Dienstag, 13. November 2018

Relative Pitch Indicator

Building a relative pitch meter

After developing an absolute pitch indicator, I asked myself "Shouldn’t there be a more general way to measure the sense of relative pitch?" After all, the expressions “I have good relative pitch,”  “I have excellent relative pitch,” and “I have bad relative pitch” are not quantitative statements.

Because relative pitch is the essential thing in musicality, I should have developed such an indicator in the first place. The idea that you cannot acquire absolute pitch after a certain age, is in my opinion not helpful in improving one's musicality. Therefore, the idea of taking away the mystique of perfect pitch arose. But only after developing a continuous absolute pitch indicator did I realized that the advantages of having a similar indicator for relative pitch, is too.

There are numerous interval test programs that can tell you how many out of a certain number of  intervals you've guessed correctly. Isn’t that good enough? After all, you get enough feedback to continue your training and improve your percentage ratio.

In most cases, the feedback is very helpful, because you know that the percentage was for a particular interval or intervals. For example, you may have tested major thirds, perfect fifths, or a combination of both. Or, in the best case, you do a test of all intervals. While such a percentage provides an overall view of relative pitch, it is not useful for beginners. Beginners are better off receiving feedback on specific intervals. This allows them to train specifically on those intervals where they need improvement. More importantly, they can better track their progress.

Why, then, should we have a relative pitch indicator?
There are two main reasons for developing a relative pitch indicator: precision and answering speed. Additionally, the indicator provides the advantage of music system independence.

Interval Precision
What exactly is relative pitch? To identify an interval, you must recognize pitch distances. That is, you must recognize that the tonal distance between a minor third and a major third is smaller. However, if you think that smaller distances are more difficult to recognize than larger distances, then you are wrong. This lies in the relationship between tones and overtone creation. Normal tones will always create overtones, and these overtones follow a simple pattern: the path of least resistance. If you pluck a string, the string will start to vibrate with its fundamental frequency. The first overtone that gets generated is always the octave and its wavelength corresponds to half the length of the string. In other words, the wavelength fits twice within the original length. The next overtone is the perfect fifth and its wavelength fits three times within the original length. Now, since the first overtone is an octave, we also hear a perfect fourth, since the perfect fourth is the inverse interval of the perfect fifth. For more information on this topic, see my video: Absolute and relative pitch – inside our methods.

In this way, pitch distance discrimination has two components: the tonal distance and the overtone relationship. While for the octave, the distance is usually the main identifier, for the perfect fifth and the perfect fourth, the overtone relationship makes the distinguishing process difficult. In fact, for most people distinguishing perfect fourths and perfect fifths is an extremely difficult task. Therefore, for learning purposes, it makes sense to follow an interval training pattern.

However, as a general measure we should still use pitch distance alone as the relative pitch indicator. How do we describe the difference between someone who has “a good sense” and someone that has “an excellence sense” of relative pitch? To answer this question, we have to go deeper – beyond the precision of half-steps. That is, we must measure pitch distance deviations. In this way, measuring pitch distance is the only way to determine relative pitch discrimination ability.  

Answering Speed
Unlike absolute pitch, it is generally accepted that relative pitch can be acquired. So, assuming that you have acquired relative pitch, then the recognition speed is still a criterion to differentiate or grade your ability. For relative pitch, speed is everything: You should continually improve relative pitch recognition speed until it is innate. Therefore, answering speed should be part of a relative pitch indicator.

Music system independence
When we speak of relative pitch, we usually mean intervals in the equal-tempered system. Thus, one must know the interval names of this system. However, there exist other music systems around the world. Furthermore, people without a musical education can also discriminate pitch distances; they just cannot name the intervals because they lack basic music theory.

Since all music systems recognize the octave, dividing the octave into equal small steps makes it possible to measure pitch distances. In the equal-tempered system, the octave is divided into 1,200 small steps. A half-step, then, consists of 100 such small steps. In the equal-tempered system, deviations from standard frequencies is given in cents. Therefore, one small step equals 1 cent. For the remainder of this post I will use the term "cents" for pitch distance statements.

