User:Moremajorthanmajor/5L 3s (15/7-equivalent): Difference between revisions
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The chain of perfect 4ths becomes: ... Ef Af Qf Ff Bf Df G C E A Q F B D ... | The chain of perfect 4ths becomes: ... Ef Af Qf Ff Bf Df G C E A Q F B D ... | ||
Thus the [[ | Thus the [[13ed15/7]] gamut is as follows: | ||
'''G/F#''' G#/Af '''A''' A#/Bf '''B/Cf''' '''C/B#''' C#/Qf '''Q''' Q#/Df '''D/Ef E/D#''' E#/Ff '''F/Gf G''' | '''G/F#''' G#/Af '''A''' A#/Bf '''B/Cf''' '''C/B#''' C#/Qf '''Q''' Q#/Df '''D/Ef E/D#''' E#/Ff '''F/Gf G''' | ||
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|1L + 2s | |1L + 2s | ||
|- | |- | ||
| colspan="8" |The chromatic 13-note MOS (either [[5L 8s (15/7-equivalent)|5L 8s]], [[8L 5s (15/7-equivalent)|8L 5s]], or [[ | | colspan="8" |The chromatic 13-note MOS (either [[5L 8s (15/7-equivalent)|5L 8s]], [[8L 5s (15/7-equivalent)|8L 5s]], or [[13ed15/7]]) also has the following intervals (from some root): | ||
|- | |- | ||
|8 | |8 | ||
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|- | |- | ||
! class="unsortable" |Degree | ! class="unsortable" |Degree | ||
!Size in [[ | !Size in [[13ed15/7]] (basic) | ||
!Size in [[18ed15/7]] (hard) | !Size in [[18ed15/7]] (hard) | ||
!Size in [[21ed15/7]] (soft) | !Size in [[21ed15/7]] (soft) | ||
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**The large step is near the Pythagorean 9/8 whole tone, somewhere between as in [[12edo]] and as in [[17edo]]. | **The large step is near the Pythagorean 9/8 whole tone, somewhere between as in [[12edo]] and as in [[17edo]]. | ||
**The major 3rd (made of two large steps) is a near-[[Pythagorean]] to [[Neogothic]] major third. | **The major 3rd (made of two large steps) is a near-[[Pythagorean]] to [[Neogothic]] major third. | ||
EDIXs that are in the hypohard range include [[ | EDIXs that are in the hypohard range include [[13ed15/7]], [[18ed15/7]], and 31ed15/7. | ||
The sizes of the generator, large step and small step of Neapolitan-oneirotonic are as follows in various hypohard Neapolitan-oneiro tunings. | The sizes of the generator, large step and small step of Neapolitan-oneirotonic are as follows in various hypohard Neapolitan-oneiro tunings. | ||
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|- | |- | ||
! | ! | ||
![[ | ![[13ed15/7]] (basic) | ||
![[18ed15/7]] (hard) | ![[18ed15/7]] (hard) | ||
!31ed15/7 (semihard) | !31ed15/7 (semihard) | ||
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|- | |- | ||
! class="unsortable" |Degree | ! class="unsortable" |Degree | ||
!Size in [[ | !Size in [[13ed15/7]] (basic) | ||
!Size in [[18ed15/7]] (hard) | !Size in [[18ed15/7]] (hard) | ||
!Size in 31ed15/7 (semihard) | !Size in 31ed15/7 (semihard) | ||
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===Hyposoft=== | ===Hyposoft=== | ||
[[Hyposoft]] Neapolitan-oneirotonic tunings (with generator between 8\21 and 5\13) have step ratios between 3/2 and 2/1. The 8\21-to-5\13 range of Neapolitan-oneirotonic tunings can be considered "meantone Neapolitan-oneirotonic”. This is because these tunings share the following features with meantone diatonic tunings: | [[Hyposoft]] Neapolitan-oneirotonic tunings (with generator between 8\21 and 5\13) have step ratios between 3/2 and 2/1. The 8\21-to-5\13 range of Neapolitan-oneirotonic tunings can be considered "meantone Neapolitan-oneirotonic”. This is because these tunings share the following features with meantone diatonic tunings: | ||
*The large step is between near the meantone and near the Pythagorean 9/8 whole tone, somewhere between as in [[19edo]] and as in [[ | *The large step is between near the meantone and near the Pythagorean 9/8 whole tone, somewhere between as in [[19edo]] and as in [[12edo]]. | ||
*The major 3rd (made of two large steps) is a near-[[Just intonation|just]] to near-[[Pythagorean]] major third. | *The major 3rd (made of two large steps) is a near-[[Just intonation|just]] to near-[[Pythagorean]] major third. | ||
The sizes of the generator, large step and small step of Neapolitan-oneirotonic are as follows in various hyposoft Neapolitan-oneiro tunings ([[ | The sizes of the generator, large step and small step of Neapolitan-oneirotonic are as follows in various hyposoft Neapolitan-oneiro tunings ([[13ed15/7]] not shown). | ||
{| class="wikitable right-2 right-3 right-4 right-5" | {| class="wikitable right-2 right-3 right-4 right-5" | ||
|- | |- | ||
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|15\38, 520.833 | |15\38, 520.833 | ||
|21\53, 522.798 | |21\53, 522.798 | ||
|25\63, 523. | |25\63, 523.588 | ||
|484.07 | |484.07 | ||
|C | |C | ||