MIDI Files of Classical and Recorder Music

The MIDI files and MP3 files presented here are all sequenced by the site owner. They are based on the instrument map of SC-88 (Roland). Please keep in mind that musical expressions intended may not be reproduced faithfully by soft-synthesizers or other sound modules. Copyright You can download and enjoy the music files, but refrain from re-distribution without permission, except for the case that  you use them at a classroom for educational purposes. Please e-mail me when you  use the file(s) as background music of your web page. Mail-address:

Recorder Midi Guitar Midi Other Classical Midi MP3 Files An attempt to the Optimum Temperament Link About me Back to Main

Recorder Midi

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Guitar Midi

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Other Classical Midi

Anonym

Russian folk song
The twelve burglars (4'10" 49K) (00.8.15) (Choir) (Pure)
 (SC-8850 recommended)

American folk song
An old military camp (1'21" 15K) (02.7.30)
Arr: O.Shimizu
(Choir) (Pure)

Bach, Johann Sebastian (1685-1750)

Air (From The Suite No.3 for Orchestra) (4'57" 69K) (01.3.23)
(Strings)
Menuet (1'42" 5K) (02.9.22)
(Harpsicord) (Mean-tone)

Chopin, Frederic (1810?-1849)

Waltz "Puppy" Op.64-1 (2'06" 15K) (04.7.11)
(Piano)

Dowland, John (1563-1626)

"Now, o now I need must part" (2'37" 25K) (00.1.22)
(Choir) (Mean-tone)

Handel, Georg Friedrich (1685-1759)

Concerto Grosso Op.6-10 in D minor (16' 20" 76K) (01.02.24)
Overture-Allegro-Air-Allegro-Allegro-Allegro moderato
(String Orchestra)
Halleluja (3' 56" 47K) (01.07.08)
(Choir, Orchestra, Organ, Harpsicord)

Lassus, Orlande de (1532?-1594)

Echo song (1'36" 41K) (00.1.22)
(Choir) (Mean-tone)

Marschner, Heinrich (1795-1861)

Standchen (2'23" 24K) (02.4.30)
(Choir) (Mean-tone)

Mozart, Leopold (1719-1787)

Kinder Symphonie (10'57" 132K) (04.03.24)
Allegro-Menuetto-Final
(Toys and Strings) (Optimum)

Mozart, Wolfgang Amadeus (1756-1791)

Divertimento No.17 K.334 Mov.3 Menuetto (04'27" 34K) (00.8.23)
(Strings and French Horns) (Mean-tone)
Serenade "Eine kleine Nachtmusik" K.525 (19'31" 175K) (04.4.18)
Allegro-Romanze(Andante)-Menuetto(Allegretto)-Rondo(Allegro)
(Strings)

Vivaldi, Antonio (1678-1741)

Concertos "The Four Seasons"

Spring Op.8-1 (10'33" 60K) (02.03.30)
Summer Op.8-2 (10'26" 85K) (01.09.29)
Autumn Op.8-3 (10'56" 67K) (01.10.12)
Winter Op.8-4 (8'51" 67K) (02.03.06)

Others

From Songs for Schoolchildren in Japan
Arranged for Music Box by Makoyan

Anonym
Chorus of Insects (1'44" 4K) (03.09.08)
Fun in Snowfall (0'54" 3K) (02.05.01)
Winter Night (0'57" 2K) (00.10.08)

Koyama, Sakunosuke (1863-1927)
Summer Has Come! (0'52" 3K) (00.10.08)

Minami, Yoshie (1881-1944)
A Festival of the Village Shrine (1'24" 15K) (02.07.21)

Okano, Tei-ichi (1878-1941)
A Brook in Spring (1'12" 3K) (02.06.01)
Night of Hazy Moon (1'21" 3K) (01.04.25)
Autumn Leaves (1'28" 3K) (00.10.08)
My Home Village (1'22" 3K) (02.05.06)

Hymn <SC88Pro, SC8850 recommended>

Converse, Charles Crozat (1868)
What a Friend (4'06" 15K) (01.02.11) (Choir and Organ) (Pure)
John Hugh McNaughto (1829-1901)
Home (3'58" 42K) (01.02.11) (Choir and Organ) (Pure)

Christmas Songs <SC88Pro, SC8850 recommended>

Gruber, Franz Xerver (1787-1863)
Silent Night (3'13" 12K) (02.11.09) (Choir and Organ)
Mendelssohn, Felix (1809-1847)
Hark! the Herald Angels Sing (3'09" 18K) (02.10.14) (Choir and Organ)
French old Carol
Gloria (3'29" 18K) (02.10.24) (Choir and Organ)
Sicilian melody
O Sanctissima, O Purissima (1'43" 10K) (02.10.30) (Choir and Organ)
English traditional melody
The first Noel the angels did say (2'42" 14K) (02.11.02) (Choir and Organ)
Latin Hymn of 17th or 18th Century
Adeste fidele laeti triumphantes (2'37" 13K) (02.11.03) (Choir and Organ)
Phillips Brooks
O little town of Bethlehem (2'35" 12K) (02.11.04) (Choir and Organ)
Willis, Richard Storrs
lt came upon the midnight clear (2'42" 13K) (02.11.10) (Choir and Organ)
Handel, Georg Friedrich (1685-1759)
Hark, the glad sound! the Saviour comes (1'55" 14K) (02.12.14) (Choir and Organ)

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MP3 Files

　Ｊ．Ｓ．Ｂａｃｈ：　Menuet <Harpsicord> 1'41" 2.374MB

　Ｇ．Ｆ．Ｈａｎｄｅｌ：　Recorder Sonata Op.1-7 in C <Recorder, Harpsicord, and Cello>

Larghetto	2'26"	3.432MB
Allegro	2'18"	3.2240MB
Larghetto	2'04"	2.927MB
A tempo di Gavotti	2'43"	3.841MB
Allegro	2'45"	3.874MB

  L.Sarony/(arr.M.Tahira):　　Swiss melody 　3.205MB (2005.12.6 revised)

  Johann Joachim Quantz:  Trio Sonata in C (Recorder, Flute, Cello, Harpsicord) (2006/06/05)

Affettuoso	3'14"	4.555MB
Alla breve	2'40"	3.754MB
Larghetto	3'31"	4.965MB
Vivace	3'37"	5.095MB

Leopord Mozart: Toy Symphony (Orchestra, Toys) (2006/06/17)

Allegro	4'32"	6.392MB
Menuetto	5'03"	7.124MB
Finale	1'29"	2.102MB

Joseph Haydn : String Quartet Op.3-5 Mov.2 "Serenade"(Alto Recorder 1, Bass Recorder 2, Great Bass Recorder 1) (2006/6/22) (3'22" 4.748MB)

Nine Songs for Japanese School Children　(Music Box) (2006/06/28) (10'50" 15.245MB)

Antonio Vivaldi : Concertos 'Four Seasons' Op. 8 (2006/07/28)

Spring (Op.8-1)	10'39"	14.986MB
Summer(Op.8-2)	10'32"	14.822MB
Fall(Op.8-3)	11'03"	15.544MB
Winter(Op.8-4)	9'43"	13.678MB

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An Attempt to the Optimum Temperament

by Makoyan (August 22, 1999)(Revised, September 8, 1999)

1. Introduction
2. Approach using the least-square method
3. Characteristics of the newly introduced temperament

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1. Introduction

Many of the widely used musical instruments, especially those with a keyboard, and MIDI sound modules are tuned in the '12-tone equal temperament', which consists of 12 tones of equal interval to make up an octave. It has an amazing advantage that it is adaptable to vast variety of tonalities, and its invention, no doubt, greatly enriched musical expressions.

Unfortunately, however, the '12-tone equal temperament' has a weak point that the consonance of the chords is somewhat imperfect. The word 'consonance' implies physically that the frequencies of two tones make a simple ratio. For example, when the ratio of frequencies of 2 tones is 3 to 2, these two tones make a consonant pair. This relationship is called 'pure 5'. Similarly, two tones with frequencies that make a ratio 5 to 4, are also consonant and called 'pure major 3'.

The intervals of 'pure 5' and 'pure major 3' are quite close to the 'perfect 5' and the 'major 3' in the equal temperament, respectively, as shown below, and the equal temperament is accepted widely with no serious problems. But, for ones that seek for more consonant music the difference is sometimes not small enough to be negligible.

According to literature, the 12-tone equal temperament had not been spread in Europe until the end of 19'th century, and musical instruments in old time were tuned in various ancient temperaments, for example, Pythagorean, Meantone, Werkmeister's and Kirnberger's. One of the common characteristics of these ancient temperaments is that some reference intervals such as 'pure 5' or 'pure major 3', all distinguishable by ear were used to determine the pitch of individual tones, because the musical instruments had to be tuned by ear. Depending on what reference intervals to be adopted and where to apply them, various types of temperaments were invented after repeated try and error.

Once a new temperament was introduced, its characteristics were examined, for example, how it can harmonize tonic, dominant and sub-dominant chords in one tonality, and how it has to sacrifice consonance of the chords in other tonalities. In general, the more a temperament is specialized in one tonality, the poorer is the consonance in other tonalities.

Recent development of technology is now making it possible to tune musical instruments with electronic methods instead of the well-trained ear. Then, in building a temperament we can forget the reference intervals. Now that we are free from the reference intervals, we can reverse the procedure. First we give the conditions of a temperament by describing the extent of specialization to one tonality. Then we seek for a unique solution that satisfies the given conditions best. We adopt a technique of the least-square method, which is popular in the Theory of Error. The new temperament thus obtained will be called the 'Optimum Temperament'.

2. Approach using the least-square method

We consider the twelve tones [C, C#, D, Eb, E, F, F#, G, Ab, A, Bb, B] that make up an octave. The pitch of these tones are denoted using lower-case characters as [c, c#, d, eb, e, f, f#, g, ab, a, bb, b]. For expressing the pitch we use a unit called 'cents'. A cent is 1/100 of the interval of semitone in the '12-tone equal temperament'. The origin is placed at C (c=0). Then, in the '12-tone equal temperament', we can write

c=0
c#=100
d=200
eb=300
e=400
f=500
f#=600
g=700
ab=800
a=900
bb=1000
b=1100

In terms of cents, the intervals of the 'pure 5' and 'pure major 3' are expressed as 702 and 386 cents, respectively, and are a little different from the 'perfect 5' (700) and 'major 3' (400) in the equal temperament. Usually most of us are not aware of the little dissonance of the chords in the equal temperament, but it is worthwhile to seek for a more consonant scale.

First, we will try to find a scale in which every 'perfect 5' is 702 cents and every 'major 3' is 386 cents. The requirements are written as,

g-c=702
ab-c#=702
a-d=702
bb-eb=702
b-e=702
c-f=702-1200
c#-f#=702-1200
d-g=702-1200
eb-ab=702-1200
e-a=702-1200
f-bb=702-1200
f#-b=720-1200

e-c=386
f-c#=386
f#-d=386
g-eb=386
ab-e=386
a-f=386
bb-f#=386
b-g=386
c-ab=386-1200
c#-a=386-1200
d-bb=386-1200
eb-b=386-1200

These are a set of simultaneous equations for the variables [c, c#, d, eb, e, f, f#, g, ab, a, bb, b]. Since we know that c=0, the number of unknowns is 11, while the number of equations is 24, and therefore, it is not possible to find solutions that strictly satisfy all of the requirements.

Then we will seek for solutions that best fit the requirements as follows. Even though the given conditions are written as a set of equalities, the left-hand side does not coincide with the right-hand side, and the small discrepancies are taken as errors. We seek for [c, c#, d, eb, e, f, f#, g, ab, a, bb, b] that makes the sum of these errors squared minimum. This is the principle of the least-square method. For detailed procedure the readers are referred to some math textbook. Anyway, the solutions that best fit the given simultaneous equations are,

c=0
c#=100
d=200
eb=300
e=400
f=500
f#=600
g=700
ab=800
a=900
bb=1000
b=1100

These are nothing but the equal temperament! In other word, if we seek for pitches of the twelve tones that apply equally to every tonality, the resulting solution is the 'equal temperament', and this is not surprising.

Now we will proceed to the next stage. In the above discussion, we gave exactly the equal importance to all of the 24 equations. Instead, we assign different importance to each of the members of the simultaneous equations. Here, we will seek for solutions favorable to C-major. We also give some considerations to A-minor as a relative key. The conditions are as follows:

(1) We assume the following equations to be five times as important. These are major 3's that appear in the tonic, dominant and sub-dominant chord in C-major.

e-c=386
a-f=386
b-g=386

(2) Similarly, we assume that the following equations are three times as important, for they appear in perfect 5 in the tonic, dominant and sub-dominant in C-major.

g-c=702
d-g=702-1200
c-f=702-1200

(3) We give some consideration to the perfect 5, D-A, which appears by extension of dominant chord further up by 5 degrees, giving it a weight 2.

a-d=702

(4) Next, we consider the consonance of A-minor. For major 3, we give a weight 3 to the following equation that appears in the dominant chord in A-minor.

ab-e=386

(5) Also, we give a weight 2 to the following two equations that appear in A-minor.

b-e=702
e-a=702-1200

(6) Finally, all other equations have a weight 1.

ab-c#=702
bb-eb=702
c#-f#=702-1200
eb-ab=702-1200
f-bb=702-1200
f#-b=720-1200
f-c#=386
f#-d=386
g-eb=386
bb-f#=386
c-ab=386-1200
c#-a=386-1200
d-bb=386-1200
eb-b=386-1200

Now we completed all the conditions by giving different weights to the members of the simultaneous equations. To give a weight 5 to some equation, for example, implies that the equation appears five times in the set of simultaneous equations. In the strict algebra, multiple description of the same equation in a set of simultaneous equations does not make sense, but in the treatment of Error it does.

The solutions that best fit the given conditions are obtained using the least-square method and the results are,

c=0
c#=93
d=196
eb=293
e=391
f=500
f#=594
g=699
ab=789
a=891
bb=996
b=1090

These are the 12 tones in the Optimum Temperament obtained under conditions (1) - (6).

3. Characteristics of the newly introduced scale

We can check the behavior of the Optimum Temperament obtained in the previous section using the Consonance Diagram as shown above. The twelve axes correspond to the twelve tones C, G, D, ..... , Bb and F, respectively. The coordinate on each axis indicates how a given interval, say, major 3 made upon the note of the axis is close to the that in just intonation. For example, take a look at the red line, which shows the consonance of major 3 in the Optimum Temperament. The coordinate of the red line on the C-axis is read as 5. This indicates the following situation. Using the conclusion in the previous section, the interval of major 3 upon C is evaluated as,

e-c=391-0=391

This is larger than the pure major 3 (386) by 5 cents. Then, the coordinate of the red line on the C-axis is 5. Similarly, the coordinate of the red line (major 3) on the G-axis is,

b-g-386=1090-699-386=5

The dark blue line indicates the consonance of perfect 5. For example, the perfect 5 on C is evaluated as,

g-c-702=699-0-702=-3

which implies that the perfect 5 on C is smaller than the pure 5 by 3 cents. Likewise the green line indicates the consonance of minor 3.

For comparison, consonance for the equal temperament is also shown on the diagram (perfect 5 by light blue line, major 3 by pink line and minor 3 by orange line).

The diagram clearly shows that the consonance of tonic (C-E-G), dominant (G-B-D) and sub-dominant (F-A-C) in C-major are much better than in the equal temperament. Chords (A-C-E), (E-As-E) and (D-F-A) in A-minor are also acceptable. The intervals of major 3 on Eb, Ab, C# is somewhat large, but these intervals seldom appear in C-major or A-minor and this does not bring about serious dissonance. Other intervals are more or less like those in the equal temperament, and the readers will easily see the advantage of the Optimum Temperament.

For guests who use a GS sound module, a MIDI file ('The Wild Roses' by Werner) is given below to compare several different scales. The same melody will be repeated three times, first in equal temperament, next in just intonation, and last in Optimum Temperament. Note that all the tuning controls are executed by sending system exclusive messages of GS format, and ignored by other sound modules.

nobara_epo.mid

Some other MIDI files tuned in the Optimum Temperament are presented on Makoyan's MIDI page. I hope you enjoy the beautifully harmonized music.

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About me

Nickname: Makoyan, or some American friends call me Mako..

Born on May 25, 1941. My birthday may have something to do with the fact
that I love 'Eine kleine Nachtmusik'(K525)!

Brought up in a beautiful, small village in Shimane Prefecture, western Japan.

Job: I used to teach Earth sciences in a teachers college. Majored in Geophysics
(Meteorology), but now retired. Received the degree of Ph.D. in Science from Kyoto University.
Major interest  has been in detecting weak infrasound, or sound waves with frequencies
lower than the limit of human audibility. Infrasound arrives from distant volcanic
eruptions, ocean waves in stormy regions, violent convective clouds, earthquakes,
etc. Indeed, I enjoy music originated by the Nature.

Other hobbies: Wandering about nearby mountains and hills. I also enjoy golf.

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