User:Moremajorthanmajor/16wtn: Difference between revisions
Jump to navigation
Jump to search
No edit summary |
m Text replacement - "{{todo|clarify|unify precision|inline=1}}" to "" |
||
| (5 intermediate revisions by 3 users not shown) | |||
| Line 1: | Line 1: | ||
'''16WTN''' is the equal division of the fifth into 8 steps of 87.7444 [[cent]]s each, alternated with a sequence of eight equal steps of another interval between 75 and 100 cents in its patent tunings making its best tunings very nearly [[88cET]]. | '''16WTN''' is optimally the equal division of the fifth into 8 steps of 87.7444 [[cent]]s each, alternated with a sequence of eight equal steps of another interval between 75 and 100 cents in its patent tunings making its best tunings very nearly [[88cET]]. | ||
== | == Patent Intervals == | ||
The best tunings of 16WTN can be interpreted as tunings for the Natural and Harmonic Minor modes of Annapolis[6L 4s]. For the notation of these modes, Greek numerals 1-10 can be used (Α,Β,Γ,Δ,Ε,Ϛ/Ϝ,Ζ,Η,Θ,Ι [J]). | The best tunings of 16WTN can be interpreted as tunings for the Natural and Harmonic Minor modes of Annapolis[6L 4s]. For the notation of these modes, Greek numerals 1-10 can be used (Α,Β,Γ,Δ,Ε,Ϛ/Ϝ,Ζ,Η,Θ,Ι [J]). | ||
{| class="wikitable" | {| class="wikitable" | ||
| Line 8: | Line 8: | ||
!Target a | !Target a | ||
!Target b | !Target b | ||
!Alternating [[EDO|edo]] and *ed(9/8) a | |||
!Alternating edo and *ed(9/8) b | |||
!Annapolis[6L 4s] | !Annapolis[6L 4s] | ||
|- | |- | ||
|1 | |||
! colspan="2" |87.7444 | ! colspan="2" |87.7444 | ||
|92.3077 | |||
|85.7143 | |||
|Α# | |Α# | ||
|- | |- | ||
|2 | |||
! colspan="2" |175.48875 | ! colspan="2" |175.48875 | ||
|184.6154 | |||
|171.4286 | |||
|Β | |Β | ||
|- | |- | ||
|3 | |||
! colspan="2" |263.2331 | ! colspan="2" |263.2331 | ||
|276.9231 | |||
|257.1429 | |||
|Γ | |Γ | ||
|- | |- | ||
|4 | |||
! colspan="2" |350.9775 | ! colspan="2" |350.9775 | ||
|369.2308 | |||
|342.8571 | |||
|Γ# | |Γ# | ||
|- | |- | ||
|5 | |||
! colspan="2" |438.7219 | ! colspan="2" |438.7219 | ||
|461.5385 | |||
|428.5714 | |||
|Δ | |Δ | ||
|- | |- | ||
|6 | |||
! colspan="2" |526.46625 | ! colspan="2" |526.46625 | ||
|553.84615 | |||
|51<span style="line-height: 1.5;">4.2857</span> | |||
|Δ# | |Δ# | ||
|- | |- | ||
|7 | |||
! colspan="2" |614.2106 | ! colspan="2" |614.2106 | ||
|646.15385 | |||
|600.000 | |||
|Ε | |Ε | ||
|- | |- | ||
|'''8''' | |||
! colspan="2" |'''701.955''' | ! colspan="2" |'''701.955''' | ||
|738.4615 | |||
|685.7143 | |||
|'''Ϛ/Ϝ''' | |'''Ϛ/Ϝ''' | ||
|- | |- | ||
| Line 45: | Line 63: | ||
|801.564 | |801.564 | ||
|784.9625 | |784.9625 | ||
|830.7692 | |||
|771.4286 | |||
|Ϛ#/Ϝ# | |Ϛ#/Ϝ# | ||
|- | |- | ||
| Line 50: | Line 70: | ||
|901.173 | |901.173 | ||
|867.97 | |867.97 | ||
|923.0769 | |||
|857.1429 | |||
|Ζ | |Ζ | ||
|- | |- | ||
| Line 55: | Line 77: | ||
|1000.782 | |1000.782 | ||
|950.9775 | |950.9775 | ||
|1015.3846 | |||
|942.8571 | |||
|Η | |Η | ||
|- | |- | ||
| Line 60: | Line 84: | ||
|1101.391 | |1101.391 | ||
|1033.985 | |1033.985 | ||
|1107.6923 | |||
|1028.5714 | |||
|Η# | |Η# | ||
|- | |- | ||
| Line 65: | Line 91: | ||
|1200 | |1200 | ||
|1116.9925 | |1116.9925 | ||
|1200 | |||
|1114.2857 | |||
|Θ | |Θ | ||
|- | |- | ||
|14 | |14 | ||
|1299.609 | |1299.609 | ||
|1200 | |||
|1267.97 | |||
|1200 | |1200 | ||
|Θ# | |Θ# | ||
| Line 75: | Line 105: | ||
|1398.218 | |1398.218 | ||
|1283.0075 | |1283.0075 | ||
|1333.94 | |||
|1301.955 | |||
|I (J) | |I (J) | ||
|- | |- | ||
| Line 80: | Line 112: | ||
|1497.827 | |1497.827 | ||
|1366.015 | |1366.015 | ||
! colspan="2" |1403.91 | |||
|A | |A | ||
|} | |} | ||
[[Category:Well tempered nonet]] | |||
Latest revision as of 09:31, 1 September 2025
16WTN is optimally the equal division of the fifth into 8 steps of 87.7444 cents each, alternated with a sequence of eight equal steps of another interval between 75 and 100 cents in its patent tunings making its best tunings very nearly 88cET.
Patent Intervals
The best tunings of 16WTN can be interpreted as tunings for the Natural and Harmonic Minor modes of Annapolis[6L 4s]. For the notation of these modes, Greek numerals 1-10 can be used (Α,Β,Γ,Δ,Ε,Ϛ/Ϝ,Ζ,Η,Θ,Ι [J]).
| Target a | Target b | Alternating edo and *ed(9/8) a | Alternating edo and *ed(9/8) b | Annapolis[6L 4s] | |
|---|---|---|---|---|---|
| 1 | 87.7444 | 92.3077 | 85.7143 | Α# | |
| 2 | 175.48875 | 184.6154 | 171.4286 | Β | |
| 3 | 263.2331 | 276.9231 | 257.1429 | Γ | |
| 4 | 350.9775 | 369.2308 | 342.8571 | Γ# | |
| 5 | 438.7219 | 461.5385 | 428.5714 | Δ | |
| 6 | 526.46625 | 553.84615 | 514.2857 | Δ# | |
| 7 | 614.2106 | 646.15385 | 600.000 | Ε | |
| 8 | 701.955 | 738.4615 | 685.7143 | Ϛ/Ϝ | |
| 9 | 801.564 | 784.9625 | 830.7692 | 771.4286 | Ϛ#/Ϝ# |
| 10 | 901.173 | 867.97 | 923.0769 | 857.1429 | Ζ |
| 11 | 1000.782 | 950.9775 | 1015.3846 | 942.8571 | Η |
| 12 | 1101.391 | 1033.985 | 1107.6923 | 1028.5714 | Η# |
| 13 | 1200 | 1116.9925 | 1200 | 1114.2857 | Θ |
| 14 | 1299.609 | 1200 | 1267.97 | 1200 | Θ# |
| 15 | 1398.218 | 1283.0075 | 1333.94 | 1301.955 | I (J) |
| 16 | 1497.827 | 1366.015 | 1403.91 | A | |