Historical Examination and Theoretical Analysis of Maqām Iṣfahān in Persian Art Music^*

Introduction

[0.1] The core of contemporary Persian art music—also referred to as Iranian classical or traditional music—is based on several radīfs (organized repertoires), a large number of which originated from the teachings of Mirza ꜥAbdullah Farahani (1843–1918). The gūshihs (musical pieces or samples) in the radīfs were initially taught and transferred aurally from the masters to the students, which resulted in the emergence of several versions with some variations.⁽¹⁾ Many of these versions were transcribed over decades in the twentieth-century. These radīfs are typically divided into seven dastgāhs (modal systems or primary groupings) and five āvāzes (derivative or secondary groupings), although such categorization is debatable. For instance, Farhat (1990, 21) questioned the subjective distinction between the primary and secondary groupings and recognized twelve dastgāhs. The term dastgāh is referred to all groupings (including iṣfahān) in this article as well.

[0.2] The seven dastgāhs in the radīf tradition comprise shūr, sigāh, chahārgāh, rāst-panjgāh, māhūr, humāyūn, and navā; the five “āvāzes” (derivative dastgāhs) include abūꜥaṭāʾ, bayāt-i turk, dashtī, afshārī, and bayāt-i iṣfahān. In this classification, bayāt-i iṣfahān (or iṣfahān in short⁽²⁾), which is likely the most popular mode across different genres in Iranian music,⁽³⁾ is considered a derivative of humāyūn, as the scale of iṣfahān (being almost identical to the harmonic minor scale) can be established on $\hat{4}$ of humāyūn (Khaleghi 1982, vol. 2, 149). In contrast, in the Systematist school of Arabic and Persian musical traditions (the thirteenth through the fifteenth century),⁽⁴⁾ iṣfahān was one the seven recognized species of fourth and one of the twelve adwār al-mashhūrah (famous cycles or scales),⁽⁵⁾ whereas humāyūn was not among the main tetrachords or even the main adwār.⁽⁶⁾ One may therefore wonder about the origins of these two maqāms (modes) and how their evolution over centuries resulted in a reversal of their relative status. In another study (Poorhaydari 2025), I report on the historical evolution and theoretical analysis of humāyūn. This article extends that work, examining iṣfahān with two main objectives. The first involves tracing it back as a distinct maqām in the Systematist school. The second entails examining its modal characteristics (such as the intervallic structure and the scale degree functions) in the contemporary radīfs and taṣnīf (metered, composed song) collections.⁽⁷⁾ As a preliminary evaluation, iṣfahān’s counterparts in the neighboring musical systems, namely, the Arabic maqāmāt and the Turkish makams, are also identified. Near the end, I propose an evolution pattern for iṣfahān and present the scalar transpositions (or repositions) of the basic form of this maqām.

[0.3] Readers should note that this article is concerned with the basic theoretical characteristics of iṣfahān as a maqām or a dastgāh, as opposed to its performance aspects.⁽⁸⁾ I would like to emphasize that in no way is this article claiming to have examined the subject absolutely completely, nor should the proposed evolution pattern and the conclusions be taken definitively. This effort, at best, represents a further step in the understanding of Persian music dastgāhs/maqāms and finding possible connections between the disconnected Systematist adwār and the modern modal systems, which has been of interest to some musicologists.⁽⁹⁾ Very little work has been done in this regard, which is likely due, in part, to the difficulties encountered in connecting the dots between the two apparently different systems.

[0.4] A further issue that should be pointed out is the gap or the decline period in the theoretical analysis of music in Iran between approximately the sixteenth and the twentieth centuries.⁽¹⁰⁾ This characterization pertains not to the number of musical writings in the post-Systematist period, but to the overall quality and the content of the writings. The writings in the decline period deal mostly with inter-relationships, extra-musical, and non-theoretical properties of maqāms and generally lack explanations of their intervallic structures.⁽¹¹⁾ Therefore, this article, which is interested in the theoretical analysis of iṣfahān and the evolution of its intervallic structure, examines and cites the writings from almost exclusively the Systematist and the modern periods. The presence of the gap, however, may lead to conjecture on the part of the researcher. Nevertheless, the proposed evolution pattern for iṣfahān appears relatively clear at the end and does not imply a significant missing link.

