisub)(octave) | |||||||
| Extreme example | dencoaltertransqianbimercsesquipertrinterfourth ncarΣwQ4T (-1795.53787428) <684 -432.5] | ||||||
Etymologies of new nominals:
- Barbaric: Greek-flavored interseptimals inspired by Zhea for the unison-inter-second, based on barbarians because the interval sounds kinda harsh. Use thalassic if you don't like it but I think the name sounds kickass.
- Tartaric: Greek-flavored interseptimals inspired by Zhea for the seventh-inter-octave, based on the Tartarus, hell of eternal suffering because yes. Rhymes with barbaric, fitting because they are octave complements.
- Trinterfourth: contraction of tritone-inter-fourth.
- Trinterfifth: contraction of tritone-inter-fifth. Technically misnomer because this is actually the octave complement of trinterfourth, the actual interval that's a true tritone-inter-fifth is sqrt(2187/1024) which here would be the semipertrinterfifth. Maybe not the best idea to keep this inconsistency.
| Alternate name | Systematic name | |
| Modifiers | neutral- | mid- |
| contra- | trans- | |
| Pythagorean comma | superunison | |
| pythcomma | ||
| Mercator's comma | mercunison | |
| mercomma | ||
| Holopythagorean nominals | octave | counison |
| tone | major second | |
| limma | minor second | |
| apotome | superminor second | |
| ditone | major third | |
| Hemipythagorean nominals | hemitone | semiperminor second |
| hemilimma | barbaric | |
| thalassic | ||
| hemifourth | chthonic | |
| hemififth | mid third | |
| hemisixth | naiadic | |
| hemioctave | semisubtritone | |
| hemitenth | cocytic | |
| hemitwelth | ouranic | |
| hemitritave | ||
| (hemipyth) meantone | semisubmajor second | |
| paramajor fourth | trinterfourth | |
| paraminor fifth | trinterfifth |
| Fifthspan | Cents | Name | Simplified |
|---|---|---|---|
| -106 | 1192.7699 | bitransmercoctave | rww1 |
| -105 | 694.7249 | transmercfifth | rw5 |
| -104 | 196.6799 | transmercmajor second | rwM2 |
| -103 | 898.6349 | transmercmajor sixth | rwM6 |
| -102 | 400.5899 | transmercmajor third | rwM3 |
| -101 | 1102.5449 | transmercmajor seventh | rwM7 |
| -100 | 604.4999 | transmerctritone | rwTT |
| -99 | 106.4549 | transmercsuperminor second | rwSm2 |
| -98 | 808.4099 | transmercsuperminor sixth | rwSm6 |
| -97 | 310.3649 | transmercsuperminor third | rwSm3 |
| -96 | 1012.3199 | transmercsuperminor seventh | rwSm7 |
| -95 | 514.2749 | transmercsuperfourth | rwS4 |
| -94 | 16.2299 | transmercsuperunison | rwS1 |
| -93 | 718.1849 | transmercsuperfifth | rwS5 |
| -92 | 220.1399 | transmercsupermajor second | rwSM2 |
| -91 | 922.0949 | transmercsupermajor sixth | rwSM6 |
| -90 | 424.0499 | transmercsupermajor third | rwSM3 |
| -89 | 1126.0049 | transmercsupermajor seventh | rwSM7 |
| -88 | 627.9599 | transmercsupertritone | rwSTT |
| -87 | 129.9149 | transmerchyperminor second | rwHm2 |
| -86 | 831.8699 | transmerchyperminor sixth | rwHm6 |
| -85 | 333.8249 | transmerchyperminor third | rwHm3 |
| -84 | 1035.7799 | transmerchyperminor seventh | rwHm7 |
| -83 | 537.7349 | transmerchyperfourth | rwH4 |
| -82 | 39.6899 | transmerchyperunison | rwH1 |
| -81 | 741.6449 | transmerchyperfifth | rwH5 |
| -80 | 243.5999 | transmerchypermajor second | rwHM2 |
| -79 | 945.5549 | merchypominor seventh | whm7 |
| -78 | 447.5099 | merchypofourth | wh4 |
| -77 | 1149.4649 | merchypoöctave | wh1 |
| -76 | 651.4199 | merchypofifth | wh5 |
| -75 | 153.3749 | merchypomajor second | whM2 |
| -74 | 855.3299 | merchypomajor sixth | whM6 |
| -73 | 357.2849 | merchypomajor third | whM3 |
| -72 | 1059.2399 | merchypomajor seventh | whM7 |
| -71 | 561.1949 | merchypotritone | whTT |
| -70 | 63.1499 | mercsubminor second | wsm2 |
| -69 | 765.1049 | mercsubminor sixth | wsm6 |
