审阅范围 · Review scope
限定范围独立审阅。请保留正文中的出处与限制；不代表全库最终验收、实际演奏或学习效果验证。
Independent review within the stated scope. Keep the evidence and limitations stated in the text in view. This is not final corpus acceptance or validation of performance or learning outcomes.
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This page preserves the author’s frozen review bytes, so prose or data may still contain candidate, pending-review or unpublished labels. This version has passed bounded independent review and repository publication; those labels record author-time status only. Acceptance covers bilingual meaning, bounded source text/stills and original fixed-fixture checks, not source audition, continuous motion, full source scores, actual performance, physical suitability or learning outcomes.
三全音代理：共同的导向音，不同的和弦与低音
先定目标，再问哪些音相同
G7接C与Db7接C，可以有相同的两条半音连接，却不是同一个完整和弦。本课先把目标明确设为C大三和弦，再核对三音、七音、根音与实际低音；“代理”表示在这个给定连接中尝试替代原属和弦的位置，不表示两个音组完全等同。
前置知识是三和弦、属七和弦、半音和八度；可先看副属和弦与和声配置链接。全课使用普通十二平均律钢琴的音高坐标作纸面计算，不需要钢琴、MIDI或麦克风。C4是中央C，b降低半音；Db写作降D，Cb写作降C，音名后的数字是八度而非指法。
先遮住拼写表和答案段，自己写G7、Db7与C的根音顺序音名；预测两种七和弦共有几个音高类，根音之间相距几个半音。允许写“不确定”。音高类暂不区分八度，实际声部连接稍后再加回音区。
既有副属课用C—D7—G—C解释局部目标，和声配置课区分身份、排列与低音。本课新增的问题是：把属七换成根音相隔三全音的另一个属七时，哪些关系保留，哪些必须重新核对？这里的C大调背景是教学条件，不是由一个连接证明的调性。
同键关系不能代替和弦拼写
G7按根音叠三度为G–B–D–F；Db7为Db–F–Ab–Cb。两者相对各自根音都是0、4、7、10半音，即大三和弦加小七度。Db到Cb跨七个字母位置，因此这里的七音应写Cb；把它改成B虽可落在同一平均律琴键上，却丢掉了这项拼写关系。
G7的三音B与七音F构成三全音；Db7的三音F与七音Cb也构成三全音。按音高类比较，它们共享F以及B/Cb；三音与七音的身份交换了。这里把决定这类七和弦性质与连接的重要三音、七音称为导向音（guide tones），不把每一个导向音都叫“导音”。
两个完整音高类集合只交于F和B/Cb。G与D并不是Db7的根音与五音，Db与Ab也不是G7的根音与五音。根音G与Db相隔6半音，不表示把G7的每个音都原地保留；本例不是G7的转位，也不是只改变同一和弦的排列。
还要检查不同的七音：Dbmaj7写Db–F–Ab–C，七音是C，不是Cb。它虽同样能以Db为低音接到C，却不具备本页Db7的同一组导向音。因此“低音高目标半音”本身不足以确认这是本例的三全音代理。
| 符号 | 根音顺序拼写 | 根音起半音 |
|---|---|---|
| G7 | G–B–D–F | 0,4,7,10 |
| Db7 | Db–F–Ab–Cb | 0,4,7,10 |
| C | C–E–G | 0,4,7 |
| Dbmaj7 | Db–F–Ab–C | 0,4,7,11 |
| 符号 | 三音 | 七音 |
|---|---|---|
| G7 | B | F |
| Db7 | F | Cb |
两种完整纸面版本
下表是本库原创四小节，不是源课谱例。A为Dm7—G7—C—C，B只把第2小节改成Db7。每版4/4，以四分音符单位q计时；四个声部同时进行，不分配左右手或指法。前3小节每音4q，第4小节每音2q后休止2q；没有踏板、反复或延音线。
全局起音为q=0、4、8、12；q=14全部进入休止，q=16结束。[a,b)包含a、不包含b。第3、4小节虽同属C，q=12仍另起音，不能自行加延音线。每版16个音符事件与4个声部休止；每声部完整覆盖16q，不能把并发声部相加称为64q长的乐句。
关键同键对照是A的B3与B的Cb4：两者都是MIDI坐标59、88键编号39。Cb4是把C4降半音，不能误写为Cb3。两个版本的V2分别是B3→C4与Cb4→C4，均上行1半音；前者按字母为小二度，后者为增一度。V3都为F4→E4，下行1半音。
在G7中，下行的F4是七音；在Db7中，它是三音，而七音Cb4在本例反而上行到C4。共同琴键与共同目标并不保证相同的和弦内身份，也不推出“每个七音都必须向下”的规则。本例只陈述这些指定声部的连接。
