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A Scale for the Measurement of the Psychological Magnitude Pitch
Abstract
A subjective scale for the measurement of pitch was constructed from determinations of the half-value of pitches at various frequencies. This scale differs from both the musical scale and the frequency scale, neither of which is subjective. Five observers fractionated tones of 10 different frequencies at a loudness level of 60 db. From these fractionations a numerical scale was constructed which is proportional to the perceived magnitude of subjective pitch. In numbering the scale the 1000-cycle tone was assigned the pitch of 1000 subjective units (mels). The close agreement of the pitch scale with an integration of the differential thresholds (DL's) shows that, unlike the DL's for loudness, all DL's for pitch are of uniform subjective magnitude. The agreement further implies that pitch and differential sensitivity to pitch are both rectilinear functions of extent on the basilar membrane. The correspondence of the pitch scale and the experimentally determined location of the resonant areas of the basilar membrane suggests that, in cutting a pitch in half, the observer adjusts the tone until it stimulates a position half-way from the original locus to the apical end of the membrane. Measurement of the subjective size of musical intervals (such as octaves) in terms of the pitch scale shows that the intervals become larger as the frequency of the mid-point of the interval increases (except in the two highest audible octaves). This result confirms earlier judgments as to the relative size of octaves in different parts of the frequency range.
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“The distance between the four orbits and the P (or the NP) vowel was equated in psychophysical terms.The metric used to equate the psychophysical distance of the orbits from P and NP was the mel scale (S. S. Stevens, Volkmann, & Newman, 1937).”
From Human adults and human infants show a “perceptual magnet effect” for the prototypes of speech categories, monkeys do not (1991) · cites this paper as S. S. Stevens, Volkmann, & Newman, 1937
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Topological Fingerprints for Audio Identification
Reise, W., Fernández, X., Dominguez, M., Harrington, H. A., & Beguerisse-Díaz, M. (2024) · SIAM Journal on Mathematics of Data Science · doi:10.1137/23m1605090 · Cited by 8
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Zhang, Y., & Yao, C. (2025) · SAGE Open · doi:10.1177/21582440251343352 · Cited by 3
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Shen, C., Hu, J., Goh, W. L., Chong, Y. S., Do, A. T., & Gao, Y. (2025) · IEEE Transactions on Circuits and Systems I Regular Papers · doi:10.1109/tcsi.2025.3594961 · Cited by 3
Music-Inspired Texture Representation
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Real Time Environmental Classification Algorithm Using Neural Network for Hearing Aids
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Robotic gaze control using reinforcement learning
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Voice Activity Detection Based on Signal Energy and Entropy-difference in Noisy Environments
Ha, D.-G., Cho, S.-J., Jin, G.-G., et al. (2008) · Journal of Advanced Marine Engineering and Technology · doi:10.5916/jkosme.2008.32.5.768 · Cited by 3
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“As a result, cepstral processing is performed using a filter bank with a mel scale [26] to maximize the efficiency in which the information available to the human ear is processed by the computer.”
MethodProduction and Perception of Voice
Singh, R. (2019) · Springer eBooks · doi:10.1007/978-981-13-8403-5_2 · Cited by 3
Speaker Verification Using Machine Learning for Door Access Control Systems
Alaliyat, S., Waaler, F. F., Dyvik, K., et al. (2021) · Advances in intelligent systems and computing · doi:10.1007/978-3-030-76346-6_61 · Cited by 3
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“The raw acoustic signal (sampled at 48 kHz for CLEAR2 and 16kHz for DAQA ′ ) is processed to create a 2D time-frequency representation with Mel scale [74] spectrograms.”
MethodAutomated respiratory sound analysis
Pessoa, D., Rocha, B., Carvalho, P., et al. (2022) · Elsevier eBooks · doi:10.1016/b978-0-12-823447-1.00003-8 · Cited by 3
Deep Learning Approaches for Classroom Audio Classification Using Mel Spectrograms
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“It is found that humans are better at detecting a difference in lower frequencies as compared to the higher frequencies [20].”
