Kite's ups and downs notation: Difference between revisions
Wikispaces>TallKite **Imported revision 588443188 - Original comment: ** |
Wikispaces>TallKite **Imported revision 588446246 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-07-31 | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-07-31 19:42:03 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>588446246</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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==__Chord names in other EDOs__== | ==__Chord names in other EDOs__== | ||
When applied to notes, the mid symbol "~"means "neither up nor down". But in chord names it means "exactly midway between major and minor". This | When applied to notes, the mid symbol "~"means "neither up nor down". But in chord names it means "exactly midway between major and minor", hence neutral. This only applies to EDOs where the sharp equals an even number of EDOsteps. For example, in 10edo, 17edo, 24edo, 31edo, etc., a sharp is two EDOsteps, upminor equals downmajor, and "mid" replaces both of them. In 20edo, 27edo, 34edo, 41edo, etc., a sharp is four EDOsteps, and double-upminor equals double-downmajor equals mid. The period is used as before to clarify whether the mid applies to the chord root or the chord name. | ||
__**Various thirds:**__ | |||
C D G = Csus2 = "C sus two" | |||
C D^ G = Csus^2 = "C sus up-two" | |||
C D^^ G = Csus^^2 = "C sus double-up two" | |||
C Ebvv G = C.vvm = "C double-downminor" or "C dot double-downminor" | |||
C Ebv G = C.vm = "C downminor" or "C dot downminor" | |||
C Eb G = Cm = "C minor" | |||
C Eb^ G = C.^m = "C upminor" or "C dot upminor' (in EDOs 10, 17, 24, 31, etc., C.~ = "C dot mid") | |||
C Eb^^ G = C.^^m = "C (dot) double-upminor" (in EDOs 20, 27, 34, 41, etc., C.~ = "C dot mid") | |||
C Evv G = C.vv = "C (dot) double-upmaior" (in EDOs 20, 27, 34, 41, etc., C.~ = "C dot mid") | |||
C Ev G = C.v = "C (dot) downmajor" (in EDOs 10, 17, 24, 31, etc., C.~ = "C dot mid") | |||
C E G = C = "C perfect" in perfect EDOs, "C major" in sweet EDOs, possibly "C minor" in fourthwards EDOs | |||
C E^ G = C.^ = "C dot up" | |||
C E^^ G = C.^^ = "C dot double-up" | |||
C Fvv G = Csusvv4 = "C sus double-down four" | |||
C Fv G = Csusv4 = "C sus down-four" | |||
C F G = Csus4 = "C sus four" | |||
__**Altered fifths:**__ | |||
C Eb Gbv = Cdim(v5) = "C dim down-five" | |||
C Eb Gb = Cdim = "C dim" | |||
C Eb Gb^ = Cdim(^5) = "C dim up-five" | |||
C Eb Gv = Cm(v5) = "C minor down-five" | |||
C E Gv = C(v5) = "C down-five" | |||
C E G^ = C(^5) = "C up-five" | |||
C E G#v = Caug(v5) = "C aug down-five" | |||
C E G# = Caug = "C aug" | |||
C E G#^ = Caug(^5) = "C aug up-five" | |||
__**Seventh chords:**__ | |||
C Eb G Bb = Cm7 = "C minor seven" | |||
C Eb G Bb = Cm7 = "C minor seven" | |||
C Eb G Bb = Cm7 = "C minor seven" | |||
14edo: D * E * F * G * A * B * C * D, zero keys per #/b. | 14edo: D * E * F * G * A * B * C * D, zero keys per #/b. | ||
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chord components: P1 m2 ~2 M2 m3 ~3 M3 P4 ^P4/d5 A4/vP5 P5 m6 ~6 M6 m7 ~7 M7 | chord components: P1 m2 ~2 M2 m3 ~3 M3 P4 ^P4/d5 A4/vP5 P5 m6 ~6 M6 m7 ~7 M7 | ||
chord roots: I v#I/bII #I/vII II bIII vIII III IV ^IV/bV #IV/vV V #V/bVI vVI VI bVII vVII VII | chord roots: I v#I/bII #I/vII II bIII vIII III IV ^IV/bV #IV/vV V #V/bVI vVI VI bVII vVII VII | ||
0-3-10 = D E A = Dsus2 | |||
0-4-10 = D F A = Dm | 0-4-10 = D F A = Dm | ||
0-5-10 = D F^ A = D.~ ("D dot mid") | 0-5-10 = D F^ A = D.~ ("D dot mid") | ||
0-6-10 = D F# A = D (or D major) | 0-6-10 = D F# A = D (or D major) | ||
0-7-10 = D G A = Dsus4 | 0-7-10 = D G A = Dsus4 | ||
0-4-9 = D F Av = Dm(v5) | |||
0-5-9 = D F^ Av = D.~(v5) | |||
