User:Eufalesio/EPN
A notation capable of notating all pythagorean, hemipyth, and then some.
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 quset 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 | Bt!4 / Cd¡4 | ~508.068 Hz |
| chthonic | 1 | -0.5 | 2i3 | χ4 | Et!4 / Fd¡4 | ~338.712 Hz | |
| naiadic | -2 | 1.5 | 3i4 | δ4 | Gd¡4 | ~381.051 Hz | |
| cocytic | 3 | -1.5 | 5i6 | κ4 | At!4 | ~451.616 Hz | |
| tartaric | -3 | 2.5 | 7i8 | τ4 | Dd¡5 | ~571.577 Hz | |
| barbaric | 4 | -2.5 | 1i2 | β4 | Dt!4 | ~301.077 Hz | |
| trinterfifth | -5 | 3.5 | Ti5 | α4 | Ad¡4 | ~428.683 Hz | |
| Modifiers | po- | -19 | 12 | p- | Dp4 | +23.46c | |
| qu- | 19 | -12 | q- | Dq4 | -23.46c | ||
| 2po | -38 | 24 | P- | DP4 | +46.92c | ||
| 2qu | 38 | -24 | Q- | DQ4 | -46.92c | ||
| semipo- | -9.5 | 6 | ¡- | D¡4 | +11.73c | ||
| semiqu- | 9.5 | -6 | !- | D!4 | -11.73 | ||
| sesquipo- | -28.5 | 18 | p¡- | Dp¡4 | +35.19c | ||
| sesquiqu- | 28.5 | -18 | q!- | Dq!4 | -35.19c | ||
| semimerc- | -42 | 26.5 | U- | DU4 | ±1.8075c | ||
| merc- | -84 | 53 | j/J- | Dj4 | ±3.615c | ||
| semiqian- | -242.5 | 153 | σ- | Dσ4 | ±0.88487c | ||
| qian- | -485 | 306 | Σ- | DΣ4 | +1.7697c | ||
| co- | 1 | 0 | c- | – | 1200c | ||
| alter- | see below | R- | DR4 | 3.615c | |||
| revol- | r- | Dr4 | 1.7697c | ||||
| ne- | 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 | |||
| -semiqusemisharp | 4 | -2.5 | -t! | +45.1125c | |||
| -semiposemiflat | -4 | 2.5 | -d¡ | -45.1125c | |||
| Syntax | interval: (den)(co)(revol)(alter)([semi]qian)([semi]merc)(po/qu/popo/ququ/semipo/semiqu/sesquipo/sesquiqu)(nominal) | ||||||
| pitch: (revol)(alter)(pitch-class)([semi]qian)([semi]merc)(po/qu/popo/ququ/semipo/semiqu/sesquipo/sesquiqu)(octave) | |||||||
| Extreme example | necorevolalterqianbimercsesquipotrinterfourth -crRΣJQ4T (-1795.53787428c just) <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.
Alter and revol
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 (thus alter-). They make the mercator and qian microalterations go in the opposite direction the interval suggests, which eliminates the need of knowing which direction you need to alter by. Alter is more than enough for the overwhelming majority of cases.
So you have the fourth -1 fifth, alterfourth +52 fifths, mercfourth is -54 fifths and altermercfourth +105 fifths. Same with revol and qian.
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.
| Alternate name | Systematic name | |
| Modifiers | neutral- | mid- |
| contra- | alter- | |
| Pythagorean comma | pounison | |
| poma | ||
| Mercator's comma | mercunison | |
| mercma | ||
| Monocot nominals | octave | counison |
| tone | major second | |
| limma | minor second | |
| apotome | pominor second | |
| ditone | major third | |
| diabolus | tritone | |
| inversus | qutritone | |
| Hemipyth nominals | hemitone | semipominor second |
| hemilimma | barbaric | |
| thalassic | ||
| hemifourth | chthonic | |
| hemififth | mid third | |
| hemisixth | naiadic | |
| hemioctave | semiqutritone | |
| hemitenth | cocytic | |
| hemitwelfth | ouranic | |
| hemitritave | ||
| (hemipyth) meantone | semiqumajor second | |
| paramajor fourth | trinterfourth |
All the hemis- can be semis- too. Nominals in italics are either negative or bigger than than an octave.
