审阅范围 · Review scope
指定内容与证据核对。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。
Specified content and evidence checks. Keep the evidence and limitations stated in the text in view. This is not final corpus acceptance or validation of performance or learning outcomes.
音高、音律与乐器状态
先把两种“快”分开：音叉每秒振动很多次，决定音高；你每秒点一次拍，决定音乐时间。把一个音持续4拍，不会因此把它的音高降低。节奏视频演示密度与拍速；本页用可离线阅读的原创数值表解释频率关系，无需先操作钢琴内部。
相同音程不是相同Hz差
【通用乐理】频率以Hz表示每秒周期数。理想十二平均律把一个八度分成12个相同的频率比；向上一个八度频率乘2。取A4=440 Hz，以它为基准向上n个半音：f = 440 * 2^(n/12)。这里A4是科学音高记号，不是手指编号；C4为中央C。
| 原创例 | 半音数n | 理想频率Hz | 比前一个A高多少Hz |
|---|---|---|---|
| A4 | 0 | 440 | — |
| A5 | 12 | 880 | 440 |
| A6 | 24 | 1760 | 880 |
相邻两行都是八度，频率比相同，差值不同。实际钢琴可能采用伸缩调律，弦的泛音也不完全是整数倍；上表不是给每架钢琴逐键验收的标准，更不能用手机测出的单个数值诊断击弦机。
【本库推导】两条理想、同时发声且频率接近的纯音440 Hz和442 Hz，拍频为差的绝对值2 Hz；这里的“拍”是干涉形成的强弱起伏，不是乐谱里每分钟多少拍。持续4秒会有约8个这种起伏周期，但不因此是8个四分音符。实际音色、泛音和环境会影响听辨；本页没有做听觉试验。
五度圈如何“闭合”
【本库推导】十二平均律的五度是7个半音，12次共84个半音，即7个八度。纯五度的频率比为3/2，连乘12次再除去7个八度，得到(3/2)^12 / 2^7 = 1.0136432648，不是1。差约23.460音分（cent）；1个十二平均律半音=100音分。纯五度约701.955音分，平均律五度700音分。这里“纯五度”特指精确3/2，不把所有谱写的完全五度都称为3/2。
这说明精确的纯五度链与闭合的12音系统不能全部兼得；不说明毕达哥拉斯律的每个八度必须失谐。可以保留纯八度，把闭合差留在某些五度中。音律选择涉及取舍，不推出某一种音律适合所有作品或人人必然听出其差别。
【翻译复核】FOPP-77第一段说小提琴其他弦已按五度调好，但“not tempered”；现有中文“未经调律”会误成根本没有调音。这里应区分“已调音”与“未按所讨论的律制修正音程”。本库用“中全音律（meantone，原译另作中庸律）”，不把平均律、纯律和所有半音音阶混为一谈。
【证据边界】FOPP-76物理207页、印刷206的表3.2图像已看过；列出的误差百分数不符合通常的100 * (ET_ratio / reference_ratio - 1)定义；原列值接近100 * (ET_ratio - reference_ratio)，两者分母不同。独立重算小三度约−0.899%、大三度+0.794%、四度+0.113%、五度−0.113%。这些是比值误差，不是音分，也不证明听觉悦耳程度。文字提取把指数压平的问题不应当算译文错误。
先描述问题，再决定练习或维护
【作者观点】FOPP-75建议把具体演奏困难告诉调律师。我们保留这个沟通方向；不采用失调必毁绝对音感、任何旧琴都无法轻奏等笼统断言。调音（tuning）调整音高关系；钢琴整音（voicing）处理琴槌与音色，和弦声部配置（chord voicing）则是安排音符；击弦机调整（regulation）涉及机构工作状态。这些不是一个动作。
【本库综合】原创任务“乐器状态单”：在熟悉且舒适的小片段上，先记录实际琴键、力度目标、是否用踏板、发生条件和不确定之处。只记录“某键难以得到预想弱音”，不要由一次失败断定是手指、琴槌或调律。改用纸面分析或别的已熟悉片段继续项目；把重复出现的问题交给合适的钢琴技术人员检查，不自己拆机或针刺琴槌。下次用相同片段及条件重新比较，再把结果放回整句练习；这是本库的项目依赖设计，不是来源证明的诊断方法。
【证据边界】FOPP-73和FOPP-74是作者的“新发现”与待研究问题清单。量子类比的记忆场、自动获得绝对音感、唯一最佳音阶、特定音律证明作曲家意图等没有因本次阅读成为科学事实；所比中文大多忠实保留原著过强语气。更准确的短解释应保留问题、写明未知，不能伪装成翻译修正后就已被证实。
前置：音程、节奏；应用：练习项目。出处见PDF-FOPP§73–77，相关正文物理198–211页（印刷197–210），逐节位置与选比译段见账本。本页不是调律教程或整章替代品。