低音另算：A的G2→C3上行5半音，是纯四度；B的Db3→C3下行1半音，是小二度。两个属七根音的音高类相隔三全音，但这里实际低音前往C的路线不同。若换转位或八度，实际低音距离会变，不能直接照抄本表的有符号数值。
V4也从D5→G4改为Ab4→G4，分别下行7与1半音。第2小节两音被换掉、一个音以等音改名，不能说两版和弦听起来必定相同，也不能凭较小的低音步距宣布B更好。若有给定旋律、其他乐器或特定风格，必须重新检查实际音组与连接。
| 版本 | 声部 | 小节1 [0,4) | 小节2 [4,8) | 小节3 [8,12) | 小节4 [12,14) | 小节4 [14,16) |
|---|---|---|---|---|---|---|
| A | V1 | D3 | G2 | C3 | C3 | 休止 |
| A | V2 | C4 | B3 | C4 | C4 | 休止 |
| A | V3 | F4 | F4 | E4 | E4 | 休止 |
| A | V4 | A4 | D5 | G4 | G4 | 休止 |
| B | V1 | D3 | Db3 | C3 | C3 | 休止 |
| B | V2 | C4 | Cb4 | C4 | C4 | 休止 |
| B | V3 | F4 | F4 | E4 | E4 | 休止 |
| B | V4 | A4 | Ab4 | G4 | G4 | 休止 |
| 版本 | 声部 | 第2小节 | 第3小节 | 有符号半音 |
|---|---|---|---|---|
| A | V1 | G2 | C3 | +5 |
| B | V1 | Db3 | C3 | -1 |
| A | V2 | B3 | C4 | +1 |
| B | V2 | Cb4 | C4 | +1 |
| A | V3 | F4 | E4 | -1 |
| B | V3 | F4 | E4 | -1 |
| A | V4 | D5 | G4 | -7 |
| B | V4 | Ab4 | G4 | -1 |
| 音名 | MIDI坐标 | 88键编号 |
|---|---|---|
| G2 | 43 | 23 |
| C3 | 48 | 28 |
| Db3 | 49 | 29 |
| D3 | 50 | 30 |
| B3 | 59 | 39 |
| Cb4 | 59 | 39 |
| C4 | 60 | 40 |
| E4 | 64 | 44 |
| F4 | 65 | 45 |
| G4 | 67 | 47 |
| Ab4 | 68 | 48 |
| A4 | 69 | 49 |
| D5 | 74 | 54 |
键号从A0=1起同时计黑白键；中央C4=40。MIDI编号只是坐标。B3与Cb4是两种拼写、同一坐标。
从局部核对回到完整乐句
纸面步骤：先在每版第2小节标根音、三音、五音、七音；再圈V2和V3，分别写出前往第3小节的有符号半音差；最后单独画V1低音线。答案应同时包含“两个共同音高类”和“不同完整和弦”，不能只写“它们一样”。不要求同时弹四个声部。
若Cb4容易写错，暂只核第2、3小节窗口[4,12)，局部原点为全局q=4，长度8q；局部0与4分别对应原第2与第3小节。先核Cb4/B3的坐标、角色和目标，再恢复第1小节以及第4小节的2q音与2q休止，完整重读[0,16)。局部正确不代替全句核对。
这是一条纸面路线，没有附加实琴作业。若只计算时间，四分音符60 BPM时1q=1秒，每版16秒、局部窗口8秒；这不是要求你按这个速度弹奏，更不是已测得的放键或声学消音时刻。谱写休止不会证明真实环境完全静音。
每次记录版本、核对前预测、答案提示是否可见、实际纸面结果或“不确定”、一个下一步，以及恢复全句后的结果。空白保持未知；本页没有真实学习者观察。隔天或另一个明确记录的延迟后，先遮答案重做同一材料并记录间隔，这只检查熟悉材料的保留。
公开答案和对照表不能随后充当陌生材料盲测；迁移另需难度相近、未看未听未练的新题。纸面拼写正确也不等于已经听见完整和弦、流畅演奏或改变了听感，记录应只说本次真正核对了什么。
局部功能与来源边界
在预先给定的C大调中，A的G7是V7，目标为C；B的Db7在同一位置作为G7的三全音代理候选。一个Db7→C连接本身不证明全曲的调，也不自动证明转调。更多旋律、前后和声、终止与持续的主音组织仍然需要分析。
“在目标根音高半音处放属七”是生成候选的一种办法；本例还明确核对了和弦结构、共同导向音与实际解决。它不是所有目标、所有旋律或所有扩展音都相容的保证。这里没有推广到属九、属十一或属十三，也没有给任何情绪或学习结果作保证。
NC-029的既有112段ASR全部已读，选看90、146、172、190、286秒五张静帧。90秒可见G7与两个红圈；146秒可见G7、Db7及三全音标注；172秒可见E7、Bb7；190秒有三全音代理标题与插入规则；286秒是带和弦符号的谱例布局。这里只确认这些可见标签与布局，没有逐音验收源谱。
ASR第36—40、43—52段提出共享三全音来替代属七，第66—73段提出目标上方半音的插入思路，均保留为未经原声听校的候选归因。ASR可能把音名与术语认错；190秒的可见规则也不证明其听感结论。没有核实ASR与每张静帧精确对齐，也没有审查连续动作。
完整四小节、音区、声部时值、根音与拼写核算、Dbmaj7反例和记录步骤均为本库原创综合，不是源课转录。有限文字／选帧审阅与原创符号核对分开记录；本页仍是待独立审阅候选，未增加已发布覆盖数。
