[Joe Monzo]

A system of temperament in which the "5th" is wider (larger) than the 12-edo "5th" of 700 cents.

(I had originally provided some examples here measured in terms of fraction-of-a-comma temperament. These have been removed in favor of the ones given below.)

. . . . . . . . .

[Paul Erlich, Yahoo tuning-math, message 2542 (Thu Jan 10, 2002 4:56 pm)]

Today, on these [internet tuning] lists, we tend to call negative systems "meantone" and positive systems "schismic". The reason 700 cents was chosen as the dividing line between "negative" and "positive" is that when the fifth is below 700 cents, the "meantone" (+4 fifths) approximation to the 5/4 is better than the "schismic" (-8 fifths) approximation to the 5/4. When the fifth is above 700 cents, the "schismic" approximation to the 5/4 is better than the "meantone" approximation to the 5/4. I might differ, saying that there is a "gray area", and also factoring the 6/5 into consideration . . . but the definitions are well-established and there is no reason to favor ones which could breed potential contradictions.

... Positive systems should be characterized by the fraction of a *schisma* that the fifths differ from just -- this is the relevant measure of them. Knowing what fraction of a syntonic comma a positive system's fifth might have been *increased* by is irrelevant for understanding the functioning of the system, and is potentially misleading.

. . . . . . . . .

Manuel Op de Coul also suggested that I add the tuning's "p"-rating, where "p" represents the Pythagorean comma in terms of number of that temperament's scale degrees:

[Manuel Op de Coul, Yahoo tuning-math message 2580 (Fri Jan 11, 2002 5:08 am)]

Ifvis the size of the fifth, andathe size of the octave, thenp= 12v- 7a. For example in 31-tET,v= 18 anda= 31, sop= -1.

A negative value indicates a negative temperament, and a positive value indicates a positive temperament. Values greater than one require an additional qualifier, as, for example, 2 designates "doubly positive", -3 is "triply negative", etc.

. . . . . . . . .

[Joe Monzo]

So taking Paul's advice and Manuel's suggestion, here is the listing of the same EDO "5ths", but giving this time their deviation from 3:2 in fractions of a skhisma, and also their "p" value:

tuningptempering of "5th" 17-EDO +1 == + 2 skhismas 22-EDO +2 == + 3 & 1/3 skhismas + 3 & 15/23 skhismas 29-EDO +1 == + 4/5 skhisma + 7/9 skhisma + 13/17 skhisma 39-EDO +3 == + 2 & 15/16 skhismas 41-EDO +1 == + 1/4 skhisma

. . . . . . . . .

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a&b temperament [a&b are numbers]

55-edo (comma) (Mozart's tuning)

1/1 or 1:1 (ratio)

2/1 or 2:1 (ratio)

a&b temperament [a&b are numbers]

apotome (Greek interval)

aristoxenean (temperament family)

atomic (temperament family)

augmented / diesic (temperament family)

augmented-2nd / aug-2 / #2 (interval)

augmented-4th / aug-4 / #4 (interval)

augmented-5th / aug-5 / #5 (interval)

augmented-6th / aug-6 / #6 (interval)

augmented-9th / aug-9 / #9 (interval)

blackjack (tuning)

cent / ¢ (unit of interval measurement)

centitone / iring (unit of interval measurement)

chromatic-semitone / augmented-prime (interval)

daseian (musical notation)

dekamu / 10mu (MIDI-unit)

diapason (Greek interval)

diapente (Greek interval)

diatessaron (Greek interval)

diatonic semitone (minor-2nd) (interval)

diesic (temperament family)

diezeugmenon (Greek tetrachord)

diminished-5th / dim5 / -5 / b5 (interval)

diminished-7th / dim7 / o7 (interval)

doamu / 2mu (MIDI-unit)

dodekamu / 12mu (MIDI-unit)

dominant-7th (dom-7, x7) (chord)

dorian (mode)

eleventh / 11th (interval)

enamu / 1mu (MIDI-unit)

endekamu / 11mu (MIDI-unit)

enharmonic semitone (interval)

ennealimmal (temperament family)

enneamu / 9mu (MIDI-unit)

farab (unit of interval measurement)

fifth / 5th (interval)

flu (unit of interval measurement)

Gentle introduction to Fokker periodicity-blocks (by Paul Erlich)

fourth / 4th (interval)

Gentle introduction to Fokker periodicity-blocks (by Paul Erlich)

grad (unit of interval measurement)

hexamu / 6mu (MIDI-unit)

Hurrian Hymn (Monzo reconstruction)

hypate (Greek note)

hypaton (Greek tetrachord)

hyperbolaion / hyperboleon (Greek tetrachord)

hypophrygian (Greek mode)

imperfect (interval quality)

iring / centitone (unit of interval measurement)

1/1 or 1:1 (ratio)

2/1 or 2:1 (ratio)

jot (unit of interval measurement)

JustMusic: A New Harmony [Monzo's book]

JustMusic prime-factor notation [Monzo essay]

kwazy (temperament family)

leimma / limma (Greek interval)

lichanos (Greek note)

limma / leimma (Greek interval)

locrian (mode)

lydian (mode)

magic (temperament family)

Mahler 7th/1 [Monzo score and analysis]

marvel (temperament family)

meantone (temperament family)

mem (unit of interval measurement)

meride (unit of interval measurement)

mese (Greek note)

meson (Greek tetrachord)

millioctave / m8ve (unit of interval measurement)

mina (unit of interval measurement)

minerva (temperament family)

miracle (temperament family)

mixolydian (mode)

monzo (prime-exponent vector)

Monzo, Joe (music-theorist)

morion / moria (unit of interval measurement)

mutt (temperament family)

mystery (temperament family)

octamu / oktamu / 8mu (MIDI-unit)

octave (interval)

oktamu / octamu / 8mu (MIDI-unit)

orwell (temperament family)

p4, perfect 4th, perfect fourth (interval)

p5, perfect 5th, perfect fifth (interval)

pantonality of Schoenberg [Monzo essay]

paramese (Greek note)

paranete (Greek note)

parhypate (Greek note)

pentamu / 5mu (MIDI-unit)

prime-factor notation (JustMusic) [Monzo essay]

proslambanomenos (Greek note)

savart (unit of interval measurement)

schismic / skhismic (temperament family)

Schoenberg's pantonality [Monzo essay]

second / 2nd (interval)

semisixths (temperament family)

semitone (unit of interval measurement)

seventh / 7th (interval)

sixth / 6th (interval)

sk (unit of interval measurement)

skhismic / schismic (temperament family)

sruti tuning [Monzo essay]

studloco (tuning)

subminor 3rd (interval)

Sumerian tuning [speculations by Monzo]

synemmenon (Greek tetrachord)

temperament-unit / tu (unit of interval measurement)

tenth / 10th (interval)

tetrachord-theory tutorial [by Monzo]

tetradekamu / 14mu (MIDI-unit)

tetramu / 4mu (MIDI-unit)

third / 3rd (interval)

thirteenth / 13th (interval)

tina (unit of interval measurement)

tone (interval, and other definitions)

tredek (unit of interval measurement)

triamu / 3mu (MIDI-unit)

tridekamu / 13mu (MIDI-unit)

trihemitone (Greek interval)

trite (Greek note)

tu / temperament-unit (unit of interval measurement)

Türk sent (unit of interval measurement)

twelfth / 12th (interval)

whole-tone (interval)

woolhouse-unit (unit of interval measurement)