Neutral third scales: Difference between revisions
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One possible temperament interpretation is that the neutral third generator can be taken to represent either 11/9 or 27/22. This means the comma 243/242 is tempered out. | One possible temperament interpretation is that the neutral third generator can be taken to represent either 11/9 or 27/22. This means the comma 243/242 is tempered out. | ||
If the fifth harmonic is used at all, it makes sense to map it to 8 generators by tempering out 81/80, making it [[ | If the fifth harmonic is used at all, it makes sense to map it to 8 generators by tempering out 81/80, making it [[Meantone family #Mohaha|a meantone system]], sometimes called [[Chromatic pairs #Mohaha|"mohaha"]]. If 7 is also mapped a particular way it is called [[mohajira]]. Alternatively, 64/63 could be tempered out, leading to a 2.3.7.11 version of [[maqamic|maqamic temperament]]. But neither of these adjustments to the farther-out intervals affects its basic nature as a "neutral thirds" scale, which equally subdivides the 3/2 into two equal parts. | ||
Any temperament tempering out 243/242 lends itself to neutral thirds; this becomes more significant when fifths are of low complexity, such as hemififths or the rank three temperament jove, but also includes miracle, harry and so forth. Nor does a scale need to be a MOS to qualify as a neutral thirds scale; that name could reasonably be given to [[Graph-theoretic properties of scales#Oktone|Oktone]], for example. | Any temperament tempering out 243/242 lends itself to neutral thirds; this becomes more significant when fifths are of low complexity, such as hemififths or the rank three temperament jove, but also includes miracle, harry and so forth. Nor does a scale need to be a MOS to qualify as a neutral thirds scale; that name could reasonably be given to [[Graph-theoretic properties of scales #Oktone|Oktone]], for example. | ||
==Interval chains== | == Interval chains == | ||
=== Basic 2.3.11 neutral thirds scale === | |||
===Basic 2.3.11 neutral thirds scale=== | |||
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===2.3.5.11 mohaha=== | === 2.3.5.11 mohaha === | ||
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===2.3.7.11 | === 2.3.7.11 suhajira === | ||
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==MOSes== | == MOSes == | ||
Neutral third scales are associated with the [[ | Neutral third scales are associated with the [[MOS Scales|MOS patterns]] [[3L 4s]] and [[7L 3s]]. | ||
In the 3L4s MOS, the large step is a 9/8 and the small step is a 12/11 neutral second. In the 7L3s MOS, the 12/11 is now the large step and the small step is a 33/32 quarter tone. | In the 3L4s MOS, the large step is a 9/8 and the small step is a 12/11 neutral second. In the 7L3s MOS, the 12/11 is now the large step and the small step is a 33/32 quarter tone. | ||
==Munits== | == Munits == | ||
Though they differ in the specifics of their temperaments, all neutral third scales have certain [[ | Though they differ in the specifics of their temperaments, all neutral third scales have certain [[munit]]s in common. | ||
* 4/3 Lss, 4/3 sLs: Rather than being divided into two large steps and one small step as in the diatonic scale, 4/3 can always be divided into one large step and two small steps. The large step is 9/8, and the two small steps are "neutral seconds" representing the sub-munit "32/27 ss". | |||
* 11/8 LsL: In contrast, two large steps and a small step make a much less consonant and more colorful interval, 11/8. | |||
< | [[Category:Temperament]] | ||
[[Category:Neutral| ]] <!-- main article --> | |||
[[Category:Rastmic]] | |||
Revision as of 07:13, 26 April 2021
Neutral third scales are characterized by the division of the 3/2 "perfect fifth" into two equal "neutral thirds". It usually refers to a MOS or MODMOS generated by a neutral third (usually from 342.9c in 7edo to 360c in 10edo).
One possible temperament interpretation is that the neutral third generator can be taken to represent either 11/9 or 27/22. This means the comma 243/242 is tempered out.
If the fifth harmonic is used at all, it makes sense to map it to 8 generators by tempering out 81/80, making it a meantone system, sometimes called "mohaha". If 7 is also mapped a particular way it is called mohajira. Alternatively, 64/63 could be tempered out, leading to a 2.3.7.11 version of maqamic temperament. But neither of these adjustments to the farther-out intervals affects its basic nature as a "neutral thirds" scale, which equally subdivides the 3/2 into two equal parts.
Any temperament tempering out 243/242 lends itself to neutral thirds; this becomes more significant when fifths are of low complexity, such as hemififths or the rank three temperament jove, but also includes miracle, harry and so forth. Nor does a scale need to be a MOS to qualify as a neutral thirds scale; that name could reasonably be given to Oktone, for example.
Interval chains
Basic 2.3.11 neutral thirds scale
| 296.85 | 647.37 | 997.90 | 148.42 | 498.95 | 849.47 | 0. | 350.53 | 701.05 | 1051.58 | 202.10 | 552.63 | 903.15 |
| 32/27 | 16/11 | 16/9 | 12/11 | 4/3 | 18/11 | 1/1 | 11/9 | 3/2 | 11/6 | 9/8 | 11/8 | 27/16 |
2.3.5.11 mohaha
| 815.25 | 1163.34 | 311.44 | 659.53 | 1007.63 | 155.72 | 503.81 | 851.91 | 0. | 348.09 | 696.19 | 1044.28 | 192.37 | 540.47 | 888.56 | 36.66 | 384.75 |
| 8/5 | 6/5 | 16/11 | 16/9~9/5 | 12/11~11/10 | 4/3 | 18/11 | 1/1 | 11/9 | 3/2 | 11/6 | 10/9~9/8 | 11/8 | 5/3 | 5/4 |
2.3.7.11 suhajira
| 414.38 | 768.34 | 1122.29 | 276.25 | 630.21 | 984.17 | 138.13 | 492.08 | 846.04 | 0. | 353.96 | 707.92 | 1061.87 | 215.83 | 569.79 | 923.75 | 77.71 | 431.66 | 785.62 |
| 14/11 | 14/9 | 7/6 | 16/11 | 7/4~16/9 | 12/11 | 4/3 | 18/11 | 1/1 | 11/9 | 3/2 | 11/6 | 9/8~8/7 | 11/8 | 12/7 | 9/7 | 11/7 |
MOSes
Neutral third scales are associated with the MOS patterns 3L 4s and 7L 3s.
In the 3L4s MOS, the large step is a 9/8 and the small step is a 12/11 neutral second. In the 7L3s MOS, the 12/11 is now the large step and the small step is a 33/32 quarter tone.
Munits
Though they differ in the specifics of their temperaments, all neutral third scales have certain munits in common.
- 4/3 Lss, 4/3 sLs: Rather than being divided into two large steps and one small step as in the diatonic scale, 4/3 can always be divided into one large step and two small steps. The large step is 9/8, and the two small steps are "neutral seconds" representing the sub-munit "32/27 ss".
- 11/8 LsL: In contrast, two large steps and a small step make a much less consonant and more colorful interval, 11/8.