副属目标 · 和声与配置 · 音程拼写 · 保留与迁移 · 来源范围 · 可复算数据
Tritone substitution: shared guide tones, different chords and basses
Set the target, then ask which notes are shared
G7–C and Db7–C can share two semitone connections without being the same complete chord. Here the target is stipulated as a C-major triad. Check thirds, sevenths, roots and actual basses separately: “substitution” means trying another chord in the original dominant’s place in this specified connection, not equating the complete sonorities.
Prerequisites are triads, dominant sevenths, semitones and octaves; start with the secondary-dominant and harmony links if needed. This paper lesson calculates with the pitch coordinates of an ordinary twelve-tone equal-tempered piano; no piano, MIDI device or microphone is needed. C4 is middle C and b lowers a note by a semitone: Db is D-flat and Cb is C-flat. The following numeral denotes the octave, not fingering.
Cover the spelling table and answer paragraphs first. Write G7, Db7 and C in root order, then predict how many pitch classes the two seventh chords share and how many semitones separate their roots. “Uncertain” is acceptable. Pitch classes temporarily disregard octave; registers return when we examine actual voice connections.
The existing secondary-dominant lesson uses C–D7–G–C to explain local targets, while the harmony lesson distinguishes identity, voicing and bass. The new question is what survives, and what must be checked again, when a dominant seventh is replaced by another dominant seventh whose root is a tritone away. The C-major background here is a teaching condition, not a key proven by a single connection.
Shared keys do not replace chord spelling
In stacked thirds from the root, G7 is G–B–D–F and Db7 is Db–F–Ab–Cb. Both have intervals 0,4,7,10 semitones above their own roots: a major triad plus minor seventh. Db to Cb spans seven letter positions, so its seventh is written Cb. B can use the same equal-tempered piano key but loses that spelling relationship.
G7’s third B and seventh F form a tritone; so do Db7’s third F and seventh Cb. As pitch classes they share F and B/Cb, with the third and seventh roles exchanged. Here “guide tones” means the thirds and sevenths important to identifying and connecting these seventh chords; it does not mean that every guide tone is a leading tone.