练习条件：先分清控制了什么
【作者观点】FOPP-70第18段讨论电子琴软件声音响应与机械部件的区别。对初学者，先问“同样的动作，声音怎样回应”，再问“琴键实际如何运动”；软件设置的名称不证明机械重量改变。本库不把原书关于品牌、寿命、购买或普遍学习效果的旧判断当作当前结论。你已有原声钢琴，练习项目不需要先购买电子琴或连接MIDI。
【翻译复核】FOPP-71第11段把capstan与jack都译成“顶杆”，容易混淆两个部件。已看FOPP-80原图（实际226页，印刷225）：capstan为图24，jack为图1；暂保留英文和编号，不自造统一中文行业名称。该节提取稿只有16个英文词的链接文字；图像与实际运动是不同证据。§11所指图5标为Center pin felt bushing，也不支持译文额外加入的立式琴比较。
【证据边界】FOPP-78第9段承认力学计算只是定性简化；其踏板／琴盖使用与琴槌问题的联系不能当作单项确诊规则。FOPP-71把多项保养笼统归入regulation，本库仍分开调音、整音和机构调整。这里不复制拆机、抛光或针刺教程，不从纸上模型推出身体用力或健康保证。
【本库综合】把“乐器状态单”具体化：用熟悉的C4、D4、E4、D4，各占一个四分音符，右手采用已经舒适的指法，左手休息；暂不用踏板。可先纸面标记或请教师示范。以四分音符为拍单位选一个舒适速度，先写“起音是否均匀”，再弹一次；下一次才查相对强弱，不同时评所有方面。记录速度、琴键、踏板、琴盖状态和未知因素；这些是观察条件，不是维修操作。次日同条件复测，再接回实际乐句。换琴后的差异先记为条件变化，不直接判为技能倒退；这一流程是本库的项目设计，未做学习效果试验。
同一个五度，拍频为何会变
【本库推导】先想象两组“几乎重合的高音成分”。在理想谐波模型中，低音的第3分音接近高音的第2分音；分音是构成复合声音的频率成分，第1分音为基音。令十二平均律A4=440 Hz，分别算C4–G4与高一八度的C5–G5。拍频模型为abs(3*f_lower - 2*f_upper)：
| 原创理想例 | 低音Hz | 高音Hz | 两分音差Hz |
|---|---|---|---|
| C4–G4 | 261.625565 | 391.995436 | 0.885824 |
| C5–G5 | 523.251131 | 783.990872 | 1.771648 |
频率全部加倍，差也加倍；两行音程仍同为五度。这不是两次钢琴录音的测量，更不是按表修琴的方法。实际弦的非谐性、伸缩调律、分音强弱和聆听环境未纳入；听不出起伏不代表学习失败。
FOPP-81的律制偏好属作者观点。“偏离精确纯五度”与“偏离选定律制目标而失调”是两回事；平均律的目标本就包含折衷。自查：低、高频率同时乘2时，上式结果如何变化？答案：也乘2，不能由此推导人人听感或某律制绝对优越。
本次新增来源为PDF-FOPP§70、71、78、80、81：相关选段实际185–195、212–214、226–230页，印刷184–194、211–213、225–229；逐段与逐页范围见账本。原图未转载，外部图链没有取得正文。
强弱目标与听力状况分开记录
【来源核对】FOPP-61实153–156／印152–155中的年龄安全保证不采用：噪声损伤可发生在任何年龄，强度、时长和距离都有关，暂时恢复也不排除残余损伤。NIDCD噪声说明
【来源核对】耳鸣与听损有关，却不是可凭响度读数的同一件事；无通用治愈不等于没有症状帮助。NIDCD耳鸣说明是本次选定文字补充，不是个人听力检查。Q-078记录原书过强概括，未采用其旧器材与药物建议。
【本库综合】练习日志分三栏：谱面强弱目标、实际听到的结果、环境与身体状况。不能把手机波形高低当触键力度，也不能把主观耳鸣强弱当测听结果。声音令人不适时停止该暴露，保留纸面预测等安静任务；出现听力变化或耳鸣，向医疗或听力专业人员咨询。下次是否回到原声任务由实际状况决定，不由“年轻”“以前能弹”或任务表自动批准。本文没有测量琴房声级、验证护耳设备或设置个人安全音量。
数字正确也不等于诊断成立
【翻译复核】FOPP-79第6段英文用inaccurate造成精度句的词误，中文按上下文写精度不够；这里应保留合理意思，不能为逐词一致反而引入原文错误。本节工具、调律动作、固定阈值和保护保证没有做实测，也不构成对初学者动手调弦的建议。
【本库推导】FOPP-83第174段把功率低30 dB说成几个百分点。按NI的相对分贝定义，功率比例为10^(-30/10) = 0.001 = 0.1%；相应振幅比例在功率与振幅平方成正比的条件下为10^(-30/20) ≈ 0.03162 = 3.162%。两者不应混写。这里是比值演算，不是人的主观响度百分比，也没有测量真实钢琴余音或证明掩蔽。
【本库综合】把“这个数是什么量、相对什么、由哪种测量得到”写进乐器状态单。若只会记录某个音听来不同，就如实记录不确定；不要先拆琴或把问题归咎于手。先完成仍可独立推进的读谱、节奏与句法任务，等待合适的乐器检查，再在原条件下复测。
Pitch, tuning systems and instrument condition
First separate two kinds of speed: a tuning fork vibrates many times per second, determining pitch; tapping once per second sets musical time. Holding a note for4 beats does not lower its pitch. The rhythm video illustrates density versus tempo; this page uses an original offline-readable numerical table for frequency relationships, with no need to work inside a piano.
Equal intervals do not have equal Hz differences
[General theory] Frequency in Hz counts cycles per second. Ideal twelve-tone equal temperament divides an octave into12 equal frequency ratios; rising an octave multiplies frequency by2. With A4=440 Hz, n semitones upward gives f = 440 * 2^(n/12). A4 uses scientific pitch notation, not a finger number; C4 is middle C.
| Original example | Semitones n | Ideal frequency Hz | Hz above the preceding A |
|---|---|---|---|
| A4 | 0 | 440 | — |
| A5 | 12 | 880 | 440 |
| A6 | 24 | 1760 | 880 |
Each adjacent pair forms an octave: equal ratio, unequal difference. An actual piano may use stretch tuning and its string partials are not exactly integer multiples. The table is not a key-by-key acceptance standard for every piano, and one phone-measured frequency cannot diagnose an action.
[Our derivation] Two ideal simultaneous nearby pure tones at440 Hz and442 Hz have a beat frequency equal to the absolute difference,2 Hz. These beats are interference-related amplitude fluctuations, not beats per minute on a score. Sustaining for4 seconds yields about8 fluctuation cycles, not necessarily8 quarter notes. Timbre, partials and surroundings affect perception; this page includes no listening trial.
How the fifths circle closes
[Our derivation] An equal-tempered fifth spans7 semitones. Repeating it12 times spans84 semitones, or7 octaves. A pure fifth has frequency ratio3/2; repeating12 times and removing7 octaves gives (3/2)^12 / 2^7 = 1.0136432648, not1. The difference is about23.460 cents;1 equal-tempered semitone=100 cents. A pure fifth is about701.955 cents, versus700 for the equal-tempered fifth. Here pure means exactly3/2; not every notated perfect fifth is assigned that exact ratio.
