晨起見藍天，漫步之林野，喜逢

雙鶴展翼翱翔而飛。隨口吟著鮑照之

  舞鶴賦

散幽經以驗物，偉胎化之仙禽。鍾浮曠之藻質，抱清迥之明心。指蓬壺而翻翰，望昆閬而揚音。澘日域以回騖，窮天步而高尋。踐神區其既遠，積靈祀而方多。精含丹而星曜，頂凝紫而煙華。引員吭之纖婉，頓修趾之洪姱。疊霜毛而弄影，振玉羽而臨霞。朝戲於芝田，夕飲乎瑤池。厭江海而游澤，掩雲羅而見羈。去帝鄉之岑寂，歸人寰之喧卑。歲崢嶸而愁暮，心惆悵而哀離。

於是窮陰殺節，急景凋年。骫沙振野，箕風動天。嚴嚴苦霧，皎皎悲泉。冰塞長河，雪滿群山。既而氛昏夜歇，景物澄廓。星翻漢回 ，曉月將落。感寒雞之早晨，憐霜雁之違漠。臨驚風之蕭條，對流光之照灼。唳清響於丹墀，舞飛容於金閣。始連軒以鳳蹌，終宛轉而龍躍。躑躅徘徊，振迅騰摧。驚身蓬集，矯翅雪飛。離綱別赴，合緒相依。將興中止，若往而歸。颯沓矜顧，遷延遲暮。逸翮後塵 ，翱翥先路。指會規翔，臨岐矩步。態有遺妍，貌無停趣。奔機逗節，角睞分形。長揚緩騖，並翼連聲。輕跡凌亂，浮影交橫。眾變繁姿，參差洊密。煙交霧凝，若無毛質。風去雨還，不可談悉。既散魂而蕩目，迷不知其所之。忽星離而雲罷，整神容而自持。仰天居之崇絕，更惆悵以驚思。

當是時也，燕姬色沮，巴童心恥。巾拂兩停，丸劍雙止。雖邯鄲其敢倫，豈陽阿之能擬。入衛國而乘軒，出吳都而傾市。守馴養於千齡，結長悲於萬里。

信步而走，不覺漸入深林，幾聲鶴鳴，方回過神來。怎到了古澤邊兒了。此間雖然聽聞絕美，四處流沙陷土極度危險。既來之，則安之。何不趁此刻細細瞧瞧，只要小心謹慎就好。此景只原夢裡有，盎然生趣是仙鄉。一時薄霧轉濃，雖然狐疑，終究不是久待之地。出林後，看那日頭，分明已過了晌午，得敢緊尋路兒歸。

 

派︰雖然夏日天光長，一溜眼兒就過。欲用『十二律 』通『五聲調式』，得加緊腳步。更別說，尚不知那『蜂鳴器』它到底行是不行？！

五聲調式，或稱五聲音階，是由5個音構成的一種調式。但不是隨意5個音構成的調式都是五聲調式，五聲調式是由按照純五度排列起來的五個音所構成。在中國音樂中，這5個音依次定名為宮、商、角（jué，ㄐㄩㄝˊ）、徵（zhǐ，ㄓˇ）、羽，大致相當於西洋音樂簡譜上的唱名（mi）、（so）、（la）、（do）、（re）。

將這五個音按高低次序移到一個八度之內，各音的名稱便是：

１　２　３　５　６

宮　商　角　徵　羽

宮、商、角、徵、羽這五個音相互間的音程關係是固定不變的。如：

五聲調式中的任何一個音均可構成一種調式，以宮音作主音構成的調式叫宮調式；以商音作主音構成的調式叫商調式；以此類推。

後來，再加上變宮（宮的低半音，即（si））和變徵（徵的低半音，即（升fa）），稱為七聲或七音。

【五聲的聲學性質】

中國音樂選定這五種相對音高做為旋律的基礎，是來自於三分損益法前五音的結果。

在司馬遷的《史記》 「律書第三」中寫到：「……九九八十一以為宮。三分去一，五十四以為徵。三分益一，七十二以為商。三分去一，四十八以為羽。三分益一，六十四以為角。」意 思是說，如果我們先取一根長度為81單位的竹管用來定為「宮音」，用三分損益法便可以依序求得「徵音」、「商音」、「羽音」、「角音」的長度分別為54、 72、48、64。中國的「三分損益」或「五度相生」，在這五個相對音高與純律所取得的結果是相同的。

聲學理論中，以上的長度可視為基音的波長（由於竹管兩端是開放端，故管長正比於基音的波長），並與其頻率音高成反比。在下面列表中可以看出前五個音之間都成簡單的整數比，而這正是構成和弦的基礎。因為這五音容易構成和諧的優點，所以古代中國便採取宮商角徵羽作為作曲旋律的基礎。

