A scale devised by Wendy Carlos, which does not have octaves, because of its equal "step size" of 63.8 ¢, with 18.809 steps per "octave".

It is "defined strictly as a local minimum of the root-mean-square error function that Wendy set up with 3/2, 5/4, 6/5, 7/4, and 11/8 as target intervals."

The Carlos Beta tuning splits a tempered "perfect-4th" into two equal parts, each of which in turn are twice divided in half - thus, the perfect-4th subtends 8 equal steps of 63.8 ¢ each. The first "8ve" of this scale is covered by the following notes in descending order:

degree cents 19 1212.2 18 1148.4 17 1084.6 16 1020.8 15 957 14 893.2 13 829.4 12 765.6 11 701.8 10 638 9 574.2 8 510.4 7 446.6 6 382.8 5 319 4 255.2 3 191.4 2 127.6 1 63.8 0 0Examples of its use can be found on the title track of her album Beauty In The Beast.

Various EDOs give approximations to the Carlos beta scale:

- 19-edo is a fairly low-cardinality tuning which gives a rough approximation of the beta tuning, with 1deg19-edo giving a passable approximation to one step of beta. But its approximation of the 3/2 ratio is 11deg19-edo, which is the same narrow 5th which acts as the generator in 19-edo's role as the 19-et approximation of 1/3-comma meantone, and the error from the beta 5th is enough to be audibly noticeable.
- 94-edo gives a much better approximation of beta, at the cost of much higher cardinality, with 5deg94-edo closely approximating one step of beta, and 55deg94-edo giving a very good approximation of the beta 5th.

Used in its lower-case form β as an additional letter-name in Erv Wilson's notations, signifying a note near "B", but with a musical function separate from "B", in whatever particular scale the notation is describing. See The Wilson Archives for examples and explanations of his notation.

[Joe Monzo]

. . . . . . . . .

The tonalsoft.com website is almost entirely the work of one person: me, Joe Monzo. Please reward me for my knowledge and effort by choosing your preferred level of financial support. Thank you.

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)