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| Line 302: |
Line 302: |
| === Website === | | === Website === |
| I have some scales ready in Scala format on my website [https://tilde.town/~tromboneboi9/scales.html here]. | | I have some scales ready in Scala format on my website [https://tilde.town/~tromboneboi9/scales.html here]. |
|
| |
| === Cumulus scales ===
| |
| I don't know about you, but I love the seventh harmonic. These [[MOS scale|MOS scales]] are named after the [[cloudy comma]], and use different [[7-limit]] intervals for generators.
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|
| |
| ====Cumulus Alpha====
| |
| '''''Cumulus Alpha''''' is a 5L6s MOS with [[7/4]] as the generator and [[2/1]] as the period. This appears to approximate a subset of [[26edo|26-EDO]]; it approximates the whole of 26-EDO when extended to a 5L21s MOS, which I dub '''''Cumulus Alpha Holo'''''.
| |
|
| |
| ''That's right. We're comparing JI to EDOs instead of the other way around.''
| |
| {| class="wikitable mw-collapsible"
| |
| ! Steps
| |
| !Ratio
| |
| !Cents
| |
| !Approx. 26-EDO Degree
| |
| |-
| |
| |0
| |
| |1/1
| |
| |0.000
| |
| |0
| |
| |-
| |
| | 1
| |
| | 16807/16384
| |
| |43.130
| |
| |1
| |
| |-
| |
| |2
| |
| |8/7
| |
| |231.174
| |
| |5
| |
| |-
| |
| |3
| |
| |2401/2048
| |
| |275.304
| |
| |6
| |
| |-
| |
| |4
| |
| |64/49
| |
| |462.348
| |
| |10
| |
| |-
| |
| |5
| |
| |343/256
| |
| |506.478
| |
| |11
| |
| |-
| |
| |6
| |
| |512/343
| |
| |693.522
| |
| |15
| |
| |-
| |
| |7
| |
| |49/32
| |
| |737.652
| |
| |16
| |
| |-
| |
| |8
| |
| |4096/2401
| |
| |924.696
| |
| |20
| |
| |-
| |
| |9
| |
| |7/4
| |
| |968.826
| |
| |21
| |
| |-
| |
| |10
| |
| |32768/16807
| |
| |1155.870
| |
| |25
| |
| |-
| |
| |11
| |
| |2/1
| |
| |1200.000
| |
| |26
| |
| |}
| |
|
| |
| ====Cumulus Beta====
| |
| '''''Cumulus Beta''''' is an 4L5s MOS with [[7/6]] as the generator and [[2/1]] as the period. Amazingly, it approximates all intervals of [[9edo|9-EDO]] within a cent, with a mean difference of about 0.409 cents.
| |
| {| class="wikitable mw-collapsible"
| |
| !Steps
| |
| !Ratio
| |
| !Cents
| |
| !9-EDO Difference
| |
| |-
| |
| | 0
| |
| |1/1
| |
| |0.000
| |
| |0.000
| |
| |-
| |
| |1
| |
| |2592/2401
| |
| |132.516
| |
| | -0.817
| |
| |-
| |
| |2
| |
| |7/6
| |
| |266.871
| |
| |0.204
| |
| |-
| |
| |3
| |
| |432/343
| |
| |399.387
| |
| | -0.613
| |
| |-
| |
| |4
| |
| |49/36
| |
| |533.742
| |
| |0.409
| |
| |-
| |
| |5
| |
| |72/49
| |
| |666.258
| |
| | -0.409
| |
| |-
| |
| |6
| |
| |343/216
| |
| |800.613
| |
| |0.613
| |
| |-
| |
| |7
| |
| |12/7
| |
| |933.129
| |
| | -0.204
| |
| |-
| |
| |8
| |
| |2401/1296
| |
| |1067.484
| |
| |0.817
| |
| |-
| |
| |9
| |
| |7/4
| |
| |1200.000
| |
| |0.000
| |
| |}
| |
|
| |
| ====Cumulus Gamma====
| |
| '''''Cumulus Gamma''''' is an 3L8s MOS with [[9/7]] as the generator and [[2/1]] as the period. It approximates all intervals of [[11edo|11-EDO]] within 7 cents, with a mean difference of 3.199 cents.
| |
| {| class="wikitable mw-collapsible"
| |
| !Steps
| |
| !Ratio
| |
| !Cents
| |
| !11-EDO Difference
| |
| |-
| |
| |0
| |
| |1/1
| |
| |0.000
| |
| |0.000
| |
| |-
| |
| |1
| |
| |729/686
| |
| |105.252
| |
| |3.839
| |
| |-
| |
| |2
| |
| |67228/59049
| |
| |224.580
| |
| | -6.398
| |
| |-
| |
| |3
| |
| |98/81
| |
| |329.832
| |
| | -2.559
| |
| |-
| |
| |4
| |
| |9/7
| |
| |435.084
| |
| |1.280
| |
| |-
| |
| |5
| |
| |6561/4802
| |
| |540.336
| |
| |5.119
| |
| |-
| |
| |6
| |
| |9604/6561
| |
| |659.664
| |
| | -5.119
| |
| |-
| |
| |7
| |
| |14/9
| |
| |764.916
| |
| | -1.280
| |
| |-
| |
| |8
| |
| |81/49
| |
| |870.168
| |
| |2.559
| |
| |-
| |
| |9
| |
| |59049/33614
| |
| |975.420
| |
| |6.398
| |
| |-
| |
| |10
| |
| |1372/729
| |
| |1094.748
| |
| | -3.839
| |
| |-
| |
| |11
| |
| |2/1
| |
| |1200.000
| |
| |0.000
| |
| |}
| |
|
| |
|
| === Blues scale in 10-EDO === | | === Blues scale in 10-EDO === |