Thus a chain of exact pure fifths and a closed12-note system cannot satisfy every relation simultaneously. This does not require every octave in Pythagorean tuning to be out of tune. Pure octaves can be retained with the closure discrepancy placed in some fifths. Tuning systems involve tradeoffs, without proving one system suits every work or that everybody must hear its differences.
[Translation review] The first paragraph of FOPP-77 describes other violin strings already tuned in fifths but not tempered. The Chinese wording implies they were not tuned at all. Distinguish tuning from adjusting intervals according to the temperament under discussion. We use 中全音律 for meantone, noting the source's alternative 中庸律; equal temperament, just intonation and all chromatic scales are not interchangeable.
[Evidence limits] The image of table3.2 in FOPP-76, physical207/printed206, was inspected. Its printed percentage errors do not match the usual 100 * (ET_ratio / reference_ratio - 1) definition; the printed values resemble 100 * (ET_ratio - reference_ratio), which uses a different denominator. Independent calculations give approximately−0.899% for the minor third,+0.794% for the major third,+0.113% for the fourth and−0.113% for the fifth. These are ratio errors, not cents or evidence of pleasantness. Flattened superscripts in text extraction are not translation errors.
Describe the problem before choosing practice or maintenance
[Author's view] FOPP-75 suggests communicating specific playing difficulties to a tuner. We retain that direction without adopting blanket claims that mistuning destroys absolute pitch or that every old piano prevents soft playing. Tuning adjusts pitch relationships; piano voicing concerns hammers and tone, whereas chord voicing arranges notes. Regulation concerns the action's operation. These are distinct tasks.
[Our synthesis] Original task, “instrument-condition record”: use a familiar comfortable short passage and record the actual key, dynamic goal, pedal use, conditions and uncertainty. Describe difficulty obtaining the intended soft tone without concluding from one failure that fingers, hammers or tuning caused it. Continue the project through paper analysis or another familiar passage. Ask a suitable piano technician to assess recurring problems; do not dismantle the action or needle hammers yourself. Compare again next time with the same passage/conditions, then reintegrate into the phrase. This project-dependency design is ours, not a source-validated diagnostic method.
[Evidence limits] FOPP-73 and FOPP-74 list the author's proposed discoveries and research questions. Quantum-like memory fields, automatic absolute pitch, one best scale and claimed proof of composer intent through a temperament have not become scientific facts through this reading. Most compared Chinese passages faithfully retain strong original wording. A better short explanation preserves the question and states uncertainty; editing a translation does not validate its claims.
Prerequisites: intervals and rhythm. Application: practice projects. Sources: PDF-FOPP§73–77, relevant bodies physical198–211 (printed197–210), with section coordinates and selected translations in the ledger. This is not a tuning manual or a replacement chapter.
Practice conditions: identify what is being controlled
[Author's view] Paragraph18 of FOPP-70 discusses electronic sound response versus mechanical components. A beginner can first ask how sound responds to an action, then how the key physically moves; a software setting’s label does not prove a mechanical-weight change. We do not treat the book’s dated brand, lifespan, purchase or universal-learning judgments as current conclusions. Your existing acoustic piano supports the practice project without first buying a digital instrument or connecting MIDI.
[Translation review] Paragraph11 of FOPP-71 translates capstan and jack with the same Chinese term 顶杆, conflating distinct parts. In the inspected original FOPP-80 diagram (physical226, printed225), capstan is label24 and jack label1. Retain English names and numbers pending standard Chinese trade-name checking. The section’s extraction contains only16 English words of link text; images and actual motion provide different evidence. Label5, referenced by§11, reads Center pin felt bushing and does not support the translation’s added upright-piano comparison.
[Evidence limits] Paragraph9 of FOPP-78 acknowledges a qualitative mechanical simplification; its association between pedal/lid use and hammer problems is not a single-symptom diagnosis. FOPP-71 groups several maintenance tasks broadly under regulation; our notes retain tuning, voicing and action regulation as distinct. We do not reproduce disassembly, polishing or needling instructions or derive bodily-force/health guarantees from a paper model.
