  # mem, 205-edo

[Joe Monzo]

A small unit of interval measurement, used mainly in connection with h-Pi Instruments, suggested by Aaron Hunt and used by him as the default tuning for his instruments.

A mem divides one degree of 41-edo into 5 logarithmically equal parts. This is approximately the size of the JND (just noticeable difference). It therefore divides the octave into 41 * 5 = 205 equal parts.

The mem is therefore calculated as the 205th root of 2, or 2(1/205), with a ratio of approximately 1:1.00338692848311. It is an irrational number.

A mem is:

• exactly 3 153/205 (= 3.7,46341... = ~ 3 3/4 ) 6mus.
• exactly 4 36/41 (= 4.87804... = ~ 4 7/8 ) millioctaves,
• exactly 5 35/41 (= 5.85365... = ~ 5 6/7 ) cents,
• exactly 4 38/123 (= 4.30894... = ~ 4 1/3 ) türk-sents,
• <-->
• exactly 12 minas,
• exactly 41 134/205 (= 41.6,53658... = ~ 41 2/3 ) tinas.
• exactly 239 157/205 (= 239.7,65853... = ~ 239 3/4 ) 12mus.
• exactly 959 13/205 (= 959.0,63414... = ~ 959 1/16 ) 14mus.

The formula for calculating the mem-value of any ratio r is: mems = log10(r) * [ 205 / log10(2) ] or mems = log2(r) * 205

A mem represents one degree of 205-edo tuning.

The 12-edo semitone is exactly 17 1/12 (= 17.08,3...) mems.

. . . . . . . . .

### mems calculator

Ratio may be entered as fraction or floating-point decimal number.
(value must be greater than 1)

For EDOs (equal-temperaments), type: "a/b" (without quotes)
where "a" = EDO degree and "b" = EDO cardinality.
(value must be less than 1)

Enter ratio: = mems

. . . . . . . . .

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