This music system independence allows for the measurement of general pitch distance and is thus suited for a general relative pitch indicator.

Idea and development
If we want to measure and quantify relative pitch, we must first identify the main quality of relative pitch. When I developed the absolute pitch indicator, I started with the assumption that everybody has absolute pitch, but some are just better than others. So, all we have to do is find a continuous measure to describe that ability. Since most people do not have absolute pitch, I have to bring them into a framework where I can say, "You have this degree of absolute pitch." Therefore, I did loosen the definition of absolute pitch. For example, if someone is never more than a half-step off from the correct answer, then this person – in my system – has absolute pitch. This assumes the absolute pitch test would be done only with whole-steps instead of half-steps. If we go even further in loosening the required recognition precision – to an octave, for example – then we can grade all possessors of non-absolute pitch. But I can also go in the other direction by defining perfect pitch as the ability to discriminate pitches by a third of a half-step. That is, there are now 36 tones to identify in an octave. A sample answer for a tested tone, then, would be "This is an 'A' plus a third of a half-step.” Now some people who have absolute pitch according to the current perceived meaning of absolute pitch would start to fail the test for the narrower definition. If we were to go even further by accepting deviations of only fractions of a cent, then at some point everybody would fail the test (e.g., if you must be able to express tones to a precision of 0.1 cent – such as: this is an “'A' plus 34.7 cents.“). For absolute pitch, measuring accuracy is, in my opinion, not the most relevant criterion, so, I decided to keep accuracy at a fixed level, and use the retention-time as the unit for the indicator. Nevertheless, the loosening of the accuracy was the first step toward the absolute pitch indicator.

Using a similar approach for a relative pitch indicator, I will start by testing to see if one can successfully identify large pitch distances. In this way, I can already start to grade people with a poor sense of relative pitch. In addition, I will take the tested range and measure the answering speed. This allows me to grade even more precisely. Going beyond the precision of half-steps in the grading lets you see your “cushion” and gives you confidence. Therefore, the main criterion will be the pitch distance, and the unit of the relative pitch meter will be cents. For example, if you are able to identify pitch distances to a third of a half step, then your relative pitch indicator is 33 cents. In other words, you can differentiate an interval from another interval that deviates by a third of a half step.

When I introduced the program listening-ear-trainer (March 2013), I also added – as a by-product – a learning box for intervals. Instead of absolute pitches, intervals are used as the “words” to memorize. A learning box is usually used for vocabulary training. Since, listening-ear-trainer is a training program, it is not suited for an evaluation test. Moreover, it is limited to pitch distances of a half-step.

So, after introducing the absolute pitch indicator, the idea for a general indicator for relative pitch was born. It is important to note that both indicators are independent of any particular music system and that the programs can also be used by non-musicians to grade them-self. This feature makes it easy to evaluate the success rate of any training program. Before releasing the program Pitch Grid Test (October 2018), I introduced the program PitchBlitz (June 2018), which is based on the same grid layout as the test but has additional training options. The test returns a continuous indicator for the relative pitch ability expressed in cents.

Defining the test and metrics
Pitch Grid Test measures the ability to distinguish pitch distances within a predefined precision. Thus, the distance itself is not part of the evaluation, only the ability to discriminate that distance within the given precision. That is, you must be able to differentiate a pitch distance from a pitch distance that is larger or smaller by the amount of the given precision.

Relative pitch tests can be done in two ways: harmonically or melodically. In a harmonically played interval, both notes are played simultaneously. In a melodically played interval, the notes are played one after the other. Harmonic intervals are simpler to test, since no melodic time delay has to be defined. Furthermore, in the melodic interval test, an additional component comes into play: The participant must keep the reference tone in mind until the second note is played. However, since relative pitch recognition also implies melodic intervals, and the main distinction between absolute and relative pitch is the presence of a reference tone, I prefer to use a separate distinguished reference tone for the test.

