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== Theory ==
== Theory ==
40ed10 is related to [[12edo]], but with 10/1 instead of 2/1 being just. The octave, which comes from [[10ed10]], is compressed from pure by about 4.1 cents.  
40ed10 is related to [[12edo]], but with 10/1 instead of 2/1 being just. The octave is compressed from pure by 4.106{{c}}, a small but significant deviation.  


=== Harmonics ===
=== Harmonics ===
{{Harmonics in equal|40|10|1|intervals=integer}}
{{Harmonics in equal|40|10|1|intervals=integer}}
{{Harmonics in equal|40|10|1intervals=integer|start=12|columns=12|collapsed=1|title=Approximation of harmonics in 40ed10 (continued)}}
{{Harmonics in equal|40|10|1intervals=integer|start=12|columns=12|collapsed=1|title=Approximation of harmonics in 40ed10 (continued)}}
=== Subsets and supersets ===
Since 40 factors into 2<sup>3</sup> × 5, 40ed10 has subset ed10's {{EDs|equave=10| 2, 4, 5, 8, 10, and 20 }}.
=== Miscellany ===
It is possible to call this division a form of '''kilobyte tuning''', as
<math>2^{10} \approx 10^{3} = 1024 \approx 1000</math>;
which lies in the obsolete practice of using a decimal prefix to an otherwise binary unit of information.


== Intervals ==
== Intervals ==
Line 13: Line 23:
|-
|-
! #
! #
! Cents value
! Cents
! Approximate ratio
! Approximate ratios
|-
|-
| 0
| 0
| 0.0000
| 0.0
| [[1/1]]
| [[1/1]]
|-
|-
| 1
| 1
| 99.6578
| 99.7
| [[18/17]]
| [[18/17]]
|-
|-
| 2
| 2
| 199.3157
| 199.3
|  
| [[9/8]]
|-
|-
| 3
| 3
| 298.9735
| 299.0
| [[19/16]]
| [[6/5]]
|-
|-
| 4
| 4
| 398.6314
| 398.6
|  
| [[5/4]]
|-
|-
| 5
| 5
| 498.2892
| 498.3
| [[4/3]]
| [[4/3]]
|-
|-
| 6
| 6
| 597.9471
| 597.9
| [[24/17]]
| [[7/5]]
|-
|-
| 7
| 7
| 697.6049
| 697.6
|  
| [[3/2]]
|-
|-
| 8
| 8
| 797.2627
| 797.3
|  
| [[8/5]]
|-
|-
| 9
| 9
| 896.9206
| 896.9
|  
| [[5/3]]
|-
|-
| 10
| 10
| 996.5784
| 996.6
| [[16/9]]
| [[7/4]]
|-
|-
| 11
| 11
| 1096.2363
| 1096.2
| [[32/17]]
| [[15/8]]
|-
|-
| 12
| 12
| 1195.8941
| 1195.9
| [[2/1]]
| [[2/1]]
|-
|-
| 13
| 13
| 1295.5520
| 1295.6
|  
| [[17/8]]
|-
|-
| 14
| 14
| 1395.2098
| 1395.2
| [[28/25|56/25]]
| [[9/4]]
|-
|-
| 15
| 15
| 1494.8676
| 1494.9
|  
| [[12/5]]
|-
|-
| 16
| 16
| 1594.5255
| 1594.5
|  
| [[5/2]]
|-
|-
| 17
| 17
| 1694.1833
| 1694.2
|  
| [[8/3]]
|-
|-
| 18
| 18
| 1793.8412
| 1793.8
|  
| [[14/5]]
|-
|-
| 19
| 19
| 1893.4990
| 1893.5
| [[112/75|224/75]]
| [[3/1]]
|-
|-
| 20
| 20
| 1993.1569
| 1993.2
|  
| [[16/5]]
|-
|-
| 21
| 21
| 2092.8147
| 2092.8
| 375/112
| [[10/3]]
|-
|-
| 22
| 22
| 2192.4725
| 2192.5
|  
| [[7/2]]
|-
|-
| 23
| 23
| 2292.1304
| 2292.1
|  
| [[15/4]]
|-
|-
| 24
| 24
| 2391.7882
| 2391.8
|  
| [[4/1]]
|-
|-
| 25
| 25
| 2491.4461
| 2491.4
|  
| [[17/4]]
|-
|-
| 26
| 26
| 2591.1039
| 2591.1
| 125/28
| [[9/2]]
|-
|-
| 27
| 27
| 2690.7618
| 2690.8
|  
| 19/4
|-
|-
| 28
| 28
| 2790.4196
| 2790.4
|  
| [[5/1]]
|-
|-
| 29
| 29
| 2890.0774
| 2890.1
| 85/16
| [[16/3]]
|-
|-
| 30
| 30
| 2989.7353
| 2989.7
| [[45/32|45/8]]
| 17/3
|-
|-
| 31
| 31
| 3089.3931
| 3089.4
|  
| [[6/1]]
|-
|-
| 32
| 32
| 3189.0510
| 3189.1
|  
| 19/3
|-
|-
| 33
| 33
| 3288.7088
| 3288.7
|  
| 20/3
|-
|-
| 34
| 34
| 3388.3667
| 3388.4
| 85/12
| [[7/1]]
|-
|-
| 35
| 35
| 3488.0245
| 3488.0
| [[15/2]]
| [[15/2]]
|-
|-
| 36
| 36
| 3587.6823
| 3587.7
|  
| [[8/1]]
|-
|-
| 37
| 37
| 3687.3402
| 3687.3
|  
| [[17/2]]
|-
|-
| 38
| 38
| 3786.9980
| 3787.0
|  
| [[9/1]]
|-
|-
| 39
| 39
| 3886.6559
| 3886.7
| 85/9
| 19/2
|-
|-
| 40
| 40
| 3986.3137
| 3986.3
| [[10/1]]
| [[10/1]]
|}
|}
=== Miscellany ===
It is possible to call this division a form of '''kilobyte tuning''', as
<math>2^{10} \approx 10^{3} = 1024 \approx 1000</math>;
which lies in the basis of using a "decimal" prefix to an otherwise binary unit of information.


== Regular temperaments ==
== Regular temperaments ==
Line 194: Line 197:


== See also ==
== See also ==
* [[7edf]] – relative edf
* [[12edo]] – relative edo
* [[12edo]] – relative edo
* [[19ed3]] – relative ed3
* [[19edt]] – relative edt
* [[28ed5]] – relative ed5
* [[28ed5]] – relative ed5
* [[31ed6]] – relative ed6
* [[31ed6]] – relative ed6
* [[34ed7]] – relative ed7
* [[34ed7]] – relative ed7
* [[42ed11]] – relative ed11
* [[42ed11]] – relative ed11
* [[76ed80]] – close to the zeta-optimized tuning for 12edo
* [[1ed18/17|AS18/17]] – relative [[AS|ambitonal sequence]]
* [[1ed18/17|AS18/17]] – relative [[AS|ambitonal sequence]]


[[Category:12edo]]
[[Category:Sonifications]]
[[Category:Sonifications]]
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