0-5-11 = D F^ A^ = D.~(^5) | |||
0-6-11 = D F# A^ = D(v5) | |||
0-4-10-14 = D F A C = Dm7 | 0-4-10-14 = D F A C = Dm7 | ||
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The name "major" refers not to the sound but to the function of the chord. If you want to play a 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 red chord. | The name "major" refers not to the sound but to the function of the chord. If you want to play a 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 red chord. | ||
In other words, I - VIm - IIm - V - I in | In other words, I - VIm - IIm - V - I in just intonation implies Iy - VIg - IIg - Vy - Iy, but this implication only holds in those EDOs in which major sounds yellow. If 22edo's downmajor chord 0-7-13 = 0¢-382¢-709¢ were called "major", you wouldn't know that it doesn't work in that progression. | ||
Another example: I7 - bVII7 - IV7 - I7. To make this work, the 7th in the I7 chord must be a minor 7th. in 22edo, that 7th sounds blue. In 19edo, it sounds green. If you want a blue 7th in 19edo, you have to use the downminor 7th, which will cause shifts or drifts in the progression. | Another example: I7 - bVII7 - IV7 - I7. To make this work, the 7th in the I7 chord must be a minor 7th. in 22edo, that 7th sounds blue. In 19edo, it sounds green. If you want a blue 7th in 19edo, you have to use the downminor 7th, which will cause shifts or drifts in the progression. | ||
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This is in addition to the trivial EDOs, 1, 2, 3, 4 and 6, which can be notated with standard notation as a subset of 12-EDO. The fifth is defined as the nearest approximation to 3/2. There is a little leeway to this in certain EDOs like 18 which have two possible fifths with nearly equal accuracy.<br /> | This is in addition to the trivial EDOs, 1, 2, 3, 4 and 6, which can be notated with standard notation as a subset of 12-EDO. The fifth is defined as the nearest approximation to 3/2. There is a little leeway to this in certain EDOs like 18 which have two possible fifths with nearly equal accuracy.<br /> | ||
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<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:4038:&lt;img src=&quot;/file/view/The%20fifth%20of%20EDOs%205-53.png/570450231/800x1035/The%20fifth%20of%20EDOs%205-53.png&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 1035px; width: 800px;&quot; /&gt; --><img src="/file/view/The%20fifth%20of%20EDOs%205-53.png/570450231/800x1035/The%20fifth%20of%20EDOs%205-53.png" alt="The fifth of EDOs 5-53.png" title="The fifth of EDOs 5-53.png" style="height: 1035px; width: 800px;" /><!-- ws:end:WikiTextLocalImageRule:4038 --><br /> | ||
The above diagram is actually a section of the Stern-Brocot tree. The tree usually has ratios, not octave fractions (i.e. 4/7, not 4\7 as above). Also it's usually arranged vertically with nodes of the same &quot;generation&quot; occurring at the same height. For example, 5\9 and 7\12 are both children of 4\7, and would usually be level with each other. Here the nodes are arranged vertically by denominator, i.e., the EDO itself. The colored regions of the tree are what I call <strong>kites</strong>, and this version of the Stern-Brocot tree I call the <strong>Tree of Kites</strong>. The heptatonic kite is blue and the pentatonic kite is orange. Every kite has a head (4\7 for the blue kite), a central spine (8\14, 12\21, etc.), a fifthward side on the right (7\12, 11\19, etc.) and a fourthward side on the left (5\9, 9\16, etc.). Every node on a spine is a <strong>spinal</strong> node. Every non-spinal node is part of three kites. It's the head of one kite and on the side of two others.<br /> | The above diagram is actually a section of the Stern-Brocot tree. The tree usually has ratios, not octave fractions (i.e. 4/7, not 4\7 as above). Also it's usually arranged vertically with nodes of the same &quot;generation&quot; occurring at the same height. For example, 5\9 and 7\12 are both children of 4\7, and would usually be level with each other. Here the nodes are arranged vertically by denominator, i.e., the EDO itself. The colored regions of the tree are what I call <strong>kites</strong>, and this version of the Stern-Brocot tree I call the <strong>Tree of Kites</strong>. The heptatonic kite is blue and the pentatonic kite is orange. Every kite has a head (4\7 for the blue kite), a central spine (8\14, 12\21, etc.), a fifthward side on the right (7\12, 11\19, etc.) and a fourthward side on the left (5\9, 9\16, etc.). Every node on a spine is a <strong>spinal</strong> node. Every non-spinal node is part of three kites. It's the head of one kite and on the side of two others.<br /> | ||
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<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:4039:&lt;img src=&quot;/file/view/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%201.jpg/570451171/800x1035/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%201.jpg&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 1035px; width: 800px;&quot; /&gt; --><img src="/file/view/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%201.jpg/570451171/800x1035/Tibia%20in%20G%20with%20%5Ev%2C%20rygb%201.jpg" alt="Tibia in G with ^v, rygb 1.jpg" title="Tibia in G with ^v, rygb 1.jpg" style="height: 1035px; width: 800px;" /><!-- ws:end:WikiTextLocalImageRule:4039 --><br /> | ||
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<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><!-- ws:end:WikiTextHeadingRule:10 --> </h2> | <!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><!-- ws:end:WikiTextHeadingRule:10 --> </h2> | ||
<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><!-- ws:end:WikiTextHeadingRule:12 --> </h2> | <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><!-- ws:end:WikiTextHeadingRule:12 --> </h2> | ||
<!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="Naming Chords-Chord names in other EDOs"></a><!-- ws:end:WikiTextHeadingRule:14 --><u>Chord names in other EDOs</u></h2> | <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="Naming Chords-Chord names in other EDOs"></a><!-- ws:end:WikiTextHeadingRule:14 --><u>Chord names in other EDOs</u></h2> | ||
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When applied to notes, the mid symbol &quot;~&quot;means &quot;neither up nor down&quot;. But in chord names it means &quot;exactly midway between major and minor&quot;. This | When applied to notes, the mid symbol &quot;~&quot;means &quot;neither up nor down&quot;. But in chord names it means &quot;exactly midway between major and minor&quot;, hence neutral. This only applies to EDOs where the sharp equals an even number of EDOsteps. For example, in 10edo, 17edo, 24edo, 31edo, etc., a sharp is two EDOsteps, upminor equals downmajor, and &quot;mid&quot; replaces both of them. In 20edo, 27edo, 34edo, 41edo, etc., a sharp is four EDOsteps, and double-upminor equals double-downmajor equals mid. The period is used as before to clarify whether the mid applies to the chord root or the chord name.<br /> | ||
<br /> | |||
<u><strong>Various thirds:</strong></u><br /> | |||
C D G = Csus2 = &quot;C sus two&quot;<br /> | |||
C D^ G = Csus^2 = &quot;C sus up-two&quot;<br /> | |||
C D^^ G = Csus^^2 = &quot;C sus double-up two&quot;<br /> | |||
C Ebvv G = C.vvm = &quot;C double-downminor&quot; or &quot;C dot double-downminor&quot;<br /> | |||
C Ebv G = C.vm = &quot;C downminor&quot; or &quot;C dot downminor&quot;<br /> | |||
C Eb G = Cm = &quot;C minor&quot;<br /> | |||
C Eb^ G = C.^m = &quot;C upminor&quot; or &quot;C dot upminor' (in EDOs 10, 17, 24, 31, etc., C.~ = &quot;C dot mid&quot;)<br /> | |||
C Eb^^ G = C.^^m = &quot;C (dot) double-upminor&quot; (in EDOs 20, 27, 34, 41, etc., C.~ = &quot;C dot mid&quot;)<br /> | |||
C Evv G = C.vv = &quot;C (dot) double-upmaior&quot; (in EDOs 20, 27, 34, 41, etc., C.~ = &quot;C dot mid&quot;)<br /> | |||
C Ev G = C.v = &quot;C (dot) downmajor&quot; (in EDOs 10, 17, 24, 31, etc., C.~ = &quot;C dot mid&quot;)<br /> | |||
C E G = C = &quot;C perfect&quot; in perfect EDOs, &quot;C major&quot; in sweet EDOs, possibly &quot;C minor&quot; in fourthwards EDOs<br /> | |||
C E^ G = C.^ = &quot;C dot up&quot;<br /> | |||
C E^^ G = C.^^ = &quot;C dot double-up&quot;<br /> | |||
C Fvv G = Csusvv4 = &quot;C sus double-down four&quot;<br /> | |||
C Fv G = Csusv4 = &quot;C sus down-four&quot;<br /> | |||
C F G = Csus4 = &quot;C sus four&quot;<br /> | |||
<br /> | |||
<u><strong>Altered fifths:</strong></u><br /> | |||
C Eb Gbv = Cdim(v5) = &quot;C dim down-five&quot;<br /> | |||
C Eb Gb = Cdim = &quot;C dim&quot;<br /> | |||
C Eb Gb^ = Cdim(^5) = &quot;C dim up-five&quot;<br /> | |||
C Eb Gv = Cm(v5) = &quot;C minor down-five&quot;<br /> | |||
C E Gv = C(v5) = &quot;C down-five&quot;<br /> | |||
C E G^ = C(^5) = &quot;C up-five&quot;<br /> | |||
C E G#v = Caug(v5) = &quot;C aug down-five&quot;<br /> | |||
C E G# <!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="Caug"></a><!-- ws:end:WikiTextHeadingRule:16 --> Caug </h1> | |||
&quot;C aug&quot;<br /> | |||
C E G#^ = Caug(^5) = &quot;C aug up-five&quot;<br /> | |||
<br /> | |||
<u><strong>Seventh chords:</strong></u><br /> | |||
C Eb G Bb = Cm7 = &quot;C minor seven&quot;<br /> | |||
C Eb G Bb = Cm7 = &quot;C minor seven&quot;<br /> | |||
C Eb G Bb = Cm7 = &quot;C minor seven&quot;<br /> | |||
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14edo: D * E * F * G * A * B * C * D, zero keys per #/b.<br /> | 14edo: D * E * F * G * A * B * C * D, zero keys per #/b.<br /> | ||
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chord components: P1 m2 ~2 M2 m3 ~3 M3 P4 ^P4/d5 A4/vP5 P5 m6 ~6 M6 m7 ~7 M7<br /> | chord components: P1 m2 ~2 M2 m3 ~3 M3 P4 ^P4/d5 A4/vP5 P5 m6 ~6 M6 m7 ~7 M7<br /> | ||
chord roots: I v#I/bII #I/vII II bIII vIII III IV ^IV/bV #IV/vV V #V/bVI vVI VI bVII vVII VII<br /> | chord roots: I v#I/bII #I/vII II bIII vIII III IV ^IV/bV #IV/vV V #V/bVI vVI VI bVII vVII VII<br /> | ||
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0-3-10 = D E A = Dsus2<br /> | |||
0-4-10 = D F A = Dm<br /> | 0-4-10 = D F A = Dm<br /> | ||
0-5-10 = D F^ A = D.~ (&quot;D dot mid&quot;)<br /> | 0-5-10 = D F^ A = D.~ (&quot;D dot mid&quot;)<br /> | ||
0-6-10 = D F# A = D (or D major)<br /> | 0-6-10 = D F# A = D (or D major)<br /> | ||
0-7-10 = D G A = Dsus4<br /> | 0-7-10 = D G A = Dsus4<br /> | ||
<br /> | |||
0-4-9 = D F Av = Dm(v5)<br /> | |||
0-5-9 = D F^ Av = D.~(v5)<br /> | |||
0-5-11 = D F^ A^ = D.~(^5)<br /> | |||
0-6-11 = D F# A^ = D(v5)<br /> | |||
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0-4-10-14 = D F A C = Dm7<br /> | 0-4-10-14 = D F A C = Dm7<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="Caug-Cross-EDO considerations"></a><!-- ws:end:WikiTextHeadingRule:18 --><strong><u>Cross-EDO considerations</u></strong></h2> | ||
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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 &quot;major 3rd&quot; 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 red and 19edo major chords sound yellow.<br /> | 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 &quot;major 3rd&quot; 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 red and 19edo major chords sound yellow.<br /> | ||
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The name &quot;major&quot; refers not to the sound but to the function of the chord. If you want to play a 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 red chord.<br /> | The name &quot;major&quot; refers not to the sound but to the function of the chord. If you want to play a 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 red chord.<br /> | ||
<br /> | <br /> | ||
In other words, I - VIm - IIm - V - I in | In other words, I - VIm - IIm - V - I in just intonation implies Iy - VIg - IIg - Vy - Iy, but this implication only holds in those EDOs in which major sounds yellow. If 22edo's downmajor chord 0-7-13 = 0¢-382¢-709¢ were called &quot;major&quot;, you wouldn't know that it doesn't work in that progression.<br /> | ||
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Another example: I7 - bVII7 - IV7 - I7. To make this work, the 7th in the I7 chord must be a minor 7th. in 22edo, that 7th sounds blue. In 19edo, it sounds green. If you want a blue 7th in 19edo, you have to use the downminor 7th, which will cause shifts or drifts in the progression.<br /> | Another example: I7 - bVII7 - IV7 - I7. To make this work, the 7th in the I7 chord must be a minor 7th. in 22edo, that 7th sounds blue. In 19edo, it sounds green. If you want a blue 7th in 19edo, you have to use the downminor 7th, which will cause shifts or drifts in the progression.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="Caug-EDOs with an inaccurate 3/2"></a><!-- ws:end:WikiTextHeadingRule:20 --><u>EDOs with an inaccurate 3/2</u></h2> | ||
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Not counting the trivial edos 2, 3, 4 and 6, there are only seven such edos. As seen in the above diagram, they are the ones to the left of the heptatonic kite's spine, plus the ones to the right of the pentatonic kite's spine. The ones on the left edge of the heptatonic kite are the fourthward ones like 16edo, and have been dealt with already. 23edo can be notated similarly to 16edo by using a fifth of 13\23 instead of 14\23. That leaves only four edos: 8, 11, 13, and 18.<br /> | Not counting the trivial edos 2, 3, 4 and 6, there are only seven such edos. As seen in the above diagram, they are the ones to the left of the heptatonic kite's spine, plus the ones to the right of the pentatonic kite's spine. The ones on the left edge of the heptatonic kite are the fourthward ones like 16edo, and have been dealt with already. 23edo can be notated similarly to 16edo by using a fifth of 13\23 instead of 14\23. That leaves only four edos: 8, 11, 13, and 18.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><h1 id="toc11"><a name="Summary of EDO notation"></a><!-- ws:end:WikiTextHeadingRule:22 --><u><strong>Summary of EDO notation</strong></u></h1> | ||
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Besides the trivial EDOs, 1, 2, 3, 4 and 6, which can be notated with standard notation as a subset of 12-EDO, there are five EDO categories, based on the size of the fifth:<br /> | Besides the trivial EDOs, 1, 2, 3, 4 and 6, which can be notated with standard notation as a subset of 12-EDO, there are five EDO categories, based on the size of the fifth:<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:24:&lt;h3&gt; --><h3 id="toc12"><a name="Summary of EDO notation--&quot;Fifth-less&quot; EDOs (8, 11, 13 and 18)"></a><!-- ws:end:WikiTextHeadingRule:24 --><u><strong>&quot;Fifth-less&quot; EDOs (8, 11, 13 and 18)</strong></u></h3> | ||
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<strong><u>8edo</u>:</strong> (generator = 1\8 = perfect 2nd = 150¢)<br /> | <strong><u>8edo</u>:</strong> (generator = 1\8 = perfect 2nd = 150¢)<br /> | ||
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E# - G# - B# - D# - F# - A# - C# - E - G - B - D - F - A - C - Eb - Gb - Bb - Db - Fb - Ab - Cb<br /> | E# - G# - B# - D# - F# - A# - C# - E - G - B - D - F - A - C - Eb - Gb - Bb - Db - Fb - Ab - Cb<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:26:&lt;h3&gt; --><h3 id="toc13"><a name="Summary of EDO notation--Alternate pentatonic notation for EDOs 8, 13 and 18"></a><!-- ws:end:WikiTextHeadingRule:26 --><u><strong>Alternate pentatonic notation for EDOs 8, 13 and 18</strong></u></h3> | ||
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All three EDOs use the same pentatonic fifthwards chain of fifths: ms3 - ms7 - P4d - P1 - P5d - Ms3 - Ms7 - A4d etc.<br /> | All three EDOs use the same pentatonic fifthwards chain of fifths: ms3 - ms7 - P4d - P1 - P5d - Ms3 - Ms7 - A4d etc.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:28:&lt;h3&gt; --><h3 id="toc14"><a name="Summary of EDO notation--Fourthward EDOs (9, 16 and 23)"></a><!-- ws:end:WikiTextHeadingRule:28 --><u>Fourthward EDOs (9, 16 and 23)</u></h3> | ||
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All fourthwards EDOs use the same chain of fifths: M2 - M6 - M3 - M7 - P4 - P1 - P5 - m2 - m6 - m3 - m7 - A4 etc.<br /> | All fourthwards EDOs use the same chain of fifths: M2 - M6 - M3 - M7 - P4 - P1 - P5 - m2 - m6 - m3 - m7 - A4 etc.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:30:&lt;h3&gt; --><h3 id="toc15"><a name="Summary of EDO notation--&quot;Perfect&quot; EDOs (7, 14, 21, 28 and 35)"></a><!-- ws:end:WikiTextHeadingRule:30 --><u>&quot;Perfect&quot; EDOs (7, 14, 21, 28 and 35)</u></h3> | ||
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All perfect EDOs use the same chain of fifths: P2 - P6 - P3 - P7 - P4 - P1 - P5 - P2 - P6 - P3 - P7 etc.<br /> | All perfect EDOs use the same chain of fifths: P2 - P6 - P3 - P7 - P4 - P1 - P5 - P2 - P6 - P3 - P7 etc.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:32:&lt;h3&gt; --><h3 id="toc16"><a name="Summary of EDO notation--Pentatonic EDOs (5, 10, 15, 20, 25 and 30)"></a><!-- ws:end:WikiTextHeadingRule:32 --><u>Pentatonic EDOs (5, 10, 15, 20, 25 and 30)</u></h3> | ||
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All pentatonic EDOs use the usual chain of fifths: m2 - m6 - m3 - m7 - P4 - P1 - P5 - M2 - M6 - M3 - M7 etc.<br /> | All pentatonic EDOs use the usual chain of fifths: m2 - m6 - m3 - m7 - P4 - P1 - P5 - M2 - M6 - M3 - M7 etc.<br /> | ||
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P1/m2 - ^m2 - ^^m2 - vvM2 - vM2 - M2/m3 - ^m3 - ^^m3 - vvM3 - vM3 - M3/P4 - ^P4 - ^^P4 - vvP5 - vP5 - P5/m6 - ^m6 - ^^m6 - vvM6 - vM6 - M6/m7 - ^m7 - ^^m7 - vvM7 - vM7 - P8<br /> | P1/m2 - ^m2 - ^^m2 - vvM2 - vM2 - M2/m3 - ^m3 - ^^m3 - vvM3 - vM3 - M3/P4 - ^P4 - ^^P4 - vvP5 - vP5 - P5/m6 - ^m6 - ^^m6 - vvM6 - vM6 - M6/m7 - ^m7 - ^^m7 - vvM7 - vM7 - P8<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:34:&lt;h3&gt; --><h3 id="toc17"><a name="Summary of EDO notation--Alternative pentatonic notation for pentatonic EDOs:"></a><!-- ws:end:WikiTextHeadingRule:34 --><u>Alternative pentatonic notation for pentatonic EDOs:</u></h3> | ||
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Pentatonic fourthwards chain of fifthoids: Ms3 - Ms7 - P4d - P1 - P5d - ms3 - ms7 - d4d etc.<br /> | Pentatonic fourthwards chain of fifthoids: Ms3 - Ms7 - P4d - P1 - P5d - ms3 - ms7 - d4d etc.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:36:&lt;h3&gt; --><h3 id="toc18"><a name="Summary of EDO notation--&quot;Sweet&quot; EDOs (12, 17, 19, 22, 24, 26, 27, 29, 31-34, and all edos 36 or higher)"></a><!-- ws:end:WikiTextHeadingRule:36 --><u>&quot;Sweet&quot; EDOs (12, 17, 19, 22, 24, 26, 27, 29, 31-34, and all edos 36 or higher)</u></h3> | ||
