Studio Design - Audio Room Setting - Theatre - Sound Texture - Acoustic - Hi Fi Arrangement

How to read and use sound texture :

Sound texture display shows the quality of stable sound as a transformed display of its waveform. This is particularly useful in checking the timbre and subtle features of the sound of a musical instrument or the sound effects of a room and hi-fi arrangement. The general rule is that sound with simple waveforms will result in simple sound texture and complex sound result in complex sound texture.

1. The variations of sound and its sound texture
The simplest sound is that of the tuning fork or whistling which is approximately a sine wave, meaning a pure tone. For the perfect sine wave, its sound texture is a circle.

The ¡§timbre¡¨ of sound is basically the combination of the harmonic contents for a note and its variation over time. The more high harmonic contents, the more complex the sound waveform, and the more complex the sound texture. Many Jazz musical instruments exhibit complex sound texture.

The waveform of a musical instrument is in general similar within a short range of frequency. Some exhibit more variation than similarity. The most notable being the violin. The violin¡¦s resonance chamber gives rise to complex resonance variation so that two very close notes can have very different waveforms. You can now appreciate the uniqueness of each violin by studying their sound texture for different notes.

The waveform of human speech is even more complex. There are voiced and unvoiced sounds. Unvoiced sounds do not have clear frequency and waveform. Their sound textures are messy. Voiced sounds are complex and are related to the formant frequencies of the sound. So the sound texture of the vowels 'a', 'e', 'I', 'o', 'u' differ. It also varies for different pitch and different people. But each has its own visual characteristic. For example, the 'a' is a smooth convoluted loop while the 'e' looks jittery. As the pitch of sound increases, they look more and more similar. It is because all tend towards the pure tone, or a sine wave. Even if a high pitched note includes rich high frequency harmonics, it still appears to us more like a sine wave because our ears are poor in hearing high frequency sound.

2. The temporal variation of sound
The waveform, and hence sound texture of a note is actually time varying as the various harmonics of a note develop over time during the attack, sustain, and decay stage. One of the most complex sounds is that of the church organ. It is produced as a result of several pipes sounding together. The slight differences in frequencies for the different pipes interact to give a time-varying waveform. So the sound texture display of a church organ literately dances while you can hear the corresponding subtle variation over time. The accordion is similarly made up of multiple sound elements. The bell also exhibit time varying waveform with drastic changing relative strength of different frequencies. Its time-varying acoustic effect and sound texture gives an intriguing hypnotic feel.

3. The spatial variation of sound
We know that the interaction of multiple loudspeakers and the reflections of sound in a room will create different reinforcement or cancellation of sound at different locations. The calibrated sound texture display on a Pocket PC enables us to see this phenomenon for the first time. The pocket PC is a small device that doesn't disturb too much the sound interactions and the miniature microphone essentially picks up sound at a single point.

4. The fusing of two or more notes
Since for a stable sound of a fixed pitch, its sound texture is a stable shape. The sound texture display can also be used to check the fusing of sound by seeing two notes appearing simultaneously create a stable sound texture. The fusing of two notes is better if they have frequencies in simple ratio such as the following :

Ratio	Notes	Distance in Cochlea
4:5	do-me (major third)	4/12 circle
3:4	do-fa (major fourth)	5/12 circle
2:3	do-so (major fifth)	7/12 circle

The ratios for one octave in the major just intonation is shown below

Note	C	D	E	F	G	A	B	C
Ratio	1.000	1.111	1.250	1.333	1.500	1.666	1.875	2.000
Ratio	8	9	10		12		15	16
Ratio	3			4		5		6
Name			Third	Fourth	Fifth			Octave

Kyle Gann has a more elaborate explanation about the ratio and mathematics related to the just intonation scale and their implications which is in his website http://www.friendsoffreedom.com/Crafts/Ocarinas/JIExplained.html.

There is a slight deviation from the ideal ratio for the ¡§equal temperament¡¨ chromatic scale. For the ¡§Just intonation¡¨ scale, the notes are designed to have simple ratios with each other and will result in perfect fusing of sound. For more about just intonation, please see the ¡§Just Intonation Network¡¨ at http://www.justintonation.net. The sound texture display is, however, a good way for you to see the beauty of the just intonation scale.

Likewise, chords are notes having essentially simple ratios. The most common major fifth chord with notes do-me-so is in approximately ratios of 4:5:6 which fuses well into one sound. If your piano is offtuned to the extent that deviation from this simple is excessive, then the sounds no longer fuse together, and the sound texture looks messy.