In addition to the pitch discrimination precision, the maximum time used to answer is also measured.

The result of the relative pitch test is expressed in cents as the amount of deviation you are still able to recognize.

The test procedure
To avoid side effects, the test should use (pure) sinus waves. In addition, pitch distance deviations should be created by calculating the appropriate frequencies. Human interactions would not be precise enough. Therefore the test can only be performed using a computer.

The test procedure is as follows: 
  1. The person who wants to test her or his ability choses a frequency range (three or four octaves ) and a starting pitch deviation (from 1,200 downto 7 cents) to be tested.
  2. The computer plays a random reference tone.
  3. After a short pause the computer plays a tone that must be identified, whereby the tone to identify is multiple times the chosen pitch deviation away from the reference tone.
  4. The candidate has to select the correct tone in a grid.
  5. If the candidate selects the correct tone, then the test continues with another tone to identify. No new reference tone is played. The last heard tone is the new reference tone.
  6. If the candidate selects a wrong answer, then the selected tone is played followed by the correct tone, and the candidate is given one more chance to pass the test. If he/she fails a second time the test is finished and the relative pitch indicator is calculated.
  7. If the candidate does not answer within six seconds, then this is recorded as a wrong answer.
  8. After ten tones have been tested, the test continues with a smaller pitch distance deviation.
  9. The test ends when you make your second error, or when you have passed the test with a pitch deviation of 7 cents.

Since a general pitch distance test has to go beyond half-steps and must be independent of any music system, building such a system based on the Western equal-tempered system does not seem like the ideal solution. However, we can still use equal-tempered frequencies as base reference points and conduct arbitrary-distance tests from these points. Using equal-tempered frequencies as starting points does not really limit our measuring quality, as we can still measure pitch distances outside of the equal-tempered interval system.
Thus, my proposal is to use a pitch grid based on the equal-tempered system. We can measure pitch distances beyond the precision of half-steps by making the grid resolution finer. If we also use reference tones that deviate from the equal-tempered frequencies by the amount of a grid resolution, the test will be generalized enough to confirm pitch distance recognition independent of the equal-tempered system

Next steps
Please let me know what you think about my proposed relative pitch indicator/relative pitch meter. Do you know of any other approaches for measuring relative pitch that also allow for measuring the sense of relative pitch in non-musicians? Also, do you have ideas for improvements?

Sonntag, 4. November 2018

Absolute Pitch Indicator

Building an absolute pitch meter

Wikipedia shows the following definition for the term absolute pitch:

"Generally, absolute pitch implies some or all of the following abilities, achieved without a reference tone:
   Identify by name individual pitches (e.g. F, A, G, C) played on various instruments.
   Name the key of a given piece of tonal music.
   Reproduce a piece of tonal music in the correct key days after hearing it.
   Identify and name all the tones of a given chord or other tonal mass.
   Accurately sing a named pitch.
   Name the pitches of common everyday sounds such as car horns and alarms.
   Name the frequency of a pitch (e.g. that G4 is 415Hz) after hearing it."

Unfortunately, the definition “some or all” is confusing and leaves room for interpretation. A simpler definition given at the beginning of the Wikipedia article says "Absolute pitch (AP), widely referred to as perfect pitch, is a rare auditory phenomenon characterized by the ability of a person to identify or recreate a given musical note without the benefit of a reference tone." This sentence is also ambiguous since it also contains an "or."

This ambiguity makes it very difficult – if not impossible – to answer this question with a "Yes, you have it" or "No, you don’t have it."  

This situation is aggravated by the fact that the Wikipedia’s definition is not precise and no other official definition exists. For example, an individual might be able to recognize notes in a very limited range or is capable of naming simple chords, yet may fail to identify very complex chord names because of the lack of knowledge in music theory. Or, how much time is allowed for recognizing a note or a chord name? Must the answer be given within a second, or is figuring it out in a minute still accepted to count as an absolute pitch possessor?

