User:Moremajorthanmajor/5L 3s (15/7-equivalent): Difference between revisions
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{{Infobox MOS | {{Infobox MOS | ||
|Tuning=5L 3s<15/7>}}{{MOS intro|Scale Signature=5L 3s<15/7>}} | |Tuning=5L 3s<15/7> | ||
}} | |||
{{MOS intro|Scale Signature=5L 3s<15/7>}} | |||
Any ed15/7 with an interval between 494.8¢ and 527.8¢ has a 5L 3s scale. [[13ed15/7]] is the smallest ed15/7 with a (non-degenerate) 5L 3s scale and thus is the most commonly used 5L 3s tuning. | Any ed15/7 with an interval between 494.8¢ and 527.8¢ has a 5L 3s scale. [[13ed15/7]] is the smallest ed15/7 with a (non-degenerate) 5L 3s scale and thus is the most commonly used 5L 3s tuning. | ||
==Standing assumptions== | ==Standing assumptions== | ||
The [[TAMNAMS]] system is used in this article to name 5L 3s<15/7> intervals and step size ratios and step ratio ranges. | The [[TAMNAMS]] system is used in this article to name 5L 3s<15/7> intervals and step size ratios and step ratio ranges. | ||
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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) | ||
| Line 278: | Line 281: | ||
**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) | ||
| Line 308: | Line 311: | ||
|- | |- | ||
! 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) | ||
| Line 420: | Line 423: | ||
|11\13, 1116.452 | |11\13, 1116.452 | ||
|15\18, 1099.536 | |15\18, 1099.536 | ||
|26\31, 1106. | |26\31, 1106.629 | ||
|Ff | |Ff | ||
|11/6, 13/7, 15/8 | |11/6, 13/7, 15/8 | ||
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|12\13, 1217.942 | |12\13, 1217.942 | ||
|17\18, 1246.140 | |17\18, 1246.140 | ||
|29\31, 1234. | |29\31, 1234.317 | ||
|F | |F | ||
|2/1 | |2/1 | ||
| Line 435: | Line 438: | ||
===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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|s (-5g + 2 minor 9ths) | |s (-5g + 2 minor 9ths) | ||
|3\29, 136.494 | |3\29, 136.494 | ||
|4\37, | |4\37, 142.642 | ||
|} | |} | ||
====Intervals==== | ====Intervals==== | ||
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| -8 | | -8 | ||
|} | |} | ||
===Parahard=== | ===Parahard=== | ||
23ed15/7 Neapolitan-oneiro combines the sound of the 15/7 minor ninth and the [[8/7]] whole tone. This is because 23ed15/7 Neapolitan-oneirotonic has a large step of 229.5¢. | 23ed15/7 Neapolitan-oneiro combines the sound of the 15/7 minor ninth and the [[8/7]] whole tone. This is because 23ed15/7 Neapolitan-oneirotonic has a large step of 229.5¢. | ||
| Line 1,024: | Line 1,028: | ||
|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 | ||
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|} | |} | ||
==Scale tree== | ==Scale tree== | ||
{{Scale | {{MOS tuning spectrum|Scale Signature=5L 3s<15/7>}} | ||