| -68 | 267.0599 | mercsubminor third | wsm3 |
| -67 | 969.0149 | mercsubminor seventh | wsm7 |
| -66 | 470.9699 | mercsubfourth | ws4 |
| -65 | 1172.9249 | mercsuboctave | ws1 |
| -64 | 674.8799 | mercsubfifth | ws5 |
| -63 | 176.8349 | mercsubmajor second | wsM2 |
| -62 | 878.7899 | mercsubmajor sixth | wsM6 |
| -61 | 380.7449 | mercsubmajor third | wsM3 |
| -60 | 1082.6999 | mercsubmajor seventh | wsM7 |
| -59 | 584.6549 | mercsubtritone | wsTT |
| -58 | 86.6099 | mercminor second | wm2 |
| -57 | 788.5650 | mercminor sixth | wm6 |
| -56 | 290.5200 | mercminor third | wm3 |
| -55 | 992.4750 | mercminor seventh | wm7 |
| -54 | 494.4300 | mercfourth | w4 |
| -53 | 1196.3850 | transmercoctave / transmercunison | rw8 / rw1 |
| -52 | 698.3400 | transfifth | r5 |
| -51 | 200.2950 | transmajor second | rM2 |
| -50 | 902.2500 | transmajor sixth | rM6 |
| -49 | 404.2050 | transmajor third | rM3 |
| -48 | 1106.1600 | transmajor seventh | rM7 |
| -47 | 608.1150 | transtritone | rTT |
| -46 | 110.0700 | transsuperminor second | rSm2 |
| -45 | 812.0250 | transsuperminor sixth | rSm6 |
| -44 | 313.9800 | transsuperminor third | rSm3 |
| -43 | 1015.9350 | transsuperminor seventh | rSm7 |
| -42 | 517.8900 | transsuperfourth | rS4 |
| -41 | 19.8450 | transsuperunison | rS1 |
| -40 | 721.8000 | transsuperfifth | rS5 |
| -39 | 223.7550 | transsupermajor second | rSM2 |
| -38 | 925.7100 | transsupermajor sixth | rSM6 |
| -37 | 427.6650 | transsupermajor third | rSM3 |
| -36 | 1129.6200 | transsupermajor seventh | rSM7 |
| -35 | 631.5750 | transsupertritone | rSTT |
| -34 | 133.5300 | transhyperminor second | rHm2 |
| -33 | 835.4850 | transhyperminor sixth | rHm6 |
| -32 | 337.4400 | transhyperminor third | rHm3 |
| -31 | 1039.3950 | transhyperminor seventh | rHm7 |
| -30 | 541.3500 | transhyperfourth | rH4 |
| -29 | 43.3050 | transhyperunison / hypominor second | rH1 |
| -28 | 745.2600 | transhyperfifth / hypominor sixth | rH5 |
| -27 | 247.2150 | transhypermajor second / hypominor third | rHM2 |
| -26 | 949.1700 | hypominor seventh | hm7 |
| -25 | 451.1250 | hypofourth | h4 |
| -24 | 1153.0800 | hypoöctave / hypounison | h8 / h1 |
| -23 | 655.0350 | hypofifth | h5 |
| -22 | 156.9900 | hypomajor second | hM2 |
| -21 | 858.9450 | hypomajor sixth | hM6 |
| -20 | 360.9000 | hypomajor third | hM3 |
| -19 | 1062.8550 | hypomajor seventh | hM7 |
| -18 | 564.8100 | hypotritone | hTT |
| -17 | 66.7650 | subminor second | sm2 |
| -16 | 768.7200 | subminor sixth | sm6 |
| -15 | 270.6750 | subminor third | sm3 |
| -14 | 972.6300 | subminor seventh | sm7 |
| -13 | 474.5850 | subfourth | s4 |
| -12 | 1176.5400 | suboctave / subunison | s8 / s1 |
| -11 | 678.4950 | subfifth | s5 |
| -10 | 180.4500 | submajor second | sM2 |
| -9 | 882.4050 | submajor sixth | sM6 |
| -8 | 384.3600 | submajor third | sM3 |
| -7 | 1086.3150 | submajor seventh | sM7 |
| -6 | 588.2700 | subtritone | sTT |
| -5 | 90.2250 | minor second | m2 |
| -4 | 792.1800 | minor sixth | m6 |
| -3 | 294.1350 | minor third | m3 |
| -2 | 996.0900 | minor seventh | m7 |
| -1 | 498.0450 | fourth | 4 |
| 0 | 0.0000 | unison / octave | 1 / 8 |
| 1 | 701.9550 | fifth | 5 |
| 2 | 203.9100 | major second | M2 |
| 3 | 905.8650 | major sixth | M6 |
| 4 | 407.8200 | major third | M3 |
| 5 | 1109.7750 | major seventh | M7 |
| 6 | 611.7300 | tritone | TT |
| 7 | 113.6850 | superminor second | Sm2 |
| 8 | 815.6400 | superminor sixth | Sm6 |
| 9 | 317.5950 | superminor third | Sm3 |
| 10 | 1019.5500 | superminor seventh | Sm7 |
| 11 | 521.5050 | superfourth | S4 |
| 12 | 23.4600 | superunison / superoctave | S1 / S8 |
| 13 | 725.4150 | superfifth | S5 |
| 14 | 227.3700 | supermajor second | SM2 |
| 15 | 929.3250 | supermajor sixth | SM6 |
| 16 | 431.2800 | supermajor third | SM3 |
| 17 | 1133.2350 | supermajor seventh | SM7 |
| 18 | 635.1900 | supertritone | STT |
| 19 | 137.1450 | hyperminor second | Hm2 |
| 20 | 839.1000 | hyperminor sixth | Hm6 |
| 21 | 341.0550 | hyperminor third | Hm3 |
| 22 | 1043.0100 | hyperminor seventh | Hm7 |
| 23 | 544.9650 | hyperfourth | H4 |
| 24 | 46.9200 | hyperunison / hyperoctave | H1 / H8 |
| 25 | 748.8750 | hyperfifth | H5 |
| 26 | 250.8300 | hypermajor second | HM2 |
| 27 | 952.7850 | transhypominor seventh / hypermajor sixth | rhm7 |
| 28 | 454.7400 | transhypofourth / hypermajor third | rh4 |
| 29 | 1156.6950 | transhypoöctave / hypermajor third | rh1 |
| 30 | 658.6500 | transhypofifth / hypermajor third | rh5 |
| 31 | 160.6050 | transhypomajor second | rhM2 |
| 32 | 862.5600 | transhypomajor sixth | rhM6 |
| 33 | 364.5150 | transhypomajor third | rhM3 |
| 34 | 1066.4700 | transhypomajor seventh | rhM7 |
| 35 | 568.4250 | transhypotritone | rhTT |
| 36 | 70.3800 | transsubminor second | rsm2 |
| 37 | 772.3350 | transsubminor sixth | rsm6 |
| 38 | 274.2900 | transsubminor third | rsm3 |
| 39 | 976.2450 | transsubminor seventh | rsm7 |
| 40 | 478.2000 | transsubfourth | rs4 |
| 41 | 1180.1550 | transsuboctave | rs1 |
| 42 | 682.1100 | transsubfifth | rs5 |
| 43 | 184.0650 | transsubmajor second | rsM2 |
| 44 | 886.0200 | transsubmajor sixth | rsM6 |
| 45 | 387.9750 | transsubmajor third | rsM3 |
| 46 | 1089.9300 | transsubmajor seventh | rsM7 |
| 47 | 591.8850 | transsubtritone | rsTT |
| 48 | 93.8400 | transminor second | rm2 |
| 49 | 795.7950 | transminor sixth | rm6 |
| 50 | 297.7500 | transminor third | rm3 |
| 51 | 999.7050 | transminor seventh | rm7 |
| 52 | 501.6600 | transfourth | r4 |
| 53 | 3.6150 | mercunison / mercoctave | w1 / w8 |
| 54 | 705.5700 | mercfifth | w5 |
| 55 | 207.5250 | mercmajor second | wM2 |
| 56 | 909.4800 | mercmajor sixth | wM6 |
| 57 | 411.4350 | mercmajor third | wM3 |
| 58 | 1113.3901 | mercmajor seventh | wM7 |
| 59 | 615.3451 | merctritone | wTT |
| 60 | 117.3001 | mercsuperminor second | wSm2 |
| 61 | 819.2551 | mercsuperminor sixth | wSm6 |
| 62 | 321.2101 | mercsuperminor third | wSm3 |
| 63 | 1023.1651 | mercsuperminor seventh | wSm7 |
| 64 | 525.1201 | mercsuperfourth | wS4 |
| 65 | 27.0751 | mercsuperunison | wS1 |
| 66 | 729.0301 | mercsuperfifth | wS5 |
| 67 | 230.9851 | mercsupermajor second | wSM2 |
| 68 | 932.9401 | mercsupermajor sixth | wSM6 |
| 69 | 434.8951 | mercsupermajor third | wSM3 |
| 70 | 1136.8501 | mercsupermajor seventh | wSM7 |
| 71 | 638.8051 | mercsupertritone | wSTT |
| 72 | 140.7601 | merchyperminor second | wHm2 |
| 73 | 842.7151 | merchyperminor sixth | wHm6 |
| 74 | 344.6701 | merchyperminor third | wHm3 |
| 75 | 1046.6251 | merchyperminor seventh | wHm7 |
| 76 | 548.5801 | merchyperfourth | wH4 |
| 77 | 50.5351 | merchyperunison | wH1 |
| 78 | 752.4901 | merchyperfifth | wH5 |
| 79 | 254.4451 | merchypermajor second | wHM2 |
| 80 | 956.4001 | transmerchypominor seventh | rwhm7 |
| 81 | 458.3551 | transmerchypofourth | rwh4 |
| 82 | 1160.3101 | transmerchypoöctave | rwh1 |
| 83 | 662.2651 | transmerchypofifth | rwh5 |
| 84 | 164.2201 | transmerchypomajor second | rwhM2 |
| 85 | 866.1751 | transmerchypomajor sixth | rwhM6 |
| 86 | 368.1301 | transmerchypomajor third | rwhM3 |
| 87 | 1070.0851 | transmerchypomajor seventh | rwhM7 |
| 88 | 572.0401 | transmerchypotritone | rwhTT |
| 89 | 73.9951 | transmercsubminor second | rwsm2 |
| 90 | 775.9501 | transmercsubminor sixth | rwsm6 |
| 91 | 277.9051 | transmercsubminor third | rwsm3 |
| 92 | 979.8601 | transmercsubminor seventh | rwsm7 |
| 93 | 481.8151 | transmercsubfourth | rws4 |
| 94 | 1183.7701 | transmercsuboctave | rws1 |
| 95 | 685.7251 | transmercsubfifth | rws5 |
| 96 | 187.6801 | transmercsubmajor second | rwsM2 |