| Fifthspan | Cents (just) | Name | Simplified |
|---|---|---|---|
| -106 | 1192.7699 | bialtermercoctave | RJP1 |
| -105 | 694.7249 | altermercfifth | RjP5 |
| -104 | 196.6799 | altermercmajor second | RjM2 |
| -103 | 898.6349 | altermercmajor sixth | RjM6 |
| -102 | 400.5899 | altermercmajor third | RjM3 |
| -101 | 1102.5449 | altermercmajor seventh | RjM7 |
| -100 | 604.4999 | altermerctritone | RjTT |
| -99 | 106.4549 | altermercpominor second | Rjpm2 |
| -98 | 808.4099 | altermercpominor sixth | Rjpm6 |
| -97 | 310.3649 | altermercpominor third | Rjpm3 |
| -96 | 1012.3199 | altermercpominor seventh | Rjpm7 |
| -95 | 514.2749 | altermercpofourth | RjpP4 |
| -94 | 16.2299 | altermercpounison | RjpP1 |
| -93 | 718.1849 | altermercpofifth | RjpP5 |
| -92 | 220.1399 | altermercpomajor second | RjpM2 |
| -91 | 922.0949 | altermercpomajor sixth | RjpM6 |
| -90 | 424.0499 | altermercpomajor third | RjpM3 |
| -89 | 1126.0049 | altermercpomajor seventh | RjpM7 |
| -88 | 627.9599 | altermercpotritone | RjpTT |
| -87 | 129.9149 | altermercpopominor second | RjPm2 |
| -86 | 831.8699 | altermercpopominor sixth | RjPm6 |
| -85 | 333.8249 | altermercpopominor third | RjPm3 |
| -84 | 1035.7799 | altermercpopominor seventh | RjPm7 |
| -83 | 537.7349 | altermercpopofourth | RjPP4 |
| -82 | 39.6899 | altermercpopounison | RjPP1 |
| -81 | 741.6449 | altermercpopofifth | RjPP5 |
| -80 | 243.5999 | altermercpopomajor second | RjPM2 |
| -79 | 945.5549 | mercququminor seventh | jQm7 |
| -78 | 447.5099 | mercququfourth | jQP4 |
| -77 | 1149.4649 | mercququöctave | jQP1 |
| -76 | 651.4199 | mercququfifth | jQP5 |
| -75 | 153.3749 | mercququmajor second | jQM2 |
| -74 | 855.3299 | mercququmajor sixth | jQM6 |
| -73 | 357.2849 | mercququmajor third | jQM3 |
| -72 | 1059.2399 | mercququmajor seventh | jQM7 |
| -71 | 561.1949 | mercququtritone | jQTT |
| -70 | 63.1499 | mercquminor second | jqm2 |
| -69 | 765.1049 | mercquminor sixth | jqm6 |
| -68 | 267.0599 | mercquminor third | jqm3 |
| -67 | 969.0149 | mercquminor seventh | jqm7 |
| -66 | 470.9699 | mercqufourth | jqP4 |
| -65 | 1172.9249 | mercquoctave | jqP1 |
| -64 | 674.8799 | mercqufifth | jqP5 |
| -63 | 176.8349 | mercqumajor second | jqM2 |
| -62 | 878.7899 | mercqumajor sixth | jqM6 |
| -61 | 380.7449 | mercqumajor third | jqM3 |
| -60 | 1082.6999 | mercqumajor seventh | jqM7 |
| -59 | 584.6549 | mercqutritone | jqTT |
| -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 | altermercoctave / altermercunison | RjP8 / RjP1 |
| -52 | 698.3400 | alterfifth | RP5 |
| -51 | 200.2950 | altermajor second | RM2 |
| -50 | 902.2500 | altermajor sixth | RM6 |
| -49 | 404.2050 | altermajor third | RM3 |
| -48 | 1106.1600 | altermajor seventh | RM7 |
| -47 | 608.1150 | altertritone | RTT |
| -46 | 110.0700 | alterpominor second | Rpm2 |
| -45 | 812.0250 | alterpominor sixth | Rpm6 |
| -44 | 313.9800 | alterpominor third | Rpm3 |
| -43 | 1015.9350 | alterpominor seventh | Rpm7 |
| -42 | 517.8900 | alterpofourth | RpP4 |
| -41 | 19.8450 | alterpounison | RpP1 |
| -40 | 721.8000 | alterpofifth | RpP5 |
| -39 | 223.7550 | alterpomajor second | RpM2 |
| -38 | 925.7100 | alterpomajor sixth | RpM6 |
| -37 | 427.6650 | alterpomajor third | RpM3 |
| -36 | 1129.6200 | alterpomajor seventh | RpM7 |
| -35 | 631.5750 | alterpotritone | RpTT |
| -34 | 133.5300 | alterpopominor second | RPm2 |
| -33 | 835.4850 | alterpopominor sixth | RPm6 |
| -32 | 337.4400 | alterpopominor third | RPm3 |
| -31 | 1039.3950 | alterpopominor seventh | RPm7 |
| -30 | 541.3500 | alterpopofourth | RPP4 |
| -29 | 43.3050 | alterpopounison / ququminor second | RPP1 |
| -28 | 745.2600 | alterpopofifth / ququminor sixth | RPP5 |
| -27 | 247.2150 | alterpopomajor second / ququminor third | RPM2 |
| -26 | 949.1700 | ququminor seventh | Qm7 |
| -25 | 451.1250 | ququfourth | QP4 |
| -24 | 1153.0800 | ququöctave / ququunison | QP8 / QP1 |
| -23 | 655.0350 | ququfifth | QP5 |
| -22 | 156.9900 | ququmajor second | QM2 |
| -21 | 858.9450 | ququmajor sixth | QM6 |
| -20 | 360.9000 | ququmajor third | QM3 |
| -19 | 1062.8550 | ququmajor seventh | QM7 |
