User:Moremajorthanmajor/5L 2s (5/3-equivalent): Difference between revisions
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| Neutral = 3L 4s | | Neutral = 3L 4s | ||
| Equave=5/3}} | | Equave=5/3}} | ||
One way of distinguishing the '''3/4''' '''diatonic''' scale is by considering it a [[MOS scale|moment of symmetry]] scale produced by a chain of "fifths" (or "fourths") with the step combination of '''5L 2s'''. Among the most well-known variants of this MOS proper are | One way of distinguishing the '''3/4''' '''diatonic''' scale is by considering it a [[MOS scale|moment of symmetry]] scale produced by a chain of "fifths" (or "fourths") with the step combination of '''5L 2s'''. Among the most well-known variants of this MOS proper are 12ED5/3's diatonic scale along with both the Pythagorean diatonic scale and the various meantone systems. Other similar scales referred to by the term "diatonic" can be arrived at different ways – for example, through just intonation procedures, or with tetrachords. However, it should be noted that at least the majority of the other scales that fall under this category – such as the just intonation scales that use more than one size of whole tone – are actually JI detemperings or tempered approximations of them that both closely resemble and are derived from this MOS. | ||
==On the term ''diatonic''== | ==On the term ''diatonic''== | ||
In [[TAMNAMS]] (which is the convention on all pages on scale patterns on the wiki), [[diatonic]] exclusively refers to 5L 2s. Other diatonic-based scales (specifically with 3 step sizes or more), such as [[Zarlino]], [[blackdye]] and [[diasem]], are called ''[[Detempering|detempered]]'' (if the philosophy is [[RTT]]-based) or ''deregularized'' (RTT-agnostic) ''diatonic scales''. The adjectives ''diatonic-like'' or ''diatonic-based'' may also be used to refer to diatonic-based scales, depending on what's contextually the most appropriate. | In [[TAMNAMS]] (which is the convention on all pages on scale patterns on the wiki), [[diatonic]] exclusively refers to 5L 2s. Other diatonic-based scales (specifically with 3 step sizes or more), such as [[Zarlino]], [[blackdye]] and [[diasem]], are called ''[[Detempering|detempered]]'' (if the philosophy is [[RTT]]-based) or ''deregularized'' (RTT-agnostic) ''diatonic scales''. The adjectives ''diatonic-like'' or ''diatonic-based'' may also be used to refer to diatonic-based scales, depending on what's contextually the most appropriate. | ||
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The 5L 2s MOS scale has this generalized form. | The 5L 2s MOS scale has this generalized form. | ||
*L L s L L L s | *L L s L L L s | ||
Insert 2 for L and 1 for s and you'll get the | Insert 2 for L and 1 for s and you'll get the 12ed5/3 diatonic of standard practice. | ||
*2 2 1 2 2 2 1 | *2 2 1 2 2 2 1 | ||
When L=3, s=1, you have | When L=3, s=1, you have 17ED5/3: 3 3 1 3 3 3 1 | ||
When L=3, s=2, you have | When L=3, s=2, you have 19ED5/3: 3 3 2 3 3 3 2 | ||
When L=4, s=1, you have | When L=4, s=1, you have 22ED5/3: 4 4 1 4 4 4 1 | ||
When L=4, s=3, you have | When L=4, s=3, you have 26ED5/3: 4 4 3 4 4 4 3 | ||
When L=5, s=1, you have | When L=5, s=1, you have 27ED5/3: 5 5 1 5 5 5 1 | ||
When L=5, s=2, you have | When L=5, s=2, you have 29ED5/3: 5 5 2 5 5 5 2 | ||
When L=5, s=3, you have | When L=5, s=3, you have 31ED5/3: 5 5 3 5 5 5 3 | ||
When L=5, s=4, you have | When L=5, s=4, you have 33ED5/3: 5 5 4 5 5 5 4 | ||
So you have scales where L and s are nearly equal, which approach | So you have scales where L and s are nearly equal, which approach 7ED5/3: | ||
*1 1 1 1 1 1 1 | *1 1 1 1 1 1 1 | ||
And you have scales where s becomes so small it approaches zero, which would give us | And you have scales where s becomes so small it approaches zero, which would give us 5ED5/3: | ||
*1 1 0 1 1 1 0 = 1 1 1 1 1 | *1 1 0 1 1 1 0 = 1 1 1 1 1 | ||
==Tuning ranges== | ==Tuning ranges== | ||
===Parasoft to ultrasoft=== | ===Parasoft to ultrasoft=== | ||
"3/4 Flattone" systems, such as | "3/4 Flattone" systems, such as 26ED5/3. | ||
===Hyposoft=== | ===Hyposoft=== | ||
"3/4 Meantone" (more properly "3/4 septimal meantone") systems, such as | "3/4 Meantone" (more properly "3/4 septimal meantone") systems, such as 31ED5/3. | ||
===Hypohard=== | ===Hypohard=== | ||
The near-just part of the region is of interest mainly for those interested in “3/4” [[Pythagorean tuning]] and large, accurate eds systems based on close-to-Pythagorean fifths, such as | The near-just part of the region is of interest mainly for those interested in “3/4” [[Pythagorean tuning]] and large, accurate eds systems based on close-to-Pythagorean fifths, such as 41ED5/3 and 53ED5/3. This class of tunings is called [[schisma|trischismic]] temperament; these tunings can approximate 5<sup>3/4</sup>-limit harmonies very accurately by [[tempering out]] a small comma called the [[schisma]]. (Technically, 12ED5/3 tempers out the schisma and thus is a schismic tuning, but it is nowhere near as accurate as schismic tunings can be.)<!--(see [[5L 2s/Temperaments#Schismic]])-->. | ||
The sharp-of-just part of this range includes so-called “3/4 [[neogothic]]" or "3/4 parapyth" systems, which tune the diatonic major third slightly flatly of [[6/5]] and the diatonic minor third slightly sharply of [[12/11]]. Good 3/4 neogothic EDSs include | The sharp-of-just part of this range includes so-called “3/4 [[neogothic]]" or "3/4 parapyth" systems, which tune the diatonic major third slightly flatly of [[6/5]] and the diatonic minor third slightly sharply of [[12/11]]. Good 3/4 neogothic EDSs include 29EDQ and 46ED5/3. 17ED5/3 is often considered the sharper end of the 3/4 neogothic spectrum; its major third at 313 cents (417 śata) is considerably more concordant than in flatter neogothic tunings. | ||
===Parahard to ultrahard=== | ===Parahard to ultrahard=== | ||
"3/4 Archy" systems such as | "3/4 Archy" systems such as 17ED5/3, 22ED5/3, and 27ED5/3. | ||
==Modes== | ==Modes== | ||
Diatonic modes have standard names from classical music theory: | Diatonic modes have standard names from classical music theory: | ||