Kite's color notation: Difference between revisions
m →Temperament names and comma names: changed wa-53 to 53wama, plus minor clarifications |
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The [[4:5:6:7|y,z7 chord]] is called the har7 ("har-seven") or h7 chord, because it's part of the harmonic series. {{nowrap|[[4:5:6:7:9|Ch9]] {{=}} Cy,z7,9}} and {{nowrap|[[4:5:6:7:9:11|Ch11]] {{=}} Cy,z7,w9,1o11}}. The [[60:70:84:105|sub7 ("sub-seven") or s7 chord]] is part of the subharmonic series. It's the first 7 subharmonics, with the 7th subharmonic becoming the root. {{nowrap|[[140:180:210:252:315|Cs9]] {{=}} Cr,g7,9}} and {{nowrap|Cs11 {{=}} C1o11(1or5,1og9)}}. Note that s9 is not s7 plus a 9th, but a completely different chord. Usually the 9th ''ascends'' from the root, but in a sub9 chord it ''descends'' from the top note, and becomes the new root. Thus the s7 chord is contained in the ''upper'' four notes of the s9 chord, not the lower four. See [[Kite's thoughts on harmonic and subharmonic nomenclature]]. | The [[4:5:6:7|y,z7 chord]] is called the har7 ("har-seven") or h7 chord, because it's part of the harmonic series. {{nowrap|[[4:5:6:7:9|Ch9]] {{=}} Cy,z7,9}} and {{nowrap|[[4:5:6:7:9:11|Ch11]] {{=}} Cy,z7,w9,1o11}}. The [[60:70:84:105|sub7 ("sub-seven") or s7 chord]] is part of the subharmonic series. It's the first 7 subharmonics, with the 7th subharmonic becoming the root. {{nowrap|[[140:180:210:252:315|Cs9]] {{=}} Cr,g7,9}} and {{nowrap|Cs11 {{=}} C1o11(1or5,1og9)}}. Note that s9 is not s7 plus a 9th, but a completely different chord. Usually the 9th ''ascends'' from the root, but in a sub9 chord it ''descends'' from the top note, and becomes the new root. Thus the s7 chord is contained in the ''upper'' four notes of the s9 chord, not the lower four. See [[Kite's thoughts on harmonic and subharmonic nomenclature]]. | ||
{{nowrap|Cs6 {{=}} Cg,r6}} {{nowrap|{{=}} [[70:84:105:120|12:10:8:7]]}}. Ch6 = Cz,y6 = 6:7:9:10. Other than | {{nowrap|Cs6 {{=}} Cg,r6}} {{nowrap|{{=}} [[70:84:105:120|12:10:8:7]]}}. Ch6 = Cz,y6 = 6:7:9:10. Other than these two chords, all harmonic/subharmonic numbers must be odd, e.g. Ch8 is invalid. For any odd number N greater than 5, ChN is 1:3:5...N and CsN is N...5:3:1 (but 1 and 3 are generally written as their octave equivalents 4 and 6). <u>Additions, a</u><u>lterations and omissions refer to degrees</u>, not harmonics or subharmonics: Ch7,11 adds w11, not 1o11. Ch9no5 omits w5, not y3. However, <u>all numbers > 13 refer to (sub)harmonics</u>, e.g. Ch9,15 adds y7 and Ch19no15 omits it. When two harmonics share the same degree, omitting that degree omits the lower harmonic. Thus Ch19no7 omits 7/4. | ||
<u>All wa chords can be named conventionally</u>, since wa is the default color. Thus {{dash|w1, w3, w5}} is both Cw and Cm. And {{dash|w1, Lw3, w5, w6}} is both CLw6 and C6. For aesthetic reasons, the conventional name is preferred only when neither "M" nor "m" appears in the name (since color notation doesn't use major/minor). This is especially true if the chord includes non-wa notes: {{dash|w1, w3, w5, y6}} is Cw,y6 not Cm,y6. | <u>All wa chords can be named conventionally</u>, since wa is the default color. Thus {{dash|w1, w3, w5}} is both Cw and Cm. And {{dash|w1, Lw3, w5, w6}} is both CLw6 and C6. For aesthetic reasons, the conventional name is preferred only when neither "M" nor "m" appears in the name (since color notation doesn't use major/minor). This is especially true if the chord includes non-wa notes: {{dash|w1, w3, w5, y6}} is Cw,y6 not Cm,y6. | ||
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Another reason is to avoid an awkward unison trill. [[File:Notation example 5a.png|992x992px]] | Another reason is to avoid an awkward unison trill. [[File:Notation example 5a.png|992x992px]] | ||
== | == Comma names and temperament names == | ||
{{Main | Color notation/Temperament names}} | {{Main | Color notation/Temperament names}} | ||
Temperaments are named after the comma(s) they temper out. Commas are named using an alternate format that replaces the degree (unison, 2nd, etc.) with the suffix "-ma" (mnemonics: com'''ma''', or -is'''ma''' as in schisma and kleisma). The degree isn't needed because the comma is assumed to be the smallest interval in cents of that color and magnitude. For example, the guma is the smallest of the 7 central gu intervals, which is [[81/80]]. Tempering out the guma creates [[Meantone]] or Guti or gT, where "-ti" and "T" stand for temperament. [[2048/2025]] is the saguguma, abbreviated sggM, and [[Srutal]] is Saguguti or sggT. [[Porcupine]] is Triyoti or 3yT. | Temperaments are named after the comma(s) they temper out. Commas are named using an alternate format that replaces the degree (unison, 2nd, etc.) with the suffix "-ma" (mnemonics: com'''ma''', or -is'''ma''' as in schisma and kleisma). The degree isn't needed because the comma is assumed to be the smallest interval in cents of that color and magnitude. For example, the guma is the smallest of the 7 central gu intervals, which is [[81/80]]. Tempering out the guma creates [[Meantone]] or Guti or gT, where "-ti" and "T" stand for temperament. [[2048/2025]] is the saguguma, abbreviated sggM, and [[Srutal]] is Saguguti or sggT. [[Porcupine]] is Triyoti or 3yT. Example usage of -ti and -ma: triyoti inflates the guma. | ||