| -18 | 564.8100 | ququtritone | QTT |
| -17 | 66.7650 | quminor second | qm2 |
| -16 | 768.7200 | quminor sixth | qm6 |
| -15 | 270.6750 | quminor third | qm3 |
| -14 | 972.6300 | quminor seventh | qm7 |
| -13 | 474.5850 | qufourth | qP4 |
| -12 | 1176.5400 | quoctave / quunison | qP8 / qP1 |
| -11 | 678.4950 | qufifth | qP5 |
| -10 | 180.4500 | qumajor second | qM2 |
| -9 | 882.4050 | qumajor sixth | qM6 |
| -8 | 384.3600 | qumajor third | qM3 |
| -7 | 1086.3150 | qumajor seventh | qM7 |
| -6 | 588.2700 | qutritone | qTT |
| -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 | pominor second | pm2 |
| 8 | 815.6400 | pominor sixth | pm6 |
| 9 | 317.5950 | pominor third | pm3 |
| 10 | 1019.5500 | pominor seventh | pm7 |
| 11 | 521.5050 | pofourth | pP4 |
| 12 | 23.4600 | pounison / pooctave | pP1 / pP8 |
| 13 | 725.4150 | pofifth | pP5 |
| 14 | 227.3700 | pomajor second | pM2 |
| 15 | 929.3250 | pomajor sixth | pM6 |
| 16 | 431.2800 | pomajor third | pM3 |
| 17 | 1133.2350 | pomajor seventh | pM7 |
| 18 | 635.1900 | potritone | pTT |
| 19 | 137.1450 | popominor second | Pm2 |
| 20 | 839.1000 | popominor sixth | Pm6 |
| 21 | 341.0550 | popominor third | Pm3 |
| 22 | 1043.0100 | popominor seventh | Pm7 |
| 23 | 544.9650 | popofourth | PP4 |
| 24 | 46.9200 | popounison / popooctave | PP1 / PP8 |
| 25 | 748.8750 | popofifth | PP5 |
| 26 | 250.8300 | popomajor second | PM2 |
| 27 | 952.7850 | alterququminor seventh / popomajor sixth | RQm7 |
| 28 | 454.7400 | alterququfourth / popomajor third | RQP4 |
| 29 | 1156.6950 | alterququöctave / popomajor third | RQP1 |
| 30 | 658.6500 | alterququfifth / popomajor third | RQP5 |
| 31 | 160.6050 | alterququmajor second | RQM2 |
| 32 | 862.5600 | alterququmajor sixth | RQM6 |
| 33 | 364.5150 | alterququmajor third | RQM3 |
| 34 | 1066.4700 | alterququmajor seventh | RQM7 |
| 35 | 568.4250 | alterququtritone | RQTT |
| 36 | 70.3800 | alterquminor second | Rqm2 |
| 37 | 772.3350 | alterquminor sixth | Rqm6 |
| 38 | 274.2900 | alterquminor third | Rqm3 |
| 39 | 976.2450 | alterquminor seventh | Rqm7 |
| 40 | 478.2000 | alterqufourth | RqP4 |
| 41 | 1180.1550 | alterquoctave | RqP1 |
| 42 | 682.1100 | alterqufifth | RqP5 |
| 43 | 184.0650 | alterqumajor second | RqM2 |
| 44 | 886.0200 | alterqumajor sixth | RqM6 |
| 45 | 387.9750 | alterqumajor third | RqM3 |
| 46 | 1089.9300 | alterqumajor seventh | RqM7 |
| 47 | 591.8850 | alterqutritone | RqTT |
| 48 | 93.8400 | alterminor second | Rm2 |
| 49 | 795.7950 | alterminor sixth | Rm6 |
| 50 | 297.7500 | alterminor third | Rm3 |
| 51 | 999.7050 | alterminor seventh | Rm7 |
| 52 | 501.6600 | alterfourth | 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 | mercpominor second | jpm2 |
| 61 | 819.2551 | mercpominor sixth | jpm6 |
| 62 | 321.2101 | mercpominor third | jpm3 |
| 63 | 1023.1651 | mercpominor seventh | jpm7 |
| 64 | 525.1201 | mercpofourth | jpP4 |
| 65 | 27.0751 | mercpounison | jpP1 |
| 66 | 729.0301 | mercpofifth | jpP5 |
| 67 | 230.9851 | mercpomajor second | jpM2 |
| 68 | 932.9401 | mercpomajor sixth | jpM6 |
| 69 | 434.8951 | mercpomajor third | jpM3 |
| 70 | 1136.8501 | mercpomajor seventh | jpM7 |
| 71 | 638.8051 | mercpotritone | jpTT |
| 72 | 140.7601 | mercpopominor second | jPm2 |
| 73 | 842.7151 | mercpopominor sixth | jPm6 |
| 74 | 344.6701 | mercpopominor third | jPm3 |
| 75 | 1046.6251 | mercpopominor seventh | jPm7 |
| 76 | 548.5801 | mercpopofourth | jPP4 |
| 77 | 50.5351 | mercpopounison | jPP1 |
| 78 | 752.4901 | mercpopofifth | jPP5 |
| 79 | 254.4451 | mercpopomajor second | jPM2 |
| 80 | 956.4001 | altermercququminor seventh | RjQm7 |
| 81 | 458.3551 | altermercququfourth | RjQP4 |
| 82 | 1160.3101 | altermercququöctave | RjQP1 |
| 83 | 662.2651 | altermercququfifth | RjQP5 |
| 84 | 164.2201 | altermercququmajor second | RjQM2 |
| 85 | 866.1751 | altermercququmajor sixth | RjQM6 |
| 86 | 368.1301 | altermercququmajor third | RjQM3 |
| 87 | 1070.0851 | altermercququmajor seventh | RjQM7 |
| 88 | 572.0401 | altermercququtritone | RjQTT |
| 89 | 73.9951 | altermercquminor second | Rjqm2 |
| 90 | 775.9501 | altermercquminor sixth | Rjqm6 |
