Musical Diary

Musical Diary - 14 February 2010 - Auckland New Zealand

My musical 'discoveries' of yesterday and today have made me think I should keep a diary to document my efforts.


Yesterday I worked out a simple 'how to use the fingers' method that enables me easily to play the natural minor scale for any major scale. Since this is the first entry, I will describe the method that I worked out before yesterday to play any major scale easily.

Preliminary: Any key (white or black that we press to make a sound) is separated from the immediately adjacent key (white if the first key is black and either black or white if the first key is white) by a semitone. If we pass over the immediately adjacent key to the next one, then the interval is a full tone. The major scale beginning from any of the twelve keys from C to the next B inclusive follows the interval sequence


where the hyphens represent the keys we press, where the T's stand for the full tone interval, and where 's' stands for the semitone interval.

Before the first semitone, we press three keys, and I do this with the first three digits of my right hand - thumb, index finger, and middle finger. At this point, which coincides with the first semitone, I switch back to the thumb. Then the next four keys are pressed with thumb through ring finger. If only one octave is to be played, and that is all I am interested in at the moment because I just want to study the scales, then the pinky strikes the last key. The second semitone is at the end going up, and at the beginning going down. The first semitone is at the thumb shift both going up and going down. These considerations apply to all twelve major scales, and this makes them easy to play, because I know where to look for the semitone, and elsewhere the interval is a full tone.

For the natural minor scales, the interval sequence is


I start on the index finger and do the thumb shift at the semitones: The shift to or from the thumb occurs after or before the middle finger is used, and this is where to look for the semitone. This ends on the middle finger which is ideal if it is desired to continue another octave. The ring finger would press the next key, and the same pattern would then be repeated. I chose to begin on the index finger because it was much less stressful for the hand.


Please consider the following image:

All three scores are for the German national anthem.

The first was copied from the internet, and it uses the major scale that begins on E-flat. I have a recording obtained from the same web page as the score. I often play along while the recording is playing using this first score. This keeps the correct tune in my head.

The other two scores were constructed while I was studying the circle of fifths. It seems that the major scale which begins on B has two signature keys, and I was intrigued by this. Consequently the second and the third score produce exactly the same sounds, and I plan to use this in my mathematical work to illustrate the concept of the equality of sets.

I decided to play the beginning of the B scale score while the recording was playing. Immediately, they sounded grossly discordant with one another. I played the first nine notes of the anthem in all twelve major scales with the recording, and they all sounded immediately grossly discordant - except the one from the first score.

But it seemed to me that I could whistle along with all twelve scales without gross discord. Consequently it seemed that my ear was automatically making me whistle in the correct scale. But it might be the case that we can't hear our own 'out of key' singing or whistling - as we can not smell our own bad breath. I look forward to doing these exercises with a musician so he or she can tell me if I am whistling in the correct scale. If so, it would be very significant, because - up to now - I have known I could carry a tune, but I have had no idea what notes I was whistling.

Post Script - 6 August 2010:   Yesterday, I did the whistling exercise with a song writer friend, and he said my whistling was ok. He said it was not uncommon for people to be able to do this, and this means that a rare gift is common. Amazing! Now I can look forward to being able to whistle while I ... know what notes I am whistling.

Musical Diary - 22 February 2010 - Auckland, New Zealand

In my musical mental meanderings (free walkabout), I have figured out a fascinating exercise for the major scales. I will briefly describe it below. Please find a picture of the circle of fifths on Wikipedia, and consider the following picture of the German anthem showing the score that uses the B major scale with signature key having 7 flats:

I play starting at the fifth line, until we come full circle to the end of the fourth line. That partial tic-tac-toe (natural) symbol removes the last flat in the signature key, so that the signature key becomes the one for the major scale G-flat, and we finish on G-flat. So i play that scale down and up a couple times, and then play the anthem again using the G-flat scale - starting with the fifth line again. Post Script - 6 August 2010: It is convenient to begin playing the anthem at the top of the scale. That means we play the scale going up, and then, instead of playing it back down, we begin the anthem at the fifth line - which descends the scale with beautiful variations. I also find it convenient to play the natural minor scale a few times while playing the major one. This uses the previous entry at 14 February 2010.

At the end of the fourth line, the last flat is removed again in the signature key, and we end on and get the signature key of the major scale D-flat. Five more cycles brings us to the C-major scale, and going on starts adding sharps. So we can go all the way around until we repeat the first four cycles using the signature keys that have the sharps.

Every three cycles or so, I need to change ends of my short keyboard. I think even on a piano with 88 keys, we might need to change ends twice. Post Script - 6 August 2010: I have looked at the piano, and it seems that only one change of ends would be required. I wonder if this exercise would help a good ear determine how well the piano is tuned.

Musical Diary - 24 February 2010 - Auckland, New Zealand

The little exercise that I described in the 22 Feb 10 entry has lead me to the picture shown below. I start the German hymn at the fifth line using the major scale that starts on B - which seems more appropreately named C-flat if we use the signature key that has 7 flats. The hymn then ends with the fourth line on the last note of the next major scale in the spiral. The process repeats all the way around. The top note of the B / C-flat scale is under the right most yellow block at the back of the keyboard. The red block indicates the last major scale.

I find this exercise to be very helpful in learning the major scales. Post Script - 6 August 2010: Below please find two representations of the spiral on paper. It seems to be a little helpful to remember that the sequence G-D-A-E-B occurse twice (from one to five o'clock and from six to ten o'clock).

Musical Diary - 26 February 2010 - Auckland, New Zealand

Note: I do not use the word 'key' as in music being in a certain key. I only use the word 'key' to refer to the levers we press on the piano to make sounds.

In the exercise described in the previous two entries, I began by playing the last two lines of the German hymn beginning at the higest B on my little keyboard. This means that I was using the major scale that begins on B, and it means that the first note in the hymn proper (the first note of the first line) is the B that is one octave lower than the B on which I started. The playing of the hymn then ended on the F-sharp that is a perfect fifth (seven semitones) above that lower B. This determined the next major scale to be used, and the process was repeated - tending to lower pitched starting notes.

The fact that F-sharp is a perfect fifth above B seems to explain the name of the circle of fifths.

In this entry, I started with the lowest B on my little keyboard, and follow the same spiral - but now tending to higher pitched starting notes. I start playing the hymn from its proper first note in the first line. At the end of the fourth line we come to the note which is a perfect fifth above the starting note. From this perfect fifth, I look to see if there is a full octave of higher keys available:

If there is a full octave available, the remaining two lines will be played beginning on that higher note. However, to accustom the ear to the different scale and to practice the scale, I play the new major scale several times before finishing the hymn.

If there is not a full octave available, the remaining two lines will be played descending from that perfect fifth. Again however the scale is played for practice and to accustome the ear to the new scale.

In both cases the hymn continues from its first line, using the new major scale that begins and ends on that perfect fifth above the original starting note.

Please see the following picture. Ignore for a moment the light blue circle above the middle B of my keyboard. (It just so happens that this B has 18 keys on each side.) The top line of blocks was placed first with that isolated black one on the left being first. The blocks are placed on the hymn's proper starting note. The next two scales are identified by the other two black blocks on the top row: F-sharp and D-flat in that order - tending to higher pitches. When there is no room to go higer, the color switches to red until there is no room higher again. Then the color switches to yellow. Note that the order 'black red yellow' is alphabetical. Then blocks are placed on the second line, followed by the third line. At the end, I found that if I use a fourth color, I can start at the middle B and follow the same procedure and get the same placement of the blocks.

Musical Diary - 28 February 2010 - Auckland New Zealand

I find that if I play the signature keys with the sharps that are shown in the circle of fifths, in the order beginning with one sharp and progressing to seven sharps, I get a sequence of notes that quickly became familiar. And I noticed that the name of the major scale is given by 'sharpening' the last note of any signature key's sequence of notes. And the minor scale's name seems to be given by the note which is three semitones below the major scale's naming note (tonic).

Doing the same exercise with the signature keys that have flats also produced a sequence of notes that quickly became familiar. However, I found that the major scale's tonic is seven semitones higer (Post Script - 6 August 2010: mnemonically better seems five semitones lower) than the last note in the sequence. But again, the minor scale's tonic seems still to be three semitones lower than the major one.

Musical Diary - 6 March 2010 - Sydney Australia

It is painfully difficult to write down things that are so easy in physical fact and sound. But I will forget, and if I do not write, then there will be no record.

I will explain below how, by reversing the naming facts referred to in the 28 Feb 2010 entry, I can recall the signature key of the major scale starting on any given note.

(1) I go one semitone lower and ask if this is the last note in one of the sharp sequences. If it is then that sequence gives the signature key.

(2) I go seven semitones lower (Post Script - 6 August 2010: five semitones higher) and ask if this is the last note in one of the flat sequences. If it is then that sequence gives the signature key.

For the four major scales at the bottom of the circle of fifths, we get two yes answers and two signature keys. For all the others (C excepted because there is no signature key), we get one yes and one no and one signature key.

Also: I have settled on the following for my multi-scale (block placing) exercise with the German Hymn (see the 26 Feb 2010 entry and picture): I play the whole hymn, becasuse I do not want to 'mess' with it. After a pause when it is finished, I repeat in isolation the fourth line, which ends on the tonic of the next major scale. I then play the natural minor and then the major scale, and then play the hymn starting with this new tonic.

Musical Diary - 9 March 2010 - Sydney Australia

Entry 1

A remarkable thing happened today: I was playing what I call the signature key sequences, and I was practicing naming the notes for the sequences of flats in preparation to talk about them over the phone with a friend. So I played and said ... B-flat, E-flat, A-flat, D-flat, G-flat, C-flat (which is B), and ... then I was looking at F and saying to myself F-flat (which is ...). And for a split second I thought to myself, looking at the lever to the left of F but not yet recalling its name, that is the letter that comes before F in the alphabet. But, before I could think of the letter that way, I looked at this lever next to F and said to myself 'Ah! That is E.'

When I started, it was the other way round: I thought of the letter first and then associated it with the lever we press to make the sound. Now I look at the levers and only think of the letters if I need them. And, looking at the lines and spaces on a score, I am beginning to see - not the lettered notes - but the keys of the keyboard. In the beginning, the letters were conspicuous middle men between the score and the keyboard: I had to translate the note on paper to a letter, and then translate the letter to a key on the keyboard.

Entry 2

While I work, I listen over and over again to the 7th piece, 'La Rousserolle effarvatte' (The Reed Warbler) of Messiaen's 'Catalogue d'oiseaux' (Catalogue of the Birds). At this point in my musical explorations, I can only play tunes that I can carry, and I have often thought of the Catalogue "This is not that sort of music. At least it seems not to be a tune I can carry." But I have found myself whistling a sequence of six of its notes! Once that happens, I have hope to figure it out on the keyboard.

Musical Diary - 29 July 2010 - Danbury Connecticut USA

I have neglected to make entries lately and will attempt to make them up here.

Entry For Early June 2010

Note: I think that all the major scales can be played easily, if we just know the difference between a tone and a semitone: Adjacent levers that we press to make a sound (black-white, or white-white) are separated by a semitone. A tone separates any pair of levers which has exactly one lever between them. Now use the following fingering to play any major scale: 1-2-3-1-2-3-4-1, where 1 through 5 represent the thumb through pinky respectively on the right hand. AND: The semitones always occur where you switch from or to the thumb. Play it slowly, and deliberately think: tone or semitone - depending on whether or not you need to switch to or from the thumb for the next note. (Post Script - 6 August 2010: Experience seems to have shown that the terms tone and semitone are HUGE obstructions that prevent people from learning how to play the twelve major scales. All that is needed are 'next key' and 'skip a key' but the deeper we go into 'What is a tone?' the further afield we get!)

Laboriously, using the fourth line of the German national anthem and my spiral of fifths exercise (see above), I was able to make the chart shown below. It shows, as we go clockwise from one major scale to the next on the circle of fifths, how only one note changes. The notes descend to the right because I was using as an aid the last part of the German anthem, which essentially just goes down the scale. The chart also uses the fact that each lever (that we press to make a sound) has two names. I emphasize that I was until today (29 July) completely unable to visualize these changes on the keyboard. Today I worked it out. See today's entry below.

Entry For Today, 29 July 2010 (see 21 September 2010 below for a better explanation)

Focus on playing the   C   scale ascending. That means, looking at the picture immediately above, that you will read to the left, rather than to the right. Play the first four notes, but then finish the scale one octave lower. Then, when you play the next scale (G) - clockwise on the circle of fifths - you will see easily (LOOKING AT THE KEYBOARD!) that all the notes are the same, except that   F   gets sharpened to   F#   at the end. I think the same process works for all the scales.

Entry Circa 20 July 2010
Recently, I had an opportunity to play at a friend's piano, and her husband asked me to teach him what I am calling the signature key sequences. For this purpose I would like to use the pictures shown below. The flat and sharp symbols are played from left to right as if they were notes on a score for which the signature key has the symbol at that line or space. (Love of symmetry made me move the two sharp symbols that are above the red x's.) We can obtain seven signature keys from each picture by playing from one to seven notes. For the flat sequences, the major scale's key note is found by lowering the final note by five semitones. Try it with three flats to obtain E-flat. For the sharp sequences, the major scale's key note is found by raising the final note by one semitone. Try it with two sharps to obtain D.


The process just described can be reversed to find signature keys given key notes. Let any lever that we press to make a sound be regarded as a major scale's key note. Then do both of the following tests: (1) Go lower by a semitone, and determine whether or not the note obtained is the final note of one of the sharp sequences. (2) Go higher by five semitones, and determine whether or not the note obtained is the final note of one of the flat sequences. Every lever except   C   will yield either one or two signature keys.   C   will yield zero signature keys because   B   does not end any of the sharp sequences and   F   does not end any of the flat sequences.

I remember the signature key sequences as follows:

Near the middle of the keyboard, focus on one of the sets of three black keys, and remember that the sequences start either on the right hand one or on the left hand one. Then recall that the full seven flat sequence consists of three descending pairs of notes - flat takes us lower - plus one left over. Therefore, the flat sequences start on the right, or high, side so they can go lower. On the other hand, the full seven sharp sequence consists of three ascending pairs of notes - sharp takes us higher - plus one left over. Therefore, the sharp sequences start on the left, or low, side so they can go higher.

Musical Diary - 6 August 2010 - Danbury Connecticut USA

Entry 1
Refer please to the last paragraph of the previous entry. I play both the flat and sharp sequences with just the thumb and middle finger - with the thumb first for the flat sequence, and with the middle finger first for the sharp sequence. I find if I play the flat sequence first, then the hand is very well positioned to play immediately the sharp sequence. They go well together.

Entry 2
Looking back at this diary, I find that I made no mention at all of my experience 'reading' music. I learned to play the German hymn without looking at the keys. Then I played it while looking at the score - very deliberately looking at each note on the score before playing it. I soon noticed that sometimes I would be about to make a mistake, but looking at the score corrected the mistake before it was made! This happened again yesterday. I also had a remarkable experience yesterday: My eyes went on to the third line of the score - when the music goes back to the first line - but my fingers went with the music back to the first line! I was not playing the recording. My fingers just were in the correct habit of playing the first two lines twice before going on to the third. My eyes just followed the habit of always going to the next line.

Musical Diary - 21 September 2010 - Auckland New Zealand

In the entry for 29 July 2010 (see the first image and the paragraph that precedes the first image), I think I mistakenly claimed to have visualized on the keyboard how successive major scales on the circle of fifths differ by only one note. Now, using the picture below, I think I have a better method. The red blocks have been placed on the major scale that begins on E. Going clockwise around the circle of fifths, the following major scale begins on B. The yellow blocks show the B major scale finished one octave lower than it started. If we think of the red blocks as representing any "given" major scale, and the yellow blocks as representing the clockwise "following" major scale on the circle, then ...

the 1st, 2nd, and 3rd of the following major scale are the same as the 5th, 6th, and 7th of the given major scale,
the 4th, 5th, and 6th of the following major scale are the same as the 1st, 2nd, and 3rd of the given major scale,
the 7th of the following major scale is a semi-tone higher than the 4th of the given major scale.

I think the word description just given applies to any "given" major scale on the circle of fifths. If we regard the scales as consisting of their seven distinct notes, then the first three of the following scale are the same as the last three of the given scale, the second three of the following scale are the same as first three of the given scale, and the 7th of the following scale is a semi-tone higher than the 4th of the given scale.


I find that I can now see and hear what has just been presented WITHOUT ANY REGARD AT ALL FOR THE NAMING OF EITHER THE NOTES OR THE SCALES: I press any key near the middle of the keyboard and regard it as the first note of the "given" major scale. I go seven semi-tones higher to find the first note of the "following" major scale. Then I play the first three notes of that following major scale - repeating those three notes several times to get the sound into my ear. Then I play all seven notes of the given major scale - and note well the last three notes by their sound. Then I play the "following" scale - finishing one octave lower. It is easy to see that the two scales overlap for three notes, and that they differ by a semitone thereafter: The fingering is 1-2-3-1 for the "given" scale, and 1-2-3-4 for the "following" one. 3-1 is a semi-tone and 3-4 is a full tone.

Musical Diary - 5 October 2010 - Sydney Australia

I think most interesting major scale is the one with two six symbol signature keys. Consequently, I wanted to make this page.

Musical Diary - 10 December 2010 - Sydney Australia

I now have a musical mnemonic device for the circle of fifths which gives all the signature keys together with the keynotes for both major and minor scales. I started the laborious process of creating a piece of sheet music, but this set things in stone. I did not want to specify which octaves to use, I did not want to specify durations for the notes, and I did not want to specify the order in which the keynotes are played. My first step was to learn to play and recognize the sound of what are called the "full" sequences shown in the table immediately below. In this table, "Lower" means to go from the note which precedes the word "Lower" to the first instance down in pitch of the note which follows the word "Lower". The meaning of "Higher" is similar.

- - - - - Full Sharp Sequence - - - - -
( any F# , Lower C# )
( Higher G# , Lower D# )
( Higher A# , Lower E# )
Higher B#
- - - - - Full Flat Sequence - - - - -
( any B except the lowest and highest, Higher E )
( Lower A , Higher D )
( Lower G , Higher C )
Lower F

I have found it useful to remember that the full sharp sequence involves three ascending pairs and "sharp" takes us higher. Similarly, the full flat sequence involves three descending pairs and "flat" takes us lower. This also helps to identify the last two notes, which are each the higher of two white keys in the full sharp sequence, and the lower of two white keys in the full flat sequence.

The sub sequences of the full sequences have the first   n   notes, where   n   is a member of the set   {1,2,3,4,5,6,7}.   I will call these sub sequences   Sn   and   Fn   where   S   and   F   stand for flat and sharp respectively. These sub sequences give the sharp and flat signature keys, although "give" does not mean that these sub sequences are identically the same as the signature keys. They simply show how the notes on scores are sharpened or flattened.

The mnemonic device is the sequence of sub sequences

S1, S2, S3, S4, S5, S6,   F1, F2, F3, F4, F5, F6, F7,   S7

together with the following rules:

(1) For the S sub sequences, the major scale keynote is one semi-tone higher than the last note of the sub sequence, and the minor scale keynote is one tone lower than the last note.

(2) For the F subsequences the major scale keynote is the last note of the previous sequence. This is why F1 follows S6, because the last note of S6 gives the major scale key note for F1. For the F sub sequences, the minor scale keynotes are two tones higher than the last note of the F sub sequence. That is for example, the minor scale key note for F1 is two tones higher than the single note that constitutes F1, and the minor scale key note for F2 is two tones higher than the last note of F2, and so on.

Musical Diary - 31 January 2011 - Sydney Australia

Some time ago I drew on paper a set of lines that enable me to play all 88 keys of the piano using the FACE mnemonic for the spaces and the EGBDF mnemonic for the lines: The blue line and dot indicate the lowest and highest keys. The red line and dot show the lowest and highest keys on my keyboard - which is too short for the grand staff.

The three sets of lines which do not have the G-clef can be eliminated by notations that indicate we should play notes two octaves higher or two or four octaves lower. This would require only one ledger line below and one above the staff that has the G-clef.

Musical Diary - 24 April 2011 - Auckland New Zealand

I have created what might be called a table of fifths for a 7-ringed circle of fifths here.