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User:BudjarnLambeth/Draft related tunings section: Difference between revisions

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→Octave stretch or compression: useless column if there's only one significant figure
→Octave stretch or compression: as I pointed out before, octave size is way better than step size. Unify to TE and 3 decimal places
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; 36edo
; 36edo
* Step size: 33.333{{c}}, octave size: 1200.0{{c}}  
* Step size: 33.333{{c}}, octave size: 1200.000{{c}}  
{{Harmonics in equal|36|2|1|intervals=integer|columns=11|collapsed=true}}
{{Harmonics in equal|36|2|1|intervals=integer|columns=11|collapsed=true}}
{{Harmonics in equal|36|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 36edo (continued)}}
{{Harmonics in equal|36|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 36edo (continued)}}
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Pure-octaves 36edo approximates all primes up to 11 within ''15.3{{c}}''.
Pure-octaves 36edo approximates all primes up to 11 within ''15.3{{c}}''.


; [[TE|36et, 11-limit TE tuning]]
; [[TE|36et, 13-limit TE tuning]]
* Step size: 33.287{{c}}, octave size: 1198.3{{c}}
* Step size: 33.304{{c}}, octave size: 1198.929{{c}}
{{Harmonics in cet|33.287|columns=11|collapsed=true|title=Approximation of harmonics in 11-limit TE tuning of 36et}}
{{Harmonics in cet|33.303596|columns=11|collapsed=true|title=Approximation of harmonics in 13-limit TE tuning of 36et}}
{{Harmonics in cet|33.287|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 11-limit TE tuning of 36et (continued)}}
{{Harmonics in cet|33.303596|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 13-limit TE tuning of 36et (continued)}}


Compressing the octave of 36edo by about 2{{c}} results in much improved primes 5 and 11, but much worse primes 7 and 13. This approximates all primes up to 11 within ''9.7{{c}}''. The 11- and 13-limit TE tunings of 36et both do this, as do their respective WE tunings.
Compressing the octave of 36edo by about 2{{c}} results in much improved primes 5 and 11, but much worse primes 7 and 13. This approximates all primes up to 11 within ''9.7{{c}}''. The 11- and 13-limit TE tunings of 36et both do this, as do their respective WE tunings.
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|+ style="white-space: nowrap;" | Comparison of stretched and compressed tunings
|+ style="white-space: nowrap;" | Comparison of stretched and compressed tunings
|-
|-
! rowspan="2" | Tuning !! rowspan="2" | Step size<br>(cents) !! colspan="6" | Prime error (cents)  
! rowspan="2" | Tuning !! rowspan="2" | Octave size<br>(cents) !! colspan="6" | Prime error (cents)  
! rowspan="2" | Mapping of primes 2–13 (steps)
! rowspan="2" | Mapping of primes 2–13 (steps)
|-
|-
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|-
|-
! 21edf
! 21edf
| 33.426
| 1203.351
| +3.3 || +3.3 || −12.0 || +7.2 || −6.5 || +5.1
| +3.3 || +3.3 || −12.0 || +7.2 || −6.5 || +5.1
| 36, 57, 83, 101, 124, 133
| 36, 57, 83, 101, 124, 133
|-
|-
! 57edt
! 57edt
| 33.368 || +1.2 || 0.0 || +16.6 || +1.3 || −13.7 || −2.6
| 1201.235
| +1.2 || 0.0 || +16.6 || +1.3 || −13.7 || −2.6
| 36, 57, 84, 101, 124, 133
| 36, 57, 84, 101, 124, 133
|-
|-
! 155zpi
! 155zpi
| 33.346
| 1200.587
| +0.6 || −1.0 || +15.1 || −0.5 || −16.0|| −5.0
| +0.6 || −1.0 || +15.1 || −0.5 || −16.0|| −5.0
| 36, 57, 83, 101, 124, 133
| 36, 57, 83, 101, 124, 133
|-
|-
! 36edo
! 36edo
| '''33.333'''
| '''1200.000'''
| '''0.0''' || '''−2.0''' || '''+13.7''' || '''−2.2''' || '''+15.3''' || '''−7.2'''
| '''0.0''' || '''−2.0''' || '''+13.7''' || '''−2.2''' || '''+15.3''' || '''−7.2'''
| '''36, 57, 84, 101, 125, 133'''
| '''36, 57, 84, 101, 125, 133'''
|-
|-
! 13-limit WE
! 13-limit TE
| 33.302
| 1198.929
| −1.1 || −3.7 || +11.1 || −5.3 || +11.4 || −11.4
| −1.1 || −3.7 || +11.2 || −5.2 || +11.6 || −11.1
| 36, 57, 84, 101, 125, 133
| 36, 57, 84, 101, 125, 133
|-
|-
! 11-limit WE
! 11-limit TE
| 33.286
| 1198.330
| −1.7 || −4.7 || +9.7 || −6.9 || +9.4 || −13.5
| −1.7 || −4.6 || +9.8 || −6.8 || +9.5 || −13.4
| 36, 57, 84, 101, 125, 133
| 36, 57, 84, 101, 125, 133
|}
|}
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