| 91 | 277.9051 | altermercquminor third | Rjqm3 |
| 92 | 979.8601 | altermercquminor seventh | Rjqm7 |
| 93 | 481.8151 | altermercqufourth | RjqP4 |
| 94 | 1183.7701 | altermercquoctave | RjqP1 |
| 95 | 685.7251 | altermercqufifth | RjqP5 |
| 96 | 187.6801 | altermercqumajor second | RjqM2 |
| 97 | 889.6351 | altermercqumajor sixth | RjqM6 |
| 98 | 391.5901 | altermercqumajor third | RjqM3 |
| 99 | 1093.5451 | altermercqumajor seventh | RjqM7 |
| 100 | 595.5001 | altermercqutritone | RjqTT |
| 101 | 97.4551 | altermercminor second | Rjm2 |
| 102 | 799.4101 | altermercminor sixth | Rjm6 |
| 103 | 301.3651 | altermercminor third | Rjm3 |
| 104 | 1003.3201 | altermercminor seventh | Rjm7 |
| 105 | 505.2751 | altermercfourth | RjP4 |
| 106 | 7.2301 | bimercunison | JP1 |
| Fifthspan | Interchromatic-central | Simplified | Interdiatonic-central | Simplified | ||
|---|---|---|---|---|---|---|
| Cents (just) | Name | Cents | Name | |||
| -53 | 1196.3850 | altermercoctave / altermercunison | RjP8 / RjP1 | 596.3850 | altermercsemiqutritone | RJ!TT |
| -52.5 | 347.3625 | altermid third | RN3 | 947.3625 | alterouranic | R6i7 |
| -52 | 698.3400 | alterfifth | RP5 | 98.3400 | altersemipominor second | R¡m2 |
| -51.5 | 1049.3175 | altermid seventh | RN7 | 449.3175 | alternaiadic | R3i4 |
| -51 | 200.2950 | altermajor second | RM2 | 800.2950 | altersemipominor sixth | R¡m6 |
| -50.5 | 551.2725 | altertrinterfourth | R4iT | 1151.2725 | altertartaric | R7i8 |
| -50 | 902.2500 | altermajor sixth | RM6 | 302.2500 | altersemipominor third | R¡m3 |
| -49.5 | 53.2275 | altersemipobarbaric | R¡1i2 | 653.2275 | altertrinterfifth | RP5T |
| -49 | 404.2050 | altermajor third | RM3 | 1004.2050 | altersemipominor seventh | R¡m7 |
| -48.5 | 755.1825 | altersemipococytic | R¡5i6 | 155.1825 | altersemipomid second | R¡N2 |
| -48 | 1106.1600 | altermajor seventh | RM7 | 506.1600 | altersemipofourth | R¡P4 |
| -47.5 | 257.1375 | altersemipochthonic | R¡2i3 | 857.1375 | altersemipomid sixth | R¡N6 |
| -47 | 608.1150 | altertritone | RTT | 8.1150 | altersemipounison | R¡P1 |
| -46.5 | 959.0925 | altersemipoouranic | R¡6i7 | 359.0925 | altersemipomid third | R¡N3 |
| -46 | 110.0700 | alterpominor second | Rpm2 | 710.0700 | altersemipofifth | R¡P5 |
| -45.5 | 461.0475 | altersemiponaiadic | R¡3i4 | 1061.0475 | altersemipomid seventh | R¡N7 |
| -45 | 812.0250 | alterpominor sixth | Rpm6 | 212.0250 | altersemipomajor second | R¡M2 |
| -44.5 | 1163.0025 | altersemipotartaric | R¡7i8 | 563.0025 | altersemipotrinterfourth | R¡4iT |
| -44 | 313.9800 | alterpominor third | Rpm3 | 913.9800 | altersemipomajor sixth | R¡M6 |
| -43.5 | 664.9575 | altersemipotrinterfifth | R¡P5T | 64.9575 | alterpobarbaric | Rp1i2 |
| -43 | 1015.9350 | alterpominor seventh | Rpm7 | 415.9350 | altersemipomajor third | R¡M3 |
| -42.5 | 166.9125 | alterpomid second | RpN2 | 766.9125 | alterpococytic | Rp5i6 |
| -42 | 517.8900 | alterpofourth | RpP4 | 1117.8900 | altersemipomajor seventh | R¡M7 |
| -41.5 | 868.8675 | alterpomid sixth | RpN6 | 268.8675 | alterpochthonic | Rp2i3 |
| -41 | 19.8450 | alterpounison | RpP1 | 619.8450 | altersemipotritone | R¡TT |
| -40.5 | 370.8225 | alterpomid third | RpN3 | 970.8225 | alterpoouranic | Rp6i7 |
| -40 | 721.8000 | alterpofifth | RpP5 | 121.8000 | altersesquipominor second | Rp¡m2 |
| -39.5 | 1072.7775 | alterpomid third | RpN7 | 472.7775 | alterponaiadic | Rp3i4 |
| -39 | 223.7550 | alterpomajor second | RpM2 | 823.7550 | altersesquipominor sixth | Rp¡m6 |
| -38.5 | 574.7325 | alterpotrinterfourth | Rp4iT | 1174.7325 | alterpotartaric | Rp7i8 |
| -38 | 925.7100 | alterpomajor sixth | RpM6 | 325.7100 | altersesquipominor third | Rp¡m3 |
| -37.5 | 76.6875 | altersesquipobarbaric | RQ1i2 | 676.6875 | alterpotrinterfifth | RpP5T |
| -37 | 427.6650 | alterpomajor third | RpM3 | 1027.6650 | altersesquipominor seventh | Rp¡m7 |
| -36.5 | 778.6425 | altersesquipococytic | RQ5i6 | 178.6425 | altersesquipomid second | Rp¡N2 |
| -36 | 1129.6200 | alterpomajor seventh | RpM7 | 529.6200 | altersesquipofourth | Rp¡P4 |
| -35.5 | 280.5975 | altersesquipochthonic | RQ2i3 | 880.5975 | altersesquipomid sixth | Rp¡N6 |
