Tetrahanson: Difference between revisions
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== Interval chain == | == Interval chain == | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |||
! Generators | ! Generators | ||
! Cents (CTE) | ! Cents (CTE) | ||
! Approximate ratios | ! Approximate ratios | ||
|- | |- | ||
| | | −7 | ||
| 1019.413 | | 1019.413 | ||
| [[9/5]] | | [[9/5]] | ||
|- | |- | ||
| | | −6 | ||
| 1902.354 | | 1902.354 | ||
| [[3/1]] | | [[3/1]] | ||
|- | |- | ||
| | | −5 | ||
| 385.295 | | 385.295 | ||
| [[5/4]] | | [[5/4]] | ||
|- | |- | ||
| | | −4 | ||
| 1268.236 | | 1268.236 | ||
| 25/12 | | 25/12 | ||
|- | |- | ||
| | | −3 | ||
| 2151.177 | | 2151.177 | ||
| 125/36 | | 125/36 | ||
|- | |- | ||
| | | −2 | ||
| 634.118 | | 634.118 | ||
| [[36/25]] | | [[36/25]] | ||
|- | |- | ||
| | | −1 | ||
| 1517.059 | | 1517.059 | ||
| [[12/5]] | | [[12/5]] | ||
| Line 73: | Line 74: | ||
In tritave-repeating tetrahanson (3.4.5 subgroup), 36/25 actually represents 1\3edt, which makes the 3rd-tritave period. | In tritave-repeating tetrahanson (3.4.5 subgroup), 36/25 actually represents 1\3edt, which makes the 3rd-tritave period. | ||
=== b39 & b15 === | === {{nowrap|b39 & b15}} === | ||
This is restriction of [[catalan]] extension. This can maintain the structure of the 3rd-octave period in 3.4.5, 3.5.11, and 3.5.13. Well, 3.4.5 and 3.5.13, which do not include 7 nor 11 in their basis, should simply be called tetrahanson (and no-twos cata, respectively). | This is restriction of [[catalan]] extension. This can maintain the structure of the 3rd-octave period in 3.4.5, 3.5.11, and 3.5.13. Well, 3.4.5 and 3.5.13, which do not include 7 nor 11 in their basis, should simply be called tetrahanson (and no-twos cata, respectively). | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! | ! !! 3.4.5 !! 3.5.11 !! 3.5.13 | ||
|- | |- | ||
| CWE || 883.071 || 879.416 || 883.808 | | CWE || 883.071 || 879.416 || 883.808 | ||
| Line 92: | Line 93: | ||
{| class="wikitable center-1 right-2" | {| class="wikitable center-1 right-2" | ||
|+ Interval chain | |+ style="font-size: 105%;" | Interval chain | ||
|- | |- | ||
! rowspan="2" | # | ! rowspan="2" | # | ||
| Line 106: | Line 107: | ||
! Approximate ratios | ! Approximate ratios | ||
|- | |- | ||
| | | −1 | ||
| 1656.6 | | 1656.6 | ||
| 125/48, [[13/5]] | | 125/48, [[13/5]] | ||
| Line 159: | Line 160: | ||
{| class="wikitable" | {| class="wikitable" | ||
|+ Chords | |+ style="font-size: 105%;" | Chords | ||
|- | |- | ||
! Mossteps !! Tonic and then every +2 mossteps | ! Mossteps !! Tonic and then every +2 mossteps | ||
| Line 175: | Line 176: | ||
{| class="wikitable center-all left-4" | {| class="wikitable center-all left-4" | ||
|+ Tuning spectrum | |+ style="font-size: 105%;" | Tuning spectrum | ||
|- | |- | ||
! ET<br />generator | ! ET<br />generator | ||