298edo

From Xenharmonic Wiki
Jump to navigation Jump to search
298edo
Prime factorization 2 × 149
Fifth 174\298 (87\149)

298 equal divisions of the octave (298edo), or 298-tone equal temperament (298tet), 298 equal temperament (298et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 298 equal parts of about 4.03 ¢ each.

Theory

Approximation of odd harmonics in 298edo
Harmonic 3 5 7 9 11 13 15 17 19 21
Error absolute (¢) -1.28 +0.26 +1.64 +1.46 +0.36 +1.08 -1.02 -0.26 +0.47 +0.36
relative (%) -32 +7 +41 +36 +9 +27 -25 -6 +12 +9
Steps
(reduced)
472
(174)
692
(96)
837
(241)
945
(51)
1031
(137)
1103
(209)
1164
(270)
1218
(26)
1266
(74)
1309
(117)

298edo has excellent representation of the 2.5.11.17.23.43.53.59 subgroup, with all the harmonics having errors of less than 10 rc. It is a double of 149edo, which is the smallest edo that is uniquely consistent within the 17-odd-limit. It supports a 17-limit extension of Sensi, 111 & 103 & 298. However, compared to 149edo, 298edo's patent val differs on the mapping of 7, 11, and 13th harmonics.

It can be viewed as a "spicy 149edo" as a result, and different temperaments can be extracted from 298edo by simply viewing its prime harmonics as variations from 149edo by its own half-step.

In the 7-limit in the patent val, it supports bison temperament and the rank 3 temperament hemiwuermity. In the 298cd val, it supports miracle.

In the patent val, 298edo tempers out 351/350, 561/560, 936/935, and 1156/1155 in the full 17-limit. In the 2.5.11.13.17 subgroup, it tempers out 2200/2197 and 6656/6655.

In the 2.5.11.17.23.43.53.59, 298edo tempers out 3176/3175, 3128/3125, 3128/3127, 32906/32065 and 76585/76582.

The concoctic scale for 298edo is a scale produced by a generator of 105 steps (paraconcoctic), and the associated rank two temperament is 105 & 298.

Rank two temperaments by generator

Note: Temperaments represented by 149edo are not included.

Periods

per octave

Generator

(reduced)

Cents

(reduced)

Associated

ratio

Temperaments
2 39\298 157.04 35/32 Bison