[0.5] The basic terms needed for the examination of iṣfahān are explained as they are introduced in the next two sections and are also summarized in the glossary section at the end of the article. To avoid complications in defining the musical terms (such as dastgāh, maqām, gūshih, radīf,āvāz, etc.), a simplified approach has been favored. One may encounter somewhat different definitions for each term in the contemporary sources. For instance, as argued by Fakhreddini (2013, 36), the terms dastgāh and maqām are literally synonymous—both meaning or referring to the position of hand on the neck of the instrument. However, the two terms typically have different connotations in modern musicology. I have used the term dastgāh in connection to the groupings in the radīf and the term maqām outside the radīf.⁽¹²⁾

[0.6] A note on nomenclature should be added here. For the species titles, I have used the Systematist nomenclature even for analyzing the contemporary maqāms. Tetrachordal analysis of the contemporary Persian maqāms/dastgāhs is a relatively new theoretical approach, and there is no consistency in the titles used to refer to the species among the musicologists. I see no compelling reason for coming up with new and subjective species titles in analyzing Persian maqāms/dastgāhs as some musicologists have (Talai 1993, 16; Hodjati 1998, 97; As’adi 2008, 48), when we can find the titles in the Systematist treatises. The use of Systematist nomenclature for examining Arabic and Turkish maqāms provides a challenge, as they have been using tetrachordal analysis for a longer period (over a century) even as the exact meaning or intervallic structure of some of the species has changed. To tackle this issue, I have provided both the medieval titles (for consistency) and the contemporary Arabic/Turkish titles in section 5.

1. Maqām Iṣfahān in the Treatises of the Systematists

[1.1] Ṣafi al-Din Urmawi (1216–1294), Quṭb al-Din Shirazi (1236–1311), ʿAli Jurjani (1339–1414), ʿAbd al-Qadir Maraghi (d. 1435), Nur al-Din ʿAbd al-Raḥman Jami (1414–1492), Muḥi al-Din Muḥammad Ladhiqi (d. 1494), and ʿAli Ibn-Muḥammad Miʿmar (known as Banayi, d. 1513) were among the main scholars in the Systematist school of music. Urmawi is the first scholar in the Muslim world to provide a systematized classification of the modal species, particularly tetrachords, pentachords, and octave species. In these species, he identifies three small intervals (Urmawi [1235] 2001, 14), namely ṭanīnī (Ṭ, whole tone), mujannab (J, neutral interval with a range of sizes averaging three-quarter tone), and baqīyyah (B, typically a semitone). Shirazi (2008, 128) recognizes two additional unnamed intervals, labelled H of 7:6 (266.9 c) and W of 6:5 (315.6), which can be referred to as half-augmented tone (close to five quarter tone) and augmented tone, respectively.⁽¹³⁾ Note that the exact sizes of these intervals depend on the fretting system applied or theoretically advocated, and have never been fixed or “standardized” in practice or even in theory.⁽¹⁴⁾

[1.2] In al-Adwār, Urmawi ([1235] 2001, 21) lists seven mulāyim (consonant) tetrachords and twelve mostly mulāyim pentachords.⁽¹⁵⁾ These species are used to establish eighty-four adwār by iterations based on the combination of a lower tetrachord and an upper pentachord. The seventh listed tetrachord is iṣfahān with the intervallic structure JJJB, which can be notated as G–A–B♭–B–C (Jurjani [1375] 1938, 298).⁽¹⁶⁾ This is the only recognized species of fourth with five tones or four intervals. Shirazi (2008, 127) added the tetrachord ḥijāz, with the intervallic structure JHB (G–A–B–C), to the seven tetrachords listed by Urmawi. These two tetrachords use the same tones (at least in notation as opposed to the actual interval sizes that could vary in practice) except for one, the third tone of iṣfahān (B♭) that is not included in the ḥijāz tetrachord. Among the twelve pentachords recognized by Urmawi, two of note include Type 7 (JJJBṬ) and Type 8 (ṬJJJB). These two species were referred to as zīrkish-i ḥussaynī and iṣfahān-i ʾaṣl (or mukhālif-i rāst), respectively, by Shirazi (2008, 127). Banayi ([1484] 1989, 34), on the other hand, referred to the former as humāyūn and to the latter as panjgāh-i zāyid or iṣfahān.⁽¹⁷⁾

