Kite's ups and downs notation: Difference between revisions

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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.

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 ~~are not recommended~~. 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 ~~20edo's~~ har7, har11no9, etc. are not.

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 ===

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.

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* {{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~~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.

@@ Line 1,431: / Line 1,431: @@
 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.
+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 are not recommended. 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 20edo's har7, har11no9, etc. are not.
+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 ===
 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.
@@ Line 1,462: / Line 1,462: @@
 * {{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~~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.