A string, many shakes一條弦，很多種振動
Watch the string shake as a whole and in halves and thirds at the same time.
看弦同時整根、一半、三分之一地振動。
Music · Unit 3 · Lesson 9 · 音樂 單元三 第九課
How Do Instruments Make Sound?樂器怎麼發出聲音？
Four stands, four families: a string, a column of air, a drumhead, and a bar. Click each one to hear it, watch what vibrates, and find out how each family goes higher.
四個展示台，四個家族：弦、空氣柱、鼓膜和一根棒。一個一個點，聽聲音、看是什麼在振動，再找出每一家怎麼變高。
Big idea · 一句話看懂
Every instrument sounds because something vibrates. We group instruments by what vibrates: a string, a column of air, a membrane, or the body of the instrument itself.
每一種樂器會發聲，都是因為有東西在振動。我們依「是什麼在振動」把樂器分組：弦、空氣柱、膜，或樂器本身。
3D Model · 3D 模型
Four Things That Vibrate 四種會振動的東西
From left to right: a string on a box, a tube of air closed at the bottom, a drum, and a bar. Click a stand to hear that family and see what vibrates. On the string, you see the string shake in halves and thirds at once. In the tube, the little dots are air, moving back and forth. On the drum, the head swells up and down in two patterns together. The bar bends, with its ends and its middle moving in opposite directions. The motion is slowed down on purpose, and our sounds are simple recipes, not recordings.
由左到右：箱子上的一條弦、下面封閉的一管空氣、一面鼓、一根棒。點一個展示台，聽那一家的聲音，看是什麼在振動。弦會同時以一半、三分之一的方式振動；管子裡的小點是空氣，前後晃動；鼓皮同時以兩種圖樣一起一伏；棒會彎曲，兩端和中間的動向相反。振動畫面是刻意放慢的，我們的聲音是簡單的配方，不是錄音。
Click a stand to play it · 點一個展示台就會發聲 Drag the background to turn · 拖曳背景旋轉 Scroll or pinch to zoom · 滾輪／雙指縮放
This 3D model needs WebGL, which this browser does not support. The buttons on this page still work, and so do the reading, the cards, and the games.
這個瀏覽器不支援 WebGL，沒辦法顯示 3D 模型。頁面上的按鈕、課文、卡片與小遊戲都還能用。
- Click a stand: it sounds and moves
點展示台：發聲，並且動起來 - Each family has its own list of overtones
每一家有自己的一組泛音
The vibrations are slowed down: the lowest tone shakes about once a second here. The ratios between the overtones are the real ones.
振動是放慢的：最低的音在這裡每秒約振動一次。泛音之間的比例是真的。
All sounds on this page are made by your browser, tone by tone. They are simple recipes for each family, not recordings of real instruments. · 本頁所有的聲音都由瀏覽器即時合成，是每一家的簡單配方，不是真樂器的錄音。
Reading · 英文閱讀
9
Unit 9: How Do Instruments Make Sound?
Every sound starts with something that vibrates. Musical instruments can be grouped by what it is. A well-known system was devised by Erich von Hornbostel and Curt Sachs and published in 1914. It uses four families: chordophones, where a string vibrates; aerophones, where air vibrates; membranophones, where a stretched membrane vibrates; and idiophones, where the body of the instrument itself vibrates. In Taiwan they are 弦鳴樂器, 氣鳴樂器, 膜鳴樂器, and 體鳴樂器.
每個聲音都始於某個東西在振動。樂器可以依「是什麼在振動」來分組。有一套著名的系統，由霍恩博斯特爾（Erich von Hornbostel）和薩克斯（Curt Sachs）提出，1914 年發表。它分成四個家族：弦鳴樂器，是弦在振動；氣鳴樂器，是空氣在振動；膜鳴樂器，是拉緊的膜在振動；體鳴樂器，是樂器本身在振動。在台灣的標準譯名是弦鳴樂器、氣鳴樂器、膜鳴樂器和體鳴樂器。
A string’s pitch depends on three things. The shorter the string, the higher the pitch. The tighter the string, the higher the pitch. And the lighter the string, the higher the pitch. A string alone barely moves the air, so most string instruments have a body. The soundboard moves a greater volume of air than the thin string, and that makes the sound louder. The body does not add energy. The string is still where the sound comes from. Strings can be plucked, bowed, or struck.