| 97 | 889.6351 | transmercsubmajor sixth | rwsM6 |
| 98 | 391.5901 | transmercsubmajor third | rwsM3 |
| 99 | 1093.5451 | transmercsubmajor seventh | rwsM7 |
| 100 | 595.5001 | transmercsubtritone | rwsTT |
| 101 | 97.4551 | transmercminor second | rwm2 |
| 102 | 799.4101 | transmercminor sixth | rwm6 |
| 103 | 301.3651 | transmercminor third | rwm3 |
| 104 | 1003.3201 | transmercminor seventh | rwm7 |
| 105 | 505.2751 | transmercfourth | rw4 |
| 106 | 7.2301 | bimercunison | ww1 |
| Fifthspan | Interchromatic-central | Simplified | Interdiatonic-central | Simplified | ||
|---|---|---|---|---|---|---|
| Cents | Name | Cents | Name | |||
| -53 | 1196.3850 | transmercoctave / transmercunison | rw8 / rw1 | 596.3850 | transmercsemisubtritone | rwzTT |
| -52.5 | 347.3625 | transmid third | rN3 | 947.3625 | transouranic | r67 |
| -52 | 698.3400 | transfifth | r5 | 98.3400 | transsemiperminor second | rZm2 |
| -51.5 | 1049.3175 | transmid seventh | rN7 | 449.3175 | transnaiadic | r34 |
| -51 | 200.2950 | transmajor second | rM2 | 800.2950 | transsemiperminor sixth | rZm6 |
| -50.5 | 551.2725 | transtrinterfourth | rT4 | 1151.2725 | transtartaric | r78 |
| -50 | 902.2500 | transmajor sixth | rM6 | 302.2500 | transsemiperminor third | rZm3 |
| -49.5 | 53.2275 | transsemiperbarbaric | rZ12 | 653.2275 | transsemipertrinterfifth | rZ5T |
| -49 | 404.2050 | transmajor third | rM3 | 1004.2050 | transsemiperminor seventh | rZm7 |
| -48.5 | 755.1825 | transsemipercocytic | rZ56 | 155.1825 | transsemipermid second | rZN2 |
| -48 | 1106.1600 | transmajor seventh | rM7 | 506.1600 | transsemiperfourth | rZ4 |
| -47.5 | 257.1375 | transsemiperchthonic | rZ23 | 857.1375 | transsemipermid sixth | rZN6 |
| -47 | 608.1150 | transtritone | rTT | 8.1150 | transsemiperunison | rZ1 |
| -46.5 | 959.0925 | transsemiperouranic | rZ67 | 359.0925 | transsemipermid third | rZN3 |
| -46 | 110.0700 | transsuperminor second | rSm2 | 710.0700 | transsemiperfifth | rZ5 |
| -45.5 | 461.0475 | transsemipernaiadic | rZ34 | 1061.0475 | transsemipermid seventh | rZN7 |
| -45 | 812.0250 | transsuperminor sixth | rSm6 | 212.0250 | transsemipermajor second | rZM2 |
| -44.5 | 1163.0025 | transsemipertartaric | rZ78 | 563.0025 | transsemipertrinterfourth | rZ4T |
| -44 | 313.9800 | transsuperminor third | rSm3 | 913.9800 | transsemipermajor sixth | rZM6 |
| -43.5 | 664.9575 | transsupertrinterfifth | rST5 | 64.9575 | transsuperbarbaric | rS12 |
| -43 | 1015.9350 | transsuperminor seventh | rSm7 | 415.9350 | transsemipermajor third | rZM3 |
| -42.5 | 166.9125 | transsupermid second | rSN2 | 766.9125 | transsupercocytic | rS56 |
| -42 | 517.8900 | transsuperfourth | rS4 | 1117.8900 | transsemipermajor seventh | rZM7 |
| -41.5 | 868.8675 | transsupermid sixth | rSN6 | 268.8675 | transsuperchthonic | rS23 |
| -41 | 19.8450 | transsuperunison | rS1 | 619.8450 | transsemipertritone | rZTT |
| -40.5 | 370.8225 | transsupermid third | rSN3 | 970.8225 | transsuperouranic | rS67 |
| -40 | 721.8000 | transsuperfifth | rS5 | 121.8000 | transsesquiperminor second | rQm2 |
| -39.5 | 1072.7775 | transsupermid third | rSN7 | 472.7775 | transsupernaiadic | rS34 |
| -39 | 223.7550 | transsupermajor second | rSM2 | 823.7550 | transsesquiperminor sixth | rQm6 |
| -38.5 | 574.7325 | transsupertrinterfourth | rST4 | 1174.7325 | transsupertartaric | rS78 |
| -38 | 925.7100 | transsupermajor sixth | rSM6 | 325.7100 | transsesquiperminor third | rQm3 |
| -37.5 | 76.6875 | transsesquiperbarbaric | rQ12 | 676.6875 | transsesquipertrinterfifth | rQ5T |
| -37 | 427.6650 | transsupermajor third | rSM3 | 1027.6650 | transsesquiperminor seventh | rQm7 |
| -36.5 | 778.6425 | transsesquipercocytic | rQ56 | 178.6425 | transsesquipermid second | rQN2 |
