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Various equal divisions of the octave have close approximations of acoustic phi, or <span><math>φ</math></span>, ≈833.090296357¢.
 
Various equal divisions of the octave have close approximations of acoustic phi, or , ≈833.090296357¢. <span><math>φ</math></span>If the <span><math>m^{th}</math></span> step of <span><math>n</math><span>ed2 is a close approximation of <span><math>φ</math></span>, the <span><math>n^{th}</math></span> step of <span><math>m</math><span>ed<span><math>φ</math></span> will be a close approximation of 2.
If the <span><math>m^{th}</math></span> step of <span><math>n</math><span>ed2 is a close approximation of <span><math>φ</math></span>, the <span><math>n^{th}</math></span> step of <span><math>m</math><span>ed<span><math>φ</math></span> will be a close approximation of 2.


For example, the 7th step of 10ed2 is 840¢, and the 10th step of 7ed<span><math>φ</math></span> is ≈1190.128995¢.  
For example, the 7th step of 10ed2 is 840¢, and the 10th step of 7ed<span><math>φ</math></span> is ≈1190.128995¢.  
Line 10: Line 9:
{| class="wikitable"
{| class="wikitable"
|+
|+
|
| rowspan="2" |'''scale step'''
| colspan="4" |'''10ed2'''
| colspan="4" |'''10ed2'''
| colspan="4" |'''7edφ or 10ed(<math>2^{\frac{10log_2{φ}}{7}} ≈ 1.988629015</math>)'''
| colspan="4" |'''7edφ or 10ed(<math>2^{\frac{10log_2{φ}}{7}} ≈ 1.988629015</math>)'''
|-
|-
|'''scale step'''
|'''frequency multiplier (definition)'''
|'''frequency multiplier (definition)'''
|'''10ed2 frequency multiplier (decimal)'''
|'''10ed2 frequency multiplier (decimal)'''
Line 123: Line 121:
|1190.128995
|1190.128995
|119.0128995
|119.0128995
|}
{| class="wikitable"
|+
| rowspan="2" |'''scale step'''
| colspan="4" |'''13ed2'''
| colspan="4" |'''9edφ or 13ed(<math>2^{\frac{10log_2{φ}}{7}} ≈ 1.988629015</math>)<math>2^{\frac{10log_2{φ}}{7}} ≈ 1.988629015</math>'''
|-
|'''frequency multiplier (definition)'''
|'''10ed2 frequency multiplier (decimal)'''
|'''pitch (¢)'''
|'''Δ (¢)'''
|'''frequency multiplier (definition)'''
|'''frequency multiplier (decimal)'''
|'''pitch (¢)'''
|'''Δ (¢)'''
|-
|'''1'''
|
|1.054766076
|92.30769231
|92.30769231
|
|1.054923213
|92.56558848
|92.56558848
|-
|'''2'''
|
|1.112531476
|184.6153846
|92.30769231
|
|1.112862986
|185.131177
|92.56558848
|-
|'''3'''
|
|1.17346046
|276.9230769
|92.30769231
|
|1.173984997
|277.6967655
|92.56558848
|-
|'''4'''
|
|1.237726285
|369.2307692
|92.30769231
|
|1.238464025
|370.2623539
|92.56558848
|-
|'''5'''
|
|1.305511698
|461.5384615
|92.30769231
|
|1.306484449
|462.8279424
|92.56558848
|-
|'''6'''
|
|1.377009451
|553.8461538
|92.30769231
|
|1.378240772
|555.3935309
|92.56558848
|-
|'''7'''
|
|1.452422856
|646.1538462
|92.30769231
|
|1.453938184
|647.9591194
|92.56558848
|-
|'''8'''
|
|1.531966357
|738.4615385
|92.30769231
|
|1.533793141
|740.5247079
|92.56558848
|-
|'''9'''
|
|1.615866144
|830.7692308
|92.30769231
|
|1.618033989
|833.0902964
|92.56558848
|-
|'''10'''
|
|1.704360793
|923.0769231
|92.30769231
|
|1.706901614
|925.6558848
|92.56558848
|-
|11
|
|1.797701946
|1015.384615
|92.30769231
|
|1.800650136
|1018.221473
|92.56558848
|-
|12
|
|1.896155029
|1107.692308
|92.30769231
|
|1.899547627
|1110.787062
|92.56558848
|-
|13
|
|2
|1200
|92.30769231
|
|2.003876886
|1203.35265
|92.56558848
|}
|}
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