[1.3] Urmawi provides more context for the peculiar five-tone iṣfahān tetrachord, which is worth reviewing. In al-Sharafīyyah (Urmawi [1267] 1938, 51–55), he explains:

The fourth is sometimes made to produce five notes; it then includes four intervals, contrary to the general rule. These intervals can be combined in various ways. The best proportioned of these combinations are of two species. The first is obtained by first deducing from the fourth the ratio interval 1 + ¹⁄₁₂, then the ratio interval 1 + ¹⁄₁₃, and finally another ratio interval 1 + ¹⁄₁₂. The complement of the fourth will then have the ratio 1 + ¹⁵⁄ ₂₇₃. We show this species below (Row 1 in Example 1). To obtain the second species (Row 2), at the interval of ratio (1+) ¹⁄₁₂ which, in the first, occupies the low end of 1 + ¹⁄₇, we substitute another having the ratio 1 + ¹⁄₁₄. We will thus have the ratio 1 + ¹⁄₆ between the first note and the third, 1 + ¹⁄₄ between the first and the fourth, and 1 + ¹⁄₃ between the first and the fifth. The intervals of this type of fourth can be combined in twenty-four different ways. The first combination, the only one used, is very well known; the others are weak in sound. I call this genus the SINGULAR or FIRST PARTICULAR. Below, in a table, (you can find) the representation of this type of fourth and all its (twenty-four) combinations (not presented here). If we remove from the previous genus (Species 2) the ratio interval 1 + ¹⁄₁₅, the rest will constitute a kind of particular, independent genus, resembling nothing at all from the others. I call this genre the SINGULAR SECOND. You know that such a genre can only have six combinations. These combinations, however, all sound the same to the ear and are only worth one because of the smallness of their intervals which are too close. Any melodic composition based on the notes of the SINGULAR FIRST genre, today well known to the masters of the art, who generally employ this genre at the top of the scale, bears the name iṣfahān. Any melodic composition based on the notes of the SINGULAR SECOND genre is called by them rāhawī. The ancient Arabs called these mazmūm.

[1.4] As shown in Example 1, Species 2 (the basis of iṣfahān according to Urmawi) should be presented as a series of four mujannabs (of somewhat different sizes), based on the interval sizes he identifies. However, Urmawi ([1235] 2001, 21; [1267] 1938, 119) presents it as a series of three mujannabs and a baqīyyah in both treatises (al-Adwār and al-Sharafīyyah), with the notes in abjad as shown in Example 2. This is problematic though, because in the third chapter of al-Adwār (Urmawi [1235] 2001, 14; Wright 1978, 133, 191) he had approximated the size of mujannab with the ratio 16:15 (111.7 c and close to the Pythagorean apotome of 113.7 c, i.e., a limma plus a comma). Following him, Banayi ([1484] 1989, 15) chose the simpler interval 16:15 to represent all mujannabs in his listed species. In the Systematist treatises, baqīyyah is typically a limma (ca. 90.2 c) but sometimes a comma (ca. 23.5 c). The reason for such representation may be the fact that Urmawi ([1235] 2001, 18) considered a sequence of four mujannabs a cause of dissonance on the basis that it would exceed a perfect fourth. (In this case, it seems likely he was considering mujannabs of larger sizes.) Representing Species 1 in Example 1 (with the last interval of 92 c close to a limma) as a series of three mujannabs and a baqīyyah would conform better to the definitions provided by the Systematists.