| -36 | 1129.6200 | transsupermajor seventh | rSM7 | 529.6200 | transsesquiperfourth | rQ4 |
| -35.5 | 280.5975 | transsesquiperchthonic | rQ23 | 880.5975 | transsesquipermid sixth | rQN6 |
| -35 | 631.5750 | transsupertritone | rSTT | 31.5750 | transsesquiperunison | rQ1 |
| -34.5 | 982.5525 | transsesquiperouranic | rQ67 | 382.5525 | transsesquipermid third | rQN3 |
| -34 | 133.5300 | transhyperminor second | rHm2 | 733.5300 | transsesquiperfifth | rQ5 |
| -33.5 | 484.5075 | transsesquipernaiadic | rQ34 | 1084.5075 | transsesquipermid seventh | rQN7 |
| -33 | 835.4850 | transhyperminor sixth | rHm6 | 235.4850 | transsesquipermajor second | rQM2 |
| -32.5 | 1186.4625 | transsesquipertartaric | rQ78 | 586.4625 | transsesquipertrinterfourth | rQ4T |
| -32 | 337.4400 | transhyperminor third | rHm3 | 937.4400 | transsesquipermajor sixth | rQM6 |
| -31.5 | 688.4175 | transhypertrinterfifth | rHT5 | 88.4175 | transhyperbarbaric | rH12 |
| -31 | 1039.3950 | transhyperminor seventh | rHm7 | 439.3950 | transsesquipermajor third | rQM3 |
| -30.5 | 190.3725 | transhypermid second | rHN2 | 790.3725 | transhypercocytic | rH56 |
| -30 | 541.3500 | transhyperfourth | rH4 | 1141.3500 | transsesquipermajor seventh | rQM7 |
| -29.5 | 892.3275 | transhypermid sixth | rHN6 | 292.3275 | transhyperchthonic | rH23 |
| -29 | 43.3050 | transhyperunison | rH1 | 643.3050 | transsesquipertritone / transsemimerctrinterfifth | rQTT |
| -28.5 | 394.2825 | transhypermid third | rHN3 | 994.2825 | transhyperouranic | rH67 |
| -28 | 745.2600 | transhyperfifth | rH5 | 145.2600 | transsemimercmid second | rvN3 |
| -27.5 | 1096.2375 | transhypermid third | rHN7 | 496.2375 | transhypernaiadic | rH34 |
| -27 | 247.2150 | transhypermajor second | rHM2 | 847.2150 | transsemimercmid sixth | rvN6 |
| -26.5 | 598.1925 | hypotrinterfifth / transhypertrinterfourth | hT5 / rHT4 | 1198.1925 | transsemimercoctave | rv8 |
| -26 | 949.1700 | hypominor seventh | hm7 | 349.1700 | semimercmid third | vN3 |
| -25.5 | 100.1475 | hypomid second | hN2 | 700.1475 | hypococytic | h56 |
| -25 | 451.1250 | hypofourth | h4 | 1051.1250 | semimercmid seventh | vN7 |
| -24.5 | 802.1025 | hypomid sixth | hN6 | 202.1025 | hypochthonic | h23 |
| -24 | 1153.0800 | hypoöctave / hypounison | h8 / h1 | 553.0800 | semimerctrinterfourth | v4T |
| -23.5 | 304.0575 | hypomid third | hN3 | 904.0575 | hypoouranic | h67 |
| -23 | 655.0350 | hypofifth | h5 | 55.0350 | sesquisubminor second | qm2 |
| -22.5 | 1006.0125 | hypomid seventh | hN7 | 406.0125 | hyponaiadic | h34 |
| -22 | 156.9900 | hypomajor second | hM2 | 756.9900 | sesquisubminor sixth | qm6 |
| -21.5 | 507.9675 | hypotrinterfourth | hT4 | 1107.9675 | hypotartaric | h78 |
| -21 | 858.9450 | hypomajor sixth | hM6 | 258.9450 | sesquisubminor third | qm3 |
| -20.5 | 9.9225 | sesquisubbarbaric | q12 | 609.9225 | sesquisubtrinterfifth | q5T |
| -20 | 360.9000 | hypomajor third | hM3 | 960.9000 | sesquisubminor seventh | qm7 |
| -19.5 | 711.8775 | sesquisubcocytic | q56 | 111.8775 | sesquisubmid second | qN2 |
| -19 | 1062.8550 | hypomajor seventh | hM7 | 462.8550 | sesquisubfourth | q4 |
| -18.5 | 213.8325 | sesquisubchthonic | q23 | 813.8325 | sesquisubmid sixth | qN6 |
| -18 | 564.8100 | hypotritone | hTT | 1164.8100 | sesquisuboctave | q8 |
| -17.5 | 915.7875 | sesquisubouranic | q67 | 315.7875 | sesquisubmid third | qN3 |
| -17 | 66.7650 | subminor second | sm2 | 666.7650 | sesquisubfifth | q5 |
| -16.5 | 417.7425 | sesquisubnaiadic | q34 | 1017.7425 | sesquisubmid seventh | qN7 |
| -16 | 768.7200 | subminor sixth | sm6 | 168.7200 | sesquisubmajor second | qM2 |
| -15.5 | 1119.6975 | sesquisubtartaric | q78 | 519.6975 | sesquisubtrinterfourth | q4T |
| -15 | 270.6750 | subminor third | sm3 | 870.6750 | sesquisubmajor sixth | qM6 |