| -35 | 631.5750 | alterpotritone | RpTT | 31.5750 | altersesquipounison | Rp¡P1 |
| -34.5 | 982.5525 | altersesquipoouranic | RQ6i7 | 382.5525 | altersesquipomid third | Rp¡N3 |
| -34 | 133.5300 | alterpopominor second | RPm2 | 733.5300 | altersesquipofifth | Rp¡P5 |
| -33.5 | 484.5075 | altersesquiponaiadic | RQ3i4 | 1084.5075 | altersesquipomid seventh | Rp¡N7 |
| -33 | 835.4850 | alterpopominor sixth | RPm6 | 235.4850 | altersesquipomajor second | Rp¡M2 |
| -32.5 | 1186.4625 | altersesquipotartaric | RQ7i8 | 586.4625 | altersesquipotrinterfourth | Rp¡4iT |
| -32 | 337.4400 | alterpopominor third | RPm3 | 937.4400 | altersesquipomajor sixth | Rp¡M6 |
| -31.5 | 688.4175 | altersesquipotrinterfifth | RQP5T | 88.4175 | alterpopobarbaric | RP1i2 |
| -31 | 1039.3950 | alterpopominor seventh | RPm7 | 439.3950 | altersesquipomajor third | Rp¡M3 |
| -30.5 | 190.3725 | alterpopomid second | RPN2 | 790.3725 | alterpopococytic | RP5i6 |
| -30 | 541.3500 | alterpopofourth | RPP4 | 1141.3500 | altersesquipomajor seventh | Rp¡M7 |
| -29.5 | 892.3275 | alterpopomid sixth | RPN6 | 292.3275 | alterpopochthonic | RP2i3 |
| -29 | 43.3050 | alterpopounison | RPP1 | 643.3050 | altersesquipotritone | Rp¡TT |
| -28.5 | 394.2825 | alterpopomid third | RPN3 | 994.2825 | alterpopoouranic | RP6i7 |
| -28 | 745.2600 | alterpopofifth | RPP5 | 145.2600 | altersemimercmid second | RUN3 |
| -27.5 | 1096.2375 | alterpopomid third | RPN7 | 496.2375 | alterpoponaiadic | RP3i4 |
| -27 | 247.2150 | alterpopomajor second | RPM2 | 847.2150 | altersemimercmid sixth | RUN6 |
| -26.5 | 598.1925 | alterpopotrinterfourth | RP4iT | 1198.1925 | altersemimercoctave | RUP8 |
| -26 | 949.1700 | ququminor seventh | Qm7 | 349.1700 | semimercmid third | UN3 |
| -25.5 | 100.1475 | ququmid second | QN2 | 700.1475 | ququcocytic | Q5i6 |
| -25 | 451.1250 | ququfourth | QP4 | 1051.1250 | semimercmid seventh | UN7 |
| -24.5 | 802.1025 | ququmid sixth | QN6 | 202.1025 | ququchthonic | Q2i3 |
| -24 | 1153.0800 | ququöctave / ququunison | QP8 / QP1 | 553.0800 | semimerctrinterfourth | U4iT |
| -23.5 | 304.0575 | ququmid third | QN3 | 904.0575 | ququouranic | Q6i7 |
| -23 | 655.0350 | ququfifth | QP5 | 55.0350 | sesquiquminor second | q!m2 |
| -22.5 | 1006.0125 | ququmid seventh | QN7 | 406.0125 | ququnaiadic | Q3i4 |
| -22 | 156.9900 | ququmajor second | QM2 | 756.9900 | sesquiquminor sixth | q!m6 |
| -21.5 | 507.9675 | ququtrinterfourth | Q4iT | 1107.9675 | ququtartaric | Q7i8 |
| -21 | 858.9450 | ququmajor sixth | QM6 | 258.9450 | sesquiquminor third | q!m3 |
| -20.5 | 9.9225 | sesquiqubarbaric | q!1i2 | 609.9225 | ququtrinterfifth | QP5T |
| -20 | 360.9000 | ququmajor third | QM3 | 960.9000 | sesquiquminor seventh | q!m7 |
| -19.5 | 711.8775 | sesquiqucocytic | q!5i6 | 111.8775 | sesquiqumid second | q!N2 |
| -19 | 1062.8550 | ququmajor seventh | QM7 | 462.8550 | sesquiqufourth | q!P4 |
| -18.5 | 213.8325 | sesquiquchthonic | q!2i3 | 813.8325 | sesquiqumid sixth | q!N6 |
| -18 | 564.8100 | ququtritone | QTT | 1164.8100 | sesquiquoctave | q!P8 |
| -17.5 | 915.7875 | sesquiquouranic | q!6i7 | 315.7875 | sesquiqumid third | q!N3 |
| -17 | 66.7650 | quminor second | qm2 | 666.7650 | sesquiqufifth | q!P5 |
| -16.5 | 417.7425 | sesquiqunaiadic | q!3i4 | 1017.7425 | sesquiqumid seventh | q!N7 |
| -16 | 768.7200 | quminor sixth | qm6 | 168.7200 | sesquiqumajor second | q!M2 |
| -15.5 | 1119.6975 | sesquiqutartaric | q!7i8 | 519.6975 | sesquiqutrinterfourth | q!4iT |
| -15 | 270.6750 | quminor third | qm3 | 870.6750 | sesquiqumajor sixth | q!M6 |
| -14.5 | 621.6525 | sesquiqutrinterfifth | q!P5T | 21.6525 | qubarbaric | q1i2 |
| -14 | 972.6300 | quminor seventh | qm7 | 372.6300 | sesquiqumajor third | q!M3 |
| -13.5 | 123.6075 | qumid second | qN2 | 723.6075 | qucocytic | q5i6 |
| -13 | 474.5850 | qufourth | qP4 | 1074.5850 | sesquiqumajor seventh | q!M7 |
| -12.5 | 825.5625 | qumid sixth | qN6 | 225.5625 | quchthonic | q2i3 |
| -12 | 1176.5400 | quoctave / quunison | qP8 / qP1 | 576.5400 | sesquiqutritone | q!TT |
| -11.5 | 327.5175 | qumid third | qN3 | 927.5175 | quouranic | q6i7 |