BackgroundHuman-Machine Cooperative Echolocation Using Ultrasound
Watanabe, H., Sumiya, M., & Terada, T. (2022) · IEEE Access · doi:10.1109/access.2022.3224468 · Cited by 5
“Since humans can better discriminate lower timbre than higher timbre [53], converting to lower frequencies may be more useful for distinguishing TABLE 1.”
BackgroundPsychoacoustic features explain creakiness classifications made by naive and non-naive listeners
Villegas, J., Lee, S. J., Perkins, J., et al. (2023) · Speech Communication · doi:10.1016/j.specom.2023.01.006 · Cited by 3
Leaky Echo State Network for Audio Classification in Construction Sites
Scarpiniti, M., Bini, E., Ferraro, M., et al. (2023) · Smart innovation, systems and technologies · doi:10.1007/978-981-99-3592-5_18 · Cited by 3
Russian Language Speech Generation from Facial Video Recordings Using Variational Autoencoder
Leonov, M. M., Soroka, A. A., & Trofimov, A. G. (2023) · Studies in computational intelligence · doi:10.1007/978-3-031-44865-2_51 · Cited by 3
Psychoacoustic features explain subjective size and shape ratings of pseudo-words
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“Pitch was computed using Stevens’ method [15] from traces of fundamental frequency ( F 0 ) extracted using Kawahara’s method [16].”
MethodUpadhyaya, S., Buyens, W., Vranken, E., Desmet, W., & Karsmakers, P. (2023) · International Conference on Machine Learning and Applications · doi:10.1109/icmla58977.2023.00141 · Cited by 5
“Subsequently, it is converted by a number of mel filter banks to a lower dimensional mel representation [11] (see Figure 2).”
BackgroundDSVAE: Disentangled Representation Learning for Synthetic Speech Detection
Yadav, A. K. S., Bhagtani, K., Xiang, Z., Bestagini, P., Tubaro, S., & Delp, E. J. (2023) · International Conference on Machine Learning and Applications · doi:10.1109/icmla58977.2023.00072 · Cited by 5
“The mel-scale correlates better with the human auditory system as compared to the Hertz scale [39].”
MethodInfluentialEmotion Recognition from Speech Signals by Mel-Spectrogram and a CNN-RNN
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“The Mel-spectrogram makes use of the Mel-scale [6] which resembles the way humans perceive sound.”
MethodCross-linguistic differences in the size of the infant vowel space
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Optimizing Human Computer Interaction for Byzantine music learning: Comparing HMMs with RDFs
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“Consequently, DFT is multiplied by triangular band-pass filters whose central frequency and width are arranged according to Mel-scale [24].”
MethodKek, X. Y., Chin, C. S., & Li, Y. (2021) · IEEE/ACIS International Conference on Software Engineering, Artificial Intelligence, Networking and Parallel/Distributed Computing (SNPD) · doi:10.1109/snpd51163.2021.9704888 · Cited by 3
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Bresolin, A. D. A., Neto, A. D. D., & Alsina, P. J. (2006) · Lecture notes in computer science · doi:10.1007/11893257_18 · Cited by 3
“Stevens and Volkmann in [ 12 ] defined the Mel scale as a frequency function of the magnitude of an auditory sensation.”
BackgroundChoi, Y., & Lee, S. Y. (2013) · Neural Networks · doi:10.1016/j.neunet.2013.02.006 · Cited by 3
“Although the Fourier transform performs a similar function, the frequency-to-place map in human auditory systems has a loglike relationship (Greenwood, 1990) that can be modeled by melfrequency components with a linear-to-mel-frequency transform (Stevens et al., 1937).”
BackgroundMusical Instrument Identication with Feature Selection Using Evolutionary Methods
Loughran, B. (2009) · Cited by 3
Dominant Audio Descriptors for Audio Classification and Retrieval
Fadeev, A., Missaoui, O., & Frigui, H. (2009) · International Conference on Machine Learning and Applications · doi:10.1109/icmla.2009.120 · Cited by 3
“Another low-level audio features that gained popularity within the research community are based on the Mel Frequency Cepstral Coefficients (MFCC) [17], [16].”
BackgroundRecognition of the Tonal Words of BODO Language
Bhattacharjee, U. (2013) · Cited by 3
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Filter bank based cepstral features for speaker recognition
Chougule, S. V., Chavan, M. S., & Gaikwad, M. (2014) · doi:10.1109/gcwcn.2014.7030857 · Cited by 3
Acoustics recognition of excavation equipment based on MF-PLPCC features and RELM
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“[9] describes how a listener judges the distance between pitches.”