| -14.5 | 621.6525 | subtrinterfifth | sT5 | 21.6525 | subbarbaric | s12 |
| -14 | 972.6300 | subminor seventh | sm7 | 372.6300 | sesquisubmajor third | qM3 |
| -13.5 | 123.6075 | submid second | sN2 | 723.6075 | subcocytic | s56 |
| -13 | 474.5850 | subfourth | s4 | 1074.5850 | sesquisubmajor seventh | qM7 |
| -12.5 | 825.5625 | submid sixth | sN6 | 225.5625 | subchthonic | s23 |
| -12 | 1176.5400 | suboctave / subunison | s8 / s1 | 576.5400 | sesquisubtritone | qTT |
| -11.5 | 327.5175 | submid third | sN3 | 927.5175 | subouranic | s67 |
| -11 | 678.4950 | subfifth | s5 | 78.4950 | semisubminor second | zm2 |
| -10.5 | 1029.4725 | submid seventh | sN7 | 429.4725 | subnaiadic | s34 |
| -10 | 180.4500 | submajor second | sM2 | 780.4500 | semisubminor sixth | zm6 |
| -9.5 | 531.4275 | subtrinterfourth | sT4 | 1131.4275 | subtartaric | s78 |
| -9 | 882.4050 | submajor sixth | sM6 | 282.4050 | semisubminor third | zm3 |
| -8.5 | 33.3825 | semisubbarbaric | z12 | 633.3825 | semisubtrinterfifth | z5T |
| -8 | 384.3600 | submajor third | sM3 | 984.3600 | semisubminor seventh | zm7 |
| -7.5 | 735.3375 | semisubcocytic | z56 | 135.3375 | semisubmid second | zN2 |
| -7 | 1086.3150 | submajor seventh | sM7 | 486.3150 | semisubfourth | z4 |
| -6.5 | 237.2925 | semisubchthonic | z23 | 837.2925 | semisubmid sixth | zN6 |
| -6 | 588.2700 | subtritone | sTT | 1188.2700 | semisuboctave | z8 |
| -5.5 | 939.2475 | semisubouranic | z67 | 339.2475 | semisubmid third | zN3 |
| -5 | 90.2250 | minor second | m2 | 690.2250 | semisubfifth | z5 |
| -4.5 | 441.2025 | semisubnaiadic | z34 | 1041.2025 | semisubmid seventh | zN7 |
| -4 | 792.1800 | minor sixth | m6 | 192.1800 | semisubmajor second | zM2 |
| -3.5 | 1143.1575 | semisubtartaric | z78 | 543.1575 | semisubtrinterfourth | z4T |
| -3 | 294.1350 | minor third | m3 | 894.1350 | semisubmajor sixth | zM6 |
| -2.5 | 645.1125 | trinterfifth | T5 | 45.1125 | barbaric | 12 |
| -2 | 996.0900 | minor seventh | m7 | 396.0900 | semisubmajor third | zM3 |
| -1.5 | 147.0675 | mid second | N2 | 747.0675 | cocytic | 56 |
| -1 | 498.0450 | fourth | 4 | 1098.0450 | semisubmajor seventh | zM7 |
| -0.5 | 849.0225 | mid sixth | N6 | 249.0225 | chthonic | 23 |
| 0 | 0.0000 | unison / octave | 1 | 600.0000 | semisubtritone | zTT |
| 0.5 | 350.9775 | mid third | N3 | 950.9775 | ouranic | 67 |
| 1 | 701.9550 | fifth | 5 | 101.9550 | semiperminor second | Zm2 |
| 1.5 | 1052.9325 | mid seventh | N7 | 452.9325 | naiadic | 34 |
| 2 | 203.9100 | major second | M2 | 803.9100 | semiperminor sixth | Zm6 |
| 2.5 | 554.8875 | trinterfourth | T4 | 1154.8875 | tartaric | 78 |
| 3 | 905.8650 | major sixth | M6 | 305.8650 | semiperminor third | Zm3 |
| 3.5 | 56.8425 | semiperbarbaric | Z12 | 656.8425 | semipertrinterfifth | Z5T |
| 4 | 407.8200 | major third | M3 | 1007.8200 | semiperminor seventh | Zm7 |
| 4.5 | 758.7975 | semipercocytic | Z56 | 158.7975 | semipermid second | ZN2 |
| 5 | 1109.7750 | major seventh | M7 | 509.7750 | semiperfourth | Z4 |
| 5.5 | 260.7525 | semiperchthonic | Z23 | 860.7525 | semipermid sixth | ZN6 |
| 6 | 611.7300 | tritone | TT | 11.7300 | semiperunison | Z1 |
| 6.5 | 962.7075 | semiperouranic | Z67 | 362.7075 | semipermid third | ZN3 |
| 7 | 113.6850 | superminor second | Sm2 | 713.6850 | semiperfifth | Z5 |
| 7.5 | 464.6625 | semipernaiadic | Z34 | 1064.6625 | semipermid seventh | ZN7 |
| 8 | 815.6400 | superminor sixth | Sm6 | 215.6400 | semipermajor second | ZM2 |
| 8.5 | 1166.6175 | semipertartaric | Z78 | 566.6175 | semipertrinterfourth | Z4T |
| 9 | 317.5950 | superminor third | Sm3 | 917.5950 | semipermajor sixth | ZM6 |
| 9.5 | 668.5725 | supertrinterfifth | ST5 | 68.5725 | superbarbaric | S12 |