[1.5] Shirazi (2008, 127) presents a different notation (the fourth tone being w (B) instead of z (B) in Example 2) for the iṣfahān tetrachord; here, the interval sizes are consistent with those of Species 2 in Example 1 and in line with the fact that the last interval is indeed a small mujannab. Yet, he shows the last interval as a baqīyyah, which is contradictory. The other Systematists repeat Urmawi’s notations.⁽¹⁸⁾ It thus appears that the most accepted and presented form of iṣfahān tetrachord was a sequence of five tones (such as G–A–B♭–B–C) with the intervallic structure of JJJB, with some ambiguity in the size and designation of the last interval (mostly a limma but in some cases a limma plus a comma). As discussed in Section 2, this ambiguity persists to the present day.

[1.6] When listing the adwār, Urmawi and Shirazi present different scales for iṣfahān, as shown in Example 3 (Wright 1978, 75–76).⁽¹⁹⁾ Here, between the prominent tones that he marked, C and F, Shirazi uses the tone sequence that, despite appearing to represent the intervallic sequence JJJB (iṣfahān tetrachord), in terms of actual sizes (ratios) corresponds to JJJJ in Example 1. Maraghi ([1418] 1966, 68) presents two scales, referring to the one consistent with Urmawi’s scale as ʾaṣl (authentic). Ladhiqi ([1485] 1939, 379) and Banayi ([1484] 1989, 51–54) repeat Urmawi’s scale, with Banayi referring to a cycle made of two disjunct iṣfahān tetrachords as shuꜥbah iṣfahān. Jami (2000, 196) recognizes both Urmawi’s and Shirazi’s versions and refers to them as iṣfahān with a baqīyyah at the high end (aḥad al-baqīyyah) and iṣfahān with a baqīyyah in the middle (waṣat al-baqīyyah), respectively. All these adwār have one species in common and that is the peculiar iṣfahān tetrachord (JJJB) at the upper ṭabaqah (shelf or register) of the scale, which was the characteristic and the main species of maqām iṣfahān according to Urmawi (underlined in [1.3]).

2. Dastgāh Iṣfahān according to the Twentieth-Century Musicologists

[2.1] The radīfs of Persian art music contain hundreds of gūshihs (ranging from approximately 100 to 500; Nettl 1992, 5–7) that appear in several dastgāhs. Each dastgāh starts with a darāmad (introduction or entry), representing the “maqām-i mādar” (main or parent mode) of the dastgāh (Alizadeh et al. 1996, 33). The other gūshihs in the dastgāh may have different characteristics from the darāmad due to modal function variation or modulation. The main and basic theoretical characteristics of each gūshih are its intervallic structure and degree functions. The characteristic degree functions are āghāz (A, the starting tone), khātimih (K, the ending tone or conclusion), shāhid (S, the prominent tone), īst (I, the temporary stop or dwelling tone), and mutighayyir (M, the variable tone). Other characteristics of gūshihs include their melodic range and progressions as well as the specific melodic patterns or motives employed (Zonis 1973, 47).

[2.2] Many musicologists have examined the modal scheme and degree functions of iṣfahān with varying theoretical perspectives or models.⁽²⁰⁾ To aid discussion, the modal schemes of iṣfahān formulated by selected prominent twentieth-century musicologists are presented in Example 4. The following points may summarize their approaches and opinions on the modal characteristics of iṣfahān:

• Different frameworks have been used to present the modal scheme of iṣfahān, such as the octave-based scale (by Hedayat 1938a and 1938b, Vaziri 1934, Khaleghi 1982 and 1999, and Barkeshli 1976), the conjunct tetrachord form (by Fakhreddini 2013, Kiani 1992, Alizadeh et al. 1996, Talai 1993 and 2017, and Hodjati 1998) and a series of ascending notes (by Farhat 1990, Massoudieh 1997 and 2003, and During 2006).

