User:Eufalesio/EPN
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Pythagorean and Hemipythagorean systematic nomenclature proposal dispersion. Open to suggestions.
Pythagorean may be used to talk about both the non-hemi and yes-hemi structures but this is ambiguous, so 3-limit or Monocotpyth shall refer only to 2.3 NOT √2.√3 or √2.3 or 2.√3. Resumed:
- Monocotpyth 2.3 (3-limit)
- Hemipyth √2.√3
- Alpha-dicotpyth 2.√3
- Dicotpyth 2.√3/2
- Diploidpyth √2.3
Hemipyth implies (P8/2, P5/2) pergen; Alpha-dicotpyth implies (P8, P4/2), (P8, P5/2) is a subset of hemipyth. The nomenclature is called EPN and EHPN (Eufa's Pythagorean Nomenclature and Eufa's HemiPythagorean Nomenclature).
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 heptatonic. 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)
Cents (c) | |
|---|---|---|---|---|---|---|---|
| Prime 2 | Prime 3 | ||||||
| Pyth-diatonic nominals | unison | 0 | 0 | 1 | D4 | 293.3 Hz | |
| fifth | -1 | 1 | 5 | A4 | 440 Hz | ||
| fourth | 2 | -1 | 4 | G4 | 391.1 Hz | ||
| major second | -3 | 2 | M2 | E4 | 330 Hz | ||
| minor seventh | 4 | -2 | m2 | C4 | 521.481 Hz | ||
| major sixth | -4 | 3 | M6 | B4 | 495 Hz | ||
| minor third | 5 | -3 | m3 | F4 | ~347.654 Hz | ||
| Pyth-chromatic nominals | major third | -6 | 4 | M3 | P4 | F#4 | ~371.25 Hz |
| minor sixth | 7 | -4 | m6 | O4 | Bb4 | ~463.539 Hz | |
| major seventh | -7 | 5 | M7 | K4 | C#4 | 556.875 Hz | |
| minor second | 8 | -5 | m2 | L4 | Eb4 | ~309.026 Hz | |
| tritone | -9 | 6 | TT | T4 | G#4 | 417.65625 Hz | |
| Hemipyth interchromatic nominals | mid third | -0.5 | 0.5 | N3 | φ4 | Ft4 | ~359.258 Hz |
| mid sixth | 1.5 | -0.5 | N6 | θ4 | Bd4 | ~479.011 Hz | |
| mid seventh | -1.5 | 1.5 | N7 | η4 | Ct4 | ~538.888 Hz | |
| mid second | 2.5 | -1.5 | N2 | λ4 | Ed4 | ~319.341 Hz | |
| trinterfourth | -3.5 | 2.5 | 4iT | γ4 | Gt4 | ~404.166 Hz | |
| Hemipyth interdiatonic nominals | ouranic | 0 | 0.5 | 6i7 | ω4 | Bf4 / Cp4 | ~508.068 Hz |
| chthonic | 1 | -0.5 | 2i3 | χ4 | Ef4 / Fp4 | ~338.712 Hz | |
| naiadic | -2 | 1.5 | 3i4 | δ4 | Gp4 | ~381.051 Hz | |
| cocytic | 3 | -1.5 | 5i6 | κ4 | Af4 | ~451.616 Hz | |
| tartaric | -3 | 2.5 | 7i8 | τ4 | Dp5 | ~571.577 Hz | |
| barbaric | 4 | -2.5 | 1i2 | β4 | Df4 | ~301.077 Hz | |
| trinterfifth | -5 | 3.5 | Ti5 | α4 | Ap4 | ~428.683 Hz | |
| Modifiers | super- | -19 | 12 | S- | DS4 | +23.46c | |
| sub- | 19 | -12 | s- | Ds4 | -23.46c | ||
| hyper- | -38 | 24 | H- | DH4 | +46.92c | ||
| hypo- | 38 | -24 | h- | Dh4 | -46.92c | ||
| semiper- | -9.5 | 6 | Z- | DZ4 | +11.73c | ||
| semisub- | 9.5 | -6 | z- | Dz4 | -11.73 | ||
| sesquiper- | -28.5 | 18 | Q- | DQ4 | +35.19c | ||
| sesquisub- | 28.5 | -18 | q- | Dq4 | -35.19c | ||
| semimerc- | -42 | 26.5 | U- | Du4 | ±1.8075c | ||
| merc- | -84 | 53 | J- | Dm4 | ±3.615c | ||
| semiqian- | -242.5 | 153 | σ- | Dσ4 | ±0.88487c | ||
| qian- | -485 | 306 | Σ- | DΣ4 | +1.7697c | ||
| co- | 1 | 0 | c- | – | 1200c | ||
| trans- | see below | R- | Dr4 | 3.615c | |||
| alter- | r- | Da4 | 1.7697c | ||||
| den- | negative interval | "-" | – | ||||
| Evo pitch accidentals | -sharp | -11 | 7 | -# | +113.685c | ||
| -flat | 11 | -7 | -b | -113.685c | |||
| -semisharp | -5.5 | 3.5 | -t | +56.8425c | |||
| -semiflat | 5.5 | -3.5 | -d | -56.8425 | |||
| -semisubsemisharp | 4 | -2.5 | -f | +45.1125c | |||
| -semipersemiflat | -4 | 2.5 | -p | -45.1125c | |||
| 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 -crRΣJQ4T (-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. Also called semiaugmented fourth by many.
- Trinterfifth: contraction of tritone-inter-fifth. NOT a semidiminished fifth, Much like the trinterfourth, this is the geometric mean of the tritone and fifth, and since the tritone isn't 600c, this can't be the complement of the trinterfourth.