BackgroundThe KanNon System - Real Time Visualization of Speech
Nakamuro, K., Ishi, M., Haruki, K., et al. (2005) · Proceedings of the ISCIE International Symposium on Stochastic Systems Theory and its Applications · doi:10.5687/sss.2005.271 · Cited by 3
Konuşmacının Yaş ve Cinsiyetine Göre Sınıflandırılmasında DVM Çekirdeğinin Etkisi
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Unsupervised Methods for Evaluating Speech Representations
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A Nonverbal Recognition Method to Assist Speech
Meloni, F., Sicchieri, B. B., Mandrá, P. P., et al. (2021) · IEEE International Symposium on Computer-Based Medical Systems (CBMS) · doi:10.1109/cbms52027.2021.00111 · Cited by 3
Vocal-Accompaniment Compatibility Estimation Using Self-Supervised and Joint-Embedding Techniques
Nakatsuka, T., Watanabe, K., Koyama, Y., et al. (2021) · IEEE Access · doi:10.1109/access.2021.3096819 · Cited by 3
“Our method (w/ VAD [32]) is superior to the method merely applying thresholds to RMS (w/ RMS threshold). mel-scaled [54] STFT (Mel-STFT), continuous wavelet transform (CWT) [55], mel-frequency cepstrum coefficient (MFCC) [56], and chromagram representations.”
MethodSpeech Emotion Recognition Using Auditory Spectrogram and Cepstral Features
Zhao, S., Yan, Y., Cohen, I., et al. (2021) · European Signal Processing Conference (EUSIPCO) · doi:10.23919/eusipco54536.2021.9616144 · Cited by 3
“MFCCs analysis is on the strength of two major auditory mechanisms: the nonlinear classification principle of the subjective perception frequency domain from human beings [24] and classification of critical bands.”
BackgroundModeling Prosody for Speaker Recognition: Why Estimating Pitch May Be a Red Herring
Laskowski, K., & Jin, Q. (2010) · Cited by 3
Towards Blind Quality Assessment of Concert Audio Recordings Using Deep Neural Networks
Simou, N., Mastorakis, Y., & Stefanakis, N. (2020) · IEEE International Conference on Acoustics Speech and Signal Processing · doi:10.1109/icassp40776.2020.9053356 · Cited by 3
“The suitability of the mel-scale spectrogram is perhaps also justified by its ability to better capture perceptually relevant information compared to the linear scale [13, 14].”
BackgroundUsing Autotagging for Classification of Vocals in Music Signals
dos Santos, N. P. H. L. (2013) · Open Repository of the University of Porto (University of Porto) · doi:10.34626/qmje-dz52 · Cited by 3
Psychophysical measurement methods.
Preston, M. G. (1938) · Psychological Bulletin · doi:10.1037/h0052485 · Cited by 3
A content-based music recommender system
Kaitila, J. (2017) · Tampere University Institutional Repository (Tampere University) · Cited by 3
Classification of musical genres using hidden Markov models
Dalin-Volsing, S. (2017) · Lund University Publications Student Papers (Lund University) · Cited by 3
Revealing structure in vocalisations of parrots and social whales
Vargas, M. F. N. R. (2018) · doi:10.53846/goediss-6992 · Cited by 3
Altered auditory feedback induces coupled changes in formant frequencies during speech productionPreprint
Tang, D.-L., Lametti, D. R., & Watkins, K. E. (2019) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/733121 · Cited by 3
“The formant alteration was applied in mels — a perceptual scale characterizing changes in frequency that are judged by listeners to correspond to equal changes in pitch (Stevens et al., 1937).”
MethodLeveraging Multimodal Haptic Sensory Data for Robust CuttingPreprint
Zhang, K., Sharma, M. K., Veloso, M., et al. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1909.12460 · Cited by 3
“The Mel frequency scale provides a rough model of human frequency perception [23].”