	宮(81)	商(72)	角(64)	徵(54)	羽(48)
宮(81)	–	8/9	64/81	2/3	16/27
商(72)	9/8	–	8/9	3/4	2/3
角(64)	81/64	9/8	–	27/32	3/4
徵(54)	3/2	4/3	32/27	–	8/9
羽(48)	27/16	3/2	4/3	9/8	–

 

生︰《  》網上講︰

Interrupter bells

Electric bell

How it works

The most widely used form is the interrupter bell, which produces a continuous sound when current is applied. See animation, above. The bell or gong (B), which is often in the shape of a cup or half-sphere, is struck by a spring-loaded arm (A) with a metal ball on the end called a clapper, actuated by an electromagnet (E). In its rest position the clapper is held away from the bell a short distance by its springy arm. When an electric current is enabled to pass through the winding of the electromagnet (via a closing of the switch (K) i.e. pressing the door bell) it creates a magnetic field that attracts the iron arm of the clapper, pulling it over to give the bell a tap. This opens a pair of electrical contacts (T) attached to the clapper arm, interrupting the current to the electromagnet. The magnetic field of the electromagnet collapses, and the clapper springs away from the bell. This closes the contacts again, allowing the current to flow to the electromagnet again, so the magnet pulls the clapper over to strike the bell again. This cycle repeats rapidly, many times per second, resulting in a continuous ringing.

The tone of the sound generated depends on the shape and size of the bell or gong resonator. Where several bells are installed together, they may be given distinctive rings by using different size or shapes of gong, even though the strike mechanisms are identical.

Another type, the single-stroke bell, has no interrupting contacts. The hammer strikes the gong once each time the circuit is closed. These are used to signal brief notifications, such as a shop door opening for a customer, rather than continuous warnings.

Buzzers

An electric buzzer uses a similar mechanism to an interrupter bell, but without the resonant bell. They are quieter than bells, but adequate for a warning tone over a small distance, such as across a desktop.

A buzzer or beeper is an audio signalling device, which may be mechanical, electromechanical, or piezoelectric. Typical uses of buzzers and beepers include alarm devices, timers and confirmation of user input such as a mouse click or keystroke.

With the development of low cost electronics from the 1970s onwards, most buzzers have now been replaced by electronic ‘sounders’. These replace the electromechanical striker of a bell with an electronic oscillator and a loudspeaker, often a piezoelectric transducer.

 

△  Buzzer circuits 蜂鳴器的驅動線路

記得 W!o 曾傳有一 圖，

，卻難按圖索驥。一般總是用『方波』，就以 PWM 實驗之，看它終究能還不能！？

△ 因測試，暫假『十二平均律』，借用『 Piano key frequencies 』作五階八度『音高』表︰

C Do 65.4064 130.813 261.626 523.251 1046.50
D Re 73.4162 146.832 293.665 587.330 1174.66
E Mi 82.4069 164.814 329.628 659.255 1318.51
F Fa 87.3071 174.614 349.228 698.456 1396.91
G So 97.9989 195.998 391.995 783.991 1567.98
A La 110.000 220.000 440.000 880.000 1760.00
B Si 123.471 246.942 493.883 987.767 1975.53

音符之『時值』以及樂曲的『速度』，以

四分音符為一拍，每分鐘七十二拍

為準。

 