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All sweet EDOs use the usual chain of fifths: m2 - m6 - m3 - m7 - P4 - P1 - P5 - M2 - M6 - M3 - M7 etc.<br /> | All sweet EDOs use the usual chain of fifths: m2 - m6 - m3 - m7 - P4 - P1 - P5 - M2 - M6 - M3 - M7 etc.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:38:&lt;h2&gt; --><h2 id="toc19"><a name="Summary of EDO notation-Ups and downs solfege"></a><!-- ws:end:WikiTextHeadingRule:38 --><u>Ups and downs solfege</u></h2> | ||
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Solfege (do-re-mi) can be adapted to indicate sharp/flat and up/down:<br /> | Solfege (do-re-mi) can be adapted to indicate sharp/flat and up/down:<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:40:&lt;h2&gt; --><h2 id="toc20"><a name="Summary of EDO notation-Rank-2 Notation"></a><!-- ws:end:WikiTextHeadingRule:40 --><u>Rank-2 Notation</u></h2> | ||
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Ups and downs can be used to notate rank-2 scales. First we must distinguish between edos and sizing frameworks. For example, keyboards with 7 white keys and 5 black keys, and fretted instruments with 12 frets per octave, predate the use of 12edo by many centuries. Such instruments use a 12-tone framework. Traditional Western notation uses a 7-note naming framework and a 12-tone sizing framework. (See the first chapter of part V of Kite's book for more on frameworks.)<br /> | Ups and downs can be used to notate rank-2 scales. First we must distinguish between edos and sizing frameworks. For example, keyboards with 7 white keys and 5 black keys, and fretted instruments with 12 frets per octave, predate the use of 12edo by many centuries. Such instruments use a 12-tone framework. Traditional Western notation uses a 7-note naming framework and a 12-tone sizing framework. (See the first chapter of part V of Kite's book for more on frameworks.)<br /> | ||
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There is no variant of D adjacent to C, and there is no 2nd with keyspan 1 or -1. Some other method of notation must be used for rank-2 fifth-generated tunings in these two frameworks.<br /> | There is no variant of D adjacent to C, and there is no 2nd with keyspan 1 or -1. Some other method of notation must be used for rank-2 fifth-generated tunings in these two frameworks.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:42:&lt;h2&gt; --><h2 id="toc21"><!-- ws:end:WikiTextHeadingRule:42 --> </h2> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:44:&lt;h2&gt; --><h2 id="toc22"><a name="Summary of EDO notation-Generators other than a fifth"></a><!-- ws:end:WikiTextHeadingRule:44 --><u>Generators other than a fifth</u></h2> | ||
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The main reason to use ups and downs is to allow fifth-generated heptatonic notation in frameworks and EDOs that aren't fully compatible with such a notation, i.e. those not on the sides of the 4\7 kite. The main reason to use a generator other than a fifth is to use a notation more compatible with one's chosen framework or EDO. Thus there is little reason to use ups and downs in such a situation.<br /> | The main reason to use ups and downs is to allow fifth-generated heptatonic notation in frameworks and EDOs that aren't fully compatible with such a notation, i.e. those not on the sides of the 4\7 kite. The main reason to use a generator other than a fifth is to use a notation more compatible with one's chosen framework or EDO. Thus there is little reason to use ups and downs in such a situation.<br /> | ||