Kite's ups and downs notation: Difference between revisions
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{{Redirect|Ups and downs notation|the notation system with attached arrows|Stein–Zimmermann–Gould notation}} | |||
Ups and | '''Ups and downs notation''' (or ^v) is a [[musical notation]] system primarily designed for [[edo]]s. The up symbol "^" and the down symbol "v" indicate raising/lowering a note (or widening/narrowing an interval) by one EDOstep. The mid symbol, "~" is for intervals exactly midway between major and minor, e.g. 3\24 is a mid 2nd. The mid 4th (~4) is midway between perfect and augmented, i.e. halfway-augmented, and the mid 5th (~5) is a halfway-diminished 5th. | ||
Ups and downs can | Ups and downs notation can be used with other tuning systems outside edos, by adjusting the definition of the arrows and perhaps also adding lifts (/) and drops (\) to accommodate finer tuning inflections. Lifts and drops can also be used with larger edos, especially [[Kite's thoughts on ring number|multi-ring]] edos where lifts and drops can be used to navigate between the rings of the edo. | ||
Ups and downs | Ups and downs notation was invented by [[Kite Giedraitis]] in early 2014. | ||
'''<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 | {{Note|'''<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]]s article.}} | ||
== Explanation (a 22edo example) == | == Explanation (a 22edo example) == | ||
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Lifts and drops (/ and \) can be used for microinflections of less than an edostep, since they look like part of an arrow. | Lifts and drops (/ and \) can be used for microinflections of less than an edostep, since they look like part of an arrow. | ||
{| class="wikitable" | {| class="wikitable" | ||
|+ | |+categories of pitch alterations | ||
|^ | |^ | ||
|up | |up | ||
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| Cvm6v9(v5) | | Cvm6v9(v5) | ||
|} | |} | ||
=== Harmonic and subharmonic chords === | |||
A chord which is the nearest approximation of a harmonic or subharmonic chord can be named using har or sub, words borrowed from [[Kite's color notation#Chord names|color notation]]. | |||
The [[4:5:6:7|4:5:6:7 chord]] is called the har7 ("har-seven") or h7 chord, because it's part of the harmonic series. [[4:5:6:7:9|Ch9]] = 4:5:6:7:9 and [[4:5:6:7:9:11|Ch11]] = 4:5:6:7:9:11. The [[60:70:84:105|sub7 ("sub-seven") or s7 chord]] 7:6:5:4 is part of the subharmonic series. It's the first 7 subharmonics, with the 7th subharmonic becoming the root. [[140:180:210:252:315|Cs9]] = 9:7:6:5:4 and Cs11 = 11:9:7:6:5:4. 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]]. | |||
Cs6 = [[70:84:105:120|12:10:8:7]]. Ch6 = 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). Additions, alterations and omissions refer to degrees, not harmonics or subharmonics: Ch7,11 adds 8/3, not 11/4. Ch9no5 omits 3/2, not 5/4. However, all numbers greater than 13 refer to (sub)harmonics, e.g. Ch9,15 adds 15/8 and Ch19no15 omits it. When two harmonics share the same degree, omitting that degree omits the lower harmonic. Thus Ch19no7 omits 7/4. | |||
Naming edo chords this way is a slight misnomer, because the chords are not actually JI chords. If the nearest direct and indirect approximations of a harmonic don't match, har and sub can be problematic. For example, 20edo's 9th harmonic maps directly to 3\20 but indirectly to 4\20 (via the 3rd harmonic 12\20). Thus a 20edo har9 chord is somewhat ambiguous. However the har7, har11no9, etc. chords are not. A har9no5 chord would perhaps use the direct mapping. | |||
=== 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 {{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. | 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. (UPDATE -- [https://stringscales.com/microtonal StringScales.com] has implemented an algorithm to name edo chords. The owner of the site, Kevin Founder, has expressed willingness to share his code.) | ||
A comma separates an added note and prevents it from merging with what comes before it. The comma is unneeded in C7v9 because the 7 can't merge with the down to make a 7v. But Cm,7 is incorrect even though the m and the 7 can merge, because Cm7 is the same chord. | A comma separates an added note and prevents it from merging with what comes before it. The comma is unneeded in C7v9 because the 7 can't merge with the down to make a 7v. But Cm,7 is incorrect even though the m and the 7 can merge, because Cm7 is the same chord. | ||
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* {{nowrap|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) | ||
* {{nowrap|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) | ||
* {{nowrap|C~~9 = C vvE G vvD}} in a sharp-4 edo (an interval can't be doubly mid) | * C~~9 = {{nowrap|C~~9 = C vvE G vvD}} in a sharp-4 edo (an interval can't be doubly mid) | ||
<nowiki/>* But beware of the minor-major chord. CvmM7 means C vEb G vB and Cvm,M7 means C vEb G B. | <nowiki/>* But beware of the minor-major chord. CvmM7 means C vEb G vB and Cvm,M7 means C vEb G B. | ||
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== Ups and downs solfege == | == Ups and downs solfege == | ||
Solfege (do-re-mi) can be adapted to indicate sharp/flat and up/down. See [[Uniform solfege| | Solfege (do-re-mi) can be adapted to indicate sharp/flat and up/down. See [[Uniform solfege]]. | ||
== For other tuning systems == | |||
Ups and downs notation was primarily designed to notate edos, but it can also be used to notate other tuning systems. | |||
=== Rank-2 temperaments === | |||
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|Triyoti 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. Triyoti is supported by both 15edo and 22edo, and both edos map 81/80 to one EDOstep. Thus if Triyoti 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 Triyoti can be converted to a piece written in 22edo by simply writing "22edo" on the top of the page. | |||
=== Rank-3 JI === | |||
{{Main|Kite's thoughts on ups and downs notation for rank-3 JI}} | |||
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 also == | == See also == | ||
* [[ | * [[Kite's thoughts on enharmonic unisons in ups and downs notation]] | ||
* [[Lambda ups and downs notation]] | * [[Lambda ups and downs notation]] | ||
== Further reading == | |||
* [http://tallkite.com/misc_files/notation%20guide%20for%20edos%205-72.pdf Notation guide for edos 5-72], which also covers chord names, slash chords, staff notation, key signatures, and scale trees | |||
{{Navbox notation}} | {{Navbox notation}} | ||
[[Category:Ups and downs notation| ]] <!-- main article --> | [[Category:Ups and downs notation| ]] <!-- main article --> | ||
[[Category:Notation]] | [[Category:Notation]] | ||