(Canasta = Spanish, "basket")
A 31-tone scale derived from an optimal generator called MIRACLE, and a subset of 72-EDO.
For its relatively small size, this scale approximates an enormous number of 3-, 5-, 7-, and 11-limit just-intonation harmonic structures.
In keeping with the name of its smaller relative, the blackjack scale, it was dubbed "canasta" on the misconception that the card game used 31 cards. Those who know the game are aware that this is not the case, and for a while the scale was called MIRACLE-31. But later, when the meaning of the Spanish word was discovered, it was decided after all that "canasta" was an entirely appropriate name to describe this scale which contains so many harmonic resources, and that MIRACLE could therefore be reserved to designate the generator itself and the whole family of tunings.
Below are graphs of the cents-values of the pitches in
a typical Canasta chain, illustrated on the left as a
scale and on the right as a chain of generators from
-15 to +15 secors.
Below are the same graphs, but this time with the y-axis
quantized into 41edo instead of 12edo, which shows how
closely 41edo approximates the 72edo version of Canasta.
(There are 4 degrees of 41edo in a
secor.)
Finally, below are the same graphs again,
but this time with the y-axis
quantized into 31edo, which shows how
closely 31edo approximates the 72edo version of Canasta.
(There are 3 degrees of 31edo in a
secor.)
Below is a tabulation of the (-15...+15) canasta in 72, 41, and 31edo. My 72edo HEWM notation, Graham Breed's decimal notation, and cents-values are also given.
HEWM 31edo 41edo 72edo cents Breed decimal degree degree degree degree C< 30 40 70 1166.&2/3 0v B+ 29 38 67 1116.&2/3 9^^ B- 28 37 65 1083.&1/3 9^ Bv 27 36 63 1050 9 Bb 26 34 60 1000 8^^ Bb< 25 33 58 966.&2/3 8^ A> 24 32 56 933.&1/3 8 A- 23 30 53 883.&1/3 7^^ Av 22 29 51 850 7^ G#+ 21 28 49 816.&2/3 7 G#< 20 26 46 766.&2/3 6^^ G> 19 25 44 733.&1/3 6^ G 18 24 42 700 6 Gv 17 22 39 650 5^^ F#+ 16 21 37 616.&2/3 5^ F#- 15 20 35 583.&1/3 5 F^ 14 19 33 550 5v F 13 17 30 500 4^ F< 12 16 28 466.&2/3 4 E> 11 15 26 433.&1/3 4v E- 10 13 23 383.&1/3 3^ Ev 9 12 21 350 3 Eb+ 8 11 19 316.&2/3 3v Eb< 7 9 16 266.&2/3 2^ D> 6 8 14 233.&1/3 2 D 5 7 12 200 2v Dv 4 5 9 150 1^ C#+ 3 4 7 116.&2/3 1 C#- 2 3 5 83.&1/3 1v C> 1 1 2 33.&1/3 0^ C 0 0 0 0 0
Note that the full set of 31edo acts simultaneously as both a closed meantone (specifically, 1/4-comma meantone) and as the canasta form of MIRACLE.
Below is a 5-limit bingo-card-lattice of 72edo, with the canasta scale shown in buff in the central periodicity-block and in pink in the blocks which are commatic equivalents. The subset of canasta which comprises the blackjack scale is shown in lighter shades.
In May 2001 I devised this mapping of almost 2
"octaves" of the Canasta
scale to the standard QWERTY computer keyboard, for
use with my
JustMusic
software. The pitches are given
in my ASCII 72-EDO notation.
See also my Blackjack webpage.
[from Joe Monzo, JustMusic: A New Harmony]
updated:
2002.10.10 -- graphs added
2002.11.04 -- tabulation of 31/41/72edo and 72edo bingo-card-lattice added
2003.07.06 -- fixed erroneous reference to "blackjack" on bingo lattice
