51edo: Difference between revisions
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→Odd harmonics: Section heading says odd harmonics, but table was displaying only prime harmonics — fixing this and adding another row |
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Using the [[patent val]], 51et [[tempering out|tempers out]] [[250/243]] in the [[5-limit]], [[225/224]] and [[2401/2400]] in the [[7-limit]], and [[55/54]] and [[100/99]] in the [[11-limit]]. It is the [[optimal patent val]] for [[sonic]], the rank-3 temperament tempering out 55/54, 100/99, and 250/243, and also for the rank-4 temperament tempering out 55/54. It provides an alternative tuning to [[22edo]] for [[porcupine]], with a nice fifth but a rather flat major third, and the optimal patent val for the 7- and 11-limit [[porky]] temperament, which is sonic plus 225/224. It contains an archeotonic ([[6L 1s]]) scale based on repetitions of 8\51, creating a scale with a whole-tone-like drive towards the tonic through the 17edo semitone at the top. | Using the [[patent val]], 51et [[tempering out|tempers out]] [[250/243]] in the [[5-limit]], [[225/224]] and [[2401/2400]] in the [[7-limit]], and [[55/54]] and [[100/99]] in the [[11-limit]]. It is the [[optimal patent val]] for [[sonic]], the rank-3 temperament tempering out 55/54, 100/99, and 250/243, and also for the rank-4 temperament tempering out 55/54. It provides an alternative tuning to [[22edo]] for [[porcupine]], with a nice fifth but a rather flat major third, and the optimal patent val for the 7- and 11-limit [[porky]] temperament, which is sonic plus 225/224. It contains an archeotonic ([[6L 1s]]) scale based on repetitions of 8\51, creating a scale with a whole-tone-like drive towards the tonic through the 17edo semitone at the top. | ||
Using the 51c val {{val| 51 81 '''119''' 143 }}, the [[5/4]] is mapped to 1\3 (400 cents), [[support]]ing [[augmented (temperament)|augmented]]. In the 7-limit it tempers out [[245/243]] and supports [[hemiaug]] and [[rodan]]. Alternatively, the 51cd val {{val| 51 81 '''119''' '''144''' }} takes the same [[7/4]] from 17edo, and supports [[augene]]. The 51ce val {{val| 51 81 '''119''' 143 '''177''' 189 }} supports a variant of rodan called [[aerodino]]. | Using the 51c val {{val| 51 81 '''119''' 143 }}, the [[5/4]] is mapped to 1\3 (400 cents), [[support]]ing [[augmented (temperament)|augmented]]. In the 7-limit it tempers out [[245/243]] and supports [[hemiaug]] and [[rodan]]. Alternatively, the 51cd val {{val| 51 81 '''119''' '''144''' }} takes the same [[7/4]] from 17edo, and supports [[augene]]. The 51ce val {{val| 51 81 '''119''' 143 '''177''' 189 }} supports a variant of rodan called [[Gamelismic_clan#Aerodino|aerodino]]. | ||
51edo's step is the closest direct approximation to the [[Pythagorean comma]] by | 51edo's step is the closest direct approximation to the [[Pythagorean comma]] by edosteps, though that comma itself is mapped to a different interval. | ||
=== Odd harmonics === | === Odd harmonics === | ||
{{Harmonics in equal|51}} | {{Harmonics in equal|51|intervals=odd|prec=2|columns=14}} | ||
{{Harmonics in equal|51|intervals=odd|columns=14|prec=2|start=15|collapsed=true|title=Approximation of odd harmonics in 51edo (continued)}} | |||
=== Subsets and supersets === | === Subsets and supersets === | ||
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If double arrows are not desirable, then arrows can be attached to quartertone accidentals: | If double arrows are not desirable, then arrows can be attached to quartertone accidentals: | ||
{{Sharpness-sharp6-qt}} | {{Sharpness-sharp6-qt-szg}} | ||
=== Kite's ups and downs notation === | === Kite's ups and downs notation === | ||
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| 235.3 | | 235.3 | ||
| 8/7 | | 8/7 | ||
| [[Rodan]] ( | | [[Rodan]] (51cf, out of tune) / aerodino (51ce) | ||
|- | |- | ||
| 1 | | 1 | ||
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| 517.6 | | 517.6 | ||
| 27/20 | | 27/20 | ||
| [[Gravity]] (51ce) | | [[Gravity]] (51ce) / [[abergravity]] (51ce) | ||
|- | |- | ||
| 1 | | 1 | ||
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== Music == | == Music == | ||
; [[Bryan Deister]] | ; [[Bryan Deister]] | ||
* [https://www.youtube.com/watch?v=sySLQUXnQ70 ''Preludio Sentimentale (microtonal improvisation in 28edo)''] (2023) | |||
* [https://www.youtube.com/watch?v=sCE0MjUyRUk ''28edo blues''] (2023) | |||
* [https://www.youtube.com/shorts/sTPJtuHUwkg ''51edo improv''] (2025-02-03) | * [https://www.youtube.com/shorts/sTPJtuHUwkg ''51edo improv''] (2025-02-03) | ||
* [https://www.youtube.com/shorts/5pM8OC0fV98 ''51edo improv''] (2025-05-02) | * [https://www.youtube.com/shorts/5pM8OC0fV98 ''51edo improv''] (2025-05-02) | ||