# 12. Learning Relative Pitch and Absolute Pitch (Sight Singing, Composing)¶

Relative pitch (RP) is the ability to identify a note, given a reference. Absolute pitch (AP), is the ability to identify a note without using a reference note. AP is used here instead of Perfect Pitch, PP, because PP can be confused with pianissimo. The quality of your AP is determined by how accurately you can reproduce a pitch, how quickly you can identify a note, and how many notes you can identify when they are played simultaneously. People with good AP will instantly (within 3- 5 seconds) identify 10 notes played simultaneously. The standard test for AP uses 2 pianos; the tester sits at one and the student at the other, and the student tries to repeat the note played by the tester. If there is only one piano, the student names the note played by the tester (do, re, mi, ... or `C, D, E, ...`). In the following exercises use `CDE` first because most theory books use this notation. However, there is nothing wrong with using doremi if that works better for you. Nobody is born with absolute pitch; it is a learned skill, because the chromatic scale is a human invention - there is no physical relationship between the pitches of the chromatic scale and nature. The only physical relationship between the chromatic scale and the ear is that both operate on a logarithmic scale in order to accommodate a large frequency range. We know that the ear operates on a logarithmic scale because harmonies have a special meaning and harmonies are ratios and ratios are easiest to manipulate on a logarithmic scale. Thus, although we are not born with AP, we are born to recognize harmonies. The effect of the logarithmic human hearing is that the ear hears a large difference in pitch between 40 and 42.4 Hz (a semitone or 100 cents), but hears almost no difference between 2000Hz and 2002.4 Hz (about 2 cents), for the same difference of 2.4 Hz. The human ear responds to all frequencies within its range and is not calibrated on an absolute scale at birth. This is in contrast to the eye, which responds to color on an absolute scale (everyone sees red as red from birth without any training, and this perception never changes with age) because color detection is achieved using chemical reactions that respond to specific quanta (wavelengths) of light. Some people who can identify certain pitches with specific colors can acquire AP by the color that the sound evokes. They are effectively calibrating the ear to an absolute reference.

Absolute and relative pitch are best learned in very early youth. Babies who cannot understand a single word will respond appropriately to a soothing voice or a lullaby or a scary sound, which demonstrates their readiness for musical training. The best way for toddlers to acquire AP is to be exposed almost daily to well tuned pianos from birth. Therefore, every parent who has a piano should keep it tuned and play it with the baby nearby. Then they should test the child from time to time for AP. This test can be performed by playing a note (when the child is not looking) and then asking her/im to find that note on the piano. Of course, you have to first teach the child the piano scale: starting with the `C major` scale near the middle, and then the fact that all the other notes are related to this scale by octaves. If the child can find it after several tries, s/he has RP; if s/he can find it the first time every time, s/he has AP. The particular temperament to which the piano is tuned (Equal, Well temperament, etc.) is not important; in fact many people with AP know nothing about temperaments and when notes on pianos tuned to different temperaments are played, they have no trouble in identifying the notes because different temperaments change most frequencies by less than 5%, and no one has AP with that kind of accuracy. RP and AP can be acquired later in life but becomes more difficult after age 20 to 30. In fact, even those with AP will slowly lose it starting around age 20, if it is not maintained. Many piano schools routinely teach AP to all their students with over 90% success. The problem with teaching a group of older students is that there is always a certain percentage of “pitch deprived” students who had never been trained in pitch and who will have difficulty learning even RP. Instructions on how to teach AP to very young children are given in b. Teaching Youngsters, Parental Involvement, Mental Play, Absolute Pitch below because they are trivially simple and are an integral part of teaching the very young; instructions for adults are given in this section, below.

Having AP is clearly an advantage. It is a great help for memorizing, sight reading, recovering from blackouts, and composing music. You can be the pitch pipe for your choir, and easily tune string or wind instruments. It is a lot of fun because you can tell how fast a car is going by listening to the tires whine, you can tell the differences between different car horns and locomotive whistles, especially by noting whether they use thirds or fifths. You can remember telephone numbers easily by their tones. However, there are disadvantages. Music played off tune can be annoying. Since so much music is played off tune, this can present quite a problem. The person can sometimes react strongly to such music; physical reactions such as teary eyes or clammy skin can occur and out-of-tune pianos can become especially difficult to play. Transposed music is OK because every note is still correct. AP is a mixed blessing.

There is a method that makes learning RP and AP quick and easy! This method is not generally taught at music schools or in the literature, although it has been used by those with AP (usually without their explicit knowledge of how they acquired it), since the beginning of music. With the method described here, the pitch skills become simple by-products of the memory process. You expend little extra effort to acquire pitch recognition because memorizing is necessary anyway, as explained in 6. Memorizing. In that section we saw that the final objective of memorizing is to be able to play the music in your mind (mental play, MP). It turns out that, by paying attention to RP and AP during the process of practicing MP, you naturally acquire the pitch skills! Thus, you do not only play music in your mind, but you must always play it at the correct pitch. This makes perfect sense because, without playing at the correct pitch, you lose so many of the benefits of MP. Conversely, MP will not work well unless it is done in AP, because MP is a memory function, and memory is associative and AP is one of the most important associations – AP is what gives music its true melodic lines, color, expression, etc. For most, memorizing two significant compositions is sufficient to acquire AP to within a semitone, which is faster than any known method being taught today; for most, this should take a few weeks to a few months. Young children will accomplish this with zero effort, almost automatically (see 16.b below); as you grow older, you will need more effort because of all the confusing sounds that are already in memory.

Two useful compositions for practicing RP and AP are Bach’s Invention #1 and Beethoven’s Moonlight Sonata, 1st Movement. The Bach gives you middle `C` (its first note) and the `C Major` scale; these are the most useful note and scale to learn in AP. The Moonlight has compelling melodies that make the memorizing process easy and enjoyable. Yet the complex chord transitions provide a variety of notes and intervals and the complexity prevents you from guessing the notes – you need a considerable amount of practice and repetition before you can play it in your mind perfectly. It is also technically simple enough for everybody. Both compositions should be practiced HS for pitch practice initially, and HT later on.

When creating notes in your mind, do not try to hum or sing them because the dynamic range of the piano is larger than your singing range and you need to train the mind to deal with these higher and lower notes. Also, the memory of each note for AP must include everything – the harmonics, timbre, etc., of your piano – you need as many memory associations as possible. Therefore, use the same piano until you feel that you have AP. Unless you have an electronic piano, make sure that the piano is in tune. Once you acquire a strong AP, it will work with any source of sound. Unless you are a singer who can sing on pitch (in which case you should have AP), you will not be able to accurately sing the pitch. The resultant incorrect sound will confuse the brain and destroy any AP that you might have acquired. Just as MP frees the pianist from the limitations of the piano, MP (instead of singing them) frees you from the limitations of the vocal chords.

Procedure for learning relative pitch and absolute pitch: After you have memorized Bach’s Inv. #1, and can play the entire piece in your head, start practicing RP. Play the first note (`C4`) on the piano, and use it as a reference to MP the first bar or two, and check the last note with the piano. Most beginners will MP all intervals narrow because the brain automatically tries to “increase the singing range”. Thus ascending notes will be sung flat and descending notes sharp. Start with one or two bars, correct any errors, and repeat until the errors disappear. Then add more bars, etc. By the time you work through the whole Bach in this way, your RP should be pretty good. Then start on AP. MP the first few bars without a reference note from the piano and see if you got the starting `C4` right. Everyone has a maximum and minimum note s/he can hum. Therefore, check your `C4` without a piano by humming up to the maximum and down to the minimum; for example, your low and high may be `F3` and `C5`; then `C4` should be a fourth above `F3`. After this check, double- check the `C4` with the piano. Repeat until your `C4` is correct to within a semitone. After that, further success depends on practice; every time you walk by the piano, try to guess `C4` (by using the first few bars of the Bach) and test it. You can find the `C4` directly by concentrating on exactly how it sounds at the piano, but it is easier with real music because music has more associations. Success depends on how many associations you can make with the note – harmonics, tone, melody, etc. When the `C4` is fairly correct, start testing notes randomly all over the piano and trying to guess what they are (white keys only). At first, you may fail miserably. There are too many notes on the piano. In order to improve the success rate, guess the notes by referencing to the `C4-C5` octave; for example, `C2` is `C4`, two octaves down. In this way, the task of memorizing 88 notes on the keyboard is reduced to just 8 notes and one interval (octave). This simplification is possible because of the logarithmic nature of the chromatic scale; further simplification of the notes within the octave is accomplished using RP (semitone, 3rd, 4th, 5th). Acquaint yourself with all the notes on the piano by playing them in octaves and training the mind to recognize all octave notes; all octave `C`‘s, `D`‘s, etc. Until you learn some rudimentary absolute pitch, practice AP mostly at the piano so that you can correct yourself as soon as you wander off key. Do not practice mentally with the wrong pitch for extended periods (this will only confuse the brain); always have the piano nearby to correct yourself. Start practicing away from the piano after your AP is at least within two semitones.

Then memorize the whole Moonlight (first movement) and start work on the black keys. Successful AP depends on how you test yourself. Invent ways to test; I’ll show you a few examples. Let’s use the first 3 RH notes of the Moonlight. Memorize the sound of these notes in AP, and check this several times a day. See if you can get the first note (`G#3`) right every time you sit down at the piano. Practice relative pitch by checking the second note, `C#4` (a fourth from `G#3`), then MP a half tone down to `C4`, and check. Go to the 3rd note, `E4`, check, then MP down to `C4` and check. From `G#3`, MP a half step down, then up to `C4`. Now jump to some arbitrary place in this movement and repeat similar procedures (these tests are easier with the Bach).

Progress may seem slow at first, but your guesses should get closer with practice. At first, identifying notes takes time because you need to check your guess by humming to your highest and lowest notes, or by recalling the beginnings of the Bach or Moonlight. Then suddenly, one day, you should experience that magical moment when you are able to identify any note directly, without any intermediate steps. You have acquired true AP! This initial AP is fragile and you may lose it and regain it several times. The next step is to strengthen your AP by practicing to identify the notes as rapidly as you can. The strength of your AP is measured by the speed with which you can identify notes. After that, start practicing with 2-note intervals, then 3, etc. Once you have a strong AP, practice humming the notes and singing on pitch, and sight reading on pitch. Congratulations, you have done it!

The biological mechanism underlying AP is not well understood. It appears to be entirely a memory function. Therefore, in order to truly acquire AP, the daily mental habits must change, just as for becoming a good memorizer. In memorizing, we saw that the change needed was to develop a mental habit of constantly inventing associations (the more outrageous or shocking, the better!) and repeating them automatically in the brain. For good memorizers, this process occurs naturally, or effortlessly, and that is why they are good. The brains of poor memorizers either become quiescent when not needed, or wander into logical or other interests instead of performing memory work. People with AP tend to continually make music mentally; music keeps running around in their heads, whether it is their own compositions or music they had heard. This is why most musicians with AP will automatically start to compose music. The brain always returns to music when it has nothing else to do. This is probably a prerequisite to acquiring permanent AP. Note that AP does not make you into a composer; MP does. Therefore, MP is more important than AP; those with strong MP can easily learn AP and maintain it, and enjoy all the advantages discussed here. As with memorization, the hardest part of acquiring permanent AP is not the practice, but the changing of your mental habits. In principle, it’s easy – MP as much as you can, and keep checking it for AP at the piano.

AP and memorizing using MP must be periodically maintained as part of the memory maintenance program. This program automatically performs maintenance on pitch recognition – check, from time to time, that your MP is on pitch. This too, should happen automatically because you should always MP at least the beginning of every piece before playing it at the piano. By first playing it in your mind, you ensure that the speed, rhythm, and expression are correct. Your music will sound more exciting when you mentally lead it, and less exciting if you play it and wait for the piano to make the music. Combining AP, MP and keyboard memory results in a powerful set of tools that will make composing music easy, both for composing in your mind and for playing it out on the piano.

Conventional methods of learning AP take a long time, typically more than 6 months, and usually, much longer, and the resultant AP is weak. One way to start is by memorizing one note. You might pick `A440` because you hear it every time at a concert and can perhaps recall it most easily. However, `A` is not a useful note for getting to the various chords of the `C major` scale, which is the most useful scale to memorize. Therefore, pick `C`, `E`, or `G`, whichever you tend to remember best; `C` is probably the best. The standard way to learn AP in music classes is via the solfege (singing exercises) route. Solfege books are readily available in stores or over the internet. It consists of increasingly complex series of exercises involving different scales, intervals, time signatures, rhythms, accidentals, etc, for voice training. It also covers pitch recognition and dictation. Solfege books are best used in a class environment with a teacher. AP is taught as an adjunct to these exercises by learning to sing them at the correct pitch. Therefore, there are no special methods for acquiring AP – you simply repeat until the correct pitch is implanted in memory. Because AP is learned together with many other things, progress is slow.

In summary, every pianist must learn AP because it is so easy, useful, and even necessary in many situations. We demonstrated above that AP is easier to learn using music instead of rote memory. AP is inseparably associated with MP, which frees you from the mechanical limitations of musical instruments. These MP and AP abilities automatically qualify you as “talented” or even “genius” by past standards, but such labels are important mainly to the audience; for yourself, it is comforting to know that you have acquired skills needed to become an accomplished musician.