Kite's ups and downs notation: Difference between revisions
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Ups and downs can also notate any [[Tour of Regular Temperaments|rank-2 temperament]], although some temperaments require an additional pair of accidentals, lifts and drops (/ and \). In this context, an up or a lift represents sharpening by a [[comma]] that has been tempered, but not tempered out. For example, in [[Porcupine|Triyo aka Porcupine]], an up/down represents raising/lowering by a tempered 81/80, and lifts/drops aren't used. In practice, the two uses of the notation often coincide perfectly. Triyo is supported by both 15edo and 22edo, and both edos map 81/80 to one EDOstep. Thus if Triyo is tuned to 15edo, an up simultaneously means both a tempered 81/80 and 1\15. Likewise, if tuned to 22edo, the up means both 81/80 and 1\22. If not tuned to an edo at all, then the up only means 81/80. Thus a piece written in Triyo can be converted to a piece written in 22edo by simply writing "22edo" on the top of the page. | Ups and downs can also notate any [[Tour of Regular Temperaments|rank-2 temperament]], although some temperaments require an additional pair of accidentals, lifts and drops (/ and \). In this context, an up or a lift represents sharpening by a [[comma]] that has been tempered, but not tempered out. For example, in [[Porcupine|Triyo aka Porcupine]], an up/down represents raising/lowering by a tempered 81/80, and lifts/drops aren't used. In practice, the two uses of the notation often coincide perfectly. Triyo is supported by both 15edo and 22edo, and both edos map 81/80 to one EDOstep. Thus if Triyo is tuned to 15edo, an up simultaneously means both a tempered 81/80 and 1\15. Likewise, if tuned to 22edo, the up means both 81/80 and 1\22. If not tuned to an edo at all, then the up only means 81/80. Thus a piece written in Triyo can be converted to a piece written in 22edo by simply writing "22edo" on the top of the page. | ||
Ups and downs can also be used to notate rank-3 just intonation subgroups such as 2.3.5 or 2.3.7 or 2.3.11. See [[Ups and | Ups and downs can also be used to notate rank-3 just intonation subgroups such as 2.3.5 or 2.3.7 or 2.3.11. See [[Kite's thoughts on ups and downs notation for rank-3 JI|Ups and downs notation for Rank-3 JI]]. | ||
'''<u>This page only discusses notation of edos.</u>''' However, the notation of chords and chord progressions applies to all situations. For notation of rank-2 and rank-3 temperaments, see the [[pergen|pergens]] article. | '''<u>This page only discusses notation of edos.</u>''' However, the notation of chords and chord progressions applies to all situations. For notation of rank-2 and rank-3 temperaments, see the [[pergen|pergens]] article. | ||
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Very large edos can go well beyond 5 arrows. The sequence of names resembles tally counting I, II, III, IIII, <s>||||</s>. But the sequence of ''symbols'' resembles roman numerals I, II, III, IV, V. Thus 4 ups is spoken quup but written v>. | Very large edos can go well beyond 5 arrows. The sequence of names resembles tally counting I, II, III, IIII, <s>||||</s>. But the sequence of ''symbols'' resembles roman numerals I, II, III, IV, V. Thus 4 ups is spoken quup but written v>. | ||
{| class="wikitable" style="text-align:center;" | |||
{| class="wikitable" style="text-align: center;" | |||
|- | |- | ||
| up<br />^ | | up<br />^ | ||
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Chord names are based on jazz chord names. See Jim Aiken's book ''A Player's Guide to Chords & Harmony''. Alterations are enclosed in parentheses, additions never are. Alterations always come last in the chord name. Examples: | Chord names are based on jazz chord names. See Jim Aiken's book ''A Player's Guide to Chords & Harmony''. Alterations are enclosed in parentheses, additions never are. Alterations always come last in the chord name. Examples: | ||