BackgroundLiminality as a lens on social meaning: A cross-variable analysis of gender in New Zealand English
Hazenberg, E. (2017) · doi:10.26686/wgtn.17061014 · Cited by 3
Zeng, Y., Niziolek, C. A., & Parrell, B. (2023) · doi:10.31234/osf.io/ceqan · Cited by 3
Generative Ai-Based Data Augmentation for Improved Bioacoustic Classification in Noisy EnvironmentsPreprint
Gibbons, A., King, E., Donohue, I., & Parnell, A. C. (2025) · SSRN Electronic Journal · doi:10.2139/ssrn.5393534 · Cited by 14
Separation and acquisition of two languages in early childhood : a multidisciplinary approach
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Language enables the acquisition of distinct sensorimotor memories for speech
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Evaluation of the Covertness of Sound Signals Mimicking Those of Marine Mammals
Jiang, S. Y., Wang, J., Niu, Q., & Shi, W. (2025) · IEEE Journal of Oceanic Engineering · doi:10.1109/joe.2024.3508036 · Cited by 2
“…and maintains uniform bandwidth on the Mel frequency scale, the discrete transfer function for each respective filter is formally defined as [47] and the center frequency f m is defined as where f l and f h are the lower limit frequency and upper limit frequency of the filter H m ( k ) ,…”
Parlak, C. (2025) · Biomimetics · doi:10.3390/biomimetics10030167 · Cited by 2
“Common examples include Mel filters [2], Lyon filters [3], PLP [4], gammatone filters [5,6], Seneff filters [7], and Meddis hair cell models [8].”
Normalization, essentialization, and the erasure of social and linguistic variation
Barreda, S. (2025) · Journal of Phonetics · doi:10.1016/j.wocn.2025.101409 · Cited by 2
A deep learning pipeline for rainfall estimation from surveillance audio
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Srikanth, P., & Behera, C. K. (2026) · Digital Signal Processing · doi:10.1016/j.dsp.2025.105861 · Cited by 2
Leveraging Kolmogorov-Arnold networks for voice liveness detection in anti-spoofing systems
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Speaker Identification and Time Scale Modification Using VOPs
Rao, K. S., & Vuppala, A. K. (2013) · Springer briefs in electrical and computer engineering · doi:10.1007/978-3-319-03116-3_6 · Cited by 2
Auditory Scale Analysis and Evaluation of Phonemes in MISING Language
Rehman, R., HAZARIKA, G. C., & Kardong, D. (2015) · International Journal of Computer Applications · doi:10.5120/19899-2001 · Cited by 2
Signal Processing of Speech and Feature Extraction
Beigi, H. (2011) · Springer eBooks · doi:10.1007/978-0-387-77592-0_5 · Cited by 2
Classification of pediatric snoring episodes using deep convolutional neural networks
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“[13] Stanley Smith Stevens, John Volkmann, and Edwin B Newman.”
BackgroundLow dimensional measurement of vowels using machine perception
Burridge, J., & Vaux, B. (2023) · The Journal of the Acoustical Society of America · doi:10.1121/10.0016845 · Cited by 3
Hermes, D. J. (2023) · Current research in systematic musicology · doi:10.1007/978-3-031-25566-3_10 · Cited by 3
Densely Connected Networks with Multiple Features for Classifying Sound Signals with Reverberation
Chen, Z., Gao, D., Sun, K., et al. (2023) · Sensors · doi:10.3390/s23167225 · Cited by 2
“Mel filter banks were used to delineate the critical bands and extract the feature coefficients to represent the human ear’s perception of isometric pitch changes [22].”
MethodConstant-Q Based Harmonic and Pitch Features for Normal vs. Pathological Infant Cry Classification
Pusuluri, A., Kachhi, A., & Patil, H. A. (2023) · Lecture notes in computer science · doi:10.1007/978-3-031-48312-7_33 · Cited by 2
Thilakan, J., Balamurali, B. T., Chen, J., et al. (2023) · Acta Acustica · doi:10.1051/aacus/2023050 · Cited by 2
Machine Learning for Monitoring Vocal Health and Performance of Professional Singers
Jones, S. P., Reni, S. K., & Kale, İ. (2024) · IEEE International Symposium on Circuits and Systems proceedings · doi:10.1109/iscas58744.2024.10557944 · Cited by 2
“Thus, the separation of frequencies in mel spectrograms in a manner which models the response of the human ear to audio signals [12] makes them a very strong contender for analysis of audio samples in this context.”
