User:Ganaram inukshuk/5L 2s: Difference between revisions

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TAMNAMS suggests the name '''diatonic''' for this scale, which commonly refers to a scale with 5 whole steps and 2 small steps.
TAMNAMS suggests the name '''diatonic''' for this scale, which commonly refers to a scale with 5 whole steps and 2 small steps.


===On the term ''diatonic''===
Under TAMNAMS and for all scale pattern pages on the wiki, '''the term ''diatonic'' exclusively refers to 5L 2s'''. Other diatonic-based scales, such as [[Zarlino]], [[blackdye]] and [[diasem]], are called ''[[Detempering|detempered]] diatonic scales'' (for an RTT-based philosophy) or ''deregularized diatonic scales'' (for an RTT-agnostic philosophy). The terms ''diatonic-like'' or ''diatonic-based'' may also be used to refer to diatonic-based scales, depending on what's contextually the most appropriate.
Under TAMNAMS and for all scale pattern pages on the wiki, '''the term ''diatonic'' exclusively refers to 5L 2s'''. Other diatonic-based scales, such as [[Zarlino]], [[blackdye]] and [[diasem]], are called ''[[Detempering|detempered]] diatonic scales'' (for an RTT-based philosophy) or ''deregularized diatonic scales'' (for an RTT-agnostic philosophy). The terms ''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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{{MOS modes|Scale Signature=5L 2s}}
{{MOS modes|Scale Signature=5L 2s}}
==Scales==
==Scales==
=== Subset and superset MOS scales ===
5L 2s has a parent scale of 2L 3s, meaning 5L 2s contains 2L 3s as a subset. 5L 2s also has two child scales that both contain 5L 2s as a subset: either 7L 5s (if the step ratio is less than 2:1) or 5L 7s (if the step ratio is greater than 2:1). A step ratio exactly 2:1 will produce 12edo, an equalized form of 5L 7s and 7L 5s.
=== MODMOS scales and muddles ===
{{main| 5L 2s MODMOSes }} ''and [[5L 2s Muddles]]''


=== Scala files ===
=== Scala files ===
* [[Meantone7]] – 19edo and 31edo tunings
* [[Meantone7]] – 19edo and 31edo tunings
* [[Nestoria7]] – 171edo tuning
* [[Nestoria7]] – 171edo tuning
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* [[Supra7]] – 56edo tuning
* [[Supra7]] – 56edo tuning
* [[Archy7]] – 472edo tuning
* [[Archy7]] – 472edo tuning
=== MODMOS scales and muddles ===
{{main| 5L 2s MODMOSes }} ''and [[5L 2s Muddles]]''
=== Parent and daughter MOS scales ===
5L 2s has a parent scale of 2L 3s, meaning 5L 2s contains 2L 3s as a subset. 5L 2s also has two daughter scales that both contain 5L 2s as a subset: either 7L 5s (if the step ratio is less than 2:1) or 5L 7s (if the step ratio is greater than 2:1). A step ratio exactly 2:1 will produce an equalized form of both 7L 5s and 5L 7s, corresponding to 12edo.


==Tuning spectrum==
==Tuning spectrum==

Revision as of 22:27, 28 June 2023

↖ 4L 1s ↑ 5L 1s 6L 1s ↗
← 4L 2s 5L 2s 6L 2s →
↙ 4L 3s ↓ 5L 3s 6L 3s ↘ 
┌╥╥╥┬╥╥┬┐
│║║║│║║││
│││││││││
└┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLsLLs
sLLsLLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 4\7 to 3\5 (685.7 ¢ to 720.0 ¢)
Dark 2\5 to 3\7 (480.0 ¢ to 514.3 ¢)
TAMNAMS information
Name diatonic
Prefix dia-
Abbrev. dia
Related MOS scales
Parent 2L 3s
Sister 2L 5s
Daughters 7L 5s, 5L 7s
Neutralized 3L 4s
2-Flought 12L 2s, 5L 9s
Equal tunings
Equalized (L:s = 1:1) 4\7 (685.7 ¢)
Supersoft (L:s = 4:3) 15\26 (692.3 ¢)
Soft (L:s = 3:2) 11\19 (694.7 ¢)
Semisoft (L:s = 5:3) 18\31 (696.8 ¢)
Basic (L:s = 2:1) 7\12 (700.0 ¢)
Semihard (L:s = 5:2) 17\29 (703.4 ¢)
Hard (L:s = 3:1) 10\17 (705.9 ¢)
Superhard (L:s = 4:1) 13\22 (709.1 ¢)
Collapsed (L:s = 1:0) 3\5 (720.0 ¢)
This is a test page. For the main page, see 5L 2s.