| 10 | 1019.5500 | superminor seventh | Sm7 | 419.5500 | semipermajor third | ZM3 |
| 10.5 | 170.5275 | supermid second | SN2 | 770.5275 | supercocytic | S56 |
| 11 | 521.5050 | superfourth | S4 | 1121.5050 | semipermajor seventh | ZM7 |
| 11.5 | 872.4825 | supermid sixth | SN6 | 272.4825 | superchthonic | S23 |
| 12 | 23.4600 | superunison / superoctave | S1 / S8 | 623.4600 | semipertritone | ZTT |
| 12.5 | 374.4375 | supermid third | SN3 | 974.4375 | superouranic | S67 |
| 13 | 725.4150 | superfifth | S5 | 125.4150 | sesquiperminor second | Qm2 |
| 13.5 | 1076.3925 | supermid third | SN7 | 476.3925 | supernaiadic | S34 |
| 14 | 227.3700 | supermajor second | SM2 | 827.3700 | sesquiperminor sixth | Qm6 |
| 14.5 | 578.3475 | supertrinterfourth | ST4 | 1178.3475 | supertartaric | S78 |
| 15 | 929.3250 | supermajor sixth | SM6 | 329.3250 | sesquiperminor third | Qm3 |
| 15.5 | 80.3025 | sesquiperbarbaric | Q12 | 680.3025 | sesquipertrinterfifth | Q5T |
| 16 | 431.2800 | supermajor third | SM3 | 1031.2800 | sesquiperminor seventh | Qm7 |
| 16.5 | 782.2575 | sesquipercocytic | Q56 | 182.2575 | sesquipermid second | QN2 |
| 17 | 1133.2350 | supermajor seventh | SM7 | 533.2350 | sesquiperfourth | Q4 |
| 17.5 | 284.2125 | sesquiperchthonic | Q23 | 884.2125 | sesquipermid sixth | QN6 |
| 18 | 635.1900 | supertritone | STT | 35.1900 | sesquiperunison | Q1 |
| 18.5 | 986.1675 | sesquiperouranic | Q67 | 386.1675 | sesquipermid third | QN3 |
| 19 | 137.1450 | hyperminor second | Hm2 | 737.1450 | sesquiperfifth | Q5 |
| 19.5 | 488.1225 | sesquipernaiadic | Q34 | 1088.1225 | sesquipermid seventh | QN7 |
| 20 | 839.1000 | hyperminor sixth | Hm6 | 239.1000 | sesquipermajor second | QM2 |
| 20.5 | 1190.0775 | sesquipertartaric | Q78 | 590.0775 | sesquipertrinterfourth | Q4T |
| 21 | 341.0550 | hyperminor third | Hm3 | 941.0550 | sesquipermajor sixth | QM6 |
| 21.5 | 692.0325 | hypertrinterfifth | HT5 | 92.0325 | hyperbarbaric | H12 |
| 22 | 1043.0100 | hyperminor seventh | Hm7 | 443.0100 | sesquipermajor third | QM3 |
| 22.5 | 193.9875 | hypermid second | HN2 | 793.9875 | hypercocytic | H56 |
| 23 | 544.9650 | hyperfourth | H4 | 1144.9650 | sesquipermajor seventh | QM7 |
| 23.5 | 895.9425 | hypermid sixth | HN6 | 295.9425 | hyperchthonic | H23 |
| 24 | 46.9200 | hyperunison / hyperoctave | H1 | 646.9200 | sesquipertritone / semimerctrinterfifth | QTT |
| 24.5 | 397.8975 | hypermid third | HN3 | 997.8975 | hyperouranic | H67 |
| 25 | 748.8750 | hyperfifth | H5 | 148.8750 | semimercmid second | vN3 |
| 25.5 | 1099.8525 | hypermid third | HN7 | 499.8525 | hypernaiadic | H34 |
| 26 | 250.8300 | hypermajor second | HM2 | 850.8300 | semimercmid sixth | vN6 |
| 26.5 | 601.8075 | hypertrinterfourth / transhypotrinterfifth | HT4 / rhT5 | 1.8075 | semimercunison | v1 |
| 27 | 952.7850 | transhypominor seventh | rhm7 | 352.7850 | transsemimercmid third | rvN3 |
| 27.5 | 103.7625 | transhypomid second | rhN2 | 703.7625 | transhypococytic | rh56 |
| 28 | 454.7400 | transhypofourth | rh4 | 1054.7400 | transsemimercmid seventh | rvN7 |
| 28.5 | 805.7175 | transhypomid sixth | rhN6 | 205.7175 | transhypochthonic | rh23 |
| 29 | 1156.6950 | transhypoöctave / transhypounison | rh8 / rh1 | 556.6950 | transsemimerctrinterfourth | rv4T |
| 29.5 | 307.6725 | transhypomid third | rhN3 | 907.6725 | transhypoouranic | rh67 |
| 30 | 658.6500 | transhypofifth | rh5 | 58.6500 | transsesquisubminor second | rqm2 |
| 30.5 | 1009.6275 | transhypomid seventh | rhN7 | 409.6275 | transhyponaiadic | rh34 |
| 31 | 160.6050 | transhypomajor second | rhM2 | 760.6050 | transsesquisubminor sixth | rqm6 |
| 31.5 | 511.5825 | transhypotrinterfourth | rhT4 | 1111.5825 | transhypotartaric | rh78 |
| 32 | 862.5600 | transhypomajor sixth | rhM6 | 262.5600 | transsesquisubminor third | rqm3 |