• Some musicologists recognize two modal schemes for iṣfahān: the qadīm (old; pre-twentieth century) and the jadīd (new; post-twentieth century). According to the most common interpretation, the scale forms for the old and the new iṣfahān can be notated (on C, as a common example) as C^K,S–D–E♭–F–G–A^I–B–C (ṬBṬṬ–JṬJ) and C^K,S–D–E♭–F–G–A^I–B–C (ṬBṬṬ–JHB), respectively. The difference is in the status of  $\hat{7}$ that makes two slightly different upper tetrachords, specifically ꜥirāq and ḥijāz.⁽²¹⁾ Hedayat (1938a and 1938b), who followed the nineteenth-century tradition, recognized only the old form as iṣfahān and called the new form rāk without mention of their relationship.⁽²²⁾ Vaziri (1934, Part 2, 158) believed the authentic form to be the old form and the new form to have been created under the influence of Western music. Some musicologists believe that the seventh tone should be played about a comma lower than the notated new form (During 2006, 300; Alizadeh et al. 1996, 70), producing an apotome last interval rather than a semitone. This issue, as discussed in [1.5], was also the dilemma for the Systematists.⁽²³⁾

• The main tetrachord in iṣfahān is the upper tetrachord (JHB in the “new” form) starting from $\hat{5}$, i.e. the namāyān (N) according to Vaziri (1934) and Khaleghi (1982 and 1999).⁽²⁴⁾

• The shāhid of maqām iṣfahān and of the darāmad in the radīf is $\hat{1}$. Note that this is not the case for all Persian dastgāhs or maqāms (such as humāyūn and abūꜥaṭāʾ).

• Iṣfahān has two common khātimihs, namely $\hat{1}$ (shāhid) and $\hat{6}$ (or more accurately, the third below the shāhid). Ending on the shāhid (the tonic of the scale form) is the complete khātimih as it produces a sense of final rest and stability (qarār, a term used primarily in Arabic maqāmāt). Ending on $\hat{6}$ (which is $\hat{2}$ of humāyūn and its shāhid according to most musicologists) provides a sense of suspense or lack of completion (Massoudieh 1997, 105);⁽²⁵⁾ as such it may be better referred to as the īst (temporary conclusion) following Vaziri (1934, Part 2, 163), Farhat (1990, 12) and Pirniakan (2010, 222). The āghāz (starting tone) is typically either the tonic or the namāyān.

• A characteristic or common mutighayyir, as seen in some other dastgāhs such as humāyūn, dashtī, and afshārī, is not generally recognized in iṣfahān; the superscript M appears only on the modal schemes of Massoudieh (1997, 2003) and Talai (1993, 2017) in Example 4.

• The main modulation from iṣfahān to other dastgāhs is a modulation to shūr—or even to the gūshih zābul of the dastgāh sigāh—through the gūshih ꜥushshāq with a shāhid established on the namāyān of iṣfahān (Khaleghi 1982, Part 2, 163; Fakhreddini 2013, 311). Because its shāhid is on $\hat{8}$ of humāyūn, ꜥushshāq acts as the owj (climax) of iṣfahān and humāyūn and moves the nucleus of activity to the first pentachord of iṣfahān (the Systematist navā that is changed to rāst upon raising $\hat{3}$ a quartertone). Another possibility is a modulation to afshārī through the gūshih ruhāb, which has a shāhid on $\hat{4}$, an īst on $\hat{3}$ (becoming a neutral 3rd instead of a minor 3rd) and a khātimih on $\hat{1}$ of iṣfahān (Fakhreddini 2013, 312). Returning to humāyūn as the primary dastgāh is, of course, part of the dastgāh/radīf tradition.⁽²⁶⁾ Some gūshihs in iṣfahān may resemble those in humāyūn and vice versa. For instance, a dwelling (īst) on $\hat{2}$ of iṣfahān occurs in the gūshih bayāt-i rājiꜥ, which resembles the gūshih bīdād of humāyūn with a shāhid on $\hat{5}$ of humāyūn (Fakhreddini 2013, 306). The khātimih would typically be the distinctive point between the similar gūshihs in humāyūn and iṣfahān (Khaleghi 1982, vol. 2, 165).