5L 2s, named diatonic in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 2 small steps, repeating every octave. Generators that produce this scale range from 685.7 ¢ to 720 ¢, or from 480 ¢ to 514.3 ¢.

Name

TAMNAMS suggests the name diatonic for this scale, which commonly refers to a scale with 5 whole steps and 2 small steps.

Under TAMNAMS and for all scale pattern pages on the wiki, the term diatonic exclusively refers to 5L 2s. Other diatonic-based scales, such as Zarlino, blackdye and diasem, are called detempered diatonic scales (for an RTT-based philosophy) or deregularized diatonic scales (for an RTT-agnostic philosophy). The terms diatonic-like or diatonic-based may also be used to refer to diatonic-based scales, depending on what's contextually the most appropriate.

Notation

Intervals

Intervals are identical to that of standard notation. As such, the usual interval qualities of major/minor and augmented/perfect/diminished apply here.

Interval class Large variety Small variety
Size Quality Size Quality
1st (unison) 0 Perfect 0 Perfect
2nd L Major s Minor
3rd 2L Major L + s Minor
4th 3L Augmented 2L + 1s Perfect
5th 3L + 1s Perfect 2L + 2s Diminished
6th 4L + 1s Major 3L + 2s Minor
7th 5L + 1s Major 4L + 2s Minor
8th (octave) 5L + 2s Perfect 5L + 2s Perfect

Note names

Note names are identical to that of standard notation. Thus, the basic gamut for 5L 2s is the following:

J, J&/K@, K, L, L&/M@, M, M&/N@, N, N&/O@, O, P, P&/J@, J

Theory

Generalizing whole and half steps

The familiar pattern of 5 whole steps and 2 half steps, commonly written as WWHWWWH for the major scale, has step sizes of 2 (whole step) and 1 (small step), producing 12edo. This can be generalized to form the pattern LLsLLLs with whole-number step sizes for L and s, where L is greater than s. The terms "large step" and "small step" are preferred as most step size pairings cannot be interpreted as "whole" and "half" steps.

Different edos are produced by using different ratios of step sizes. A few examples are shown below.

Step ratio (L:s) Step pattern EDO
4:3 4 4 3 4 4 4 3 26edo
3:2 3 3 2 3 3 3 2 19edo
5:3 5 5 3 5 5 5 3 31edo
2:1 2 2 1 2 2 2 1 12edo (standard tuning)
5:2 5 5 2 5 5 5 2 29edo
3:1 3 3 1 3 3 3 1 17edo
4:1 4 4 1 4 4 4 1 22edo

Edos that are multiples of the examples above can be reached by entering non-simplified step ratios. For example, edos that are multiples of 12 are reached by using larger values whose ratio simplifies to 2:1, such as 4:2 for 24edo and 12:6 for 72edo. The step sizes may be called whole and half in this case.

A spectrum of step ratios can be produced by starting with the ratios 1:1 and 1:0 and repeatedly finding the mediants between adjacent ratios. The first three iterations are shown below, yielding the step ratios previously mentioned.