碼︰無 習。

☿ 行︰就先從音頻音域探索開始︰

pi@raspberrypi ~ $ sudo -s
root@raspberrypi:/home/pi# python3
Python 3.2.3 (default, Mar  1 2013, 11:53:50) 
[GCC 4.6.3] on linux2
Type "help", "copyright", "credits" or "license" for more information.
>>> import RPi.GPIO as GPIO
>>> GPIO.setmode(GPIO.BCM)
>>> from time import sleep
>>> 針碼 = 11
>>> GPIO.setup(11, GPIO.OUT, initial=GPIO.HIGH)
>>> 音符 = [130.8, 146.8, 164.8, 174.6, 195.9, 220.0, 246.9]
#
>>> 音響 = GPIO.PWM(11, 0)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
ValueError: frequency must be greater than 0.0
#
>>> 音響 = GPIO.PWM(11, 130.8)
>>> 音響.start(100)
>>> 音響.start(0)
>>> 音響.start(100)
>>> def 測試(音符):
...     for 音 in 音符:
...         音響.ChangeFrequency(音)
...         音響.start(50)
...         sleep(60/72)
...         音響.start(100)
... 
>>> 音符一 = [65.4, 73.4, 82.4, 87.3, 97.9, 110.0, 123.4]
>>> 測試(音符一)
>>> 音符二 = [130.8, 146.8, 164.8, 174.6, 195.9, 220.0, 246.9]
>>> 測試(音符二)
>>> 音符三 = [261,6, 293.6, 329.6, 349.2, 391.9, 440.0, 493.8]
>>> 測試(音符三)
>>> 測試(音符三)
>>> 音符四 = [523.2, 587.3, 659.2, 698.4, 783.9, 880.0, 987.7]
>>> 測試(音符四)
>>> 測試(音符四)
>>> 音符五 = [1046.5, 1174.6, 1318.5, 1396.9, 1567.9, 1760.0, 1975.5]
>>> 測試(音符五)
>>> 測試(音符五)
>>> 測試(音符二)
>>> 測試(音符一)
>>> 測試(音符三)
>>> 測試(音符四)
>>> 測試(音符五)
# 
>>> 音符六 = [2*1046.5, 2*1174.6, 2*1318.5, 2*1396.9, 2*1567.9, 2*1760.0, 2*1975.5]
>>> 測試(音符六)
>>> 測試(音符六)
>>> 音符七 = [4*1046.5, 4*1174.6, 4*1318.5, 4*1396.9, 4*1567.9, 4*1760.0, 4*1975.5]
>>> 測試(音符七)
>>> 測試(音符七)
>>> 音符八 = [8*1046.5, 8*1174.6, 8*1318.5, 8*1396.9, 8*1567.9, 8*1760.0, 8*1975.5]
>>> 測試(音符八)
>>> 測試(音符八)
>>> 測試(音符六)
>>> 測試(音符七)
>>> 測試(音符五)
>>> 測試(音符八)
>>> 

，音階聽來是高頻的較準。接著嘗試音符響應速度︰

>>> 音高表 = {"C-":2*1046.5, "D-":2*1174.6, "E-":2*1318.5, "F-":2*1396.9, "G-":2*1567.9, "A-":2*1760.0, "B-":2*1975, 
...           "C":4*1046.5, "D":4*1174.6, "E":4*1318.5, "F":4*1396.9, "G":4*1567.9, "A":4*1760.0, "B":4*1975, 
...           "C+":8*1046.5, "D+":8*1174.6, "E+":8*1318.5, "F+":8*1396.9, "G+":8*1567.9, "A+":8*1760.0, "B+":8*1975,}
>>> 小蜜蜂音高 = ["C","E","E","F","D","D","C","D","E","F","G","G","G","G","E","E","F","D","D","C","E","G","G","E","D","D","D","D","D","E","F","E","E","E","E","E","F","G","G","E","E","F","D","D","C","E","G","G","C"]
>>> 小蜜蜂時值 = [1,1,2,1,1,2,1,1,1,1,1,1,2,1,1,2,1,1,2,1,1,1,1,2,1,1,1,1,1,1,2,1,1,1,1,1,1,2,1,1,2,1,1,2,1,1,1,1,4]

>>> def 播歌(音高列,時值列):
...     for 指標 in range(len(音高列)):
...         音響.ChangeFrequency(音高表[音高列[指標]])
...         音響.start(50)
...         sleep(60/72 * 時值列[指標])
...         音響.start(100)
... 
>>> 播歌(小蜜蜂音高, 小蜜蜂時值)

>>> def 播歌一(音高列,時值列):
...     for 指標 in range(len(音高列)):
...         音響.ChangeFrequency(音高表[音高列[指標]+"-"])
...         音響.start(50)
...         sleep(60/72 * 時值列[指標])
...         音響.start(100)
... 
>>> 播歌一(小蜜蜂音高, 小蜜蜂時值)

>>> def 播歌二(音高列,時值列):
...     for 指標 in range(len(音高列)):
...         音響.ChangeFrequency(音高表[音高列[指標]+"+"])
...         音響.start(50)
...         sleep(60/72 * 時值列[指標])
...         音響.start(100)
... 
>>> 播歌二(小蜜蜂音高, 小蜜蜂時值)
>>> 

，怕是五音不全的耶！大概真的只能作『 Beeper 』嗶嗶响用了？

 

訊︰☿☹☺ 卻憶起《世說新語‧言語》:

謝太傅寒雪日內集，與兒女講論文義。俄而雪驟，公欣然曰：白雪紛紛何所似？兄子胡兒曰：撒鹽空中差可擬。兄女曰：未若柳絮因風起。公大笑樂。即公大兄無奕女，左將軍王凝之妻也。

也許真真是為難了那一個『小哨子』的吧！！☺☺