[Our synthesis] Make the instrument-condition record concrete: use familiar C4, D4, E4, D4, each lasting one quarter note, with already comfortable right-hand fingering and the left hand resting; initially use no pedal. Paper marking or a teacher model is an alternative. Select a comfortable tempo with the quarter note as beat unit, write “Are attacks evenly spaced?”, then play once. Check relative dynamics on another attempt, without grading everything together. Log tempo, keys, pedal, lid position and unknown factors as observation conditions, not maintenance procedures. Retest under the same conditions next day and return to the actual phrase. Initially record a difference after changing pianos as a condition change, not proof of lost skill. This is our project design, without a learner-effectiveness trial.
Why the same fifth can have a different beat rate
[Our derivation] Imagine two nearly coincident high-frequency components. In an ideal harmonic model, the lower tone’s3rd partial lies near the upper tone’s2nd partial; partials are the frequency components of a complex sound, with the1st being the fundamental. Set equal-tempered A4=440 Hz and compare C4–G4 with C5–G5 an octave higher. The beat model is abs(3*f_lower - 2*f_upper):
| Original ideal example | Lower Hz | Upper Hz | Partial difference Hz |
|---|---|---|---|
| C4–G4 | 261.625565 | 391.995436 | 0.885824 |
| C5–G5 | 523.251131 | 783.990872 | 1.771648 |
Doubling every frequency doubles the difference; both intervals remain fifths. These are neither measurements of two piano recordings nor instructions for adjusting an instrument. Real-string inharmonicity, stretch tuning, partial amplitudes and the listening environment are outside the model. Failure to hear fluctuations is not learning failure.
The temperament preferences in FOPP-81 belong to the author. Departure from an exact pure fifth differs from mistuning relative to a selected temperament: equal temperament intentionally incorporates compromises. Self-check: when both frequencies double, what happens to the formula? Answer: its result doubles too; this does not establish everyone’s perception or the absolute superiority of a temperament.
New sources are PDF-FOPP§70,71,78,80,81: selected relevant bodies at physical185–195,212–214,226–230, printed184–194,211–213,225–229. See the ledger for paragraph/page scopes. The original diagram is not reproduced; no body was obtained from its external diagram link.
Log dynamic goals separately from hearing status
[Source check] We do not adopt the age-based safety guarantee in FOPP-61, physical153–156/printed152–155. Noise damage can occur at any age; level, duration and distance matter, and temporary recovery does not exclude residual damage. NIDCD noise information
[Source check] Tinnitus relates to hearing loss without being the same thing measured by perceived loudness; no general cure does not mean no symptom help. NIDCD tinnitus information is a bounded text supplement, not an individual hearing examination. Q-078 records overstrong book generalizations without adopting dated equipment or medication advice.
[Our synthesis] Keep three log columns: notated dynamic goal, heard result, and environment/body conditions. A phone waveform’s height is not touch force, and perceived tinnitus loudness is not an audiogram. Stop an uncomfortable sound exposure and retain quiet tasks such as paper prediction; seek medical or hearing-professional advice about hearing changes or tinnitus. Returning to the acoustic task depends on actual circumstances, not automatic permission from youth, past ability or a checklist. No room sound level was measured, hearing-protection device tested or personal safe volume set here.
Correct arithmetic does not establish a diagnosis
[Translation review] Paragraph6 of FOPP-79 uses inaccurate in a precision sentence where the context points to a lexical error; Chinese conveys insufficient precision. Preserve the reasonable meaning instead of importing the source error for word-for-word agreement. Tools, tuning movements, fixed thresholds and protective assurances here were not experimentally checked and do not advise beginners to adjust strings.
[Our derivation] Paragraph174 of FOPP-83 calls power30 dB lower a few percent. Using NI’s relative-decibel definition, the power ratio is 10^(-30/10) = 0.001 = 0.1%; the corresponding amplitude ratio, where power is proportional to amplitude squared, is 10^(-30/20) ≈ 0.03162 = 3.162%. Do not conflate them. This is ratio arithmetic, not a percentage of subjective loudness, a real-piano after-sound measurement or a masking demonstration.
[Our synthesis] Add “what quantity, relative to what, from which measurement” to the instrument-condition log. If you can only say that a note sounds different, record uncertainty honestly; do not first dismantle the piano or blame the hand. Continue independent reading, rhythm and phrase tasks, await suitable instrument assessment, then retest under the original conditions.