弦的音高取決於三件事：弦越短，音越高；弦越緊，音越高；弦越輕，音越高。弦自己幾乎推不動空氣，所以大多數弦樂器有琴身。共鳴板比細細的弦推動更多的空氣，聲音就變大聲。琴身不會增加能量；聲音的來源還是弦。弦可以撥、可以用弓拉，也可以敲。
In a wind instrument the air inside a tube vibrates, and the player starts it in one of three ways: by blowing across an edge, as in a flute, by making a reed vibrate, as in a clarinet, or by buzzing the lips, as in a trumpet. The pitch depends on the length of the tube. Finger holes, valves, and slides change the effective length. A tube that is closed at one end makes only the odd harmonics, 1, 3, 5, and so on, and sounds an octave lower than an open tube of the same length. A clarinet behaves roughly like that, and a flute behaves like an open tube.
管樂器是管子裡的空氣在振動，演奏者用三種方式讓它開始：吹過邊緣，如長笛；讓簧片振動，如單簧管；或用嘴唇嗡嗡振動，如小號。音高取決於管子的長度，按音孔、活塞和滑管會改變有效長度。一端封閉的管子只有奇數諧波 1、3、5……，基音比同長度的開管低一個八度。單簧管大致像這樣；長笛則像開管。
A drum has a stretched membrane. When you tighten the head, the pitch goes up. A circular membrane does not vibrate in whole-number multiples. For an ideal drumhead the overtones are about 1.59, 2.14, 2.30, and 2.92 times the lowest frequency. That makes a drum sound different from a string, and many drums have no clear pitch. But some, such as the timpani, are tuned to definite pitches with a pedal that changes the tension of the head.
鼓有一張拉緊的膜。把鼓皮拉緊，音就變高。圓形的膜不是整數倍地振動：理想鼓皮的泛音大約是最低頻率的 1.59、2.14、2.30、2.92 倍。這讓鼓聽起來和弦不同，許多鼓沒有明確的音高。不過有些鼓，例如定音鼓，用踏板改變鼓皮的張力，可以調到確定的音高。
In a marimba or a xylophone, the bar itself vibrates. A free bar has overtones at about 2.76, 5.40, and 8.93 times its lowest frequency, which are not whole numbers either. Makers tune a marimba bar by taking wood from the middle of its underside, which lowers the pitch. The shorter the bar, the higher the pitch. A bell is a body too. A well-tuned bell has a hum, a strike tone, a tierce, a quint, and a nominal.
在馬林巴琴或木琴裡，是琴鍵那根棒本身在振動。兩端自由的棒，泛音大約是最低頻率的 2.76、5.40、8.93 倍，也不是整數倍。製作者調馬林巴琴鍵的音，是從琴鍵底面中間削掉木頭，音會變低。棒越短，音越高。鐘也是體鳴樂器。調好音的鐘有低音（hum）、敲擊音（strike）、小三度音（tierce）、五度音（quint）和高八度音（nominal）。
So the family is not about the material. A saxophone is usually made of brass, but it is a woodwind, because a reed starts the vibration. Our ears also use more than the overtones to tell instruments apart. Researchers say the timbre depends mainly on the frequency spectrum, but also on the attack and on how the sound changes in time. The sounds on this page are our own simple recipes, so real instruments sound richer.
所以家族和材料沒有關係。薩克斯風通常是銅做的，但它是木管樂器，因為開始振動的是簧片。我們的耳朵也不只靠泛音來分辨樂器。研究者說，音色主要取決於頻率頻譜，但也取決於起音和聲音隨時間的變化。本頁的聲音是我們自己的簡單配方，所以真樂器聽起來更豐富。
Read aloud · 課文朗讀
Questions · 閱讀理解
Why is a saxophone a woodwind, even though it is usually made of brass?