*[[19edo | * [[19edo chords]] | ||
*[[22edo | * [[22edo chords]] | ||
*[[24edo | * [[24edo chord names]] | ||
*[[31edo | * [[31edo chord names]] | ||
*[[41edo | * [[41edo chord names]] | ||
*[[Kite Guitar | * [[Kite Guitar chord shapes (downmajor tuning)]] | ||
In [[Sharpness|sharp-0]] edos aka perfect edos (7, 14, 21, 28 and 35), every interval is perfect, and there is no major or minor. In the following lists of chord names, omit major, minor, dim and aug. Substitute up for upmajor and upminor, and down for downmajor and downminor. The C-E-G chord is called "C perfect" or simply "C". | In [[Sharpness|sharp-0]] edos aka perfect edos (7, 14, 21, 28 and 35), every interval is perfect, and there is no major or minor. In the following lists of chord names, omit major, minor, dim and aug. Substitute up for upmajor and upminor, and down for downmajor and downminor. The C-E-G chord is called "C perfect" or simply "C". | ||
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| C<sup>ø</sup>(v3) | | C<sup>ø</sup>(v3) | ||
| '''Cvd,d7''' | | '''Cvd,d7''' | ||
| | | Cv<sup>o</sup>d7 | ||
| Cv,6 | | Cv,6 | ||
| Cvm,6 | | Cvm,6 | ||
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| C<sup>ø</sup>(v3v5) | | C<sup>ø</sup>(v3v5) | ||
| '''Cvd,d7(v5)''' | | '''Cvd,d7(v5)''' | ||
| | | Cv<sup>o</sup>d7(v5) | ||
| Cv,6(v5) | | Cv,6(v5) | ||
| Cvm,6(v5) | | Cvm,6(v5) | ||
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Various unusual tetrads: | Various unusual tetrads: | ||
*C vE G ^Bb = Cv^7 = "C down up-seven" (in sharp-2 edos 17, 24, 31, etc. C~7 = "C mid-seven") | * {{nowrap|C vE G ^Bb {{=}} Cv^7 {{=}} "C down up-seven"}} (in sharp-2 edos 17, 24, 31, etc. {{nowrap|C~7 {{=}} "C mid-seven"}}) | ||
*C E G A# = C,#6 or C,A6 = "C add sharp-six" or "C add aug-six" | * {{nowrap|C E G A# {{=}} C,#6}} or {{nowrap|C,A6 {{=}} "C add sharp-six"}} or "C add aug-six" | ||
*C E G Ab = C,b6 or C,m6 = "C add flat-six" or "C add minor-six" | * {{nowrap|C E G Ab {{=}} C,b6}} or {{nowrap|C,m6 {{=}} "C add flat-six"}} or "C add minor-six" | ||
*C E G Bbb = C,bb7 or C,d7 = "C add double-flat-seven" or "C add dim-seven" (19edo's 4:5:6:7 chord) | * {{nowrap|C E G Bbb {{=}} C,bb7}} or {{nowrap|C,d7 {{=}} "C add double-flat-seven"}} or "C add dim-seven" (19edo's 4:5:6:7 chord) | ||
*C E G B# = C,#7 or C,A7 = "C add sharp-seven" or "C add aug-seven" | * {{nowrap|C E G B# {{=}} C,#7}} or {{nowrap|C,A7 {{=}} "C add sharp-seven"}} or "C add aug-seven" | ||
*C E G Cb = C,b8 or C,d8 = "C add flat-eight" or "C add dim-eight" | * {{nowrap|C E G Cb {{=}} C,b8}} or {{nowrap|C,d8 {{=}} "C add flat-eight"}} or "C add dim-eight" | ||
=== Ninth chords === | === Ninth chords === | ||
As in conventional chord naming, a sharp-9 or flat-9 chord is always named as a 7th chord with an added 9th. Thus B D# F# A C is named B7b9 (not Bb9 which would be Bb D F A C). Likewise C#7b9 not C#b9, even thought the latter is clearly the same flat-9 chord as the former. Likewise Cm7b9 not Cmb9, etc. | As in conventional chord naming, a sharp-9 or flat-9 chord is always named as a 7th chord with an added 9th. Thus {{nowrap|B D# F# A C}} is named B7b9 (not Bb9 which would be {{nowrap|Bb D F A C}}). Likewise C#7b9 not C#b9, even thought the latter is clearly the same flat-9 chord as the former. Likewise Cm7b9 not Cmb9, etc. | ||
Double alterations need only a single pair of parentheses, e.g. C E vG vB D is named CM9(v5v7). Double additions mostly need only a single comma, e.g. C E G vBb vD is named C,v7v9. But certain 6/9 chords require two commas. In '''bolded''' 6/9 chords, the comma between the 6 and the 9 is <u>not</u> spoken as "add". However any comma before "6" is, e.g. Cv,6,9 is "C down add six nine". | Double alterations need only a single pair of parentheses, e.g. C E vG vB D is named CM9(v5v7). Double additions mostly need only a single comma, e.g. C E G vBb vD is named C,v7v9. But certain 6/9 chords require two commas. In '''bolded''' 6/9 chords, the comma between the 6 and the 9 is <u>not</u> spoken as "add". However any comma before "6" is, e.g. Cv,6,9 is "C down add six nine". | ||