| -11 | 678.4950 | qufifth | qP5 | 78.4950 | semiquminor second | !m2 |
| -10.5 | 1029.4725 | qumid seventh | qN7 | 429.4725 | qunaiadic | q3i4 |
| -10 | 180.4500 | qumajor second | qM2 | 780.4500 | semiquminor sixth | !m6 |
| -9.5 | 531.4275 | qutrinterfourth | q4iT | 1131.4275 | qutartaric | q7i8 |
| -9 | 882.4050 | qumajor sixth | qM6 | 282.4050 | semiquminor third | !m3 |
| -8.5 | 33.3825 | semiqubarbaric | !1i2 | 633.3825 | qutrinterfifth | qP5T |
| -8 | 384.3600 | qumajor third | qM3 | 984.3600 | semiquminor seventh | !m7 |
| -7.5 | 735.3375 | semiqucocytic | !5i6 | 135.3375 | semiqumid second | !N2 |
| -7 | 1086.3150 | qumajor seventh | qM7 | 486.3150 | semiqufourth | !P4 |
| -6.5 | 237.2925 | semiquchthonic | !2i3 | 837.2925 | semiqumid sixth | !N6 |
| -6 | 588.2700 | qutritone | qTT | 1188.2700 | semiquoctave | !P8 |
| -5.5 | 939.2475 | semiquouranic | !6i7 | 339.2475 | semiqumid third | !N3 |
| -5 | 90.2250 | minor second | m2 | 690.2250 | semiqufifth | !P5 |
| -4.5 | 441.2025 | semiqunaiadic | !3i4 | 1041.2025 | semiqumid seventh | !N7 |
| -4 | 792.1800 | minor sixth | m6 | 192.1800 | semiqumajor second | !M2 |
| -3.5 | 1143.1575 | semiqutartaric | !7i8 | 543.1575 | semiqutrinterfourth | !4iT |
| -3 | 294.1350 | minor third | m3 | 894.1350 | semiqumajor sixth | !M6 |
| -2.5 | 645.1125 | semiqutrinterfifth | !P5T | 45.1125 | barbaric | 1i2 |
| -2 | 996.0900 | minor seventh | m7 | 396.0900 | semiqumajor third | !M3 |
| -1.5 | 147.0675 | mid second | N2 | 747.0675 | cocytic | 5i6 |
| -1 | 498.0450 | fourth | P4 | 1098.0450 | semiqumajor seventh | !M7 |
| -0.5 | 849.0225 | mid sixth | N6 | 249.0225 | chthonic | 2i3 |
| 0 | 0.0000 | unison / octave | P1 | 600.0000 | semiqutritone | !TT |
| 0.5 | 350.9775 | mid third | N3 | 950.9775 | ouranic | 6i7 |
| 1 | 701.9550 | fifth | P5 | 101.9550 | semipominor second | ¡m2 |
| 1.5 | 1052.9325 | mid seventh | N7 | 452.9325 | naiadic | 3i4 |
| 2 | 203.9100 | major second | M2 | 803.9100 | semipominor sixth | ¡m6 |
| 2.5 | 554.8875 | trinterfourth | 4iT | 1154.8875 | tartaric | 7i8 |
| 3 | 905.8650 | major sixth | M6 | 305.8650 | semipominor third | ¡m3 |
| 3.5 | 56.8425 | semipobarbaric | ¡1i2 | 656.8425 | trinterfifth | P5T |
| 4 | 407.8200 | major third | M3 | 1007.8200 | semipominor seventh | ¡m7 |
| 4.5 | 758.7975 | semipococytic | ¡5i6 | 158.7975 | semipomid second | ¡N2 |
| 5 | 1109.7750 | major seventh | M7 | 509.7750 | semipofourth | ¡P4 |
| 5.5 | 260.7525 | semipochthonic | ¡2i3 | 860.7525 | semipomid sixth | ¡N6 |
| 6 | 611.7300 | tritone | TT | 11.7300 | semipounison | ¡P1 |
| 6.5 | 962.7075 | semipoouranic | ¡6i7 | 362.7075 | semipomid third | ¡N3 |
| 7 | 113.6850 | pominor second | pm2 | 713.6850 | semipofifth | ¡P5 |
| 7.5 | 464.6625 | semiponaiadic | ¡3i4 | 1064.6625 | semipomid seventh | ¡N7 |
| 8 | 815.6400 | pominor sixth | pm6 | 215.6400 | semipomajor second | ¡M2 |
| 8.5 | 1166.6175 | semipotartaric | ¡7i8 | 566.6175 | semipotrinterfourth | ¡4iT |
| 9 | 317.5950 | pominor third | pm3 | 917.5950 | semipomajor sixth | ¡M6 |
| 9.5 | 668.5725 | semipotrinterfifth | ¡P5T | 68.5725 | pobarbaric | p1i2 |
| 10 | 1019.5500 | pominor seventh | pm7 | 419.5500 | semipomajor third | ¡M3 |
| 10.5 | 170.5275 | pomid second | pN2 | 770.5275 | pococytic | p5i6 |
| 11 | 521.5050 | pofourth | pP4 | 1121.5050 | semipomajor seventh | ¡M7 |
| 11.5 | 872.4825 | pomid sixth | pN6 | 272.4825 | pochthonic | p2i3 |
| 12 | 23.4600 | pounison / pooctave | pP1 / pP8 | 623.4600 | semipotritone | ¡TT |
| 12.5 | 374.4375 | pomid third | pN3 | 974.4375 | poouranic | p6i7 |
| 13 | 725.4150 | pofifth | pP5 | 125.4150 | sesquipominor second | p¡m2 |
| 13.5 | 1076.3925 | pomid third | pN7 | 476.3925 | ponaiadic | p3i4 |
| 14 | 227.3700 | pomajor second | pM2 | 827.3700 | sesquipominor sixth | p¡m6 |
| 14.5 | 578.3475 | potrinterfourth | p4iT | 1178.3475 | potartaric | p7i8 |
| 15 | 929.3250 | pomajor sixth | pM6 | 329.3250 | sesquipominor third | p¡m3 |
| 15.5 | 80.3025 | sesquipobarbaric | Q1i2 | 680.3025 | potrinterfifth | pP5T |
| 16 | 431.2800 | pomajor third | pM3 | 1031.2800 | sesquipominor seventh | p¡m7 |
