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| Rodan is naturally a [[detemperament]] of the [[5edo|5 equal temperament]]. The diagram on the right shows a 46-tone detempered scale, with a generator range of -22 to +23. 46 is the largest number of tones for a mos where intervals in the 5 categories do not overlap. Each category is divided into eight or nine qualities separated by 5 generator steps, which represent the syntonic comma. | | Rodan is naturally a [[detemperament]] of the [[5edo|5 equal temperament]]. The diagram on the right shows a 46-tone detempered scale, with a generator range of -22 to +23. 46 is the largest number of tones for a mos where intervals in the 5 categories do not overlap. Each category is divided into eight or nine qualities separated by 5 generator steps, which represent the syntonic comma. |
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| Notice also the little interval between the largest of a category and the smallest of the next, which represents the differences between 16/15 and 14/13, between 11/9 and 16/13, between 7/5 and 45/32, between 13/8 and 18/11, and between 13/7 and 15/8. It spans 41 generator steps, so it vanishes in 41edo, but is tuned to the same size as the syntonic comma in 46edo. 87edo tunes it to one half the size of the syntonic comma, which may be seen as a good compromise. | | Notice also the little interval between the largest of a category and the smallest of the next, which represents the differences between 16/15 and 14/13, between 11/9 and 16/13, between 7/5 and 45/32, between 13/8 and 18/11, and between 13/7 and 15/8. It spans 41 generator steps, so it vanishes in 41edo, but is tuned to the same size as the quark/syntonic comma in 46edo. 87edo tunes it to one half the size of the syntonic comma, which may be seen as a good compromise. |
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| [[File: Rodan 5et Detempering.png|thumb|Rodan as a 46-tone 5et detempering]]
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| === As a detemperament of 5et ===
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| Rodan is naturally a [[detemperament]] of the [[5edo|5 equal temperament]]. The diagram on the right shows a 46-tone detempered scale, with a generator range of -22 to +23. 46 is the largest number of tones for a mos where intervals in the 5 categories do not overlap. Each category is divided into eight or nine qualities separated by 5 generator steps, which represent the syntonic comma.
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| Notice also the little interval between the largest of a category and the smallest of the next, which represents the differences between 16/15 and 14/13, between 11/9 and 16/13, between 7/5 and 45/32, between 13/8 and 18/11, and between 13/7 and 15/8. It spans 41 generator steps, so it vanishes in 41edo, but is tuned to the same size as the syntonic comma in 46edo. 87edo tunes it to one half the size of the syntonic comma, which may be seen as a good compromise.
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| == Notation == | | == Notation == |
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| == Tunings == | | == Tunings == |
| === Tuning spectrum ===
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| {| class="wikitable center-all left-4 left-5"
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| |-
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| ! Edo<br>generator
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| ! [[Eigenmonzo|Eigenmonzo<br>(unchanged interval)]]*
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| ! Generator (¢)
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| ! Comments
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| |-
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| | [[8/7]]
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| | 231.174
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| | Untempered tuning
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| |-
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| | '''[[31edo|6\31]]'''
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| | '''232.258'''
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| | 31ceffgg val, '''lower bound of 5-odd-limit diamond monotone'''
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| |-
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| | '''[[36edo|7\36]]'''
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| | '''233.333'''
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| | 36cfg val, '''lower bound of 7- and 9-odd-limit diamond monotone'''
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| |-
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| | [[3/2]]
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| | 233.985
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| | 1/3-comma
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| |-
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| | '''[[41edo|8\41]]'''
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| | '''234.146'''
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| | '''Lower bound of 11- to 17-odd-limit diamond monotone'''
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| |-
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| | [[128edo|25\128]]
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| | 234.375
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| |-
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| | [[55/32]]
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| | 234.408
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| | As SM6
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| |-
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| | [[87edo|17\87]]
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| | 234.483
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| |-
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| | [[63/32]]
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| | 234.547
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| | 2/5-comma
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| |-
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| | [[133edo|26\133]]
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| | 234.586
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| |-
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| | '''[[46edo|9\46]]'''
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| | '''234.783'''
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| | '''Upper bound of 11- to 17-odd-limit diamond monotone'''
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| |-
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| | [[51edo|10\51]]
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| | 235.294
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| | 51ceg val
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| |-
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| | [[21/16]]
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| | 235.390
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| | 1/2-comma
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| |-
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| | '''[[5edo|1\5]]'''
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| | '''240.000'''
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| | 5f val, '''upper bound of 5- to 9-odd-limit diamond monotone'''
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| |}
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| <nowiki/>* Besides the octave
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| === Tuning spectrum === | | === Tuning spectrum === |
| {| class="wikitable center-all left-4" | | {| class="wikitable center-all left-4" |