2444edo: Difference between revisions
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m changed EDO intro to ED intro |
m Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ED intro}} | {{ED intro}} | ||
==Theory== | == Theory == | ||
2444edo is an excellent 2.5.7.11.13.19 subgroup tuning. | 2444edo is an excellent 2.5.7.11.13.19 subgroup tuning. | ||
In the 13-limit, 2444edo tempers out [[6656/6655]] and in light of having 52 as a divisor, it is a tuning for the [[french deck]] temperament. | In the 13-limit, 2444edo tempers out [[6656/6655]] and in light of having 52 as a divisor, it is a tuning for the [[french deck]] temperament. | ||
===Harmonics=== | |||
=== Harmonics === | |||
{{harmonics in equal|2444}} | {{harmonics in equal|2444}} | ||
== Regular temperament properties == | == Regular temperament properties == | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
!Periods<br>per 8ve | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
! Generator | |- | ||
! Cents | ! Periods<br />per 8ve | ||
! Associated<br> | ! Generator* | ||
! Cents* | |||
! Associated<br />ratio* | |||
! Temperaments | ! Temperaments | ||
|- | |- | ||
| 52 | | 52 | ||
| 804\2444<br>(5\2444) | | 804\2444<br />(5\2444) | ||
| 394.73662<br>(2.455) | | 394.73662<br />(2.455) | ||
| 134560000/107132311<br>(?) | | 134560000/107132311<br />(?) | ||
| [[French deck]] | | [[French deck]] | ||
|} | |} | ||
<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 | |||
Latest revision as of 13:32, 13 March 2026
| ← 2443edo | 2444edo | 2445edo → |
2444 equal divisions of the octave (abbreviated 2444edo or 2444ed2), also called 2444-tone equal temperament (2444tet) or 2444 equal temperament (2444et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2444 equal parts of about 0.491 ¢ each. Each step represents a frequency ratio of 21/2444, or the 2444th root of 2.
Theory
2444edo is an excellent 2.5.7.11.13.19 subgroup tuning.
In the 13-limit, 2444edo tempers out 6656/6655 and in light of having 52 as a divisor, it is a tuning for the french deck temperament.
Harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.173 | +0.102 | -0.086 | -0.146 | +0.073 | +0.062 | -0.216 | +0.118 | +0.032 | +0.087 | +0.204 |
| Relative (%) | +35.2 | +20.8 | -17.5 | -29.7 | +14.9 | +12.5 | -44.1 | +24.1 | +6.5 | +17.6 | +41.5 | |
| Steps (reduced) |
3874 (1430) |
5675 (787) |
6861 (1973) |
7747 (415) |
8455 (1123) |
9044 (1712) |
9548 (2216) |
9990 (214) |
10382 (606) |
10735 (959) |
11056 (1280) | |
Regular temperament properties
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated ratio* |
Temperaments |
|---|---|---|---|---|
| 52 | 804\2444 (5\2444) |
394.73662 (2.455) |
134560000/107132311 (?) |
French deck |
* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct