Semester 1, Academic Year 2017/2018

Two lectures a week (BOTH to be attended):
Monday from 2 pm to 4 pm at LT27 and
Thursday from 2 pm to 4 pm at LT27. 

Lecturer: Prof Bernard Tan, email:
Tutor: Ms Lydia Lam, email:

Class tutorials will be held at the Computer Lab 1 at Block S13, i.e. S13-M-09. 

The tutorial class list is here.


Tutorial set no. 1 and the answers.

Tutorial set no. 2 and the answers.

Tutorial set no. 2.5 with answers.

Tutorial set no. 3 and the answers.

Tutorial set no. 4 and the answers.

Tutorial set no. 5 and the answers.

Tutorial set no. 6 with answers.


Prof Bernard Tan will be attending a Government international panel meeting on Thursday 7 September 2017, and will also be overseas in the second half of September 2017 to attend an international conference as a representative of the Government.

The lectures on Thursday 7 September 2017, Monday 18 September 2017 and Thursday 21 September 2017 will carry on as usual. However, these three lectures will feature video lectures prepared by Prof Tan in place of his lectures. The lecture slides for these three lectures will be posted in advance. Lectures by Prof Tan will resume as usual on Monday 2 October 2017.

Video lecture no. 8 on YouTube.

Video lecture no. 11 on YouTube.

Video lecture no. 12 on YouTube.

Video lecture no. 13 on YouTube.


Mid-term Test: Monday 9 October 2017 (week 8), 2 pm to 4 pm.

The venue and seating plan for the Mid-term Test are here, and also posted outside S12-04-02.

The Mid-term Test will cover all the topics dealt with in lectures 1 to 11 as defined by the Powerpoint slides.

End-of-term Test: Thursday 16 November 2017 (week 13), 2 pm to 4 pm.

The venue and seating plan for the End-of-term Test are here, and also posted outside S12-04-02.

The End-of-term Test will cover all the topics dealt with in the entire series of lectures.

The venues and seating plans for the both Tests will be announced a few days before each Test. Both tests are within scheduled lecture slots.

The tests will be open book tests.

Both tests will consist of multiple-choice questions. Answers are to be given on a computer mark card, using a pencil.

Please bring your matriculation card and NRIC with you for identification.

Make-up tests for students who have valid reasons for missing the tests, i.e. either a valid MC or official leave granted by the University, will be scheduled in the week following each test.

MCs must be submitted within 24 hours of a Test to the Lecturer, Tutor or to Mdm Pang at the 1st year Physics Laboratory, S12, level 4.

Mid-term Test answers and results.


Every student is required to submit an essay as an individual project.

The essay should be on the following topic:

Attend a musical concert or any live musical performance, which could be an SSO concert, a musical or an opera, a pop/rock concert, a jazz concert, a Chinese orchestra concert or any concert, performance or event in which the LIVE performance of music is the main focus (this excludes plays or ballet/dance performances), and say in your own words how and why you have enjoyed (or not enjoyed) the performance. You should include some comments on how and why science and/or technology may have had an effect (positive or otherwise) on your musical experience and why, but the main focus of the essay should be on your personal views of the concert performance. The essay should be written from the point of view of a member of the audience, and NOT as one of the performers.

In addition to concerts which you plan to attend, you may also write about a concert you have recently attended (within the last 3 months). This will include concerts during the months of May, June and July 2016. The concert should be a formal performance by live performers for an audience lasting at least 45 minutes. The concert may be either in an indoor or outdoor venue, and need not be a ticketed fee-paying performance.

You need not confine your essay to the content of the lectures. The essay should express your own opinions, and will be graded on content and writing ability.

The essay should have not less than 200 words or more than 800 words and should be written in English. If other languages are used in, for examples, titles of musical pieces, an English translation should be provided. The essay should consist only of text and should NOT include any photographs or illustrations. Any references or bibliography should be included in the word count.

It MUST be entirely your own and unaided work.

The essay should be submitted as a Microsoft Word file with the name:
where xxxxxxxxx is your matriculation number. Please put the number of words and your matric. number at the end of your essay but do NOT include your name.

The submission deadline is at the end of week 10 of the semester, at midnight of Saturday 28 October 2017 i.e. the midnight between Saturday 28 October and Sunday 29 October.

The IVLE workbin for the submission of the Essay project files will be open a few days before the submission deadline. Please do NOT email your essay files to me.


Yong Siew Toh Conservatory of Music.

The Centre for the Arts.

Singapore Symphony Orchestra.

Singapore Chinese Orchestra.

The Esplanade - Theatres on the Bay.


Every student is required to submit a MIDI music composition as an individual project.

The MIDI music composition is an electronic/computer music piece in MIDI format lasting at least 20 seconds, but not more than 60 seconds. MIDI files lasting less than 20 seconds and more than 60 seconds will be penalized.

The piece MUST be an original piece and NOT an arrangement of an existing piece of music.

It should be for at least two different General MIDI (GM) instruments, and for not more than five different General MIDI (GM) instruments. You are permitted to use any GM instruments except for instruments no. 121 to 128. Whatever number of GM instruments you choose to use from two to five, they should all be different instruments i.e. if you use the same instrument twice for more than one track/channel, it will be considered one instrument.

Your MIDI piece must begin with not more than two GM instruments, and continue thus for at least 8 seconds. Additional GM instruments should only enter the music after 8 seconds. (You are of course free to use only two instruments for the entire piece.)

If you intend to use the channel 10 percussion instruments, this will count as one instrument.

The list of GM instruments is in this file.

The piece MUST be entirely your own and unaided work.

The completed MIDI piece should be submitted in the form of a computer file in Standard MIDI format (SMF) with the name:


where xxxxxxxxx is your matriculation number.

You may use any music software to write the piece, as long as it is submitted as a MIDI in Standard MIDI format.

One freely available piece of software which you can use is Anvil Studio, which is only available for Windows. Mac OS X users can use MidiSwing or Melody Assistant (which is also available for Windows). To obtain these freeware/shareware software packages, please see the links below.
Please note that to export Melody Assistant files to MIDI format, you will need to register and pay a fee of US$20.

The submission deadline is midnight of Saturday 18 November 2017 i.e. the midnight between Saturday 18 November and Sunday 19 November.

MIDI files are to be submitted into the IVLE MIDI workbin which will be open a few days before the submission deadline.

MIDI sequencers

Anvil Studio for Windows.

MidiSwing for Mac OS X.

Melody Assistant for Windows and Mac (OS 8, 9 and X).

MuseScore, a freeware music notation program with MIDI output.


25% Mid-term Class Test
25% End-of-term Class Test
20% Essay Project
20% MIDI Music Project
10% Tutorial Attendance

Please note:

1. For students who have missed a test with valid reasons, a make-up test will be organised and administered within the following week.

2. For tutorial attendance, there will be no more accepting of MCs. If students are ill on the day of the tutorial, they must attend another tutorial in the same cycle to make up.

3. For homework assignments, again no MCs will be accepted as an excuse for not submitting the assignments.


Lecture 1 in ppt format.

Lecture 2 in ppt format.

Lecture 3 in ppt format.

Lecture 4 in ppt format.

Lecture 5 in ppt format.

Lecture 6 in ppt format.

Lecture 7 in ppt format.
Please note corrections in slide 18 to the ratios for the notes G and A.

Lecture 8 in ppt format.

Lecture 9 in ppt format.

Lecture 10 in ppt format.
Please note that a more up-to-date version of Lecture 10 has just been uploaded.

Lecture 11 in ppt format.

Lecture 12 in ppt format.

Lecture 13 in ppt format.

Lecture 14 in ppt format.

Lecture 15 in ppt format.

Lecture 16 in ppt format.

Lecture 17 in ppt format.

Lecture 18 in ppt format.

Lecture 19 in ppt format.

Lecture 20 in ppt format.
Please note the correct version of lecture 20 has now been posted. The incorrect version had slides 2 to 8 which were not meant to be released.

Lecture 21 in ppt format.

Lecture 22 in ppt format.

Musical Examples from YouTube

Beethoven's Symphony No. 5, 1st Movement.
Performance by BBC Symphony Orchestra conducted by Daniel Barenboim.
Performance by Gothenburg Symphony Orchestra conducted by Gustavo Dudamel.

Example of 3/4 time signature: Tchaikovsky's Symphony No. 5, 3rd Movement.
Performed by Amsterdam Symphony Orchestra conducted by Peter Santa.

Example of 5/4 time signature: Tchaikovsky's Symphony No. 6, 2nd Movement.
Performed by State Symphony Orchestra of Tatarstan conducted by Feodor Gluschenko.
Performed by Orchestra del Teatro alLa Scala Milan Tatarstan conducted by Yuri Temirkanov.

Example of 5/4 time signature in jazz: Take Five.
Dave Brubeck Quartet (1961).

Example of melody with several notes of the same pitch: One Note Samba by Antonio Carlos Jobim.
Performed by Sharon Clark Quintet.

Example of choral piece demonstrating unison singing: Khwaja Mere Khwaja by A R Rahman.
Excerpt from movie Jodhaa Akbar.

Example of choral piece demonstrating harmonic and contrapuntal aspects of music: Hallelujah Chorus from Handel's Messiah
Performance showing musical score.
Performance by Choir of King's College Cambridge.
Performance by Kampong Kapor Methodist Church Chancel Choir.

Example of how music is built from notes of a scale:
Do Re Mi from Rodger's and Hammerstein's The Sound of Music sung by Julie Andrews.

The Pitch Helix

Two diagrams showing the pitch helix are here.

Musical examples from the dulcimer, clavichord, harpsichord and fortepiano and videos of buskers

Katsutaga Tsutsiu's webpage with examples from Japanese made replicas of antique keyboard instruments and actual antique pianos.

The Classical Harpsichord Music Page.

Cimbalom player in Salzburg, September 2009.

Cimbalon player in Vienna, September 2010.

Bottle organ/marimba player in Vienna, September 2011.

Barrel organ player in Prague, September 2011.

Trio consisting of cimbalon, contrabass balalaika and accordion in Vienna, September 2012.

Online Webpianos

Webpiano from a guitar teaching website.

Daniel Laberge's webpiano.

88-key realistic virtual piano.

Webpiano for online piano lessons using Macromedia flash.

Tuning and Temperament webpages

Scale (an elementary explanation).

Alternate Temperaments: Theory and Philosophy.

Just Temperament and Others.

The Theory Behind Chinese Music.

Listening to Balinese Gamelan.

Rainer Pusch's Guide to Talas and Ragas.

Links to piano action diagrams and animations

YouTube video of Cristofori piano action.

K. Wayne Land's piano action page.

Upright piano action.

Steve's Piano Service piano action page.

The piano deconstructed.

Physics and sound webpages

University of New South Wales webpage on Physics of Music.

Website on the Mexican wave (La Ola).

Beats demonstration.

Video demonstration on beats.

Automatic pianos at the Musee Mecanique, San Francisco (2004)

A player piano showing its mechanism.

Close-up of the paper roll mechanism.

Another view of the paper roll.

Another player piano, with the paper roll in place of the keyboard.

Musee Mecanique website.

Youtube video on manufacture of player piano rolls.

Miscellaneous photographs of exhibits at the Haus der Musik (House of Music) Vienna (2009)

A dancing master's violin.

A square piano with a keyboard of 5 and half octaves, probably dating from the time of Beethoven.

An early six-string guitar dating from the time of Schubert.

A mechanical music box cylinder mechanism with the music of a Viennese waltz.

Weblink to the Haus der Musik (House of Music), Vienna.

YouTube videos on music boxes

How a music box works.

Reuge 72 note 15 song music box .

Reuge 144 note Grand Cartel music box.

Paper roll music box.

MIDI files

Large MIDI music archive.

Composers Offering MIDI Files on the Net.

Classical Piano MIDI Files.

Jazz MIDI Files.

Links to FM MIDI players and FM software synthesizers

The fmmidi download page.
Fmmidi is a MIDI player (with versions for Windows, Mac OS X and Java) which emulates the OPL4, a 2/4-operator FM synthesis chip. Simply drag your MIDI file onto the fmmidi window, and it will start to play. Please note that the Windows version has menus in Japanese, and the names of the GM instruments are also in Japanese. However, you can deduce which GM instruments are being played from the number of the instrument (with number 0 for Acoustic Grand Piano).

Home page of the FM8.
The FM8 is the successor to the FM7, a software synthesizer created by Native Instruments which emulates all the functions of the legendary 6-operator Yamaha DX7 FM synthesizer. The FM8 costs US$199.

Dave Benson's DX7 page.
His excellent book on Mathematics and Music can be found here.


Intervals and Scales

Equal-tempered fifth followed by Pythagorean/Just fifth

Pythagorean scale
Just scale
Equal-tempered scale

Back to Bernard Tan's home page