User:Moremajorthanmajor/8L 3s (perfect twelfth-equivalent): Difference between revisions
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The [[TAMNAMS]] system is used in this article to refer to 8L 3s (perfect twelfth equivalent) step size ratios and step ratio ranges. | The [[TAMNAMS]] system is used in this article to refer to 8L 3s (perfect twelfth equivalent) step size ratios and step ratio ranges. | ||
The notation used in this article is GHJKLABCDEFG = LLsLLLsLLLs (Ionian #11), #/f = up/down by chroma (mnemonic f = F molle in Latin). | The notation used in this article is GHJKLABCDEFG = LLsLLLsLLLs (Ionian #11) or LLLsLLsLLLs (Lydian), #/f = up/down by chroma (mnemonic f = F molle in Latin). | ||
Thus the [[19edt]] gamut is as follows: | Thus the [[19edt]] gamut is as follows: | ||
'''G/F#''' G#/Hf '''H''' H#/Jf '''J K''' K#/Lf '''L''' L#/Af '''A''' ''A#/Bf'' '''B C''' C#/Df '''D''' D#/Ef '''E''' ''E#/Ff'' '''F/Gf''' | '''G/F#''' G#/Hf '''H''' H#/Jf '''J K''' K#/Lf '''L''' L#/Af '''A''' ''A#/Bf'' '''B C''' C#/Df '''D''' D#/Ef '''E''' ''E#/Ff'' '''F/Gf''' | ||
'''G/F#''' G#/Hf '''H''' H#/Jf '''J''' J#/Kf '''K''' '''L''' L#/Af '''A''' ''A#/Bf'' '''B C''' C#/Df '''D''' D#/Ef '''E''' ''E#/Ff'' '''F/Gf''' | |||
The [[27edt]] gamut is notated as follows: | The [[27edt]] gamut is notated as follows: | ||
'''G''' F#/Hf G# '''H''' Jf H#/Kf '''J K''' J#/Lf K# '''L''' Af L# '''A''' ''Bf'' A#/Cf '''B''' '''C''' B#/Df C# '''D''' Ef D# '''E''' ''Ff'' E#/Gf '''F''' | '''G''' F#/Hf G# '''H''' Jf H#/Kf '''J K''' J#/Lf K# '''L''' Af L# '''A''' ''Bf'' A#/Cf '''B''' '''C''' B#/Df C# '''D''' Ef D# '''E''' ''Ff'' E#/Gf '''F''' | ||
'''G''' F#/Hf G# '''H''' Jf H#/Kf '''J''' Kf J#/Lf '''K''' '''L''' Af L# '''A''' ''Bf'' A#/Cf '''B''' '''C''' B#/Df C# '''D''' Ef D# '''E''' ''Ff'' E#/Gf '''F''' | |||
The [[30edt]] gamut: | The [[30edt]] gamut: | ||
'''G''' G# Hf '''H''' H# Jf '''J''' J#/Kf '''K''' K# Lf '''L''' L# Af '''A''' A# ''Bf'' '''B''' B#/Cf '''C''' C# Df '''D''' D# Ef '''E''' E# ''Ff'' '''F''' F#/Gf | '''G''' G# Hf '''H''' H# Jf '''J''' J#/Kf '''K''' K# Lf '''L''' L# Af '''A''' A# ''Bf'' '''B''' B#/Cf '''C''' C# Df '''D''' D# Ef '''E''' E# ''Ff'' '''F''' F#/Gf | ||
'''G''' G# Hf '''H''' H# Jf '''J''' J#Kf '''K''' K#/Lf '''L''' L# Af '''A''' A# ''Bf'' '''B''' B#/Cf '''C''' C# Df '''D''' D# Ef '''E''' E# ''Ff'' '''F''' F#/Gf | |||
==Intervals== | ==Intervals== | ||
| Line 67: | Line 73: | ||
|6L+2s | |6L+2s | ||
| -2 | | -2 | ||
|K | |K(f) | ||
|natural 4th | |natural 4th | ||
|2L+1s | |2L+1s | ||
| Line 126: | Line 132: | ||
|- | |- | ||
|9 | |9 | ||
|K# | |K(#) | ||
|augmented 4th | |augmented 4th | ||
|3L | |3L | ||
| Line 268: | Line 274: | ||
|7\27, 494.12 | |7\27, 494.12 | ||
|8\30, 505,26 | |8\30, 505,26 | ||
|K | |K, Kf | ||
| -2 | | -2 | ||
|- | |- | ||
| Line 275: | Line 281: | ||
|9\27, 635.29 | |9\27, 635.29 | ||
|9\30, 568.42 | |9\30, 568.42 | ||
|K# | |K, K# | ||
|9 | |9 | ||
|- | |- | ||
| Line 455: | Line 461: | ||
|7\27, 494.12 | |7\27, 494.12 | ||
|12\46, 496.55 | |12\46, 496.55 | ||
|K | |K, Kf | ||
| -2 | | -2 | ||
|- | |- | ||
| Line 462: | Line 468: | ||