On the other hand, how important is it to know if you have absolute pitch or not?

Of course, having the ability to identify absolute pitches is fascinating. However, music lives from change. That is, pitch changes relative to other notes. Absolute pitch associates a name to a particular frequency, thus is isolated. Creating harmony in music involves relations to other notes.

Being able to recognize notes, intervals, chords, and keys requires knowledge of the underlying musical system. Detecting keys or chords requires several notes; detecting intervals requires two notes. These notes are then set in relation to each other. The underlying music system assigns these constellations interval names, chord names, or a key name. Therefore, these abilities have more to do with music theory and relative pitch skills than with absolute pitch abilities.

This is also the main reason why it is generally accepted that relative pitch is more important than absolute pitch. Many well-known musicians did not have absolute pitch. Or maybe they just did not care about it because harmony in music is always relative, and absolute pitch frequencies are irrelevant for that matter.

Why, then, should we have an Absolute Pitch indicator?
The only reason I can think of is to have a musical goal. Ear training is an important aspect for any music student. There are our ears with which we can judge if we are in tune with others or not. If we are playing a solo, the ability to keep a fundamental note over a longer period in our mind is a useful skill: it prevents us from drifting off the key.

Not having a single, continuous indicator for absolute pitch makes it difficult to bring absolute pitch in line with a training program. The road to absolute pitch may be long, and only a "Yes, you have it" or "No, you don’t have it" answer does not leave room for a step-by-step progress.

To make gradual progress, we need better feedback. We can break up the Wikipedia criteria for absolute pitch in separate tasks and measure progress in each category. However, we still have to guess our progress toward absolute pitch. More importantly, how do we measure the criterion: "identify a pitch without a reference tone"?

The main problem here is "without a reference tone." If we are given a reference pitch and then listen to a piece of music, chances are that we still can remember the reference tone after the piece has finished. This is because we stay in a musical context. Therefore, we would solve absolute pitch questions after the piece has finished still through relative pitch skills.

To overcome this problem, we need to define a musical absence time, before we can answer absolute pitch questions. Tests have shown that after a quarter of an hour of musical absence, in most cases, the reference tone has vanished – is no longer accessible through our short-term memory.

Now, this restriction of a mandatory musical absence makes it nearly impossible to develop a test for testing the absolute pitch skill “recognizing a pitch without a reference tone”

Even so, we have good possibilities for measuring the other criteria for absolute pitch; we are still missing a method for measuring pitch retention abilities. Since “without a reference tone” is where people have most difficulties, the task of an absolute pitch indicator will be providing a pitch retention metric.

Directly measuring retention abilities is difficult since any test taken will interrupt the retention process. Thus, you would have to start measuring with a very large time, and if you fail then you would have to restart the test with a decreased time period until a successful feedback is generated. Such a test would be very long and therefore unpractical.

However, we can speed up this measurement if we can measure how pitch retention deteriorated during a specified time. To develop a continuous indicator, we must depart from the idea that we can only measure absolute pitch ability without a reference tone, if that "without" means a musical absence of fifteen minutes or more. By testing at lower time periods, we can get a picture of pitch retention deterioration.

Measuring how long you can retain a pitch with precision will complete a musical test. Being able to retain a pitch for a longer time has many positive implications on musicality. Therefore, an absolute pitch indicator still has its justification in a musical evaluation process. Trying to improve this indicator is a valid musical goal, even if we do not achieve absolute pitch as defined by Wikipedia.

Idea and development
In Wikipedia, the term perfect pitch is redirected to absolute pitch. This bringing together of the two terms is unfortunate. Perfect suggests that no errors are allowed. Perfect pitch implies many other abilities that are related to pitch. This implication has led to the definition of absolute pitch that there is no simple way of testing this ability. As a consequence, numerous rumors about absolute pitch have emerged. The biggest rumor is that you cannot acquire it: you must be born with absolute pitch. Since the requirements are not clearly defined, some people will not accept progress towards absolute pitch and will speak of pseudo absolute pitch, if for example; someone learns to identify pitches after singing a reference tone. They argue: It takes too long: it must be immediate. It must be magic. Unfortunately, this "Yes" or "No”"view is not helping people to see absolute pitch as a goal worth pursuing. Accepting imperfection and using a continuous indicator could make absolute pitch training a challenge and lead to a better ear.

The assumption that absolute pitch can be learned like foreign languages has led to the development of the program Listening Ear Trainer. Both absolute pitch and foreign languages use voice to express an idea. Both rely on retaining sound patterns in memory for references and analyses. Therefore, it stands to reason that absolute pitch can be learned the same way foreign languages can. The product Listening-Ear-Trainer (March 2013) introduced the learning box—used for vocabulary training—for learning absolute pitches. Keeping an eye on the precise pitch (singing) reproduction improves the retention skills and confidence in your musical discrimination ability.

Since no silence period between exercises in Listening-Ear-Trainer is mandatory, the training is not really for absolute but relative pitch. Therefore, in August 2015, I released the program TuneCrack. A direct application of keeping a pitch in mind is during the tuning process of an instrument. Therefore the idea was: Cracking the tuning problem by giving people a training program to increase their pitch retention skills.

The program TuneCrack recommends internalizing a pitch by taking it over to your voice. However, singing is not mandatory since only the precision-identifying ability is tested.

Since I believe that singing is the closest way you can get to music, I searched for a method to get a reliable way of measuring what I think is the most important criterion of absolute pitch: accurately sing a named pitch without a reference tone. This criterion includes singing and accurate pitch retention. The result was the introduction of the program SamePitchPlease (May 2016).

To improve the pitch retention training, the programs TuneCrack and SamePitchPlease introduced a silence period. However, these two programs are training programs that guide you through incremental exercises to better performance. If we want a tool that measures an individual’s absolute pitch ability in a more general way, then we have to build an absolute pitch meter that can be evaluated through a single test.

Restricting the program SamePitchPlease to four notes and a 25-cent deviation led to the Pitch Ability Test (November 2016), which returns an indicator on the pitch retention and reproduction ability. Both abilities are required for absolute pitch; therefore, the indicator can be used as a continuous measure for absolute pitch instead of only a "Yes, you have it" or "No, you don’t have it" answer.

Defining the test and metrics
The Pitch Ability Test defines the ability to reproduce a given pitch after a specified time period within a frequency precision of 25 cents as the measure. Thus, the Pitch Ability Test fixes the note accuracy for the reproduction and uses only the time as an indicator.

As with any test, the more precise a result should be, the more time is needed to determine the result. Therefore, a careful selection between time and accuracy should be considered. In the Pitch Ability Test, a decision to keep a single evaluation below 20 minutes was made. This limits the number of tones that can be tested during that time frame. Since the test should also prove that you can locate non-tested tones over a larger range, the test requires four different notes. Having four notes as fixed points ensures that you can orientate yourself by building distances between the tested notes and the directions: up or down.

The restriction of keeping a single test below 20 minutes leads to a maximum of 4 minutes for each note. That is, the best result you can get for the Pitch Ability Test is 4 minutes. While longer times can be easily measured, increasing the time does not make sense. Most people will have difficulty reaching this 4-minute limit—without training anyway. However, to make it clear that you have reached this 4-minute limit, and probably can reproduce pitches way beyond this point, the 4-minute point has a special name: Felix’s Pitch Point.

The result of the Pitch Ability Test is the silence time between the sounding of the reference sound and the accurate reproduction of the pitch with your voice. Pitch ability is expressed in seconds.

The test procedure
The requirements for administering the test are a stopwatch and a person with a good ear. This person  does not need to have absolute pitch. Playing the correct note on an instrument and comparing the pitch with the sung note can evaluate accuracy.