The logic for M and T being upper case is that in color notation abbreviations, nouns are always capitalized and adjectives are generally not. | The logic for M and T being upper case is that in color notation abbreviations, nouns are always capitalized and adjectives are generally not. Color notation nouns: M and T, note names A B C D E F G, roman numerals I II III IV V VI VII, and degrees 1 2 3 etc. (L for large is an exception to this rule, because otherwise Ly7 would be ly7, which looks like a y7 chord on the tonic.) | ||
Some commas over 90¢ (but not all) are the ''2nd'' smallest interval in cents of that color and magnitude. These use the -bi- syllable. For example, [[Schismic]] is Layoti or LyT, but [[Mavila]] is Layobiti or LybT, where "-bi-" and "-b-" indicate it's the 2nd largest layo interval. Likewise 135/128 is named layobima or LybM. | |||
Most wa commas use yet another alternate format, e.g. [[Mercator's comma]] is 53wama or 53wM. The only exceptions are lawama (LwM = A1), sawama (swM = m2) and lalawama (LLwM = pythagorean comma). | Most wa commas use yet another alternate format, e.g. [[Mercator's comma]] is 53wama or 53wM. The only exceptions are lawama (LwM = A1), sawama (swM = m2) and lalawama (LLwM = pythagorean comma). | ||
Multi-comma temperaments have multiple commas in their name. [[Meantone family#Septimal meantone | Septimal Meantone]] is | Multi-comma temperaments have multiple commas in their name. [[Meantone family#Septimal meantone | Septimal Meantone]] is gu & ruyoyoti or g&ryyT, and [[Meantone family#Dominant | Dominant Meantone]] is gu & ruguti or g&rgT. Untempered primes are included with a plus sign. The 2.3.5.7 prime subgroup with 81/80 tempered out is Guti + za = gT+z, and [[Blackwood]] is Sawati + ya = swT+y. | ||
MOS and MODMOS scales can be named as e.g. Triyoti[8]. Individual modes can be named as 2nd Triyoti[8], 3rd Triyoti[7] b7, etc. See [[Genchain mode numbering]]. | MOS and MODMOS scales can be named as e.g. Triyoti[8]. Individual modes can be named as 2nd Triyoti[8], 3rd Triyoti[7] b7, etc. See [[Genchain mode numbering]]. | ||
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| colspan="2" | -a- | | colspan="2" | -a- | ||
| delimits an exponent such as bi-, tri-, etc. | | delimits an exponent such as bi-, tri-, etc. | ||
| | | trizoguma = 3zgM = 1029/1000, but trizo-aguma = 3zagM = 343/320 | ||
|- | |- | ||
| co- | | co- | ||
| Line 789: | Line 789: | ||
| T | | T | ||
| the temperament that tempers out that comma | | the temperament that tempers out that comma | ||
| guma = 81/80, | | guma = 81/80, guti = meantone | ||
|- | |- | ||
| -bi | | -bi | ||
| style="text-align: center;" | b | | style="text-align: center;" | b | ||
| as a suffix, 2nd smallest comma in the row segment | | as a suffix, 2nd smallest comma in the row segment | ||
| | | guti = gT is Meantone, but gubiti = gbT is [[Father]] (16/15 vanishes) | ||
|- | |- | ||
| | | -wama | ||
| | | wM | ||
| alternate interval format, only used for 3-limit commas | | alternate interval format, only used for 3-limit commas | ||
| [[Mercator's comma]] = | | [[Mercator's comma]] = 53wama = 53wM | ||
|- | |- | ||
| colspan="2" | nowa | | colspan="2" | nowa | ||
| remove 3 (wa) from the prime subgroup, i.e. no-threes | | remove 3 (wa) from the prime subgroup, i.e. no-threes | ||
| 2.5.7 = yaza nowa, 2.5.7 & 50/49 = | | 2.5.7 = yaza nowa, 2.5.7 & 50/49 = biruyoti nowa | ||
|- | |- | ||
| colspan="2" | noca | | colspan="2" | noca | ||
| remove 2 (clear) from the prime subgroup, i.e. non-8ve | | remove 2 (clear) from the prime subgroup, i.e. non-8ve | ||
| 3.5.7 = yaza noca, 3.5.7 & 245/243 = | | 3.5.7 = yaza noca, 3.5.7 & 245/243 = zozoyoti noca | ||
|- | |- | ||
| colspan="2" | nowaca | | colspan="2" | nowaca | ||
| Line 816: | Line 816: | ||
| style="text-align: center;" | + | | style="text-align: center;" | + | ||
| add an untempered prime to the temperament | | add an untempered prime to the temperament | ||
| Blackwood = 2.3.5 with 256/243 tempered out = | | Blackwood = 2.3.5 with 256/243 tempered out = sawati + ya = swT+y | ||
|- | |- | ||
| and | | and | ||
| style="text-align: center;" | & | | style="text-align: center;" | & | ||
| joins commas that are tempered out | | joins commas that are tempered out | ||
| 7-limit Porcupine = 2.3.5.7 with 250/243 & 64/63 = | | 7-limit Porcupine = 2.3.5.7 with 250/243 & 64/63 = triyo & ruti = 3y&rT | ||
|- | |- | ||
| -ward | | -ward | ||