3. Musical Analysis of Gūshihs and Taṣnīfs in Iṣfahān

Methodology and Sources

[3.1] The statistical analysis of the gūshihs and taṣnīfs in iṣfahān, in terms of the characteristic degree functions āghāz, khātimih and shāhid, was performed on three renowned radīfs and two taṣnīf collections. The most prominent tones in terms of duration and frequency of appearance, as indicators of emphasis (Talai 2017, 23), were determined through statistical analysis. To this end, an eighth note was given a value of 1 unit for duration and the other notes were given proportional values. The notes were then tallied and used to establish tone distribution graphs. Similar methods have been used by Vaziri (1934, Part 2, 22), Wright (1992, 502), and Djafarzadeh (2013, 62) to determine the shāhid.⁽²⁷⁾

[3.2] The first source examined was the vocal radīf of Mahmud Karimi (1927–1984). This radīf was initially transcribed by Massoudieh in 1977, for which Arshad Tahmasbi (b. 1958) provided an instrumental response in 1995 by slightly modifying the notations (removing some of the vocal ornamentations, which would not affect my analysis). This study primarily relies on Tahmasbi’s transcriptions for analysis, while checking those of Massoudieh. The other two radīfs examined were the vocal radīf of ꜥAbdollah Davami (1891–1980) and the instrumental radīf collected by Musa Maꜥrufi (1889–1965). Faramarz Payvar (1933–2009) published a transcription of Davami’s radīf in 1960, which was reportedly approved by Davami himself (Payvar 2011, 7–10). Maꜥrufi gathered a large collection of gūshihs mostly attributed to the Farahani’s brothers, Mirza ꜥAbdullah (1843–1918) and Aqa Hussayn Qoli (1853–1916), and published the collection in 1963.⁽²⁸⁾

[3.3] The two taṣnīf collections examined were Davami’s nineteenth-century taṣnīfs,⁽²⁹⁾ transcribed by Payvar, and the twentieth-century taṣnīfs gathered and published by Habibollah Nasirifar (2001). Some twentieth-century taṣnīfs labeled as iṣfahān conformed to either the harmonic minor scale (i.e., tempered iṣfahān⁽³⁰⁾) or the natural minor scale; I grouped these as “minor” (referred to as mīnur in Iran) and analyzed them separately from those conforming to untempered iṣfahān. Examination of the prominent tones was carried out on a fraction of the untempered and tempered iṣfahān songs, and the songs in natural minor scale were excluded. Examination of the āghāz and khātimih was performed on all songs in the two groups.

Main Gūshih Types and a Taṣnīf Example

[3.4] Karimi’s radīf contains eleven gūshihs in iṣfahān, including two darāmads. Example 5 shows the first darāmad. The first segment of the piece clearly introduces the ḥijāz tetrachord with emphases on $\hat{5}$ (D, namāyān) and the tonic (G). These two notes correspond to the prominent tones marked by Shirazi (2008), encompassing the Systematists iṣfahān tetrachord (Example 3). The rest of the piece shows melodic movement pivoting around $\hat{1}$. The two histograms in Example 6 are essentially similar and indicate both that the most prominent tone (shāhid) is $\hat{1}$ and that the nucleus of activity is the ḥijāz tetrachord (as opposed to the other tetrachord of iṣfahān, i.e., navā, which in this piece would be from G4 to C5). Example 7 presents the tone duration of every gūshih in order, showing a progression of shāhid from $\hat{1}$ to $\hat{5}$ and then back to $\hat{1}$. The progression of shāhid is more clearly demonstrated in Example 8, which exhibits an overall arch-shaped progression particularly in terms of tone duration.⁽³¹⁾

[3.5] The second gūshih to be treated is bayāt-i rājiꜥ as it appears (with some variance) in the three radīfs examined in this study. Karimi’s version is a relatively long piece with a short range of notes between $\hat{1}$ and $\hat{6}$ of iṣfahān that can be divided into five parts alternating between two distinguishable modes. The initial, representative phrases of Part 1 and the entire Part 2 are shown in Example 9. The main mode (Parts 1, 3, and 5) is that of bayāt-i rājiꜥ with an indistinct shāhid between $\hat{2}$ and $\hat{4}$ (Example 10; with some emphasis on $\hat{2}$ in Part 1), a predominantly minor 3rd tone (occasionally changing to a neutral 3rd) and an īst (the ending note of each part) on $\hat{2}$ of iṣfahān. The indistinct prominence among three consecutive tones is likely a result of a dual emphasis on $\hat{2}$ and $\hat{4}$, which results in frequent passages through $\hat{3}$. The second mode (Parts 2 and 4) exhibits very distinct shāhid (Example 10) and īst on $\hat{4}$ as well as a characteristic neutral 3rd tone consistent with the lower tetrachord of the Systematist iṣfahān. The most prominent tone of the entire piece was $\hat{4}$ as well (Example 11). The main tetrachord and the center of activity in all parts is formed between $\hat{1}$ and $\hat{4}$ (i.e., predominantly navā for Mode 1 and rāst for Mode 2).