The Pythagorus tonal Temperament is based on the interplay of major fifth (2:3) and the octave (1:2). Therefore, many note pairs in this scale gives very well fused sound, which means good consonance. The Pentatonic Temperament consists of two intervals of 8:9 (204 cents) and 27:32 (294 cents) respectively. You can view them as the C D E G A tones in the Pythagorus scale. In modern piano, a shifted version is made up of the black keys in the piano. So the intervals are one whole-note or 1.5 whole-note respectively.

For the interested reader, a summary of common tonal scales and their mathematical relationships is also included in our website. Please go to our 'Musical Temperaments and Ratios' page. There you will find description of Pentatonic, Pythagorus, Chromatic, Mean-Tone, Just, Chromatic, 53 Equal Temperament, and non-standard scales. Their method of construction, basic intervals, and basic frequency ratios are summarized.

5. Precision tuning
One major value of sound texture is in precision tuning. Making use of the fact that when two notes with their frequencies in simple ratio (such as 2:3 for a fifth) gives rise to a stable waveform and sound texture, we can use the sound texture to tune two notes to almost exact ratio. The speed of variation when two notes interact is related to their frequency differences from the simple ratio. To our ears, this gives rise to the ¡§beating¡¨ effect. Trained ears can hear beating of complex sounds. On the other hand, all of us with reasonably good eyes are able to perceive the pattern change even if it has a slow cycle time of 10 seconds or more. So by tuning two notes to give a visually stable sound texture, we can tune two notes into the ideal simple ratio with an accuracy of better than 0.1 Hertz. This is particularly important when you need to tune instruments into perfect harmony for the just intonation scale. Skilled piano tuning experts in the past use their ears to detect the beating effect to achieve harmony among notes. Now you can do this easily with sound texture display.

6. Study of beating, consonance and tonality
Ideally, the music tonal scale should consist of only notes that are in simple ratios. However, it is by no means simple and the musical scales that we use is a matter of choice between different compromises. In the past, music theorists use the frequency ratios to predict the quality of a musical scale for its various intervals and musicians use their ears to feel the consonance and dissonance. Now the sound texture enable the visual anatomy of the beating effect.

When two notes are close to simple ratio, then their deviation from the simple ratio gives rise to beating. For example, a note of 200Hz and another of 300Hz fuses to become a note of 100Hz. However, if the 200Hz note is changed to 205Hz, then they are not in exact simple ratios. If their loudness is about the same, then you can hear a sound of fluctuating loudness. The frequency of the fluctuation cycle in this case is 2.5. This figure is obtained by dividing 205Hz by 2 and 300Hz by 3. So the first note appears to be the harmonic of a note with a fundamental of 102.5Hz and the 300Hz note appears at the 3rd harmonic of a 100Hz fundamental note. When the two fundamentals are in alignment, the resulting sound is loudest. It is quietest when they are in reverse alignment that cancels each other. From the above calculation, this appears 2.5 times a second.

To our ears, two notes that beats slowly is the same as one note with fluctuating loudness. What is regarded slow is for most ears less than approximately 10 cycles a second. When the two notes appears together, their interaction results in slow cycling of loudness that massages our nerves to give a soothing effect. Beyond 10 cycles a second, the beating is too fast for us to follow and imposes an annoying stimulation to our nerves. However, if the deviation from simple ratios is too far, then we can obtain a theoetical 'beating' frequency that is say, 30 cycles a second or more. In such cases, our ears actually perceive them as two distinct notes that doesn't mix.

The sound texture cycles in step with the beating. Particularly for the consonant sounds, you can see a slowly changing pattern that cycles at the same speed of the sound's beating. This can be used to study the relationship between different notes for a chosen music tonal scale. For example, in the chromatic scale, the frequency ratio for two notes that are a fifth apart is 1.4983. The frequency of C4 is 261.63Hz and G4 is 392.00 Hz. So they beats at 261.63/2-392/3 = 0.15Hz. This is small enough for these two notes to be considered consonant. Check this out by stepping on the sustain pedal of your piano and then hit on these two notes to see the sound texture display of their interaction. It takes more than 6 seconds for the cycling of loudness. Try using C5 and G5 and you can both hear and see that the cycling shortened to 3 seconds. You see, consonance and dissonance is a complicated matter. But you see, it is easy to check them using sound texture.

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