| 16.5 | 782.2575 | sesquipococytic | Q5i6 | 182.2575 | sesquipomid second | p¡N2 |
| 17 | 1133.2350 | pomajor seventh | pM7 | 533.2350 | sesquipofourth | p¡P4 |
| 17.5 | 284.2125 | sesquipochthonic | Q2i3 | 884.2125 | sesquipomid sixth | p¡N6 |
| 18 | 635.1900 | potritone | pTT | 35.1900 | sesquipounison | p¡P1 |
| 18.5 | 986.1675 | sesquipoouranic | Q6i7 | 386.1675 | sesquipomid third | p¡N3 |
| 19 | 137.1450 | popominor second | Pm2 | 737.1450 | sesquipofifth | p¡P5 |
| 19.5 | 488.1225 | sesquiponaiadic | Q3i4 | 1088.1225 | sesquipomid seventh | p¡N7 |
| 20 | 839.1000 | popominor sixth | Pm6 | 239.1000 | sesquipomajor second | p¡M2 |
| 20.5 | 1190.0775 | sesquipotartaric | Q7i8 | 590.0775 | sesquipotrinterfourth | p¡4iT |
| 21 | 341.0550 | popominor third | Pm3 | 941.0550 | sesquipomajor sixth | p¡M6 |
| 21.5 | 692.0325 | sesquipotrinterfifth | QP5T | 92.0325 | popobarbaric | P1i2 |
| 22 | 1043.0100 | popominor seventh | Pm7 | 443.0100 | sesquipomajor third | p¡M3 |
| 22.5 | 193.9875 | popomid second | PN2 | 793.9875 | popococytic | P5i6 |
| 23 | 544.9650 | popofourth | PP4 | 1144.9650 | sesquipomajor seventh | p¡M7 |
| 23.5 | 895.9425 | popomid sixth | PN6 | 295.9425 | popochthonic | P2i3 |
| 24 | 46.9200 | popounison / popooctave | PP1 | 646.9200 | sesquipotritone | p¡TT |
| 24.5 | 397.8975 | popomid third | PN3 | 997.8975 | popoouranic | P6i7 |
| 25 | 748.8750 | popofifth | PP5 | 148.8750 | semimercmid second | UN3 |
| 25.5 | 1099.8525 | popomid third | PN7 | 499.8525 | poponaiadic | P3i4 |
| 26 | 250.8300 | popomajor second | PM2 | 850.8300 | semimercmid sixth | UN6 |
| 26.5 | 601.8075 | popotrinterfourth | P4iT | 1.8075 | semimercunison | UP1 |
| 27 | 952.7850 | alterququminor seventh | RQm7 | 352.7850 | altersemimercmid third | RUN3 |
| 27.5 | 103.7625 | alterququmid second | RQN2 | 703.7625 | alterququcocytic | RQ5i6 |
| 28 | 454.7400 | alterququfourth | RQP4 | 1054.7400 | altersemimercmid seventh | RUN7 |
| 28.5 | 805.7175 | alterququmid sixth | RQN6 | 205.7175 | alterququchthonic | RQ2i3 |
| 29 | 1156.6950 | alterququöctave / alterququunison | RQP8 / RQP1 | 556.6950 | altersemimerctrinterfourth | RU4iT |
| 29.5 | 307.6725 | alterququmid third | RQN3 | 907.6725 | alterququouranic | RQ6i7 |
| 30 | 658.6500 | alterququfifth | RQP5 | 58.6500 | altersesquiquminor second | Rq!m2 |
| 30.5 | 1009.6275 | alterququmid seventh | RQN7 | 409.6275 | alterququnaiadic | RQ3i4 |
| 31 | 160.6050 | alterququmajor second | RQM2 | 760.6050 | altersesquiquminor sixth | Rq!m6 |
| 31.5 | 511.5825 | alterququtrinterfourth | RQ4iT | 1111.5825 | alterququtartaric | RQ7i8 |
| 32 | 862.5600 | alterququmajor sixth | RQM6 | 262.5600 | altersesquiquminor third | Rq!m3 |
| 32.5 | 13.5375 | altersesquiqubarbaric | Rq!1i2 | 613.5375 | alterququtrinterfifth | RQP5T |
| 33 | 364.5150 | alterququmajor third | RQM3 | 964.5150 | altersesquiquminor seventh | Rq!m7 |
| 33.5 | 715.4925 | altersesquiqucocytic | Rq!5i6 | 115.4925 | altersesquiqumid second | Rq!N2 |
| 34 | 1066.4700 | alterququmajor seventh | RQM7 | 466.4700 | altersesquiqufourth | Rq!P4 |
| 34.5 | 217.4475 | altersesquiquchthonic | Rq!2i3 | 817.4475 | altersesquiqumid sixth | Rq!N6 |
| 35 | 568.4250 | alterququtritone | RQTT | 1168.4250 | altersesquiquoctave | Rq!P8 |
| 35.5 | 919.4025 | altersesquiquouranic | Rq!6i7 | 319.4025 | altersesquiqumid third | Rq!N3 |
| 36 | 70.3800 | alterquminor second | Rqm2 | 670.3800 | altersesquiqufifth | Rq!P5 |
| 36.5 | 421.3575 | altersesquiqunaiadic | Rq!3i4 | 1021.3575 | altersesquiqumid seventh | Rq!N7 |
| 37 | 772.3350 | alterquminor sixth | Rqm6 | 172.3350 | altersesquiqumajor second | Rq!M2 |
| 37.5 | 1123.3125 | altersesquiqutartaric | Rq!7i8 | 523.3125 | altersesquiqutrinterfourth | Rq!4iT |
| 38 | 274.2900 | alterquminor third | Rqm3 | 874.2900 | altersesquiqumajor sixth | Rq!M6 |
| 38.5 | 625.2675 | altersesquitrinterfifth | Rq!P5T | 25.2675 | alterqubarbaric | Rq1i2 |
| 39 | 976.2450 | alterquminor seventh | Rqm7 | 376.2450 | altersesquiqumajor third | Rq!M3 |
| 39.5 | 127.2225 | alterqumid second | RqN2 | 727.2225 | alterqucocytic | Rq5i6 |