[3.6] Examples 12 and 13 show the main part of the gūshih bayāt-i rājiꜥ in Davami’s radīf along with its tone distribution curves. This piece also exhibits a somewhat indistinct emphasis on $\hat{2}$, $\hat{3}$, and $\hat{4}$ (Example 13), but with phrase endings on $\hat{2}$ throughout the piece. Therefore, Karimi’s and Davami’s versions of bayāt-i rājiꜥ exhibit a characteristic īst, but a somewhat indistinct shāhid, on $\hat{2}$, and a nucleus of activity in the first tetrachord of the scale with a (predominantly) minor $\hat{3}$.

[3.7] Maꜥrufi presents two gūshihs of bayāt-i rājiꜥ. The first piece is similar to Davami’s version of bayāt-i rājiꜥ in terms of phrase endings (including the khātimih) on $\hat{2}$ as well as the overall tone distribution curves. The second piece (Example 14), however, conforms best to modern descriptions of bayāt-i rājiꜥ ([2.9]; As’adi 2008, 49); i.e., it exhibits distinct prominence on $\hat{2}$ (Example 15). The second piece ends on $\hat{1}$ of iṣfahān (which can be considered a cadence or furūd to the maqām iṣfahān), as opposed to $\hat{2}$ as in the other examples. These two examples by Maʾrufi demonstrate the two types of khātimih in bayāt-i rājiꜥ, as also pointed out by Fakhreddini (2013, 306).

[3.8] The third gūshih type to be examined concerns a number of gūshihs in iṣfahān that exhibit a significant emphasis on $\hat{4}$ of iṣfahān; this is especially notable, in that there is rarely a mention or explicit demonstration of a $\hat{4}$ shāhid in iṣfahān in the literature.⁽³²⁾ In addition to the second mode identified in Karimi’s bayāt-i rājiꜥ (Example 9), two gūshih examples with some emphasis on $\hat{4}$ include Davami’s gūshih ꜥirāq (Examples 16 and 17) and Maꜥrufi’s gūshih ḥazīn (Examples 18 and 19). The gūshih ꜥirāq exhibits a very clear emphasis on $\hat{4}$ (Example 17) and a neutral $\hat{3}$ (rāst tetrachord). The gūshih ḥazīn’s emphasis, on the other hand, is less distinctive (rivaled by $\hat{3}$; Example 19) and appears with a minor $\hat{3}$ (navā tetrachord). Both examples ended on $\hat{2}$ of iṣfahān, which is to say an īst or incomplete conclusion with respect to iṣfahān.

[3.9] A representative example of a taṣnīf in iṣfahān is the nineteenth-century composition by Ali-Akbar Shayda (1843–1945) known as “ey mah-i man” (O’ My Moon) or “but-i chīn” (the Chinese Idol). The piece is usually followed by a ring (also transliterated as reng), a fast-tempo, typically-instrumental dance piece. A simplified notation of the taṣnīf along with the tone distribution curves for the taṣnīf and the ring are presented in Examples 20 to 22.⁽³³⁾ The taṣnīf can be divided into three sections, each comprising a verse (solo) and the refrain (chorus). Sections A and B are generally similar and represent the basic maqām of iṣfahān with a shāhid on $\hat{1}$ (Example 21) and a minor $\hat{3}$. The verse of section C (mm. 45–50) can be considered a modulation to ꜥushshāq (owj) with a shāhid on $\hat{5}$, a neutral $\hat{3}$, and an ending on $\hat{1}$. The second part of Verse 3 (mm. 51–54) returns to the basic mode of iṣfahān. All three sections have an īst on $\hat{6}$ (a third below the shāhid). The piece ending on $\hat{6}$ leaves the listener in waiting for another piece, the ring, that ends on $\hat{1}$ (the main khātimih of iṣfahān) and provides a sense of resolution and completion. The shāhid of the ring is also $\hat{1}$ (Example 22), consistent with basic maqām iṣfahān.