Trans and alter
These prefixes are used to described intervals beyond ±26 fifths and beyond ±153 fifths, as to think a similar interval, but from the other side (literally what trans means). They make the mercator and qian microalterations go in the opposite direction as the interval.
So you have the fourth -1 fifth, transfourth +52 fifths, mercfourth is -54 fifths and transmercfourth +105 fifths. Same with alter.
See the tables for better understanding because it all makes sense in my head but probably not yours. I don't know how convoluted this feels so I invite you to shit on me in the discussion page if this is dumb.
Up and down, etc...
Use another set of accidentals for mapping rank-3 temperaments (such as septischismic) or complex rank-2 temperaments more simply (such as newt). An example of usage is here with User:Eufalesio/Ultimate#Nomenclature and notation for more info.
| Alternate name | Systematic name | |
| Modifiers | neutral- | mid- |
| contra- | trans- | |
| Pythagorean comma | superunison | |
| poma | ||
| Mercator's comma | mercunison | |
| mercma | ||
| Monocot nominals | octave | counison |
| tone | major second | |
| limma | minor second | |
| apotome | superminor second | |
| ditone | major third | |
| diabolus | tritone | |
| inversus | subtritone | |
| Hemipyth nominals | hemitone | semiperminor second |
| hemilimma | barbaric | |
| thalassic | ||
| hemifourth | chthonic | |
| hemififth | mid third | |
| hemisixth | naiadic | |
| hemioctave | semisubtritone | |
| hemitenth | cocytic | |
| hemitwelfth | ouranic | |
| hemitritave | ||
| (hemipyth) meantone | semisubmajor second | |
| paramajor fourth | trinterfourth |
Nominals in italics are either negative or bigger than than an octave.
| Fifthspan | Cents (just) | Name | Simplified |
|---|---|---|---|
| -106 | 1192.7699 | bitransmercoctave | RJJP1 |
| -105 | 694.7249 | transmercfifth | RJP5 |
| -104 | 196.6799 | transmercmajor second | RJM2 |
| -103 | 898.6349 | transmercmajor sixth | RJM6 |
| -102 | 400.5899 | transmercmajor third | RJM3 |
| -101 | 1102.5449 | transmercmajor seventh | RJM7 |
| -100 | 604.4999 | transmerctritone | RJTT |
| -99 | 106.4549 | transmercsuperminor second | RJSm2 |
| -98 | 808.4099 | transmercsuperminor sixth | RJSm6 |
| -97 | 310.3649 | transmercsuperminor third | RJSm3 |
| -96 | 1012.3199 | transmercsuperminor seventh | RJSm7 |
| -95 | 514.2749 | transmercsuperfourth | RJSP4 |
| -94 | 16.2299 | transmercsuperunison | RJSP1 |
| -93 | 718.1849 | transmercsuperfifth | RJSP5 |
| -92 | 220.1399 | transmercsupermajor second | RJSM2 |
| -91 | 922.0949 | transmercsupermajor sixth | RJSM6 |
| -90 | 424.0499 | transmercsupermajor third | RJSM3 |
| -89 | 1126.0049 | transmercsupermajor seventh | RJSM7 |
| -88 | 627.9599 | transmercsupertritone | RJSTT |
| -87 | 129.9149 | transmerchyperminor second | RJHm2 |
| -86 | 831.8699 | transmerchyperminor sixth | RJHm6 |
| -85 | 333.8249 | transmerchyperminor third | RJHm3 |
| -84 | 1035.7799 | transmerchyperminor seventh | RJHm7 |
| -83 | 537.7349 | transmerchyperfourth | RJHP4 |
| -82 | 39.6899 | transmerchyperunison | RJHP1 |
| -81 | 741.6449 | transmerchyperfifth | RJHP5 |
| -80 | 243.5999 | transmerchypermajor second | RJHM2 |
| -79 | 945.5549 | merchypominor seventh | Jhm7 |
| -78 | 447.5099 | merchypofourth | JhP4 |
| -77 | 1149.4649 | merchypoöctave | JhP1 |
| -76 | 651.4199 | merchypofifth | JhP5 |
| -75 | 153.3749 | merchypomajor second | JhM2 |
| -74 | 855.3299 | merchypomajor sixth | JhM6 |
| -73 | 357.2849 | merchypomajor third | JhM3 |
| -72 | 1059.2399 | merchypomajor seventh | JhM7 |
| -71 | 561.1949 | merchypotritone | JhTT |
| -70 | 63.1499 | mercsubminor second | Jsm2 |
| -69 | 765.1049 | mercsubminor sixth | Jsm6 |
| -68 | 267.0599 | mercsubminor third | Jsm3 |
| -67 | 969.0149 | mercsubminor seventh | Jsm7 |
| -66 | 470.9699 | mercsubfourth | JsP4 |
| -65 | 1172.9249 | mercsuboctave | JsP1 |
| -64 | 674.8799 | mercsubfifth | JsP5 |
| -63 | 176.8349 | mercsubmajor second | JsM2 |
| -62 | 878.7899 | mercsubmajor sixth | JsM6 |
| -61 | 380.7449 | mercsubmajor third | JsM3 |
| -60 | 1082.6999 | mercsubmajor seventh | JsM7 |
| -59 | 584.6549 | mercsubtritone | JsTT |
| -58 | 86.6099 | mercminor second | Jm2 |
| -57 | 788.5650 | mercminor sixth | Jm6 |
| -56 | 290.5200 | mercminor third | Jm3 |
| -55 | 992.4750 | mercminor seventh | Jm7 |
| -54 | 494.4300 | mercfourth | JP4 |
| -53 | 1196.3850 | transmercoctave / transmercunison | RJP8 / RJP1 |
| -52 | 698.3400 | transfifth | RP5 |
| -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 | RSP4 |
| -41 | 19.8450 | transsuperunison | RSP1 |
| -40 | 721.8000 | transsuperfifth | RSP5 |
| -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 | RHP4 |
| -29 | 43.3050 | transhyperunison / hypominor second | RHP1 |
| -28 | 745.2600 | transhyperfifth / hypominor sixth | RHP5 |
| -27 | 247.2150 | transhypermajor second / hypominor third | RHM2 |
| -26 | 949.1700 | hypominor seventh | hm7 |
| -25 | 451.1250 | hypofourth | hP4 |
| -24 | 1153.0800 | hypoöctave / hypounison | hP8 / hP1 |
| -23 | 655.0350 | hypofifth | hP5 |
| -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 | sP4 |
| -12 | 1176.5400 | suboctave / subunison | sP8 / sP1 |
| -11 | 678.4950 | subfifth | sP5 |
| -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 | P4 |
| 0 | 0.0000 | unison / octave | P1 / P8 |
| 1 | 701.9550 | fifth | P5 |
| 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 | SP4 |
| 12 | 23.4600 | superunison / superoctave | SP1 / SP8 |
| 13 | 725.4150 | superfifth | SP5 |
| 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 | HP4 |
| 24 | 46.9200 | hyperunison / hyperoctave | HP1 / HP8 |
| 25 | 748.8750 | hyperfifth | HP5 |
| 26 | 250.8300 | hypermajor second | HM2 |
| 27 | 952.7850 | transhypominor seventh / hypermajor sixth | Rhm7 |
| 28 | 454.7400 | transhypofourth / hypermajor third | RhP4 |
| 29 | 1156.6950 | transhypoöctave / hypermajor third | RhP1 |
| 30 | 658.6500 | transhypofifth / hypermajor third | RhP5 |
| 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 | RsP4 |
| 41 | 1180.1550 | transsuboctave | RsP1 |
| 42 | 682.1100 | transsubfifth | RsP5 |
| 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 | RP4 |
| 53 | 3.6150 | mercunison / mercoctave | JP1 / JP8 |
| 54 | 705.5700 | mercfifth | JP5 |
| 55 | 207.5250 | mercmajor second | JM2 |
| 56 | 909.4800 | mercmajor sixth | JM6 |
| 57 | 411.4350 | mercmajor third | JM3 |
| 58 | 1113.3901 | mercmajor seventh | JM7 |
| 59 | 615.3451 | merctritone | JTT |
| 60 | 117.3001 | mercsuperminor second | JSm2 |
| 61 | 819.2551 | mercsuperminor sixth | JSm6 |
| 62 | 321.2101 | mercsuperminor third | JSm3 |
| 63 | 1023.1651 | mercsuperminor seventh | JSm7 |
| 64 | 525.1201 | mercsuperfourth | JSP4 |
| 65 | 27.0751 | mercsuperunison | JSP1 |
| 66 | 729.0301 | mercsuperfifth | JSP5 |
| 67 | 230.9851 | mercsupermajor second | JSM2 |
| 68 | 932.9401 | mercsupermajor sixth | JSM6 |
| 69 | 434.8951 | mercsupermajor third | JSM3 |
| 70 | 1136.8501 | mercsupermajor seventh | JSM7 |
| 71 | 638.8051 | mercsupertritone | JSTT |
| 72 | 140.7601 | merchyperminor second | JHm2 |
| 73 | 842.7151 | merchyperminor sixth | JHm6 |
| 74 | 344.6701 | merchyperminor third | JHm3 |
| 75 | 1046.6251 | merchyperminor seventh | JHm7 |
| 76 | 548.5801 | merchyperfourth | JHP4 |
| 77 | 50.5351 | merchyperunison | JHP1 |
| 78 | 752.4901 | merchyperfifth | JHP5 |
| 79 | 254.4451 | merchypermajor second | JHM2 |
| 80 | 956.4001 | transmerchypominor seventh | RJhm7 |
| 81 | 458.3551 | transmerchypofourth | RJhP4 |
| 82 | 1160.3101 | transmerchypoöctave | RJhP1 |
| 83 | 662.2651 | transmerchypofifth | RJhP5 |
| 84 | 164.2201 | transmerchypomajor second | RJhM2 |
| 85 | 866.1751 | transmerchypomajor sixth | RJhM6 |
| 86 | 368.1301 | transmerchypomajor third | RJhM3 |
| 87 | 1070.0851 | transmerchypomajor seventh | RJhM7 |
| 88 | 572.0401 | transmerchypotritone | RJhTT |
| 89 | 73.9951 | transmercsubminor second | RJsm2 |
| 90 | 775.9501 | transmercsubminor sixth | RJsm6 |
| 91 | 277.9051 | transmercsubminor third | RJsm3 |
| 92 | 979.8601 | transmercsubminor seventh | RJsm7 |
| 93 | 481.8151 | transmercsubfourth | RJsP4 |
| 94 | 1183.7701 | transmercsuboctave | RJsP1 |
| 95 | 685.7251 | transmercsubfifth | RJsP5 |
| 96 | 187.6801 | transmercsubmajor second | RJsM2 |
| 97 | 889.6351 | transmercsubmajor sixth | RJsM6 |
| 98 | 391.5901 | transmercsubmajor third | RJsM3 |
| 99 | 1093.5451 | transmercsubmajor seventh | RJsM7 |
| 100 | 595.5001 | transmercsubtritone | RJsTT |
| 101 | 97.4551 | transmercminor second | RJm2 |
| 102 | 799.4101 | transmercminor sixth | RJm6 |
| 103 | 301.3651 | transmercminor third | RJm3 |
| 104 | 1003.3201 | transmercminor seventh | RJm7 |
| 105 | 505.2751 | transmercfourth | RJP4 |
| 106 | 7.2301 | bimercunison | JJP1 |
| Fifthspan | Interchromatic-central | Simplified | Interdiatonic-central | Simplified | ||
|---|---|---|---|---|---|---|
| Cents (just) | Name | Cents | Name | |||
| -53 | 1196.3850 | transmercoctave / transmercunison | RJP8 / RJP1 | 596.3850 | transmercsemisubtritone | RJzTT |
| -52.5 | 347.3625 | transmid third | RN3 | 947.3625 | transouranic | R6i7 |
| -52 | 698.3400 | transfifth | RP5 | 98.3400 | transsemiperminor second | RZm2 |
| -51.5 | 1049.3175 | transmid seventh | RN7 | 449.3175 | transnaiadic | R3i4 |
| -51 | 200.2950 | transmajor second | RM2 | 800.2950 | transsemiperminor sixth | RZm6 |
| -50.5 | 551.2725 | transtrinterfourth | R4iT | 1151.2725 | transtartaric | R7P8 |
| -50 | 902.2500 | transmajor sixth | RM6 | 302.2500 | transsemiperminor third | RZm3 |
| -49.5 | 53.2275 | transsemiperbarbaric | RZ1i2 | 653.2275 | transtrinterfifth | RP5T |
| -49 | 404.2050 | transmajor third | RM3 | 1004.2050 | transsemiperminor seventh | RZm7 |
| -48.5 | 755.1825 | transsemipercocytic | RZ5i6 | 155.1825 | transsemipermid second | RZN2 |
| -48 | 1106.1600 | transmajor seventh | RM7 | 506.1600 | transsemiperfourth | RZP4 |
| -47.5 | 257.1375 | transsemiperchthonic | RZ2i3 | 857.1375 | transsemipermid sixth | RZN6 |
| -47 | 608.1150 | transtritone | RTT | 8.1150 | transsemiperunison | RZP1 |
| -46.5 | 959.0925 | transsemiperouranic | RZ6i7 | 359.0925 | transsemipermid third | RZN3 |
| -46 | 110.0700 | transsuperminor second | RSm2 | 710.0700 | transsemiperfifth | RZP5 |
| -45.5 | 461.0475 | transsemipernaiadic | RZ3i4 | 1061.0475 | transsemipermid seventh | RZN7 |
| -45 | 812.0250 | transsuperminor sixth | RSm6 | 212.0250 | transsemipermajor second | RZM2 |
| -44.5 | 1163.0025 | transsemipertartaric | RZ7P8 | 563.0025 | transsemipertrinterfourth | RZ4iT |
| -44 | 313.9800 | transsuperminor third | RSm3 | 913.9800 | transsemipermajor sixth | RZM6 |
| -43.5 | 664.9575 | transsemipertrinterfifth | RZP5T | 64.9575 | transsuperbarbaric | RS1i2 |
| -43 | 1015.9350 | transsuperminor seventh | RSm7 | 415.9350 | transsemipermajor third | RZM3 |
| -42.5 | 166.9125 | transsupermid second | RSN2 | 766.9125 | transsupercocytic | RS5i6 |
| -42 | 517.8900 | transsuperfourth | RSP4 | 1117.8900 | transsemipermajor seventh | RZM7 |
| -41.5 | 868.8675 | transsupermid sixth | RSN6 | 268.8675 | transsuperchthonic | RS2i3 |
| -41 | 19.8450 | transsuperunison | RSP1 | 619.8450 | transsemipertritone | RZTT |
| -40.5 | 370.8225 | transsupermid third | RSN3 | 970.8225 | transsuperouranic | RS6i7 |
| -40 | 721.8000 | transsuperfifth | RSP5 | 121.8000 | transsesquiperminor second | RQm2 |
| -39.5 | 1072.7775 | transsupermid third | RSN7 | 472.7775 | transsupernaiadic | RS3i4 |
| -39 | 223.7550 | transsupermajor second | RSM2 | 823.7550 | transsesquiperminor sixth | RQm6 |
| -38.5 | 574.7325 | transsupertrinterfourth | RS4iT | 1174.7325 | transsupertartaric | RS7P8 |
| -38 | 925.7100 | transsupermajor sixth | RSM6 | 325.7100 | transsesquiperminor third | RQm3 |
| -37.5 | 76.6875 | transsesquiperbarbaric | RQ1i2 | 676.6875 | transsupertrinterfifth | RSP5T |
