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User:UnbihexiumFan/Temperaments: Difference between revisions

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table & extensions
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Each half-period can be taken to represent
'''Bolded''' ratios are 7/4-reduced harmonics up to 21.
 
=== High-accuracy 7/4.2.3.11/5.13.17 extension ===


'''Bolded''' ratios are 7/4-reduced harmonics up to 21.
The 17th harmonic can be added by equating [[17/12]] and [[24/17]] with the half-octave, tempering [[442/441]], the 13th harmonic can be added by equating [[27/26]] and [[28/27]], tempering [[729/728]], and the interval [[11/5]] can be added by equating [[54/49]] with [[11/10]], tempering out [[540/539]]. This provides a high-accuracy temperament with a [[comma basis]] of 442/441, 729/728, 289/288, and 540/539.


=== Extensions ===
{| class="wikitable"
! # Gens
! Cents<ref name="SSW">Optimal generator from the [https://sevish.com/scaleworkshop Sevish Scale Workshop]</ref>
! Approximate ratios
! # Gens
! Cents<ref name="SSW" />
! Approximate ratios
|-
| +0
| 0.0
|
| -0
| 968.83
|
|-
| +1
| 701.04
|
| -1
| 267.78
|
|-
| +2
| 433.26
|
| -2
| 535.57
|
|-
| +3
| 165.47
|
| -3
| 803.35
|
|-
| +4
| 866.52
|
| -4
| 102.31
|
|-
| +5
| 598.73
|
| -5
| 370.09
|
|-
| +6
| 330.95
|
| -6
| 637.88
|
|-
| +7
| 63.16
|
| -7
| 905.66
|
|-
| +8
| 764.21
|
| -8
| 204.62
|
|-
| +9
| 496.42
|
| -9
| 472.40
|
|-
| +10
| 228.64
|
| -10
| 740.19
|
|-
| +11
| 929.68
|
| -11
| 39.15
|
|-
| +12
| 661.90
|
| -12
| 306.93
|
|-
| +13
| 394.11
|
| -13
| 574.71
|
|-
| +14
| 126.33
|
| -14
| 842.50
|
|-
| +15
| 827.37
|
| -15
| 141.46
|
|-
| +16
| 559.59
|
| -16
| 409.24
|
|-
| +17
| 291.80
|
| -17
| 677.02
|
|-
| +18
| 24.02
|
| -18
| 944.81
|
|-
| +19
| 725.06
|
| -19
| 243.77
|
|-
| +20
| 457.28
|
| -20
| 511.55
|
|}


The 17th harmonic can be added by equating [[17/12]] and [[24/17]] with the half-octave, tempering [[442/441]] and the 13th harmonic can be added by equating [[27/26]] and [[28/27]], tempering [[729/728]]. This provides a [[comma basis]] of 442/441, 729/728, and 289/288.
'''Bolded''' ratios are 7/4-reduced harmonics up to 21.
Retrieved from "https://en.xen.wiki/w/User:UnbihexiumFan/Temperaments"