Tetrameantone: Difference between revisions
Why did you document an interval in a temperament page?? |
Rework intro and invert the interval chain since 3/1 and 5/1 (or 5/4) are more recognizable |
||
| Line 1: | Line 1: | ||
The '''tetrameantone''' temperament is a [[nonoctave]] [[ | The '''tetrameantone''' temperament is a [[nonoctave]] [[regular temperament|temperament]] [[tempering out]] [[81/80]] in the 4.3.5-[[subgroup]]. It is similar to [[meantone]] but repeats at the double octave [[4/1]]. It is generated by [[3/1]] and, like in normal meantone temperament, four of them make a [[5/1]] plus two double octaves. | ||
== Interval chain == | == Interval chain == | ||
In the following table, odd harmonics 1–5 are '''bolded'''. | |||
{| class="wikitable center-1 right-2" | {| class="wikitable center-1 right-2" | ||
! | ! # | ||
! Cents | ! Cents* | ||
! Approximate | ! Approximate Ratios | ||
|- | |- | ||
| 0 | | 0 | ||
| 0.000 | | 0.000 | ||
| | | '''1/1''' | ||
|- | |- | ||
| 1 | | 1 | ||
| | | 1896.239 | ||
| | | '''3/1''' | ||
|- | |- | ||
| 2 | | 2 | ||
| | | 1392.477 | ||
| | | 9/4, 20/9 | ||
|- | |- | ||
| 3 | | 3 | ||
| | | 888.716 | ||
| | | 5/3 | ||
|- | |- | ||
| 4 | | 4 | ||
| | | 384.955 | ||
| | | '''5/4''' | ||
|- | |- | ||
| 5 | | 5 | ||
| | | 2281.193 | ||
| | | 15/4 | ||
|- | |- | ||
| 6 | | 6 | ||
| | | 1777.432 | ||
| | | 45/16 | ||
|- | |- | ||
| 7 | | 7 | ||
| | | 1273.671 | ||
| | | 25/12 | ||
|} | |} | ||
<nowiki>*</nowiki> in 4.3.5-subgroup POTE tuning | |||
== Tetrameantone on tritave == | == Tetrameantone on tritave == | ||
Tritave-repeating tetrameantone (3.4.5 subgroup) is made by cutting off the 4/3 interval range of the tetratave scale. extension will start at 3.4.5.14 subgroup. If we want strict no-twos subgroup, will be 3.5.13. | Tritave-repeating tetrameantone (3.4.5 subgroup) is made by cutting off the 4/3 interval range of the tetratave scale. extension will start at 3.4.5.14 subgroup. If we want strict no-twos subgroup, will be 3.5.13. | ||