| -37 | 427.6650 | transsupermajor third | RSM3 | 1027.6650 | transsesquiperminor seventh | RQm7 |
| -36.5 | 778.6425 | transsesquipercocytic | RQ5i6 | 178.6425 | transsesquipermid second | RQN2 |
| -36 | 1129.6200 | transsupermajor seventh | RSM7 | 529.6200 | transsesquiperfourth | RQP4 |
| -35.5 | 280.5975 | transsesquiperchthonic | RQ2i3 | 880.5975 | transsesquipermid sixth | RQN6 |
| -35 | 631.5750 | transsupertritone | RSTT | 31.5750 | transsesquiperunison | RQP1 |
| -34.5 | 982.5525 | transsesquiperouranic | RQ6i7 | 382.5525 | transsesquipermid third | RQN3 |
| -34 | 133.5300 | transhyperminor second | RHm2 | 733.5300 | transsesquiperfifth | RQP5 |
| -33.5 | 484.5075 | transsesquipernaiadic | RQ3i4 | 1084.5075 | transsesquipermid seventh | RQN7 |
| -33 | 835.4850 | transhyperminor sixth | RHm6 | 235.4850 | transsesquipermajor second | RQM2 |
| -32.5 | 1186.4625 | transsesquipertartaric | RQ7P8 | 586.4625 | transsesquipertrinterfourth | RQ4iT |
| -32 | 337.4400 | transhyperminor third | RHm3 | 937.4400 | transsesquipermajor sixth | RQM6 |
| -31.5 | 688.4175 | transsesquipertrinterfifth | RQP5T | 88.4175 | transhyperbarbaric | RH1i2 |
| -31 | 1039.3950 | transhyperminor seventh | RHm7 | 439.3950 | transsesquipermajor third | RQM3 |
| -30.5 | 190.3725 | transhypermid second | RHN2 | 790.3725 | transhypercocytic | RH5i6 |
| -30 | 541.3500 | transhyperfourth | RHP4 | 1141.3500 | transsesquipermajor seventh | RQM7 |
| -29.5 | 892.3275 | transhypermid sixth | RHN6 | 292.3275 | transhyperchthonic | RH2i3 |
| -29 | 43.3050 | transhyperunison | RHP1 | 643.3050 | transsesquipertritone | RQTT |
| -28.5 | 394.2825 | transhypermid third | RHN3 | 994.2825 | transhyperouranic | RH6i7 |
| -28 | 745.2600 | transhyperfifth | RHP5 | 145.2600 | transsemimercmid second | RUN3 |
| -27.5 | 1096.2375 | transhypermid third | RHN7 | 496.2375 | transhypernaiadic | RH3i4 |
| -27 | 247.2150 | transhypermajor second | RHM2 | 847.2150 | transsemimercmid sixth | RUN6 |
| -26.5 | 598.1925 | transhypertrinterfourth | RH4iT | 1198.1925 | transsemimercoctave | RUP8 |
| -26 | 949.1700 | hypominor seventh | hm7 | 349.1700 | semimercmid third | UN3 |
| -25.5 | 100.1475 | hypomid second | hN2 | 700.1475 | hypococytic | h5i6 |
| -25 | 451.1250 | hypofourth | hP4 | 1051.1250 | semimercmid seventh | UN7 |
| -24.5 | 802.1025 | hypomid sixth | hN6 | 202.1025 | hypochthonic | h2i3 |
| -24 | 1153.0800 | hypoöctave / hypounison | hP8 / hP1 | 553.0800 | semimerctrinterfourth | U4iT |
| -23.5 | 304.0575 | hypomid third | hN3 | 904.0575 | hypoouranic | h6i7 |
| -23 | 655.0350 | hypofifth | hP5 | 55.0350 | sesquisubminor second | qm2 |
| -22.5 | 1006.0125 | hypomid seventh | hN7 | 406.0125 | hyponaiadic | h3i4 |
| -22 | 156.9900 | hypomajor second | hM2 | 756.9900 | sesquisubminor sixth | qm6 |
| -21.5 | 507.9675 | hypotrinterfourth | h4iT | 1107.9675 | hypotartaric | h7P8 |
| -21 | 858.9450 | hypomajor sixth | hM6 | 258.9450 | sesquisubminor third | qm3 |
| -20.5 | 9.9225 | sesquisubbarbaric | q1i2 | 609.9225 | hypotrinterfifth | hP5T |
| -20 | 360.9000 | hypomajor third | hM3 | 960.9000 | sesquisubminor seventh | qm7 |
| -19.5 | 711.8775 | sesquisubcocytic | q5i6 | 111.8775 | sesquisubmid second | qN2 |
| -19 | 1062.8550 | hypomajor seventh | hM7 | 462.8550 | sesquisubfourth | qP4 |
| -18.5 | 213.8325 | sesquisubchthonic | q2i3 | 813.8325 | sesquisubmid sixth | qN6 |
| -18 | 564.8100 | hypotritone | hTT | 1164.8100 | sesquisuboctave | qP8 |
| -17.5 | 915.7875 | sesquisubouranic | q6i7 | 315.7875 | sesquisubmid third | qN3 |
| -17 | 66.7650 | subminor second | sm2 | 666.7650 | sesquisubfifth | qP5 |
| -16.5 | 417.7425 | sesquisubnaiadic | q3i4 | 1017.7425 | sesquisubmid seventh | qN7 |
| -16 | 768.7200 | subminor sixth | sm6 | 168.7200 | sesquisubmajor second | qM2 |
| -15.5 | 1119.6975 | sesquisubtartaric | q7P8 | 519.6975 | sesquisubtrinterfourth | q4iT |