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=== Rules for punctuation usage === | === Rules for punctuation usage === | ||
Tetrads, pentads, etc. often require a comma (the actual punctuation mark) to ensure correct parsing of the chord name. Only use a comma when needed, to reduce clutter and standardize chord names. A comma is needed in Cv,7 = C vE G Bb because omitting it makes Cv7 = C vE G vBb, a different chord. But C7,v9 is incorrect because C7v9 is the same chord. | Tetrads, pentads, etc. often require a comma (the actual punctuation mark) to ensure correct parsing of the chord name. Only use a comma when needed, to reduce clutter and standardize chord names. A comma is needed in {{nowrap|Cv,7 {{=}} C vE G Bb}} because omitting it makes {{nowrap|Cv7 {{=}} C vE G vBb}}, a different chord. But C7,v9 is incorrect because C7v9 is the same chord. | ||
The rule is, omit the comma unless doing so changes the chord. This simple rule suffices in most situations. What follows is a detailed analysis, designed to aid in writing computer code that automates chord naming. | The rule is, omit the comma unless doing so changes the chord. This simple rule suffices in most situations. What follows is a detailed analysis, designed to aid in writing computer code that automates chord naming. | ||
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A comma is always needed to separate a number from a number (Cv6,9). It's usually needed to separate an adjective from a number (Cv,7). The only exception is for certain conventional chords like Cm7 where separation is unneeded. A comma is always needed to separate the root of a plain major chord from an adjective (D,v7) or a number (Eb,9). It's never needed to separate a number from an adjective (C7^9). It's needed to separate an adjective from an adjective only if the two adjectives could apply to a single noun. There are six types of such adjective pairs. | A comma is always needed to separate a number from a number (Cv6,9). It's usually needed to separate an adjective from a number (Cv,7). The only exception is for certain conventional chords like Cm7 where separation is unneeded. A comma is always needed to separate the root of a plain major chord from an adjective (D,v7) or a number (Eb,9). It's never needed to separate a number from an adjective (C7^9). It's needed to separate an adjective from an adjective only if the two adjectives could apply to a single noun. There are six types of such adjective pairs. | ||
*up followed by any adjective except down (C^,^9 or C^,~7 or C^,#9 or C^,b9 or C^,M7 or C^,m6 or C^,a7 or C^,d7) | * up followed by any adjective except down (C^,^9 or C^,~7 or C^,#9 or C^,b9 or C^,M7 or C^,m6 or C^,a7 or C^,d7) | ||
*down followed by any adjective except up | * down followed by any adjective except up | ||
*sharp followed by sharp (C#,#9) | * sharp followed by sharp (C#,#9) | ||
*flat followed by flat (Bb,b9) | * flat followed by flat (Bb,b9) | ||
*aug followed by aug (Ca,a7) | * aug followed by aug (Ca,a7) | ||
*dim followed by dim (Cd,d9) | * dim followed by dim (Cd,d9) | ||
No other adjective pair can apply to a single noun, thus the comma is omitted: | No other adjective pair can apply to a single noun, thus the comma is omitted: | ||
* Cv^9 = C vE G ^D (an interval can't be both upped and downed) | * {{nowrap|Cv^9 {{=}} C vE G ^D}} (an interval can't be both upped and downed) | ||
* CmM7 = C Eb G B (an interval can't be both minor and major) * | * {{nowrap|CmM7 {{=}} C Eb G B}} (an interval can't be both minor and major) * | ||
* Cma7 = C Eb | * {{nowrap|Cma7 {{=}} C Eb G B#}} (an interval can't be both minor and aug) ** | ||
* Cm#11 = C Eb G F# (an interval can't be both minor and sharp) | * {{nowrap|Cm#11 {{=}} C Eb G F#}} (an interval can't be both minor and sharp) | ||
* Cvmm6 = C vEb G Ab (an interval can't be doubly minor) | * {{nowrap|Cvmm6 {{=}} C vEb G Ab}} (an interval can't be doubly minor) | ||
* Cmv7 = C Eb G vBb (an interval can be downminor, but it can't be minordown) | * {{nowrap|Cmv7 {{=}} C Eb G vBb}} (an interval can be downminor, but it can't be minordown) | ||
* C~v7 = C vvE G vBb in a sharp-4 edo (an interval can be downmid, but it can't be middown) | * {{nowrap|C~v7 {{=}} C vvE G vBb}} in a sharp-4 edo (an interval can be downmid, but it can't be middown) | ||
* C~~9 = C vvE G vvD in a sharp-4 edo (an interval can't be doubly mid) | * {{nowrap|C~~9 = C vvE G vvD}} in a sharp-4 edo (an interval can't be doubly mid) | ||
<nowiki>* | <nowiki/>* But beware of the minor-major chord. CvmM7 means C vEb G vB and Cvm,M7 means C vEb G B. | ||
<nowiki>** | <nowiki/>**But since Cma7 can be read as an alternate spelling of Cmaj7, adding a comma is wise: Cm,a7. | ||
In the spoken name, a comma is almost always pronounced as "add". The only exceptions are: | In the spoken name, a comma is almost always pronounced as "add". The only exceptions are: | ||
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In 22edo, the major chord is 0-8-13 = 0¢-436¢-709¢. In 19edo, it's 0-6-11 = 0¢-379¢-695¢. The two chords sound quite different, because "major 3rd" is defined only in terms of the fifth, not in terms of what JI ratios it approximates. To describe the sound of the chord, color notation can be used. 22edo major chords sound ru (7-under) and 19edo major chords sound yo (5-over). | In 22edo, the major chord is 0-8-13 = 0¢-436¢-709¢. In 19edo, it's 0-6-11 = 0¢-379¢-695¢. The two chords sound quite different, because "major 3rd" is defined only in terms of the fifth, not in terms of what JI ratios it approximates. To describe the sound of the chord, color notation can be used. 22edo major chords sound ru (7-under) and 19edo major chords sound yo (5-over). | ||
A chord quality like "major" refers not to the sound but to the function of the chord. If you want to play a I | A chord quality like "major" refers not to the sound but to the function of the chord. If you want to play a {{nowrap|{{dash|I, VIm, IIm, V, I}}}} progression without pitch shifts or tonic drift, you can do that in any edo, as long as you use only major and minor chords. The notation tells you what kind of chord can be used to play that progression. In 22edo, the chord that you need sounds like a ru chord. | ||
In other words, I | In other words, {{nowrap|{{dash|I, VIm, IIm, V, I}}}} in just intonation implies {{nowrap|{{dash|Iy, VIg, IIg, Vy, Iy}}}}, but this implication only holds in those edos in which major sounds yo. Because 22edo's yo chord {{nowrap|{{dash|0, 7, 13}} {{=}} {{dash|0{{c}}, 382{{c}}, 709{{c}}}}}} is <u>down</u>major, it doesn't work in that progression. | ||
Another example: I7 | Another example: {{nowrap|{{dash|I7, bVII7, IV7, I7}}}}. To play this progression without shifts or drifts, the 7th in the I7 chord must be a minor 7th. in 22edo, that 7th sounds zo (7-over, thus 7/4). In 19edo, it sounds gu (5-under, thus 9/5). | ||
== Ups and downs solfege == | == Ups and downs solfege == | ||
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== See also == | == See also == | ||
* [[Enharmonic unisons in ups and downs notation]] | * [[Enharmonic unisons in ups and downs notation]] | ||
* [[Lambda ups and downs notation]] | * [[Lambda ups and downs notation]] | ||
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{{Navbox notation}} | {{Navbox notation}} | ||
{{ | {{Todo|intro}} | ||
[[Category:Ups and downs notation| ]] <!-- main article --> | [[Category:Ups and downs notation| ]] <!-- main article --> | ||
[[Category:Notation]] | [[Category:Notation]] | ||