| 32.5 | 13.5375 | transsesquisubbarbaric | rq12 | 613.5375 | transsesquisubtrinterfifth | rq5T |
| 33 | 364.5150 | transhypomajor third | rhM3 | 964.5150 | transsesquisubminor seventh | rqm7 |
| 33.5 | 715.4925 | transsesquisubcocytic | rq56 | 115.4925 | transsesquisubmid second | rqN2 |
| 34 | 1066.4700 | transhypomajor seventh | rhM7 | 466.4700 | transsesquisubfourth | rq4 |
| 34.5 | 217.4475 | transsesquisubchthonic | rq23 | 817.4475 | transsesquisubmid sixth | rqN6 |
| 35 | 568.4250 | transhypotritone | rhTT | 1168.4250 | transsesquisuboctave | rq8 |
| 35.5 | 919.4025 | transsesquisubouranic | rq67 | 319.4025 | transsesquisubmid third | rqN3 |
| 36 | 70.3800 | transsubminor second | rsm2 | 670.3800 | transsesquisubfifth | rq5 |
| 36.5 | 421.3575 | transsesquisubnaiadic | rq34 | 1021.3575 | transsesquisubmid seventh | rqN7 |
| 37 | 772.3350 | transsubminor sixth | rsm6 | 172.3350 | transsesquisubmajor second | rqM2 |
| 37.5 | 1123.3125 | transsesquisubtartaric | rq78 | 523.3125 | transsesquisubtrinterfourth | rq4T |
| 38 | 274.2900 | transsubminor third | rsm3 | 874.2900 | transsesquisubmajor sixth | rqM6 |
| 38.5 | 625.2675 | transsubtrinterfifth | rsT5 | 25.2675 | transsubbarbaric | rs12 |
| 39 | 976.2450 | transsubminor seventh | rsm7 | 376.2450 | transsesquisubmajor third | rqM3 |
| 39.5 | 127.2225 | transsubmid second | rsN2 | 727.2225 | transsubcocytic | rs56 |
| 40 | 478.2000 | transsubfourth | rs4 | 1078.2000 | transsesquisubmajor seventh | rqM7 |
| 40.5 | 829.1775 | transsubmid sixth | rsN6 | 229.1775 | transsubchthonic | rs23 |
| 41 | 1180.1550 | transsuboctave | rs1 | 580.1550 | transsesquisubtritone | rqTT |
| 41.5 | 331.1325 | transsubmid third | rsN3 | 931.1325 | transsubouranic | rs67 |
| 42 | 682.1100 | transsubfifth | rs5 | 82.1100 | transsemisubminor second | rzm2 |
| 42.5 | 1033.0875 | transsubmid seventh | rsN7 | 433.0875 | transsubnaiadic | rs34 |
| 43 | 184.0650 | transsubmajor second | rsM2 | 784.0650 | transsemisubminor sixth | rzm6 |
| 43.5 | 535.0425 | transsubtrinterfourth | rsT4 | 1135.0425 | transsubtartaric | rs78 |
| 44 | 886.0200 | transsubmajor sixth | rsM6 | 286.0200 | transsemisubminor third | rzm3 |
| 44.5 | 36.9975 | transsemisubbarbaric | rz12 | 636.9975 | transsemisubtrinterfifth | rz5T |
| 45 | 387.9750 | transsubmajor third | rsM3 | 987.9750 | transsemisubminor seventh | rzm7 |
| 45.5 | 738.9525 | transsemisubcocytic | rz56 | 138.9525 | transsemisubmid second | rzN2 |
| 46 | 1089.9300 | transsubmajor seventh | rsM7 | 489.9300 | transsemisubfourth | rz4 |
| 46.5 | 240.9075 | transsemisubchthonic | rz23 | 840.9075 | transsemisubmid sixth | rzN6 |
| 47 | 591.8850 | transsubtritone | rsTT | 1191.8850 | transsemisuboctave | rz8 |
| 47.5 | 942.8625 | transsemisubouranic | rz67 | 342.8625 | transsemisubmid third | rzN3 |
| 48 | 93.8400 | transminor second | rm2 | 693.8400 | transsemisubfifth | rz5 |
| 48.5 | 444.8175 | transsemisubnaiadic | rz34 | 1044.8175 | transsemisubmid seventh | rzN7 |
| 49 | 795.7950 | transminor sixth | rm6 | 195.7950 | transsemisubmajor second | rzM2 |
| 49.5 | 1146.7725 | transsemisubtartaric | rz78 | 546.7725 | transsemisubtrinterfourth | rz4T |
| 50 | 297.7500 | transminor third | rm3 | 897.7500 | transsemisubmajor sixth | rzM6 |
| 50.5 | 648.7275 | transtrinterfifth | rT5 | 48.7275 | transbarbaric | r12 |
| 51 | 999.7050 | transminor seventh | rm7 | 399.7050 | transsemisubmajor third | rzM3 |
| 51.5 | 150.6825 | transmid second | rN2 | 750.6825 | transcocytic | r56 |
| 52 | 501.6600 | transfourth | r4 | 1101.6600 | transsemisubmajor seventh | rzM7 |
| 52.5 | 852.6375 | transmid sixth | rN6 | 252.6375 | transchthonic | r23 |
| 53 | 3.6150 | mercunison / mercoctave | w1 / w8 | 603.6150 | mercsemisubtritone | wzTT |