| -15 | 270.6750 | subminor third | sm3 | 870.6750 | sesquisubmajor sixth | qM6 |
| -14.5 | 621.6525 | sesquisubtrinterfifth | qP5T | 21.6525 | subbarbaric | s1i2 |
| -14 | 972.6300 | subminor seventh | sm7 | 372.6300 | sesquisubmajor third | qM3 |
| -13.5 | 123.6075 | submid second | sN2 | 723.6075 | subcocytic | s5i6 |
| -13 | 474.5850 | subfourth | sP4 | 1074.5850 | sesquisubmajor seventh | qM7 |
| -12.5 | 825.5625 | submid sixth | sN6 | 225.5625 | subchthonic | s2i3 |
| -12 | 1176.5400 | suboctave / subunison | sP8 / sP1 | 576.5400 | sesquisubtritone | qTT |
| -11.5 | 327.5175 | submid third | sN3 | 927.5175 | subouranic | s6i7 |
| -11 | 678.4950 | subfifth | sP5 | 78.4950 | semisubminor second | zm2 |
| -10.5 | 1029.4725 | submid seventh | sN7 | 429.4725 | subnaiadic | s3i4 |
| -10 | 180.4500 | submajor second | sM2 | 780.4500 | semisubminor sixth | zm6 |
| -9.5 | 531.4275 | subtrinterfourth | s4iT | 1131.4275 | subtartaric | s7P8 |
| -9 | 882.4050 | submajor sixth | sM6 | 282.4050 | semisubminor third | zm3 |
| -8.5 | 33.3825 | semisubbarbaric | z1i2 | 633.3825 | subtrinterfifth | sP5T |
| -8 | 384.3600 | submajor third | sM3 | 984.3600 | semisubminor seventh | zm7 |
| -7.5 | 735.3375 | semisubcocytic | z5i6 | 135.3375 | semisubmid second | zN2 |
| -7 | 1086.3150 | submajor seventh | sM7 | 486.3150 | semisubfourth | zP4 |
| -6.5 | 237.2925 | semisubchthonic | z2i3 | 837.2925 | semisubmid sixth | zN6 |
| -6 | 588.2700 | subtritone | sTT | 1188.2700 | semisuboctave | zP8 |
| -5.5 | 939.2475 | semisubouranic | z6i7 | 339.2475 | semisubmid third | zN3 |
| -5 | 90.2250 | minor second | m2 | 690.2250 | semisubfifth | zP5 |
| -4.5 | 441.2025 | semisubnaiadic | z3i4 | 1041.2025 | semisubmid seventh | zN7 |
| -4 | 792.1800 | minor sixth | m6 | 192.1800 | semisubmajor second | zM2 |
| -3.5 | 1143.1575 | semisubtartaric | z7P8 | 543.1575 | semisubtrinterfourth | z4iT |
| -3 | 294.1350 | minor third | m3 | 894.1350 | semisubmajor sixth | zM6 |
| -2.5 | 645.1125 | semisubtrinterfifth | zP5T | 45.1125 | barbaric | 1i2 |
| -2 | 996.0900 | minor seventh | m7 | 396.0900 | semisubmajor third | zM3 |
| -1.5 | 147.0675 | mid second | N2 | 747.0675 | cocytic | 5i6 |
| -1 | 498.0450 | fourth | P4 | 1098.0450 | semisubmajor seventh | zM7 |
| -0.5 | 849.0225 | mid sixth | N6 | 249.0225 | chthonic | 2i3 |
| 0 | 0.0000 | unison / octave | P1 | 600.0000 | semisubtritone | zTT |
| 0.5 | 350.9775 | mid third | N3 | 950.9775 | ouranic | 6i7 |
| 1 | 701.9550 | fifth | P5 | 101.9550 | semiperminor second | Zm2 |
| 1.5 | 1052.9325 | mid seventh | N7 | 452.9325 | naiadic | 3i4 |
| 2 | 203.9100 | major second | M2 | 803.9100 | semiperminor sixth | Zm6 |
| 2.5 | 554.8875 | trinterfourth | 4iT | 1154.8875 | tartaric | 7P8 |
| 3 | 905.8650 | major sixth | M6 | 305.8650 | semiperminor third | Zm3 |
| 3.5 | 56.8425 | semiperbarbaric | Z1i2 | 656.8425 | trinterfifth | P5T |
| 4 | 407.8200 | major third | M3 | 1007.8200 | semiperminor seventh | Zm7 |
| 4.5 | 758.7975 | semipercocytic | Z5i6 | 158.7975 | semipermid second | ZN2 |
| 5 | 1109.7750 | major seventh | M7 | 509.7750 | semiperfourth | ZP4 |
| 5.5 | 260.7525 | semiperchthonic | Z2i3 | 860.7525 | semipermid sixth | ZN6 |
| 6 | 611.7300 | tritone | TT | 11.7300 | semiperunison | ZP1 |
| 6.5 | 962.7075 | semiperouranic | Z6i7 | 362.7075 | semipermid third | ZN3 |
| 7 | 113.6850 | superminor second | Sm2 | 713.6850 | semiperfifth | ZP5 |
| 7.5 | 464.6625 | semipernaiadic | Z3i4 | 1064.6625 | semipermid seventh | ZN7 |
| 8 | 815.6400 | superminor sixth | Sm6 | 215.6400 | semipermajor second | ZM2 |
| 8.5 | 1166.6175 | semipertartaric | Z7P8 | 566.6175 | semipertrinterfourth | Z4iT |
| 9 | 317.5950 | superminor third | Sm3 | 917.5950 | semipermajor sixth | ZM6 |
| 9.5 | 668.5725 | semipertrinterfifth | ZP5T | 68.5725 | superbarbaric | S1i2 |
| 10 | 1019.5500 | superminor seventh | Sm7 | 419.5500 | semipermajor third | ZM3 |
| 10.5 | 170.5275 | supermid second | SN2 | 770.5275 | supercocytic | S5i6 |