BackgroundMethodOoba, H., Maki, J., & Masuyama, H. (2025) · Discover Mental Health · doi:10.1007/s44192-025-00138-0 · Cited by 2
“Given that human auditory perception is more sensitive to lower frequencies [21], we created mel spectrograms by applying an mel filter bank with 128 filters to the original spectrograms.”
Detection of Chronic Musculoskeletal Pain Using Voice Characteristics
Higuchi, M., Iidaka, T., Horii, C., Tanegashima, G., Oka, H., Hashizume, H., Yamada, H., Yoshida, M., Tanaka, S., Yoshimura, N., et al. (2025) · IEEE Journal of Translational Engineering in Health and Medicine · doi:10.1109/jtehm.2025.3553892 · Cited by 3
“Note that the mel-frequency, reported in Table 3, is a frequency that takes into account human auditory characteristics and is calculated by adjusting the original frequency to a scale that measures the pitch of a sound as perceived by humans (the mel scale [26]).”
CNN-Transformer Feature Aggregation Networks for Underwater Acoustic Target Recognition
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“This study explores three methods for generating spectrograms: Mel spectrogram, Constant-Q Transform (CQT) [11-15] spectrogram, and Short-Time Fourier Transform (STFT).”
Deep Learning System for Speech Command Recognition
Vujičić, D., Damnjanović, Đ., Marković, D., et al. (2025) · Electronics · doi:10.3390/electronics14193793 · Cited by 2
BBANet: Bilateral biological auditory-inspired neural network for heart sound classification
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The Acoustic characteristics and classification variables of two Hyponasal groups
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Improving Speech Recognition with Drop-in Replacements for f-Bank Features
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Analysis of the MFC Singuliarities of Speech Signals Using Big Data Methods
Skuratovskii, R., & Osadchyy, V. (2021) · Lecture notes in networks and systems · doi:10.1007/978-3-030-80126-7_70 · Cited by 2
Two Step Recognition of Raags in Hindustani Classical Music Using Supervised Deep Learning
Banerjee, S., Hota, G., Sanyal, R., et al. (2022) · IEEE International Conference on Data, Decision and Systems (ICDDS) · doi:10.1109/icdds56399.2022.10037397 · Cited by 2
“The authors in [13] proposed Mel Scale in which equal distances in pitch were perceived equally by a human.”
BackgroundCombining Timbric And Rhythmic Features For Semantic Music Tagging.
Orio, N., & Piva, R. (2013) · Padua Research Archive (University of Padova) · doi:10.5281/zenodo.1415833 · Cited by 2
A Survey of Music Structure Analysis Techniques for Music Applications
Maddage, N. C., Li, H., & Kankanhalli, M. (2009) · Studies in computational intelligence · doi:10.1007/978-3-642-02900-4_21 · Cited by 2
Emotion Recognition Using Prosodic Information
Krothapalli, S. R., & Koolagudi, S. G. (2012) · Springer briefs in electrical and computer engineering · doi:10.1007/978-1-4614-5143-3_5 · Cited by 3
Low-Complex Environmental Sound Recognition Algorithms for Power-Aware Wireless Sensor Networks
Zhan, Y. (2012) · Cited by 2
Background and Literature Review
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Analyzing a multimodal biometric system using real and virtual users
Scheidat, T., & Vielhauer, C. (2007) · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · doi:10.1117/12.703873 · Cited by 2
“As it is known the higher the frequency of two sounds the more difficult it becomes to distinguish them, a logarithmic scale – the mel scale [13] – for the perceived pitch is used.”
BackgroundWord level automatic alignment of music and lyrics using vocal synthesis
Maddage, N. C., Sim, K. C., & Li, H. (2010) · ACM Transactions on Multimedia Computing Communications and Applications · doi:10.1145/1823746.1823753 · Cited by 2
“Octave scales that arrange the audible frequencies in octaves have been used for early music content analysis research [Brown and Puckette 1992; Maddage et al. 2006; Nwe and Wang 2004; Stevens et al. 1937].”