The test procedure is as follows:
  1. The person who wants to test his or her ability tells the tester four different notes that he or she thinks he or she can sing well and announces the period of silence for which he or she wants to take the test.
  2. The tester plays the first note for about two seconds.
  3. The tester starts the stopwatch.
  4. The person taking the test is allowed to sing back the note immediately for about two seconds. No feedback is given.
  5. The tester monitors whether no pitched sounds can be heard during the following period of silence.
  6. About five seconds before the announced test time is due, the tester signals to the candidate (with a visual sign or non-pitched sound) that he or she should prepare for the singing back of the note.
  7. When the time is due, the candidate should sing the note steadily for about a second. The tester listens carefully, compares the sung pitch with the original pitch, and decides whether the pitch did not deviate more than 25 cents from the original pitch.
  8. The tester repeats steps 2 to 7 for the remaining three notes.
  9. If the candidate succeeds with all four notes, then he or she has fulfilled the Pitch Ability Test for the chosen period of silence.

To determine pitch ability, the test uses an unconventional approach: the retention time gets measured in a similar way as the height in high-jump sports gets measured. This approach allows you to measure the retention time of the pitch with enough precision. If you select a low-enough time, you will always pass. If you come to your limits, the results will start to vary. Reaching Felix’s Pitch Point is not easy, but to acquire absolute pitch (or perfect pitch), you must pass this point. Therefore, the Pitch Ability Test is a useful tool for giving you feedback on where you stand on the road to absolute pitch. Most people who want to acquire absolute pitch are far away from Felix’s Pitch Point; thus, they can improve their ability.

A computer-based implementation
Since the wait—until you are allowed to reproduce the pitch—is very boring for the tester and the determination of the pitch accuracy is often non-neutral, a computer-based implementation of the procedure was made. The program Pitch Ability Test executes the above-described procedure and automatically suggests that you take a test for a higher time limit if you passed all four notes. This procedure is similar to that in high-jump sports, where you set your targeted goal and continue until you fail. Therefore, you should select your silence period with care. Starting with a very short period may fatigue and hinder you from reaching your best performance. Starting with a very long period poses the risk of getting no result at all.

Next steps
Please let me know what you think about my proposed absolute pitch indicator/absolute pitch meter. Do you know other approaches for measuring absolute pitch? Or do you have ideas for improvements?

Dienstag, 11. September 2018

Measuring Relative Pitch Abilities

Same Pitch, Please
In the last blog post, I wrote about demystifying perfect pitch (or absolute pitch). Instead of fighting for or against myths about perfect pitch, I proposed a scientific way to measure one’s achievement toward perfect pitch. The post reduced the scope and focused only on one aspect of perfect pitch: the ability to produce a desired pitch without a reference tone.

While this is probably the most important aspect of perfect pitch – conceptualizing a tone with your “inner ear” – the proposed measurement method is no indicator of your musicality, nor is the possession of absolute pitch.

Musicality is based on harmony. Harmony can only exist if the tones relative to each other are in a harmonic relationship. Therefore, I emphasize the importance of relative pitch. Here's my standard example: if an old organ in a church is not tuned to equal-tempered frequencies, then you must adapt to this situation, since you cannot retune the old organ. Equal-tempered frequencies have no relevance in this situation.

So, absolute pitch is more or less useless, except for giving you anchor pitches. But, then, why is it so common in musicality discussions? Because it means that you can hear a melody with your “inner ear” simply by reading sheet music. Here, “inner ear” is the key word as well as the reason why I have developed the program SamePitchPlease. SamePitchPlease is a training program that focuses on this very aspect: conceptualizing a tone with your “inner ear.” So, the main goal of SamePitchPlease has more to do with keeping a reference tone in mind than with acquiring absolute pitch. To help improve your musicality, SamePitchPlease assists you with finding the reference tones you can remember best and challenges your pitch memory.

Picture: Measuring pitch memory with a forced silence period.

SamePitchPlease measures deviations from the reference tone after a specified silence period. Deviations are always relative to a reference. But this use of "relative pitch" has almost nothing to do with the term "relative pitch" as used in music. Relative pitch in music refers to identifying the interval between two notes.

Relative Pitch Distances
Having found a way to measure the most important aspect of absolute pitch ability, this post now looks at relative pitch. Can we find a similar way to measure the much more important ability of relative pitch?

Easy! In a test, just present some intervals and calculate the percentage of correct answers. Is such a percentage score useful? Of course, if this percentage increases in later tests, then you know you've made progress.

But, we could have done the same for absolute pitch tests. If, in an absolute pitch test, the percentage of correct notes identified increases compared to the previous test, then you've made progress. So, I could have stopped researching the subject. However, since a mere percentage score does not really help you make systematic progress, I tried to investigate the core ability needed for absolute pitch: pitch memory. Measuring and giving feedback for this quality allows for systematic progress by helping you find your current limit and sense the critical shortcomings. Then, it aids you with finding the tones you can keep in mind for the longest period of time. Try to figure out what sensations are responsible for the tones you have success with over the longest period of time. Finally, apply your findings to other tones.

The same is true for relative pitch tests. A general test that assesses perfect, major, and minor intervals and assigns a percentage score is not very helpful in improving your relative pitch identification ability. To speed up progress, more detailed feedback is necessary. Splitting up the test into categories for interval pairs, such as testing minor second vs. major second, eases the learning progress. A step-by-step learning approach is a far better method than trying to improve your ability through an un-guided overall evaluation score. By undertaking such tests, you will find that some interval pairs are more prone to confusion than others. One such a pair is the perfect fourth and the perfect fifth. For this reason, I recommend first learning to differentiate the perfect fifth from the perfect fourth. See my YouTube video: Absolute and Relative Pitch - Inside our Methods.

At this point, our discussion is already deep into a musical system, in this case the Western equal-tempered system. However, pitch ability is independent of any specific system. So, what should we look for to define a measurement for relative pitch ability?

Let's start with someone who possesses relative pitch. A person with good relative pitch can identify all intervals in an octave as well as spell interval names for compound intervals (= intervals larger than an octave). That is, such a person can hear pitch distances to the precision of one half-step.

Now, in real life, there are slides and bends that do not start or end on an equal-tempered frequency. Yet, a person with very good relative pitch ability can nonetheless name such deviations. Naturally, a person that can recognize pitch distances beyond half-steps should be given a better grade.

So, to assess someone’s relative pitch ability, we can measure their pitch-distance recognition accuracy. Pitch-distance accuracy is independent of a music system. The Western music system introduced the term "cents" to describe pitch distances. In the equal-tempered system, the octave is divided into 12 half-steps, and each half-step has a distance of 100 cents from one note to the next. All music systems know the octave as a divider for the pitch room. Therefore, for scientific calculations, we can use this unit in all music systems to name pitch distances.

Microtonality and Larger Intervals
Wikipedia defines micro tonality as follows: "Microtonal music or microtonality is the use in music of microtones—intervals smaller than a semitone, also called 'microintervals'. " (A semitone equals one half-step.)

Picture: Microtonality expressed with a grid resolution of 33 cents.

With microtonality we can describe deviations from standard interval distances. Since the measurement of pitch distances in cents is universal, larger distances than half-steps can also be expressed in cents. For example, a whole step has a distance of 200 cents. This universality lets us describe and measure the main aspect of relative pitch: the ability to discriminate pitch distances. People who do not possess relative pitch may fail to identify pitch distances by a half-step, a whole step, or even more. People who can, during tests, identify pitch distances within a whole step do not possess a good sense of relative pitch. However, they are still better than people that miss the pitch-distance estimation by three or more half-steps.

Thus, we can grade relative pitch ability through one's pitch-distance-discrimination ability. Measuring this ability and receiving feedback can therefore help improve your ability.