| 11 | 521.5050 | superfourth | SP4 | 1121.5050 | semipermajor seventh | ZM7 |
| 11.5 | 872.4825 | supermid sixth | SN6 | 272.4825 | superchthonic | S2i3 |
| 12 | 23.4600 | superunison / superoctave | SP1 / SP8 | 623.4600 | semipertritone | ZTT |
| 12.5 | 374.4375 | supermid third | SN3 | 974.4375 | superouranic | S6i7 |
| 13 | 725.4150 | superfifth | SP5 | 125.4150 | sesquiperminor second | Qm2 |
| 13.5 | 1076.3925 | supermid third | SN7 | 476.3925 | supernaiadic | S3i4 |
| 14 | 227.3700 | supermajor second | SM2 | 827.3700 | sesquiperminor sixth | Qm6 |
| 14.5 | 578.3475 | supertrinterfourth | S4iT | 1178.3475 | supertartaric | S7P8 |
| 15 | 929.3250 | supermajor sixth | SM6 | 329.3250 | sesquiperminor third | Qm3 |
| 15.5 | 80.3025 | sesquiperbarbaric | Q1i2 | 680.3025 | supertrinterfifth | SP5T |
| 16 | 431.2800 | supermajor third | SM3 | 1031.2800 | sesquiperminor seventh | Qm7 |
| 16.5 | 782.2575 | sesquipercocytic | Q5i6 | 182.2575 | sesquipermid second | QN2 |
| 17 | 1133.2350 | supermajor seventh | SM7 | 533.2350 | sesquiperfourth | QP4 |
| 17.5 | 284.2125 | sesquiperchthonic | Q2i3 | 884.2125 | sesquipermid sixth | QN6 |
| 18 | 635.1900 | supertritone | STT | 35.1900 | sesquiperunison | QP1 |
| 18.5 | 986.1675 | sesquiperouranic | Q6i7 | 386.1675 | sesquipermid third | QN3 |
| 19 | 137.1450 | hyperminor second | Hm2 | 737.1450 | sesquiperfifth | QP5 |
| 19.5 | 488.1225 | sesquipernaiadic | Q3i4 | 1088.1225 | sesquipermid seventh | QN7 |
| 20 | 839.1000 | hyperminor sixth | Hm6 | 239.1000 | sesquipermajor second | QM2 |
| 20.5 | 1190.0775 | sesquipertartaric | Q7P8 | 590.0775 | sesquipertrinterfourth | Q4iT |
| 21 | 341.0550 | hyperminor third | Hm3 | 941.0550 | sesquipermajor sixth | QM6 |
| 21.5 | 692.0325 | sesquipertrinterfifth | QP5T | 92.0325 | hyperbarbaric | H1i2 |
| 22 | 1043.0100 | hyperminor seventh | Hm7 | 443.0100 | sesquipermajor third | QM3 |
| 22.5 | 193.9875 | hypermid second | HN2 | 793.9875 | hypercocytic | H5i6 |
| 23 | 544.9650 | hyperfourth | HP4 | 1144.9650 | sesquipermajor seventh | QM7 |
| 23.5 | 895.9425 | hypermid sixth | HN6 | 295.9425 | hyperchthonic | H2i3 |
| 24 | 46.9200 | hyperunison / hyperoctave | HP1 | 646.9200 | sesquipertritone | QTT |
| 24.5 | 397.8975 | hypermid third | HN3 | 997.8975 | hyperouranic | H6i7 |
| 25 | 748.8750 | hyperfifth | HP5 | 148.8750 | semimercmid second | UN3 |
| 25.5 | 1099.8525 | hypermid third | HN7 | 499.8525 | hypernaiadic | H3i4 |
| 26 | 250.8300 | hypermajor second | HM2 | 850.8300 | semimercmid sixth | UN6 |
| 26.5 | 601.8075 | hypertrinterfourth | H4iT | 1.8075 | semimercunison | UP1 |
| 27 | 952.7850 | transhypominor seventh | Rhm7 | 352.7850 | transsemimercmid third | RUN3 |
| 27.5 | 103.7625 | transhypomid second | RhN2 | 703.7625 | transhypococytic | Rh5i6 |
| 28 | 454.7400 | transhypofourth | RhP4 | 1054.7400 | transsemimercmid seventh | RUN7 |
| 28.5 | 805.7175 | transhypomid sixth | RhN6 | 205.7175 | transhypochthonic | Rh2i3 |
| 29 | 1156.6950 | transhypoöctave / transhypounison | RhP8 / RhP1 | 556.6950 | transsemimerctrinterfourth | RU4iT |
| 29.5 | 307.6725 | transhypomid third | RhN3 | 907.6725 | transhypoouranic | Rh6i7 |
| 30 | 658.6500 | transhypofifth | RhP5 | 58.6500 | transsesquisubminor second | Rqm2 |
| 30.5 | 1009.6275 | transhypomid seventh | RhN7 | 409.6275 | transhyponaiadic | Rh3i4 |
| 31 | 160.6050 | transhypomajor second | RhM2 | 760.6050 | transsesquisubminor sixth | Rqm6 |
| 31.5 | 511.5825 | transhypotrinterfourth | Rh4iT | 1111.5825 | transhypotartaric | Rh7P8 |
| 32 | 862.5600 | transhypomajor sixth | RhM6 | 262.5600 | transsesquisubminor third | Rqm3 |
| 32.5 | 13.5375 | transsesquisubbarbaric | Rq1i2 | 613.5375 | transhypotrinterfifth | RhP5T |
| 33 | 364.5150 | transhypomajor third | RhM3 | 964.5150 | transsesquisubminor seventh | Rqm7 |
| 33.5 | 715.4925 | transsesquisubcocytic | Rq5i6 | 115.4925 | transsesquisubmid second | RqN2 |
