Méride is a term coined by Joseph Saveur to designate the larger of his two interval measurements, the smaller being the heptaméride.

A meride is calculated as the 43rd root of 2, or 2^{(1/43)}, with a ratio of approximately 1:1.016250325. It is an irrational number.

A meride is exactly 27^{39}/_{43} or 27.906976744186046511627... cents, or just a bit larger than several of the most common commas.

The formula for calculating the meride-value of any ratio is: `merides = log _{10}(ratio) * [43 / log_{10}(2)]` or

`merides = log`.

_{2}(ratio) * 43This interval therefore divides the octave, which is assumed to have the ratio 2:1, into 43 equal parts. Thus a meride represents one degree in 43-edo tuning.

One potential defect of using merides is that the familiar 12-edo semitone does not come out with an integer number of merides, since 43 is a prime number and therefore does not divide evenly by 12. Thus, the 12-EDO semitone is ~3.583333333, or exactly 3 & 7/12, merides.

Note that 7 * 43 = 301, so both of Saveur's units, the merides and heptamerides, did divide evenly.

The interval which functions as the 5th in 43-edo is nearly identical to the 1/5-comma meantone "5th":

43-edo "5th" = 2^{(25/43)}= 25 merides = ~697.6744186 cents. 1/5-comma meantone "5th" = (3/2) / ( (81/80)^(1/5) ) = 2^{-(5/5)}* 3^{(5/5)}* 5^{(0/5)}Pythagorean "perfect 5th", ratio 3:2 - 2^{-(4/5)}* 3^{(4/5)}* 5^{-(1/5)}1/5 syntonic comma ---------------------------- 2^{-(1/5)}* 3^{(1/5)}* 5^{(1/5)}= ~24.99925912 (= 24^{~1349}/_{1350}) merides = ~697.6537429 cents. Difference between 43-edo and 1/5-comma "5ths": = 2^{-(125/215)}43-edo "5th" - 2^{-(43/215)}* 3^{(1/5)}* 5^{(1/5)}1/5-comma meantone "5th" ------------------------------- 2^{(168/215)}* 3^{-(1/5)}* 5^{-(1/5)}= ~0.020675659 (= ~1/50) cent = ~1/2 jot.

Here is a graph of a 44-tone cycle of 1/5-comma meantone, centered on "C" as the reference (= generator 0):

Note that the pitches represented as Fbbb (-22 generators) and C### (+21 generators) are nearly identical:

Fbbb = ( (3/2)^{-22}/ ( (81/80)^{(-22/5)}) ) * 2^{13}= 2^{(87/5)}* 3^{-(22/5)}* 5^{-(22/5)}= ~251.6176552 cents C### = ( (3/2)^{21}/ ( (81/80)^{(21/5)}) ) / 2^{12}= 2^{-(81/5)}* 3^{(21/5)}* 5^{(21/5)}= ~250.7286019 cents 2^{(87/5)}* 3^{-(22/5)}* 5^{-(22/5)}Fbbb - 2^{-(81/5)}* 3^{(21/5)}* 5^{(21/5)}C### ---------------------------- 2^{(168/5)}* 3^{(-43/5)}* 5^{(-43/5)}= ~0.88905332 (=^{~8}/_{9}) cent. 0.88905332 / 43 = 0.020675659 --> compare with above.

Thus, limiting the meantone cycle to 43 pitches and distributing this difference equally among them, results in 43-edo. The chromatic semitone = 3 merides, the diatonic semitone = 4 merides, and the whole-tone = 7 merides.

These are Gene Ward Smith's 7-limit MT reduced bases for 43-edo: 43: [81/80, 126/125, 12288/12005], which can also be written as a matrix of monzos thus:

2,3,5,7-monzo [-4 4, -1 0 > = 81/80 [ 1 2, -3 1 > = 126/125 [12 1, -1 -4 > = 12288/12005

1/5-comma meantone was first described by Abraham Verheyen in a letter to Simon Stevin, around 1600.

Below is a lattice which shows one pattern by which the plane of the [3 5] lattice is tiled by 43-edo: