8103edo: Difference between revisions
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== Theory == | |||
8103edo is [[consistent]] in the [[21-odd-limit]]. In the 13-limit, it tempers out [[123201/123200]], and in the 17-limit, it tempers out [[12376/12375]]. | |||
It is divisible by 37, and inherits the precise 11th harmonic present in [[37edo]], although the error has accumulated up to 23% at this point. | |||
=== Prime harmonics === | |||
{{harmonics in equal|8103}} | |||
== Regular temperament properties == | |||
=== Rank-2 temperaments === | |||
{| class="wikitable center-all left-5" | |||
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |||
|- | |||
! Periods<br />per 8ve | |||
! Generator* | |||
! Cents* | |||
! Associated<br />ratio* | |||
! Temperaments | |||
|- | |||
| 111 | |||
| 3363\8103<br>(5\8103) | |||
| 498.0377<br>0.7405 | |||
| 4/3<br>(2657205/2656192) | |||
| [[Roentgenium]] | |||
|} | |||
<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct | |||
== Music == | == Music == | ||
* [https://www.youtube.com/watch?v=FaI74-ZPVaw Etude in C Roentgenium, Op. 2, No.1] by [[Eliora]] | |||
[[Category:Equal divisions of the octave|####]] <!-- 4-digit number --> | |||
[[Category:Listen]] | |||
Latest revision as of 13:31, 13 March 2026
| ← 8102edo | 8103edo | 8104edo → |
8103 equal divisions of the octave (abbreviated 8103edo or 8103ed2), also called 8103-tone equal temperament (8103tet) or 8103 equal temperament (8103et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 8103 equal parts of about 0.148 ¢ each. Each step represents a frequency ratio of 21/8103, or the 8103rd root of 2.
Theory
8103edo is consistent in the 21-odd-limit. In the 13-limit, it tempers out 123201/123200, and in the 17-limit, it tempers out 12376/12375.
It is divisible by 37, and inherits the precise 11th harmonic present in 37edo, although the error has accumulated up to 23% at this point.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000 | +0.0072 | +0.0617 | +0.0005 | +0.0334 | +0.0499 | +0.0427 | +0.0064 | -0.0626 | -0.0326 | +0.0218 |
| Relative (%) | +0.0 | +4.9 | +41.7 | +0.3 | +22.6 | +33.7 | +28.9 | +4.3 | -42.3 | -22.0 | +14.7 | |
| Steps (reduced) |
8103 (0) |
12843 (4740) |
18815 (2609) |
22748 (6542) |
28032 (3723) |
29985 (5676) |
33121 (709) |
34421 (2009) |
36654 (4242) |
39364 (6952) |
40144 (7732) | |
Regular temperament properties
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated ratio* |
Temperaments |
|---|---|---|---|---|
| 111 | 3363\8103 (5\8103) |
498.0377 0.7405 |
4/3 (2657205/2656192) |
Roentgenium |
* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct