L7 Loudness and Pitch Study Notes

Objectives

目標

• Upon studying this chapter, the student will be able to:
  學習本章後，學生將能夠：

  • Describe the perceptual concepts of loudness and pitch and relate them to the physical measurements of intensity and frequency, respectively.
    描述響度和音高的知覺概念，並將它們分別與強度和頻率的物理測量聯繫起來。

  • Identify the differences between a phon and a sone as units of measurement.
    識別宋和方作為測量單位的差異。

  • Describe ordinal and interval scales and how they differ from each other.
    描述序數和區間量表及其相互差異。

  • Define noise and identify the different variables that affect noise perception.
    定義噪音並識別影響噪音感知度的不同變數。

  • Explain the mel scale in terms of the relationship of pitch and frequency.
    從音高和頻率的關係角度解釋梅爾尺度（mel scale）。

  • Describe residue pitch and the acoustics underlying this phenomenon.
    描述殘餘音高（residue pitch）及其底層聲學原理。

  • Define difference and summation tones and how these phenomena are perceived.
    定義差頻和和頻（difference and summation tones）以及這些現象如何被感知。

  • Identify how and why timbre is perceived differently from pitch.
    識別音色（timbre）為何以及如何與音高被感知得不同。

Loudness & Pitch

響度與音高

• Loudness and pitch are the psychological perception of:
  響度和音高是以下兩者的心理感知：

  • Intensity (loudness)
    強度（響度）

  • Frequency (pitch)
    頻率（音高）

• Physical measures for quantifying intensity and frequency:
  量化強度和頻率的物理測量：

  • Intensity measured in decibels (dB)
    強度以分貝 (dB) 測量

  • Frequency measured in hertz (Hz)
    頻率以赫茲 (Hz) 測量

• Note: Quantification of the perception of loudness and pitch is not straightforward.
  註：響度和音高感知的量化並非直接。

Auditory Sensitivity

聽覺敏感度

• Sensitivity varies across frequency, represented by:
  敏感度隨頻率變化，由以下表示：

  • MAF (Minimal Audible Field) and MAP (Minimal Audible Pressure) curves
    MAF（最小可聽聲場）和 MAP（最小可聽聲壓）曲線

• Fletcher & Munson (Phon curve):
  弗萊徹與芒森（方曲線）：

  • At any point along any of the curves, perceived loudness remains constant.
    在任何曲線的任何一點上，感知響度保持不變。

  • Unit of measurement: phon
    測量單位：方

  • Example:
    例子：

  • At 40 phons, a 1 kHz tone is 40 dB SPL.
    在40方時，1 kHz音調的聲壓級為40分貝。

  • A 100 Hz tone is approximately 55 dB SPL.
    100 Hz音調的聲壓級約為55分貝。

  • Both judged as equally loud.
    兩者都被判斷為同樣響亮。

Q&A on Fidelity in Stereo Systems

關於立體聲系統保真度的問答

• Question: Does playing music at a lower level than recorded result in a perceived loss in fidelity?
  問題：以低於錄音時的音量播放音樂會導致感知上的保真度損失嗎？

• Answer: Yes.
  答案：會的。

  • At the 40-phon contour, frequencies between 3 kHz and 5 kHz are around the same dB SPL, while those outside that range vary significantly.
    在40方的等響度曲線中，3 kHz到5 kHz之間的頻率大致具有相同的聲壓級，而超出該範圍的頻率則差異顯著。

  • At very high levels, the phon curves flatten, resulting in perceived better fidelity, but risk of hearing damage increases.
    在非常高的音量下，方曲線會變平，導致感知上的保真度更好，但聽力損傷的風險會增加。

  • Electronic Compensating Mechanisms:
    電子補償機制：

  • Manufacturers of stereo equipment have designed mechanisms to amplify low-frequency and high-frequency ends for compensation of biological filtering at lower intensities.
    立體聲設備製造商設計了放大低頻和高頻端點的機制，以補償在較低強度下的生物過濾效應。

Sone

宋

• Reference for sone scale:
  宋尺度（sone scale）的參考點：

  • 1 kHz pure tone at 40 dB sensation level (SL)
    1 kHz純音在40分貝感覺級（SL）下

• Units and Measurements:
  單位和測量：

  • 1 sone equates to 40 phons.
    1宋等於40方。

  • Two types of measurements used:
    使用兩種測量類型：

  • Magnitude estimation
    量值估計

  • Magnitude production
    量值生成

• Benefits of Sone Scale:
  宋尺度的優點：

  • Specifies the comparative loudness between different sones: e.g., 1 sone is one loudness unit, 2 sones is double, 4 sones is double 2 sones, etc.
    明確了不同宋之間的比較響度：例如，1宋是一個響度單位，2宋是1宋的兩倍，4宋是2宋的兩倍，等等。

• Difference Between Phon and Sone:
  方與宋的區別：

  • The phon scale is ordinal (shows order of magnitude but not quantification).
    方尺度是序數的（顯示量級順序而非量化）。

  • The sone scale is interval (provides order and quantifiable differences in magnitude).
    宋尺度是區間的（提供順序和量化的量級差異）。

  • For example, 4 sones is half as loud as 8 sones.
    例如，4宋的響度是8宋的一半。

Clinical Note: Listening Effort

臨床筆記：聽力努力

• An audiogram is a graphical representation of hearing sensitivity across frequencies, tested in quiet conditions.
  聽力圖是聽力敏感度在不同頻率上的圖形表示，在安靜條件下進行測試。

• Limitations of audiograms:
  聽力圖的局限性：

  • Provides limited information regarding real-world interactions in non-optimal environments (noise, reverberation).
    在非最佳環境（噪音、混響）中，對於現實世界互動的資訊有限。

• Tools for assessing speech recognition in noise are available, along with evaluations of listening effort.
  評估噪音中語音識別能力的工具有，以及聽力努力的評估方法。

• Listening Effort Definition: Attentional requirements to process speech signals (Hicks & Tharpe, 2002).
  聽力努力定義：處理語音信號所需的注意力要求（Hicks & Tharpe, 2002）。

• Measurement Method: Typically assessed using a dual-task paradigm.
  測量方法：通常使用雙任務範式進行評估。

  • Example: Listening to and repeating words in noise (primary task) while recalling those words (secondary task).
    例子：在噪音中聽並重複單詞（主要任務），同時回憶這些單詞（次要任務）。

  • Limited cognitive capacity means increased difficulty on the primary task results in reduced performance on secondary tasks.
    有限的認知能力意味著主要任務難度增加會導致次要任務表現下降。

• This paradigm is becoming popular in research and clinical assessments, reinforcing the evaluation of listening effort.
  這種範式在研究和臨床評估中越來越受歡迎，強化了聽力努力的評估。

Pitch

音高

• Psychological perception of frequency.
  頻率的心理感知。

• Generally, a higher signal frequency leads to a higher perceived pitch.
  通常，較高的信號頻率會導致感知到的音高更高。

• Quantification often involves:
  量化通常涉及：

  • Using pure tones
    使用純音

  • Complex sounds (e.g., musical melodies).
    複雜聲音（例如，音樂旋律）。

• Observations:
  觀察結果：

  • Listeners adjusted five sounds to assess differences in pitch leading to the development of the mel scale.
    聽者調整了五種聲音以評估音高差異，從而發展出梅爾尺度。

Mel Scale

梅爾尺度

• Characteristics:
  特點：

  • Interval scale (with order and quantifiable differences).
    區間尺度（具有順序和量化的差異）。

  • Example: 2000 mels is twice that of 1000 mels.
    例子：2000梅爾是1000梅爾的兩倍。

• Pitch and frequency relationship is not 1:1.
  音高和頻率的關係不是1:1的。

  • To increase from 1000 to 2000 mels, the frequency must increase from 1000 to 3000 Hz.
    要從1000梅爾增加到2000梅爾，頻率必須從1000 Hz增加到3000 Hz。

Residue Pitch

殘餘音高

• Pitch is often perceived from the lowest harmonics.
  音高通常從最低諧波中感知。

• Schouten (1940) described a phenomenon where low-frequency pitch perception is created by higher-frequency harmonics, referred to as residue pitch.
  Schouten (1940) 描述了一種現象，即低頻音高感知是由高頻諧波產生的，這被稱為殘餘音高。

• Missing Fundamental Case: Refers to maintaining pitch perception in the absence of the fundamental frequency:
  基頻缺失案例：指在基頻缺失的情況下仍能維持音高感知：

  • Differences in timbre are noted.
    觀察到音色差異。

  • Pitch preservation is linked to signal periodicity.
    音高保持與信號週期性相關聯。

Waveform Comparison

波形比較

• Upper waveform: Contains full harmonic signal.
  上方波形：包含完整的諧波信號。

• Lower waveform: Lacks fundamental frequency.
  下方波形：缺乏基頻。

  • Notable differences exist in the waveform, yet periodicity is preserved.
    波形中存在顯著差異，但週期性仍得以保留。

Q&A on Telephones

關於電話的問答

• Question: How can the sex of a speaker be identified over telephones with limited frequency bandwidth?
  問題：在頻率帶寬有限的電話中，如何識別說話者的性別？

• Answer:
  答案：

  • Male F0 averages around 125 Hz; female F0 around 250 Hz (both are below 300-3400 Hz bandwidth).
    男性基頻（F0）平均約為125 Hz；女性基頻約為250 Hz（兩者都低於300-3400 Hz的帶寬）。

  • Auditory systems utilize higher frequencies that are multiples of F0 for identification, e.g., third and fourth harmonics (375 Hz and 500 Hz).
    聽覺系統利用基頻的倍數的高頻進行識別，例如，第三和第四諧波（375 Hz和500 Hz）。

  • Current telephone systems now transmit wider bandwidths (50 Hz to 7000 Hz; referred to as HD voice).
    目前的電話系統現在傳輸更寬的帶寬（50 Hz至7000 Hz；稱為高清語音）。

Q&A on Musical Instruments

關於樂器的問答

• Question: Do differences in pitch help differentiate musical instruments?
  問題：音高差異有助於區分樂器嗎？

• Answer: No, musical notes sounded by different instruments (e.g., piano vs. violin) may have the same pitch.
  答案：不，不同樂器（例如鋼琴與小提琴）演奏的音符可能具有相同的音高。

  • Difference is in timbre—the quality of sound perceived, described as richness or body, and does not relate to pitch differences.
    差異在於音色——感知到的聲音品質，被描述為豐富度或厚實感，且與音高差異無關。

Summary

總結

• Loudness and pitch are complex psychophysical phenomena that have qualitative and quantitative dimensions.
  響度和音高是複雜的心理物理現象，具有質性和量性維度。

• Scales:
  尺度：

  • Loudness (in phons and sones)
    響度（以方和宋為單位）

  • Pitch (in mels)
    音高（以梅爾為單位）

• Neither loudness nor pitch vary directly with physical intensity or frequency; they are influenced primarily by those physical properties.
  響度或音高都不會直接隨物理強度或頻率變化；它們主要受這些物理屬性的影響。

• Pitch perception typically arises from low-frequency harmonics; higher harmonics can evoke low-frequency pitch in absence of low-frequency spectral energy (residue pitch).
  音高感知通常源自低頻諧波；在高頻諧波的存在下，低頻頻譜能量缺失時（殘餘音高），仍可喚起低頻音高。

• While signal pitch is preserved, the timbre will vary significantly.
  雖然信號音高得以保留，但音色會顯著變化。