User:Eufalesio/EPN

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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:

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.

Table of synonyms
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.

Table of Monocot up to ±106 fifths
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
Table of Hemipyth up to ±53 fifths
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
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