240edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|240}} | |||
==Theory== | |||
240edo's patent val tempers out the [[225/224]] in the 7-limit, with low resultant errors (two cents flat for the fifth, a little over a cent flat and sharp, respectively, for the major third and the 7/4.) Retuning 5-limit scales to 240edo is a simple way to to make them function as 7-limit scales while retaining very accurate tuning. One important use for it is in tuning marvel temperament and marvel's extension to spectacle temperament. | |||
From a regular temperament theory perspective in the 7-limit, 240edo is similar to [[197edo]]. The main difference is that 197edo, despite a flatter third, gives generally better results and may be preferred, whitherfore a compromise between good results and an accurate 5 may be worked out by means of retuning 5-limit scales to the 197 & 240 temperament, whhich has a comma basis {225/224, {{monzo|-49 19 -10 15}}} in the 7-limit. | |||
For higher limits, 240edo tempers out 243/242 in the 11-limit, 351/350 in the 13-limit, and 375/374 in the 17-limit, and adding these to the mix converts marvel temperament into spectacle temperament. This is still a planar temperament, but more complex as two unidecimal neutral thirds of 11/9 make up a fifth (which is in fact the same fifth as that of 12edo, and the 11/9 is the 350 cent interval often employed in 24edo versions of Arabic music.) Musical intervals are therefore generated by octaves, major thirds, and neutral thirds in spectacle. We have: | For higher limits, 240edo tempers out 243/242 in the 11-limit, 351/350 in the 13-limit, and 375/374 in the 17-limit, and adding these to the mix converts marvel temperament into spectacle temperament. This is still a planar temperament, but more complex as two unidecimal neutral thirds of 11/9 make up a fifth (which is in fact the same fifth as that of 12edo, and the 11/9 is the 350 cent interval often employed in 24edo versions of Arabic music.) Musical intervals are therefore generated by octaves, major thirds, and neutral thirds in spectacle. We have: | ||
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==Scales== | ==Scales== | ||
Here are some examples of scales retuned to 240edo and hence exhibiting marvel temperament. | Here are some examples of scales retuned to 240edo and hence exhibiting marvel temperament. | ||
* 23 17 23 14 23 17 23 23 14 26 14 23 - Ellis's Duodene genus [33355] retuned to 240edo | |||
* 23 17 14 23 23 17 23 23 14 17 23 23 - Carl Lumma's scale | |||
* 14 9 14 17 23 23 23 17 14 9 14 23 17 23 - Pum[14] scale | |||
* 16 10 7 7 16 7 7 16 7 10 7 16 7 7 16 7 7 10 16 7 7 16 7 - Ellis duodene union 11/9 times the duodene | |||
Ellis's Duodene | |||
Carl Lumma's scale | |||
9 | |||
16 | |||
10 | |||
16 | |||
Ellis duodene union 11/9 times the duodene | |||
==Links== | ==Links== | ||