The complete pitch-class collections intersect only at F and B/Cb. G and D are not Db7’s root and fifth, and Db and Ab are not G7’s root and fifth. Roots G and Db are six semitones apart; that does not keep every G7 note in place. This is neither an inversion of G7 nor merely a new voicing of the same chord.
Check a different seventh too: Dbmaj7 is Db–F–Ab–C, with C rather than Cb. It could likewise move from a Db bass to C, but it lacks this page’s Db7 guide-tone pair. A bass one semitone above the target is therefore insufficient to identify this particular tritone substitution.
| Symbol | Root-order spelling | Semitones from root |
|---|---|---|
| G7 | G–B–D–F | 0,4,7,10 |
| Db7 | Db–F–Ab–Cb | 0,4,7,10 |
| C | C–E–G | 0,4,7 |
| Dbmaj7 | Db–F–Ab–C | 0,4,7,11 |
| Symbol | Third | Seventh |
|---|---|---|
| G7 | B | F |
| Db7 | F | Cb |
Two complete paper versions
The following four bars are original to this repository, not a source-score transcription. A is Dm7–G7–C–C; B changes only bar 2 to Db7. Each version is in 4/4 with quarter-note unit q. Four voices run concurrently, without hand or fingering assignments. Every note in bars 1–3 lasts 4q; each note in bar 4 lasts 2q followed by a 2q rest. There is no pedal, repeat or tie.
Global attacks occur at q=0,4,8,12; all voices enter rests at q=14 and finish at q=16. [a,b) includes a and excludes b. Bars 3 and 4 both use C, but q=12 is a fresh attack; do not silently add ties. Each version has 16 note events and four voice-rest events. Every voice covers 16q; concurrent voices do not make a 64q-long phrase.
The crucial shared-key comparison is A’s B3 and B’s Cb4: both have MIDI coordinate 59 and 88-key number 39. Cb4 lowers C4 by a semitone; do not substitute Cb3. V2 moves B3→C4 in A and Cb4→C4 in B, each up one semitone; the former is spelled a minor second, the latter an augmented unison. V3 moves F4→E4 down one semitone in both.
In G7 the descending F4 is the seventh; in Db7 it is the third, while that chord’s seventh Cb4 rises to C4 in this example. Shared keys and a shared target do not imply identical chord roles or a rule that every seventh must descend. We are describing these specified voice connections.
Calculate the bass separately: A’s G2→C3 rises five semitones, a perfect fourth; B’s Db3→C3 falls one semitone, a minor second. The two seventh-chord root pitch classes are a tritone apart, but their actual bass routes to C differ here. Different inversions or octaves change the actual bass distances, so these signed numbers cannot simply be reused.
V4 also changes from D5→G4 to Ab4→G4, descending seven and one semitones respectively. Bar 2 replaces two pitches and respells another enharmonically. Neither identical sound nor a better B version follows from the smaller bass step. A prescribed melody, other instruments or a specific style requires checking the actual collection and connections again.
| Version | Voice | Bar1 [0,4) | Bar2 [4,8) | Bar3 [8,12) | Bar4 [12,14) | Bar4 [14,16) |
|---|---|---|---|---|---|---|
| A | V1 | D3 | G2 | C3 | C3 | rest |
| A | V2 | C4 | B3 | C4 | C4 | rest |
| A | V3 | F4 | F4 | E4 | E4 | rest |
| A | V4 | A4 | D5 | G4 | G4 | rest |
| B | V1 | D3 | Db3 | C3 | C3 | rest |
| B | V2 | C4 | Cb4 | C4 | C4 | rest |
| B | V3 | F4 | F4 | E4 | E4 | rest |
| B | V4 | A4 | Ab4 | G4 | G4 | rest |
| Version | Voice | Bar2 | Bar3 | Signed semitones |
|---|---|---|---|---|
| A | V1 | G2 | C3 | +5 |
| B | V1 | Db3 | C3 | -1 |
| A | V2 | B3 | C4 | +1 |
| B | V2 | Cb4 | C4 | +1 |
| A | V3 | F4 | E4 | -1 |
| B | V3 | F4 | E4 | -1 |
| A | V4 | D5 | G4 | -7 |
| B | V4 | Ab4 | G4 | -1 |
| Pitch | MIDI coordinate | 88-key number |
|---|---|---|
| G2 | 43 | 23 |
| C3 | 48 | 28 |
| Db3 | 49 | 29 |
| D3 | 50 | 30 |
| B3 | 59 | 39 |
| Cb4 | 59 | 39 |
| C4 | 60 | 40 |
| E4 | 64 | 44 |
| F4 | 65 | 45 |
| G4 | 67 | 47 |
| Ab4 | 68 | 48 |
| A4 | 69 | 49 |
| D5 | 74 | 54 |
Key numbering counts black and white keys from A0=1; middle C4=40. MIDI numbers are coordinates only. B3 and Cb4 are two spellings of one coordinate.