| 40 | 478.2000 | alterqufourth | RqP4 | 1078.2000 | altersesquiqumajor seventh | Rq!M7 |
| 40.5 | 829.1775 | alterqumid sixth | RqN6 | 229.1775 | alterquchthonic | Rq2i3 |
| 41 | 1180.1550 | alterquoctave | RqP1 | 580.1550 | altersesquiqutritone | Rq!TT |
| 41.5 | 331.1325 | alterqumid third | RqN3 | 931.1325 | alterquouranic | Rq6i7 |
| 42 | 682.1100 | alterqufifth | RqP5 | 82.1100 | altersemiquminor second | R!m2 |
| 42.5 | 1033.0875 | alterqumid seventh | RqN7 | 433.0875 | alterqunaiadic | Rq3i4 |
| 43 | 184.0650 | alterqumajor second | RqM2 | 784.0650 | altersemiquminor sixth | R!m6 |
| 43.5 | 535.0425 | alterqutrinterfourth | Rq4iT | 1135.0425 | alterqutartaric | Rq7i8 |
| 44 | 886.0200 | alterqumajor sixth | RqM6 | 286.0200 | altersemiquminor third | R!m3 |
| 44.5 | 36.9975 | altersemiqubarbaric | R!1i2 | 636.9975 | alterqutrinterfifth | RqP5T |
| 45 | 387.9750 | alterqumajor third | RqM3 | 987.9750 | altersemiquminor seventh | R!m7 |
| 45.5 | 738.9525 | altersemiqucocytic | R!5i6 | 138.9525 | altersemiqumid second | R!N2 |
| 46 | 1089.9300 | alterqumajor seventh | RqM7 | 489.9300 | altersemiqufourth | R!P4 |
| 46.5 | 240.9075 | altersemiquchthonic | R!2i3 | 840.9075 | altersemiqumid sixth | R!N6 |
| 47 | 591.8850 | alterqutritone | RqTT | 1191.8850 | altersemiquoctave | R!P8 |
| 47.5 | 942.8625 | altersemiquouranic | R!6i7 | 342.8625 | altersemiqumid third | R!N3 |
| 48 | 93.8400 | alterminor second | Rm2 | 693.8400 | altersemiqufifth | R!P5 |
| 48.5 | 444.8175 | altersemiqunaiadic | R!3i4 | 1044.8175 | altersemiqumid seventh | R!N7 |
| 49 | 795.7950 | alterminor sixth | Rm6 | 195.7950 | altersemiqumajor second | R!M2 |
| 49.5 | 1146.7725 | altersemiqutartaric | R!7i8 | 546.7725 | altersemiqutrinterfourth | R!4iT |
| 50 | 297.7500 | alterminor third | Rm3 | 897.7500 | altersemiqumajor sixth | R!M6 |
| 50.5 | 648.7275 | altersemiqutrinterfifth | R!P5T | 48.7275 | alterbarbaric | R1i2 |
| 51 | 999.7050 | alterminor seventh | Rm7 | 399.7050 | altersemiqumajor third | R!M3 |
| 51.5 | 150.6825 | altermid second | RN2 | 750.6825 | altercocytic | R5i6 |
| 52 | 501.6600 | alterfourth | RP4 | 1101.6600 | altersemiqumajor seventh | R!M7 |
| 52.5 | 852.6375 | altermid sixth | RN6 | 252.6375 | alterchthonic | R2i3 |
| 53 | 3.6150 | mercunison / mercoctave | jP1 / jP8 | 603.6150 | mercsemiqutritone | J!TT |
How to use for temps in/and higher limits
EPN can handle tons of temperaments that are based on the chain of fifths, obviously the rank-2 monocots, dicots, alpha-dicots, and hemipyth ones; but also rank-3 ones with a free generator for other primes. However, there is a special case when the septischisma is tempered out due to the prevalence of the super/sub usage for septimal.
General case
Can be used not 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 qu/po prefixes, the meantone diesis
- Fifths flatter than 11\19 have to use aug/dim fractions because the mapped meantone diesis is far too wide.
Septischismic
Use the rightward names and symbols if the septischisma is tempered out since the poma is closer to 64/63 (the septischismic column). In there, the pomas and merccommas become are equated and often sound much closer to rumas and buzzardsmas. If not, keep po and super distinct. There is no equivalent for septimal comma qian, on purpose. Assume ^/v are always aberschismas. This gives you a solid 13-limit basis that can be extended to olympic.
- P1 — M2 — ^sM3 — HP4 — P5 — vHm6 — sm7 — ^sM7 — P8: 8afdo in Ultimate (see here for specifics of notation)
| Pyth or distinct | 64/63 or septischismic | Aberschismas | Septi(schismas) | |||||
|---|---|---|---|---|---|---|---|---|
| po | p | (su)per | S | up | ^ | Schisma | / | bi |
| qu | q | sub | s | down | v | \ | bo | |
| popo | P | hyper | H | dup | ^^ | // | bibi | |
| ququ | Q | hypo | h | dud | w | \\ | bobo | |
| semipo | ¡ | semiper | Z | trup | 3^ | Septischis | ^\ | gi |
| semiqu | ! | semisub | z | trud | 3v | v/ | go | |
| sesquipo | p¡ | sesquiper | SZ | quup | 4^ | ^^\\ | gi | |
| sesquiqu | q! | sesquisub | sz | quud | 4v | w// | go | |
| alter | R | trans | L | quip | 5^ | |||
| merc | J | buzz | Γ | quid | 5v | |||