| 34 | 1066.4700 | transhypomajor seventh | RhM7 | 466.4700 | transsesquisubfourth | RqP4 |
| 34.5 | 217.4475 | transsesquisubchthonic | Rq2i3 | 817.4475 | transsesquisubmid sixth | RqN6 |
| 35 | 568.4250 | transhypotritone | RhTT | 1168.4250 | transsesquisuboctave | RqP8 |
| 35.5 | 919.4025 | transsesquisubouranic | Rq6i7 | 319.4025 | transsesquisubmid third | RqN3 |
| 36 | 70.3800 | transsubminor second | Rsm2 | 670.3800 | transsesquisubfifth | RqP5 |
| 36.5 | 421.3575 | transsesquisubnaiadic | Rq3i4 | 1021.3575 | transsesquisubmid seventh | RqN7 |
| 37 | 772.3350 | transsubminor sixth | Rsm6 | 172.3350 | transsesquisubmajor second | RqM2 |
| 37.5 | 1123.3125 | transsesquisubtartaric | Rq7P8 | 523.3125 | transsesquisubtrinterfourth | Rq4iT |
| 38 | 274.2900 | transsubminor third | Rsm3 | 874.2900 | transsesquisubmajor sixth | RqM6 |
| 38.5 | 625.2675 | transsesquitrinterfifth | RqP5T | 25.2675 | transsubbarbaric | Rs1i2 |
| 39 | 976.2450 | transsubminor seventh | Rsm7 | 376.2450 | transsesquisubmajor third | RqM3 |
| 39.5 | 127.2225 | transsubmid second | RsN2 | 727.2225 | transsubcocytic | Rs5i6 |
| 40 | 478.2000 | transsubfourth | RsP4 | 1078.2000 | transsesquisubmajor seventh | RqM7 |
| 40.5 | 829.1775 | transsubmid sixth | RsN6 | 229.1775 | transsubchthonic | Rs2i3 |
| 41 | 1180.1550 | transsuboctave | RsP1 | 580.1550 | transsesquisubtritone | RqTT |
| 41.5 | 331.1325 | transsubmid third | RsN3 | 931.1325 | transsubouranic | Rs6i7 |
| 42 | 682.1100 | transsubfifth | RsP5 | 82.1100 | transsemisubminor second | Rzm2 |
| 42.5 | 1033.0875 | transsubmid seventh | RsN7 | 433.0875 | transsubnaiadic | Rs3i4 |
| 43 | 184.0650 | transsubmajor second | RsM2 | 784.0650 | transsemisubminor sixth | Rzm6 |
| 43.5 | 535.0425 | transsubtrinterfourth | Rs4iT | 1135.0425 | transsubtartaric | Rs7P8 |
| 44 | 886.0200 | transsubmajor sixth | RsM6 | 286.0200 | transsemisubminor third | Rzm3 |
| 44.5 | 36.9975 | transsemisubbarbaric | Rz1i2 | 636.9975 | transsubtrinterfifth | RsP5T |
| 45 | 387.9750 | transsubmajor third | RsM3 | 987.9750 | transsemisubminor seventh | Rzm7 |
| 45.5 | 738.9525 | transsemisubcocytic | Rz5i6 | 138.9525 | transsemisubmid second | RzN2 |
| 46 | 1089.9300 | transsubmajor seventh | RsM7 | 489.9300 | transsemisubfourth | RzP4 |
| 46.5 | 240.9075 | transsemisubchthonic | Rz2i3 | 840.9075 | transsemisubmid sixth | RzN6 |
| 47 | 591.8850 | transsubtritone | RsTT | 1191.8850 | transsemisuboctave | RzP8 |
| 47.5 | 942.8625 | transsemisubouranic | Rz6i7 | 342.8625 | transsemisubmid third | RzN3 |
| 48 | 93.8400 | transminor second | Rm2 | 693.8400 | transsemisubfifth | RzP5 |
| 48.5 | 444.8175 | transsemisubnaiadic | Rz3i4 | 1044.8175 | transsemisubmid seventh | RzN7 |
| 49 | 795.7950 | transminor sixth | Rm6 | 195.7950 | transsemisubmajor second | RzM2 |
| 49.5 | 1146.7725 | transsemisubtartaric | Rz7P8 | 546.7725 | transsemisubtrinterfourth | Rz4iT |
| 50 | 297.7500 | transminor third | Rm3 | 897.7500 | transsemisubmajor sixth | RzM6 |
| 50.5 | 648.7275 | transsemisubtrinterfifth | RzP5T | 48.7275 | transbarbaric | R1i2 |
| 51 | 999.7050 | transminor seventh | Rm7 | 399.7050 | transsemisubmajor third | RzM3 |
| 51.5 | 150.6825 | transmid second | RN2 | 750.6825 | transcocytic | R5i6 |
| 52 | 501.6600 | transfourth | RP4 | 1101.6600 | transsemisubmajor seventh | RzM7 |
| 52.5 | 852.6375 | transmid sixth | RN6 | 252.6375 | transchthonic | R2i3 |
| 53 | 3.6150 | mercunison / mercoctave | JP1 / JP8 | 603.6150 | mercsemisubtritone | JzTT |
General case
Not used necessarily with just fifths, can use ideally with fifths between 24\41 and 38\65 inclusive.
- Use normally for any tunings with fifths inside that range
- Fifths wider than 10\17 have to use m2 fractions as the mapped poma is far too big
- Compton has to use aug/dim fractions
- Fifths flatter than 7\12 now use d2 to refer to sub/super prefixes, the meantone diesis
- Fifths flatter than 11\19 have to use aug/dim fractions because the mapped meantone diesis is far too wide