Because a vibrating reed starts the sound. The family depends on how the vibration is started, not on the material.
What happens to a string’s pitch when you make the string half as long?
The frequency doubles, so the pitch goes up one octave. This is the 2 to 1 ratio from lesson 1.
What makes the overtones of a drum different from those of a string?
A string’s overtones are whole-number multiples, 1, 2, 3… times the lowest. A drumhead’s overtones are not: about 1, 1.59, 2.14, 2.30, 2.92.
Words & Phrases · 生字及片語
vibrate(v.)振動A guitar string vibrates when you pluck it.你撥吉他弦，弦就會振動。tension(n.)張力（拉緊的程度）More tension makes the pitch of a string higher.張力越大，弦的音高越高。membrane(n.)膜A drum has a stretched membrane, called the head.鼓有一張拉緊的膜，叫鼓皮。reed(n.)簧片A clarinet player makes a reed vibrate.吹單簧管的人讓簧片振動。air column(n.)空氣柱The air column in a flute gets shorter when you open a hole.打開一個孔，長笛裡的空氣柱就變短。soundboard(n.)共鳴板A piano’s soundboard makes the strings sound louder.鋼琴的共鳴板讓弦的聲音變大。overtone(n.)泛音A drum has overtones that are not whole-number multiples.鼓的泛音不是整數倍。tune(v.)調音A timpanist can tune the drum with a pedal.定音鼓手可以用踏板為鼓調音。
Quick Check · 小測驗
1. What vibrates to make the sound of a flute?
2. Which family does a drum belong to?
3. How can you make a string’s pitch higher?
4. The overtones of a drumhead are…
5. A trumpet is an aerophone because…
Try It in the Model · 在模型裡試試
Four things to try 四件值得試的事
Then try the sliders in the next section: which family needs the biggest change to go up by an octave?
然後試試下一節的滑桿：哪一家要改變最多，才能高一個八度？
Air in a closed tube封閉管裡的空氣
The dots near the bottom hardly move, and the ones at the open top swing the most.
下面的點幾乎不動，開口上面的點晃得最大。
A drumhead鼓皮
Two patterns at once: the whole head moves, and the two halves rock against each other.
兩種圖樣同時發生：整張皮一起動，和兩半一上一下。
A bar一根棒
The ends move up while the middle moves down. The two posts sit where the bar hardly moves.
兩端往上時，中間往下。兩根支柱放在棒幾乎不動的地方。
Try It · 試試看
How Can You Make It Higher? 怎麼讓它變高？
Each family has its own way to go higher. Move a slider and listen. The numbers come from the proportions in the notes below each card: a string and a tube go up as they get shorter, a drum as its head gets tighter, and a bar as it gets shorter. How far must each one change to go up a full octave?
每一家都有自己變高的方法。拖動滑桿，聽聽看。數字來自每張卡下面的比例關係：弦和管子越短越高，鼓皮越緊越高，棒越短越高。每一家要改變多少，才能高一個完整的八度？
🎻 String 弦
f ∝ 1 ÷ length
🎷 Air column 空氣柱
f ∝ 1 ÷ length
🥁 Membrane 膜
f ∝ √tension
🔔 Body 體
f ∝ thickness ÷ length²
Game · 小遊戲
Which Family Is It? 這是哪一家的聲音？
Six questions. Each one plays a sound from one of the four families. Choose which one is vibrating. If you cannot hear the sound, press “Show the overtones”: whole numbers 1, 2, 3 are a string, odd numbers are a closed pipe, and numbers that are not whole belong to a drum, a bar, or a bell.