The Pitch Grid Test uses this measuring approach and starts by testing whether one can discriminate large pitch distances. The first test starts with a pitch distance of an octave. With a little training, everybody should pass this test. In this way, everybody gets an initial score. From there, the test continues with smaller interval distances: six half-steps, three half-steps, two half-steps, and finally, one half-step. But the test does not stop when it reaches a half-step. By making the resolution even finer than a half-step, we can grade even relative pitch possessors. Thus, the test verifies one’s relative pitch ability and illustrates the path for improvement.

The Program PitchBlitz
Since relative pitch also includes compound intervals – that is, intervals that are larger than an octave – beginners face difficulties if the test is conducted with a range of several octaves. Large pitch distances increase the probability of errors for small-distance deviations. Using the analogy of measuring the physical distances of two points, we can say that measuring a distance with a precision of one millimeter is much easier if the distance is less than one meter; for distances above a kilometre, such precision can only be reached with advanced technology.

Applying this knowledge to pitch-distance learning gave rise to the development of the program PitchBlitz.

The program PitchBlitz, allows you to narrow down the tested range by letting you select the octave(s) you want to train. Additionally, PitchBlitz also offers other options. For example, people often try to solve relative pitch problems with absolute pitch skills. Since they usually don't possess absolute pitch, it turns into more of a guessing game. Let me explain:

Because you hear the note to identify after the reference tone, many people think they can forget about the reference tone and simply build the answer from the last tone they heard. They ignore the information of the reference tone. Since the Pitch Grid Test presents the notes in a grid, this layout can easily be misinterpreted as an invitation to select the note to identify through absolute pitch skills. Therefore, the training program PitchBlitz has an option that forces you to focus on distances: you must select a distance instead of a note in the grid.

The grid layout was chosen because the basic idea behind measuring pitch distances is to increase the distance precision beyond a half-step. The finer the resolution, the greater detail that can be observed. Making the grid resolution coarser gets less experienced users on board. In this way, the grid resolution can be used as a universal tool for measuring pitch-distance recognition ability.

The goal of improving one’s sense of relative pitch is to automate interval recognition. If you want to automate something, speed is everything. Therefore, the Pitch Grid Test evaluates your answering speed. By incorporating answer speed into the score, the evaluation lets you also see your progress in speed. In this way, you can observe small progress. That's why the training program was named PitchBlitz.

The term “having a good relative ear” is not very precise. To improve an ability, you need better feedback: feedback that measures your current standing. The measurement of pitch-distance recognition ability is independent of a music system. Therefore, the measurement does not stop at the distance of a half-step. And if you haven’t reached the precision of a half-step, the measurement shows you how far away you are from that goal.

A general test to measure one’s distance-hearing ability requires some time. However, you cannot compare this effort to a loudness and frequency-response measurement. Pitch-distance recognition is not limited by physical circumstances. Assuming you can hear all the tones between C2 and C6, it is a mental ability and can therefore be trained and improved. If the feedback you get from the test is precise and informative, it can be directly used to improve your ability.

The presented Pitch Grid Test and the related training program PitchBlitz are based on a grid that has its roots in the equal-tempered system. Despite looking like an absolute pitch test, it is a relative pitch test and is independent of a music system. The universally usable unit of “cents” is used to measure pitch-distance recognition.

Especially for beginners, the possibility to see the progress of one’s pitch-distance hearing ability is a motivation to continue ear training. The test offers beginners having difficulty getting started with interval identification simple-to-understand feedback. Even low-precision detection ability can be assessed. And, with training, you can observe even slight progress (fewer errors, faster answer times, using forced distance naming, etc.).

The confidence-building is further supported by neutral feedback from a computer, which eliminates the need for a second person, and means errors during the journey to success are allowed without other personal involvement.

Feedback is the only way to improve your abilities. Reaching a precision of a half-step reflects a high grade, but it also lets you know you can improve beyond this mark.

For more information visit http://www.pitch-ability.com

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