MethodDoherty, J., Curran, K. J., & McKevitt, P. (2015) · ACM Transactions on Intelligent Systems and Technology · doi:10.1145/2663358 · Cited by 2
“MFCCs [Stevens et al. 1937] are derived from a cepstral representation of an audio clip.”
BackgroundA Post-processing for Binary Mask Estimation Toward Improving Speech Intelligibility in Noise
Kim, G. (2013) · Journal of Broadcast Engineering · doi:10.5909/jbe.2013.18.2.311 · Cited by 2
“인간의청각 특성을 반영하기 위해 mel 스케일주파수([20]) 를 기반으로 한 25개의 필터로 구성된 필터뱅크를 전력 스 펙트럼에 적용한다.”
Power-law distribution in encoded MFCC frames of speech, music, and environmental sound signals
Haro, M., Serrà, J., Corral, Á. J., & Herrera, P. (2012) · International World Wide Web Conference (WWW) · doi:10.1145/2187980.2188220 · Cited by 2
“The MFCC descriptor is obtained by mapping the short-time power spectrum to the Mel scale [33].”
MethodYazawa, K., Ozaki, Y., Short, G., et al. (2015) · International Conference Oriental COCOSDA held jointly with Conference on Asian Spoken Language Research and Evaluation · doi:10.1109/icsda.2015.7357872 · Cited by 2
“The and were first calculated in Hz from measurements of all the vowels in all 20 target words in the corpus, and then converted into mel using (2) [16] to calculate the mean formant frequencies in mel, not mean mel frequencies.”
MethodSpeaker Identification in Medical Simulation Data Using Fisher Vector Representation
Jiang, S., Frigui, H., & Calhoun, A. W. (2015) · IEEE International Conference on Machine Learning and Applications (ICMLA) · doi:10.1109/icmla.2015.187 · Cited by 2
“We have also experimented with three different low-level spectral features: MFCC, PLP and LPCC.”
BackgroundMethodInfluentialOrder reduction and efficient implementation of nonlinear nonlocal cochlear response models
Filo, M., Karameh, F. N., & Awad, M. (2016) · Biological Cybernetics · doi:10.1007/s00422-016-0703-9 · Cited by 2
“…particularly the cochlea, lead to the development of the nowclassical audio frequency decompositions (the Mel spectrum) which had a salient impact in the automated processing, storage , and understanding of sound signals (Eronen and Klapuri 2000; Hasan et al. 2004; Logan 2000; Stevens et al. 1937).”
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Zhong, J., Zhang, P., & Li, X. (2018) · Lecture notes in computer science · doi:10.1007/978-3-319-77383-4_54 · Cited by 2
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“For instance, Stevens et al. (1937) famously argued that perceived pitches cannot be identified with response- independent frequencies, on the grounds that the relations (in particular, equal intervals) among apparent pitches do not match those among frequencies.”
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Metadata
- Authors
- Stevens, S. S., Volkmann, J., & Newman, E. B.
- Affiliations
- Harvard University (US)
- Swarthmore College (US)
- ORCID
- Volkmann, J.
- Venue
- The Journal of the Acoustical Society of America
- Publisher
- Acoustical Society of America (ASA)
- Published
- 1937-01-01
- Volume
- 8
- Issue
- 3
- Pages
- 185-190
- ISSN
- 0001-4966 (ISSN-L)
- 1520-8524
- OpenAlex
- W2103869314
- Cited by
- 1,107
- References
- 0
- Citations by year
- 2026: 41 · 2025: 68 · 2024: 73 · 2023: 78 · 2022: 77 · 2021: 96 · 2020: 72 · 2019: 68 · 2018: 51 · 2017: 43 · 2016: 45 · 2015: 55 · 2014: 30 · 2013: 53 · 2012: 46
- FWCI
- 1.33
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- The Journal of the Acoustical Society of America (publishedVersion)
- Topics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Neuroscience and Music Perception
- Life Sciences › Neuroscience › Sensory Systems › Hearing, Cochlea, Tinnitus, Genetics
- Physical Sciences › Physics and Astronomy › Acoustics and Ultrasonics › Human auditory perception and evaluation
- Keywords
- Mel scale, basilar membrane, sound localization, musical intervals, frequency perception
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