六道題。每一題播放四個家族之一的聲音。選出是什麼在振動。如果聽不到聲音，按「看泛音」：整數 1、2、3 是弦，奇數是封閉的管，不是整數的是鼓、棒或鐘。
Question 1 of 6 · 第 1 題（共 6 題）
Right on the first try · 第一次就答對 0 / 0
Stories Behind the Notes · 音符背後的故事
A system, eight sounds, a flute with a skin, and a carved bar 一套系統、八音、一支有膜的笛，和一根削過的琴鍵
Four short stories about how people have grouped and built instruments.
關於人們怎麼把樂器分組、怎麼製作樂器的四個小故事。
A System · 一套系統
Four families, then a fifth四個家族，後來又多一個
The Hornbostel–Sachs system was first published in 1914. It builds on an earlier classification by Mahillon, who divided instruments by the sound-producing material: an air column, a string, a membrane, or the body of the instrument. In 1940 Sachs added a fifth group, the electrophones, for instruments that use electricity.
霍恩博斯特爾—薩克斯系統在 1914 年首次發表。它建立在馬約（Mahillon）更早的分類上：他依發聲的材料把樂器分成空氣柱、弦、膜和樂器本身。1940 年薩克斯加上第五類，電鳴樂器，給使用電的樂器。
Eight Sounds · 八音
Classifying by material依材質分類
Ancient China had its own system, called the eight sounds: metal, stone, silk, bamboo, gourd, clay, hide, and wood. Taiwan’s dictionary gives examples: bells are metal, chimes stone, the zither silk, flutes bamboo, the sheng gourd, the xun clay, the drum hide, and the zhu and yu wood. It sorts by what an instrument is made of, which is a different principle from the four families.
中國古代有自己的系統，叫八音：金、石、絲、竹、匏、土、革、木。台灣的辭典舉例：鐘屬金、磬屬石、琴瑟屬絲、簫笛屬竹、笙屬匏、塤屬土、鼓屬革、柷敔屬木。它依樂器的材料分類，和四個家族的原則不同。
A Flute with a Skin · 有膜的笛
The bangdi梆笛
Taiwan’s dictionary describes the bangdi, a bamboo flute played sideways, as having one blow hole, one membrane hole, and six finger holes. So an instrument that is played by blowing has a hole made for a membrane. The erhu has a membrane too, but in another place: it is a bowed string instrument, with a python skin stretched over its resonator.
台灣的辭典描述梆笛是橫吹的竹笛，有一個吹孔、一個膜孔、六個按音孔。也就是說，這支用吹的樂器，有一個為膜而開的孔。二胡也有膜，但在別的地方：它是擦弦樂器，在琴筒上蒙著蟒皮。
A Carved Bar · 削過的琴鍵
Tuning by taking wood away削掉木頭來調音
A marimba maker tunes a bar by taking wood from the middle of its underside, which lowers the pitch. On a vibraphone, the arch ground under the bar makes the first overtones line up in consonant intervals: for an F3 bar, the bar gives F3, its first overtone is F5, and its second is A6. A glockenspiel, by comparison, has no arch at all, and a xylophone has a shallower one.
馬林巴琴的製作者，從琴鍵底面中間削掉木頭來調音，音會變低。在顫音琴上，琴鍵底下磨出的弧度，讓前幾個泛音排成協和的音程：以 F3 的琴鍵為例，基音是 F3，第一個泛音是 F5，第二個是 A6。相較之下，鋼片琴完全沒有弧度，木琴的弧度比較淺。
In the Curriculum · 對應課綱
Where this lesson fits 這一課對應的課綱
The curriculum names the classification of instruments in grades 5 to 6 and how instruments make sound in junior high school. It does not use the words for the four families, or any words about vibration.
