Goldfish
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The goldfish scale is a 7-tone MOS scale.
It is a specific case of the fish scale (the 2|4 mode of 3L 4s).
In the goldfish scale, the ratio of step sizes L:s is equal to the golden ratio (1.6180339887...:1)
The goldfish scale occurs within the golden suhajira temperament.
List of intervals
It is impossible to provide a numerical list of intervals for the 'pure' goldfish scale, but here is a list of intervals for the 788edo goldfish scale, which is indistinguishably close, for most intents and purposes:
- 44.162 (29\788)
- 385.279 (253\788)
- 429.442 (282\788)
- 770.558 (506\788)
- 814.721 (535\788)
- 858.883 (564\788)
- 1200.000 (788\788)
Modes
Rotating the goldfish scale gives the following modes (in order of rotation):
- Goldgill (5|1)
- Goldjewel (1|5)
- Goldteeth (4|2)
- Gold LED (0|6)
- Goldbish (3|3)
- Golddrill (6|0)
Based on the mode names by Andrew Heathwaite but modified slightly to fit the humorous nature of this scale's title.
Supporting EDOs
EDOs that support goldfish are any EDOs which contain exactly this number of steps:
n(4f)+n(3g)
Where f is a Fibonacci number and g is the next Fibonacci number after f. And n can be any number.
No EDOs include the 'pure' goldfish scale, but the approximations get increasingly accurate with increasingly large values of f.
You can calculate a list of optimal EDOs for the goldfish scale using the formula 4x+3(((1+sqrt(5))/2)x)) where x is a fibonacci number... This gives EDOs: 9, 18, 27, 44, 71, 115, 185, 301, 486, 788...
Trivia
Budjarn Lambeth described the goldfish scale after observing an interaction between the wiki editors, on the Xenharmonic Alliance Discord server:
Lériendil informed the Discord that they had just completed the page on the sensamagic-gariboh equivalence continuum. CompactStar noted that he had initially misread the title as “sensamagic-goldfish equivalence continuum”, possibly due to the multiple “spog” reactions on Lériendil‘s post (an emote which indicates genuine approval, but in a somewhat playful and whimsical manner).