Return from the local check to the whole phrase
On paper, label root, third, fifth and seventh in bar 2 of each version. Circle V2 and V3 and calculate their signed semitone moves to bar 3; then draw V1’s bass line separately. Your answer must include both “two shared pitch classes” and “different complete chords,” not just “they are the same.” Playing four voices together is not required.
If Cb4 causes difficulty, inspect only bars 2–3 on [4,12), an 8q window whose local origin is global q=4. Local 0 and 4 correspond to original bars 2 and 3. Check the coordinates, roles and targets of Cb4/B3, then restore bar 1 and bar 4’s 2q notes plus 2q rests and reread all of [0,16). A correct local check does not replace the whole-phrase check.
This is a paper route with no additional piano assignment. For time arithmetic alone, quarter note=60 BPM gives one second per q, sixteen seconds per version and eight seconds for the local window. It is neither a playing-tempo requirement nor a measured key release or acoustic cutoff. A notated rest does not establish absolute silence in a real environment.
Record the version, prediction before checking, whether answers were visible, actual paper result or “uncertain,” one next step and the whole-phrase result after restoration. Blank entries stay unknown; this page contains no real learner observations. After the next day or another recorded delay, hide the answers and revisit the same material, recording the interval; this tests retention of familiar material only.
Published answers and comparison tables cannot later serve as unseen blind-test material; transfer needs comparably difficult material not previously seen, heard or practiced. Correct paper spelling also does not establish hearing the complete chord, fluent playing or changed perception. Record only what this attempt actually checked.
Local function and source limits
In the stipulated C major, A’s G7 is V7 targeting C; B’s Db7 is a tritone-substitution candidate for G7 in the same position. Db7→C alone proves neither the key of a whole piece nor a modulation. Melody, preceding and following harmony, cadences and sustained tonic organization still need analysis.
“Place a dominant seventh a semitone above the target root” is one way to generate a candidate. This example also checks chord structure, shared guide tones and actual resolutions. It does not guarantee compatibility with every target, melody or extension. No extension to ninths, elevenths or thirteenths, required emotional response or learning guarantee is supplied here.
All 112 existing NC-029 ASR segments were read, with five stills inspected at 90,146,172,190 and 286 seconds. The 90-second frame shows G7 with two red circles; 146 shows G7, Db7 and tritone labels; 172 shows E7 and Bb7; 190 displays the substitution title and insertion rule; 286 shows a score layout with chord symbols. Only these visible labels and layouts are confirmed, not a note-by-note source-score audit.
ASR segments 36–40 and 43–52 propose replacing a dominant seventh through a shared tritone; segments 66–73 propose inserting a chord a semitone above the target. These remain candidate attributions not checked against source audio. ASR may misrecognize pitch names and terms; the visible rule at 190 seconds also does not prove its sound-quality claim. Precise ASR-to-still alignment and continuous motion were not verified.
The complete four bars, registers, voice durations, root and spelling calculations, Dbmaj7 counterexample and recording steps are original synthesis, not a source transcription. Limited text/still review and original symbolic checks are recorded separately. This page remains a candidate pending independent review and does not increase published coverage.
Secondary-dominant targets · Harmony and voicing · Interval spelling · Retention and transfer · Source scope · Recomputable data