課綱在國小高年級寫到樂器的分類，在國中寫到樂器的發音原理。課綱本文沒有出現四個家族的名稱，也沒有「振動」這類詞。
音 E-Ⅱ-2藝術領域・音樂（國小三、四年級） · Arts, music (grades 3–4)
簡易節奏樂器、曲調樂器的基礎演奏技巧。
Playing simple rhythm and melody instruments is where the lesson starts.從演奏簡易的節奏樂器與曲調樂器開始。
音 E-Ⅲ-2藝術領域・音樂（國小五、六年級） · Arts, music (grades 5–6)
樂器的分類、基礎演奏技巧，以及獨奏、齊奏與合奏等演奏形式。
Classifying instruments is named here. The four families are one way to do it.這裡寫到樂器的分類。四個家族就是分類的一種方式。
音 E-Ⅳ-2藝術領域・音樂（國中七至九年級） · Arts, music (grades 7–9)
樂器的構造、發音原理、演奏技巧，以及不同的演奏形式。
How instruments are built and how they make sound is junior-high content.樂器的構造與發音原理是國中的學習內容。
Myth vs. Fact · 常見迷思
Four things people get wrong 四個常見的誤會
✗ Myth · 迷思A drum has no pitch.鼓沒有音高。
✓ Fact · 事實Some drums, such as the timpani, are tuned to definite pitches. Many other percussion instruments, like snare drums and cymbals, have no pitch you can name.有些鼓，例如定音鼓，是調到確定音高的。很多其他打擊樂器，像小鼓和鈸，沒有可以說出名字的音高。
✗ Myth · 迷思The body of a violin makes the sound.小提琴的琴身發出聲音。
✓ Fact · 事實The string is where the sound starts. The body vibrates too, and it moves more air, which makes the sound louder, but it adds no energy.聲音是從弦開始的。琴身也會振動，它推動更多的空氣，讓聲音變大聲，但它沒有增加能量。
✗ Myth · 迷思Woodwinds are made of wood and brass instruments of brass.木管樂器是木頭做的、銅管樂器是銅做的。
✓ Fact · 事實The family depends on how the vibration starts. A saxophone is usually brass but is a woodwind, because a reed vibrates. A wooden cornett is a brass instrument, because the player’s lips vibrate.家族取決於振動怎麼開始。薩克斯風通常是銅做的，卻是木管樂器，因為振動的是簧片；木製的短號是銅管樂器，因為振動的是演奏者的嘴唇。
✗ Myth · 迷思A wind instrument just blows air.管樂器只是把空氣吹進去。
✓ Fact · 事實Blowing is only the start. The player uses an edge, a reed, or buzzing lips to make the air inside the tube vibrate.吹氣只是開始。演奏者靠邊緣、簧片或嘴唇的振動，讓管子裡的空氣振動。
Remember It · 記憶口訣
Instruments in a sentence 一句話記住樂器
What vibrates?是什麼在振動？
String, air column, membrane, body.
弦、空氣柱、膜、體。
Shorter, higher越短越高
Strings, tubes, and bars all go up when they are shorter.
弦、管子和棒，縮短都會變高。
Whole numbers: string and pipe整數倍：弦和管
1, 2, 3 for a string. 1, 3, 5 for a closed pipe.
弦是 1、2、3；封閉的管是 1、3、5。
Not whole: drum, bar, bell不是整數：鼓、棒、鐘
Their overtones fall in between.
它們的泛音落在整數之間。
Protect Your Ears · 保護耳朵
Before you listen 聽之前
- Start with the volume low and turn it up a little at a time. The drum and bar sounds on this page start with a sharp attack, so be careful with the volume.先把音量調小，再一點一點調大。本頁鼓和棒的聲音一開始有尖銳的起音，音量要特別小心。
- With headphones, keep the volume at no more than 60% of maximum, and use personal audio devices for less than one hour a day, as the World Health Organization suggests.戴耳機時，音量不要超過最大音量的 60%，個人音響裝置每天使用少於一小時，這是世界衛生組織的建議。
- Real drums, cymbals, and bells are much louder than this page. Do not put your ear close to them when they are played.真的鼓、鈸和鐘比本頁大聲得多。有人敲打時，不要把耳朵靠近它們。
Classroom Activity 1 · 課堂活動一
Sort the Sounds 把聲音分家族
You need · 準備材料
- Safe, ordinary things: a rubber band, a ruler, a drinking straw, a plastic bottle, a paper cup, a spoon, a glass jar安全的日常物品：橡皮筋、尺、吸管、塑膠瓶、紙杯、湯匙、玻璃罐
- Four sheets of paper labeled string, air, membrane, body四張紙，分別寫著弦、空氣、膜、體
Steps · 步驟
- In small groups, make a sound with each object. Gently: pluck the rubber band, blow across the top of the bottle, tap the stretched surface of a cup or jar lid, tap the spoon on a jar.小組輪流用每個東西發出聲音。要輕：撥橡皮筋、對著瓶口吹、輕敲繃緊的杯面或罐蓋、用湯匙輕敲玻璃罐。
- Ask: what is vibrating? Put each object on the sheet for its family.問：是什麼在振動？把每一個東西放在它那一家的紙上。
- Find an object that could fit two families. Argue for each side, then decide what starts the vibration.找一個可能屬於兩個家族的東西。為兩邊辯論，再決定是什麼開始振動。
- Share your sorted sheets with another group. Did you put anything differently?把分好類的紙給另一組看。你們有沒有放得不一樣的？
Keep everything gentle and keep glass on the table. Do not stretch rubber bands near anyone’s face.
動作要輕，玻璃放在桌上。不要在別人臉旁邊拉橡皮筋。
Classroom Activity 2 · 課堂活動二
The Rubber-Band Guitar 橡皮筋吉他
You need · 準備材料
- An open box or a plastic container一個開口的盒子或塑膠盒
- Rubber bands of different thickness不同粗細的橡皮筋
- A pencil to use as a bridge一支鉛筆當琴馬
Steps · 步驟
- Stretch several rubber bands over the box. Pluck each one and listen. Which sounds higher?把幾條橡皮筋套在盒子上。每一條撥一撥，聽聽看。哪一條比較高？
- Slide the pencil under the bands to make them shorter. What happens to the pitch?把鉛筆塞到橡皮筋下面，讓振動的部分變短。音高怎麼變？
- Stretch one band tighter. What happens now?把一條橡皮筋拉得更緊。這時候會怎樣？
- Write down what makes the pitch go higher. Compare with the “How can you make it higher?” sliders on this page.寫下什麼讓音高變高。和本頁「怎麼讓它變高」的滑桿比較。
Use thin, new rubber bands and do not stretch them far, so they do not snap. Keep the box low and away from your face.
用細細、新的橡皮筋，不要拉得太長，免得彈斷。盒子放低，離臉遠一點。
Go Further · 延伸閱讀
Before, around, and after this lesson 這一課的前面、旁邊和後面
Music · Lesson 8 · 音樂・第八課Why Do Some Notes Sound Good Together?為什麼有些音放在一起很好聽？The overtones of a closed pipe and a string follow simple ratios.封閉的管與弦的泛音，遵循簡單的比。Go to the lesson · 前往這一課 →Music · Lesson 2 · 音樂・第二課Why Does a Piano Sound Different from a Violin?同一個音，鋼琴和小提琴為什麼聽起來不一樣？The string’s harmonics, and where you pluck, come from that lesson.弦的諧波，和撥弦的位置，來自那一課。Go to the lesson · 前往這一課 →Music · Lesson 1 · 音樂・第一課Why Are Some Notes High and Some Low?為什麼有的音高、有的音低？A string half as long sounds an octave higher.弦長減半，音高一個八度。Go to the lesson · 前往這一課 →Music · Lesson 10 · 音樂・第十課What Happens Inside a Piano?鋼琴裡面發生了什麼？Next: press a key, and a small hammer strikes a string.接下來：按下琴鍵，小槌敲弦。Go to the lesson · 前往這一課 →
Sources · 資料出處
Names, numbers, and quotations on this page were checked against these sources (October 2026). The shapes of the vibrations are our own simplified drawings, and the sounds are our own simple recipes; the ratios and proportions in the code are covered by automatic tests. · 本頁的名稱、數字與引文依下列資料查證（2026 年 10 月）；振動的形狀是我們自己畫的簡化圖形，聲音是我們自己的簡單配方；程式裡的比例與比例關係有自動測試。
- A system of classification devised by Erich Moritz von Hornbostel and Curt Sachs, first published in 1914; Mahillon divided instruments into four categories by the nature of the sound-producing material; electrophones added by Sachs in 1940; definitions of chordophones, aerophones, membranophones, idiophones霍恩博斯特爾與薩克斯提出的分類，1914 年首次發表；馬約依發聲材料分成四類；電鳴樂器 1940 年由薩克斯加入；弦鳴、氣鳴、膜鳴、體鳴樂器的定義Wikipedia, “Hornbostel–Sachs” ↗
- f = (1/2L)·√(T/μ); the shorter, the tighter, the lighter the string, the higher the frequency of the fundamentalf = (1/2L)·√(T/μ)；弦越短、越緊、越輕，基音頻率越高Wikipedia, “String vibration” and “Mersenne’s laws” ↗
- The greater surface area of the soundboard moves a greater volume of air, producing a louder sound; no amplification occurs, because musicians add no external energy共鳴板的表面積較大，推動較多的空氣，聲音較大聲；沒有放大，因為演奏者沒有加入外來的能量Wikipedia, “Soundboard (music)” and “Acoustic guitar” ↗
- Strings may be struck, plucked, or bowed; bowing causes a stick-slip phenomenon; a longer string gives a lower pitch弦可以敲、撥或用弓拉；拉弓造成黏滑現象；弦越長音越低Wikipedia, “String instrument” ↗
- Open pipes: n = 1, 2, 3…; a closed pipe produces only odd harmonics and sounds an octave lower than an open one; flutes behave as open pipes and clarinets as closed pipes; practical pipes are only approximately harmonic開管 n＝1、2、3……；閉管只有奇數諧波，比開管低一個八度；長笛像開管，單簧管像閉管；實際的管子只是近似諧波Wikipedia, “Acoustic resonance” ↗
- Vibration is started by a reed, by buzzing lips, or by air across an edge; saxophones are typically brass but are woodwinds because of the reed; the pitch depends on the length of the tube; slides and valves change the length振動由簧片、嘴唇或吹過邊緣的氣流開始；薩克斯風通常是銅做的卻是木管樂器，因為簧片；音高取決於管長；滑管與活塞改變長度Wikipedia, “Wind instrument”, “Woodwind instrument”, and “Brass instrument” ↗
- The head’s tension can be adjusted; increased tension raises the frequency; timpani are tuned to specific pitches with a pedal鼓皮的張力可以調整；張力增加頻率升高；定音鼓用踏板調到確定的音高Wikipedia, “Drum” and “Timpani” ↗
- An idealized drumhead is modeled as a circular membrane; zeros 2.40483, 3.83171, 5.13562, 5.52008, 7.01559; the first overtone of the timpano is about 1.6 times its fundamental理想的鼓皮用圓形膜來模擬；貝索函數零點 2.40483、3.83171、5.13562、5.52008、7.01559；定音鼓的第一個泛音約是基音的 1.6 倍Wikipedia, “Vibrations of a circular membrane” and “Overtone” ↗
- Mode frequencies 1.593, 2.135, 2.295, 2.917 times the (0,1) mode; struck at the center a large drum gives a thump with no definite pitch, off center a definite pitch各模式頻率是 (0,1) 模式的 1.593、2.135、2.295、2.917 倍；大鼓在中心敲是沒有確定音高的「碰」，偏離中心敲有確定音高Daniel A. Russell, Penn State, “Vibrational modes of a circular membrane” ↗
- The fundamental depends on tension and density; f01 = (0.766/D)·√(T/σ)基頻取決於張力與密度；f01 = (0.766/D)·√(T/σ)HyperPhysics, “Circular membrane” ↗
- Free-free beam: β₁L = 1.50562π, β₂L = 2.49975π, β₃L = 3.50001π, β₄L = 4.50000π; ω ∝ β²·√(EI/μ)兩端自由的梁：β₁L＝1.50562π、β₂L＝2.49975π、β₃L＝3.50001π、β₄L＝4.50000π；ω ∝ β²·√(EI/μ)Wikipedia, “Euler–Bernoulli beam theory” ↗
- Wood is taken from the middle underside of the bar to lower the pitch; bars are longer at low pitches; the deep arch aligns the modes into consonant intervals: F3, F5, A6從琴鍵底面中間削木頭來降低音高；低音的琴鍵較長；深的弧度讓模式排成協和音程：F3、F5、A6Wikipedia, “Marimba” and “Vibraphone” ↗
- Partials of a well-tuned bell: hum (an octave below the named note), strike tone, tierce (a minor third above), quint (a fifth above), nominal (an octave above)調好音的鐘的泛音：hum（比名義音低八度）、strike（敲擊音）、tierce（高小三度）、quint（高五度）、nominal（高八度）Wikipedia, “Bell (instrument)” ↗
- Timbre depends primarily on the frequency spectrum, although also on the sound pressure and the temporal characteristics of the sound; attack matters for identifying a piano or trumpet音色主要取決於頻率頻譜，也取決於聲壓和聲音在時間上的特性；起音對辨認鋼琴或小號很重要Wikipedia, “Timbre” ↗
- chordophone 弦（絃）鳴樂器, aerophone 氣鳴樂器, membranophone 膜鳴樂器, idiophone 體鳴樂器, electrophone 電鳴樂器chordophone 弦（絃）鳴樂器、aerophone 氣鳴樂器、membranophone 膜鳴樂器、idiophone 體鳴樂器、electrophone 電鳴樂器國家教育研究院「學術名詞資訊網」（音樂名詞） ↗
- 八音: ancient classification by material: metal, stone, silk, bamboo, gourd, clay, hide, wood; bells metal, chimes stone, qin and se silk, xiao and di bamboo, sheng gourd, xun clay, drum hide, zhu and yu wood八音：古代依材料分的樂器分類：金、石、絲、竹、匏、土、革、木；鐘屬金、磬屬石、琴瑟屬絲、簫笛屬竹、笙屬匏、塤屬土、鼓屬革、柷敔屬木教育部《重編國語辭典修訂本》「八音」 ↗
- 管樂器: the air in the tube vibrates, started by breath or lips; pitch set by the length of the tube; 弦樂器: instruments that sound by vibrating strings, usually with a resonance box to increase loudness; 鼓: percussion, skin over hollow wood管樂器：管內空氣振動，由吹氣或振脣開始，音高取決於管長；弦樂器：以弦振動發聲，多有共鳴箱增加響度；鼓：打擊樂器，皮革蒙在中空木桶上教育部《重編國語辭典修訂本》「管樂器」「弦樂器」「鼓」 ↗
- 二胡: bowed string instrument, python skin over the resonator; 梆笛: bamboo, played sideways, one blow hole, one membrane hole, six finger holes二胡：擦弦樂器，琴筒蒙蟒皮；梆笛：竹製、橫吹，一個吹孔、一個膜孔、六個按音孔教育部《重編國語辭典修訂本》「二胡」「梆笛」 ↗
- Taiwan's 12-year curriculum: arts (music) 音 E-Ⅱ-2, 音 E-Ⅲ-2, 音 E-Ⅳ-2十二年國民基本教育課程綱要藝術領域：音 E-Ⅱ-2、音 E-Ⅲ-2、音 E-Ⅳ-2國家教育研究院，十二年國教藝術領域課綱 ↗
- Safe listening: headphone volume to 60% of maximum, personal audio devices less than one hour a day安全聆聽：耳機音量不超過最大的 60%、個人音響裝置每天少於一小時WHO, Make Listening Safe brochure (2021) ↗