Ratios
1/1
2/1
1/0
Ratios
1/1
3/2
2/1
3/1
1/0
Ratios
1/1
4/3
3/2
5/3
2/1
5/2
3/1
4/1
1/0

Larger edos, such as 53edo (step ratio 9:4), can be reached by repeatedly expanding the tuning spectrum. A larger tuning spectrum can be found in this page's tuning spectrum section.

The step ratios 1:1 and 1:0 represent the extremes of the tuning spectrum. A step ratio that approaches 1:1, where the large and small step are equal to one another, approaches 7edo, and a step ratio that approaches 1:0, where the size of the small step approaches 0 relative to the size of the large step, approaches 5edo.

Temperament interpretations

Main article: 5L 2s/Temperaments

5L 2s has several temperament interpretations, such as:

  • Flattone, with a generator size around 694¢, corresponding to a step ratio within the ultrasoft to parasoft range (6:5 to 3:2).
  • Meantone, with a generator size around 696¢, corresponding to a step ratio within the hyposoft range (3:2 to 2:1).
  • Schismic, with a generator size around 702¢ (just perfect 5th, or 3/2), corresponding to a step ratio within the hypohard range (2:1 to 3:2).
  • Parapyth, with a generator size ranging between 702¢ and 705¢, corresponding to a step ratio within the quasihard to range (5:2 to 3:1).
  • Archy, with a generator size greater than 705¢, corresponding to a step ratio within the parahard to ultrahard range (greater than 3:1).

Step ratios

Parasoft to ultrasoft

Hyposoft

Hyposoft tunings correspond to meantone temperaments, characterized by flattening the perfect 5th from just (3/2) to achieve a diatonic major 3rd that approximates 5/4 (386¢). Examples of this include 19edo (step ratio 3:2) and 31edo (step ratio 5:3).

User:MOS degrees is deprecated. Please use Template:MOS tunings instead.
Scale degree of 5L 2s
Scale degree 19edo (Soft, L:s = 3:2) 31edo (Semisoft, L:s = 5:3) Approx. JI Ratios
Steps Cents Steps Cents
Perfect 0-diadegree (unison) 0 0 0 0 1/1 (exact)
Minor 1-diadegree 2 126.3 3 116.1
Major 1-diadegree 3 189.5 5 193.5
Minor 2-diadegree 5 315.8 8 309.7
Major 2-diadegree 6 378.9 10 387.1
Perfect 3-diadegree 8 505.3 13 503.2
Augmented 3-diadegree 9 568.4 15 580.6
Diminished 4-diadegree 10 631.6 16 619.4
Perfect 4-diadegree 11 694.7 18 696.8
Minor 5-diadegree 13 821.1 21 812.9
Major 5-diadegree 14 884.2 23 890.3
Minor 6-diadegree 16 1010.5 26 1006.5
Major 6-diadegree 17 1073.7 28 1083.9
Perfect 7-diadegree (octave) 19 1200 31 1200 2/1 (exact)

Hypohard

Parahard to ultrahard

Modes

Diatonic modes have standard names from classical music theory:


Modes of 5L 2s
UDP Cyclic
order		 Step
pattern		 Mode names
6|0 1 LLLsLLs Lydian
5|1 5 LLsLLLs Ionian (major)
4|2 2 LLsLLsL Mixolydian
3|3 6 LsLLLsL Dorian
2|4 3 LsLLsLL Aeolian (minor)
1|5 7 sLLLsLL Phrygian
0|6 4 sLLsLLL Locrian

Scales

Subset and superset MOS scales

5L 2s has a parent scale of 2L 3s, meaning 5L 2s contains 2L 3s as a subset. 5L 2s also has two child scales that both contain 5L 2s as a subset: either 7L 5s (if the step ratio is less than 2:1) or 5L 7s (if the step ratio is greater than 2:1). A step ratio exactly 2:1 will produce 12edo, an equalized form of 5L 7s and 7L 5s.

MODMOS scales and muddles

Main article: 5L 2s MODMOSes
 and 5L 2s Muddles

Scala files

Tuning spectrum

Template:Scale tree

See also

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