|9\27, 635.29 | |9\27, 635.29 | ||
|15\46, 620.69 | |15\46, 620.69 | ||
|K# | |K, K# | ||
|9 | |9 | ||
|- | |- | ||
| Line 633: | Line 639: | ||
|8\30, 505,26 | |8\30, 505,26 | ||
|13\49, 503.23 | |13\49, 503.23 | ||
|K | |K, Kf | ||
|4/3 | |4/3 | ||
| -2 | | -2 | ||
| Line 640: | Line 646: | ||
|9\30, 568.42 | |9\30, 568.42 | ||
|15\49, 580.65 | |15\49, 580.65 | ||
|K# | |K, K# | ||
|7/5 | |7/5 | ||
|9 | |9 | ||
| Line 836: | Line 842: | ||
|diminished 4th | |diminished 4th | ||
|10\41, 461.54 | |10\41, 461.54 | ||
|Kff | |Kf, Kff | ||
|[[21/16]], [[13/10]] | |[[21/16]], [[13/10]] | ||
| -13 | | -13 | ||
| Line 842: | Line 848: | ||
|natural 4th | |natural 4th | ||
|11\41, 507.69 | |11\41, 507.69 | ||
|Kf | |K, Kf | ||
|[[75/56]], [[4/3]] | |[[75/56]], [[4/3]] | ||
| -2 | | -2 | ||
| Line 848: | Line 854: | ||
|augmented 4th | |augmented 4th | ||
|12\41, 553.85 | |12\41, 553.85 | ||
|K | |K, K# | ||
|[[11/8]], [[18/13]] | |[[11/8]], [[18/13]] | ||
|9 | |9 | ||
| Line 854: | Line 860: | ||
|doubly augmented 4th, doubly diminished 5th | |doubly augmented 4th, doubly diminished 5th | ||
|13\41, 600.00 | |13\41, 600.00 | ||
|K#, Lff | |K#, Kx, Lff | ||
|[[7/5]], [[10/7]] | |[[7/5]], [[10/7]] | ||
|20,-21 | |20,-21 | ||
| Line 1,088: | Line 1,094: | ||
|diminished 4th | |diminished 4th | ||
|6\35, 327.27 | |6\35, 327.27 | ||
|Kff | |Kf, Kff | ||
|[[6/5]], [[17/14]], [[11/9]] | |[[6/5]], [[17/14]], [[11/9]] | ||
| -13 | | -13 | ||
| Line 1,094: | Line 1,100: | ||
|natural 4th | |natural 4th | ||
|9\35, 490.91 | |9\35, 490.91 | ||
|Kf | |K, Kf | ||
|[[4/3]] | |[[4/3]] | ||
| -2 | | -2 | ||
| Line 1,100: | Line 1,106: | ||
|augmented 4th | |augmented 4th | ||
|12\35, 654.55 | |12\35, 654.55 | ||
|K | |K, K# | ||
|[[16/11]], [[22/15]] | |[[16/11]], [[22/15]] | ||
|9 | |9 | ||
| Line 1,307: | Line 1,313: | ||
!Size in PHTE tuning | !Size in PHTE tuning | ||
!Note name on D | !Note name on D | ||
!Note name on H | |||
! class="unsortable" |Approximate ratios | ! class="unsortable" |Approximate ratios | ||
!#Gens up | !#Gens up | ||
| Line 1,317: | Line 1,324: | ||
|0.00 | |0.00 | ||
|D | |D | ||
|H | |||
|1/1 | |1/1 | ||
|0 | |0 | ||
| Line 1,327: | Line 1,335: | ||
|230.55 | |230.55 | ||
|E | |E | ||
|J | |||
|8/7 | |8/7 | ||
| +3 | | +3 | ||
| Line 1,337: | Line 1,346: | ||
|461.10 | |461.10 | ||
|F | |F | ||
|K | |||
|13/10, 9/7 | |13/10, 9/7 | ||
| +6 | | +6 | ||
| Line 1,347: | Line 1,357: | ||
|482.06 | |482.06 | ||
|G | |G | ||
|L | |||
|4/3 | |4/3 | ||
| -2 | | -2 | ||
| Line 1,357: | Line 1,368: | ||
|712.61 | |712.61 | ||
|H | |H | ||
|A | |||
|3/2 | |3/2 | ||
| +1 | | +1 | ||
| Line 1,367: | Line 1,379: | ||
|943.16 | |943.16 | ||
|J | |J | ||
|B | |||
|12/7, 26/15 | |12/7, 26/15 | ||
| +4 | | +4 | ||
| Line 1,377: | Line 1,390: | ||
|964.12 | |964.12 | ||
|K | |K | ||
|C | |||
|7/4 | |7/4 | ||
| -4 | | -4 | ||
| Line 1,387: | Line 1,401: | ||
|1194.67 | |1194.67 | ||
|L | |L | ||
|D | |||
|2/1 | |2/1 | ||
| -1 | | -1 | ||
| Line 1,397: | Line 1,412: | ||
|1425.22 | |1425.22 | ||
|A | |A | ||
|E | |||
|16/7 | |16/7 | ||
| +2 | | +2 | ||
| Line 1,407: | Line 1,423: | ||
|1655.77 | |1655.77 | ||
|B | |B | ||
|F | |||
|13/5, 18/7 | |13/5, 18/7 | ||
| +5 | | +5 | ||
| Line 1,419: | Line 1,436: | ||
|1676.32 | |1676.32 | ||
|C | |C | ||
|G | |||
|4/3 | |4/3 | ||
| -3 | | -3 | ||
| Line 1,477: | Line 1,495: | ||
{| class="wikitable" | {| class="wikitable" | ||
|+ | |+ | ||
!Spelling | !Spelling 1 | ||
!Spelling 2 | |||
!'''Mode''' | !'''Mode''' | ||
![[Modal UDP Notation|'''UDP''']] | ![[Modal UDP Notation|'''UDP''']] | ||
| Line 1,483: | Line 1,502: | ||
|- | |- | ||
|GHJKLABCDEFG | |GHJKLABCDEFG | ||
|LABCDEFGHJKL | |||
|LLsLLLsLLLs | |LLsLLLsLLLs | ||
| style="text-align:center;" |<nowiki>8|2</nowiki> | | style="text-align:center;" |<nowiki>8|2</nowiki> | ||
| Line 1,488: | Line 1,508: | ||
|- | |- | ||
|HJKLABCDEFGH | |HJKLABCDEFGH | ||
|ABCDEFGHJKLA | |||
|LsLLLsLLLsL | |LsLLLsLLLsL | ||
| style="text-align:center;" |<nowiki>5|5</nowiki> | | style="text-align:center;" |<nowiki>5|5</nowiki> | ||
| Line 1,493: | Line 1,514: | ||
|- | |- | ||
|JKLABCDEFGHJ | |JKLABCDEFGHJ | ||
|BCDEFGHJKLAB | |||
|sLLLsLLLsLL | |sLLLsLLLsLL | ||
| style="text-align:center;" |<nowiki>2|8</nowiki> | | style="text-align:center;" |<nowiki>2|8</nowiki> | ||
| Line 1,498: | Line 1,520: | ||
|- | |- | ||
|KLABCDEFGHJK | |KLABCDEFGHJK | ||
|CDEFGHJKLABC | |||
|LLLsLLLsLLs | |LLLsLLLsLLs | ||
| style="text-align:center;" |<nowiki>10|0</nowiki> | | style="text-align:center;" |<nowiki>10|0</nowiki> | ||
| Line 1,503: | Line 1,526: | ||
|- | |- | ||
|LABCDEFGHJKL | |LABCDEFGHJKL | ||
|DEFGHJKLABCD | |||
|LLsLLLsLLsL | |LLsLLLsLLsL | ||
| style="text-align:center;" |<nowiki>7|3</nowiki> | | style="text-align:center;" |<nowiki>7|3</nowiki> | ||
| Line 1,508: | Line 1,532: | ||
|- | |- | ||
|ABCDEFGHJKLA | |ABCDEFGHJKLA | ||
|EFGHJKLABCDE | |||
|LsLLLsLLsLL | |LsLLLsLLsLL | ||
| style="text-align:center;" |<nowiki>4|6</nowiki> | | style="text-align:center;" |<nowiki>4|6</nowiki> | ||
| Line 1,513: | Line 1,538: | ||
|- | |- | ||
|BCDEFGHJKLAB | |BCDEFGHJKLAB | ||
|FGHJKLABCDEF | |||
|sLLLsLLsLLL | |sLLLsLLsLLL | ||
| style="text-align:center;" |<nowiki>1|9</nowiki> | | style="text-align:center;" |<nowiki>1|9</nowiki> | ||
| Line 1,518: | Line 1,544: | ||
|- | |- | ||
|CDEFGHJKLABC | |CDEFGHJKLABC | ||
|GHJKLABCDEFG | |||
|LLLsLLsLLLs | |LLLsLLsLLLs | ||
| style="text-align:center;" |<nowiki>9|1</nowiki> | | style="text-align:center;" |<nowiki>9|1</nowiki> | ||
| Line 1,523: | Line 1,550: | ||
|- | |- | ||
|DEFGHJKLABCD | |DEFGHJKLABCD | ||
|HJKLABCDEFGH | |||
|LLsLLsLLLsL | |LLsLLsLLLsL | ||
| style="text-align:center;" |<nowiki>6|4</nowiki> | | style="text-align:center;" |<nowiki>6|4</nowiki> | ||
| Line 1,528: | Line 1,556: | ||
|- | |- | ||
|EFGHJKLABCDE | |EFGHJKLABCDE | ||
|JKLABCDEFGHJ | |||
|LsLLsLLLsLL | |LsLLsLLLsLL | ||
| style="text-align:center;" |<nowiki>3|7</nowiki> | | style="text-align:center;" |<nowiki>3|7</nowiki> | ||
| Line 1,533: | Line 1,562: | ||
|- | |- | ||
|FGHJKLABCDEF | |FGHJKLABCDEF | ||
|KLABCDEFGHJK | |||
|sLLsLLLsLLL | |sLLsLLLsLLL | ||
| style="text-align:center;" |<nowiki>0|10</nowiki> | | style="text-align:center;" |<nowiki>0|10</nowiki> | ||