Degree Functions in the Analysed Sources

[3.10] Examples 23 to 26 summarize the scale-degree function distributions in the gūshihs and taṣnīfs from the selected Persian sources. The āghāz was most frequently $\hat{5}$, $\hat{1}$, or $\hat{4}$ (Example 23). This distinguishes it slightly from its Western counterpart (i.e., the harmonic minor mode as examined in a selected repertoire but not presented here for reasons of brevity), in which $\hat{3}$, not $\hat{4}$, frequently serves also as a starting tone.⁽³⁴⁾ It is quite possible that the significant reduction of an āghāz on $\hat{4}$ in Nasirifar’s twentieth-century taṣnīfs compared to the nineteenth-century taṣnīfs is a result of Western music influence. The khātimih was in most cases $\hat{1}$ (followed by $\hat{5}$) in Karimi’s radīf and Nasirifar’s taṣnīfs (Example 24), whereas a khātimih on $\hat{1}$ was less predominant in the other two radīfs and in the nineteenth-century taṣnīfs; instead, $\hat{6}$ and/or $\hat{2}$ frequently appear as the concluding tone. A conclusion on $\hat{2}$, similar to one on $\hat{6}$, can be considered a temporary/incomplete stop (i.e., īst) or a complete stop for a mode established on $\hat{2}$ of iṣfahān (i.e., its first scalar transposition, as discussed in [5.8]).

[3.11] Although there was some progression of the shāhid among the gūshihs (as demonstrated for Karimi’s radīf in Example 8), Example 25 shows that the most prominent tone remained predominantly $\hat{1}$ in the selected radīfs. The predominance of shāhid on $\hat{1}$ was most pronounced in Davami’s nineteenth-century taṣnīfs. In contrast, the predominance decreased in the twentieth-century taṣnīfs, where $\hat{3}$ and $\hat{5}$ were often the most prominent tones, overall. This change may again be due to Western music influence, where members of the tonic triad are generally most prominent.

[3.12] Example 26 shows the results of the analysis of the twentieth-century taṣnīfs that were in the minor mode (mostly harmonic minor) but labelled as iṣfahān in the collection. The āghāz was most frequently $\hat{1}$ or $\hat{5}$, as was also the case for the untempered iṣfahān (Example 23). The khātimih was also predominantly $\hat{1}$, but with no occurrence on $\hat{6}$. Similarly, shāhid was most frequently $\hat{1}$ or $\hat{5}$, with an increase in the percentage of $\hat{5}$ (i.e., the dominant in the minor mode). Overall, it may be concluded that the pieces in tempered iṣfahān showed relatively similar characteristics to those in untempered iṣfahān in Nasirifar’s collection (as well as the Western art pieces examined; see note 34).

4. Iṣfahān Counterparts in Arabic and Turkish Musical Systems

[4.1] Since iṣfahān is a very popular musical mode in Iran and its scale is very close to the harmonic minor scale, it is natural to ask whether there is a (popular) mode similar or close to iṣfahān in the Arabic maqāmāt or the Turkish makams. These are three closely related musical systems with common theoretical roots in the Systematist treatises. A thorough examination of these musical systems is beyond the scope of this investigation, but the results of a preliminary inquiry centering on a few selected sources will be presented here.

[4.2] The main counterpart maqām to the Persian iṣfahān in Arabic music (at least in the scale form) appears to be nahāvand (or nahāwand).⁽³⁵⁾ In all classifications of the principal Arabic maqāmāt—which may vary from 8 to 12 octave species in the treatises of the last century—nahāvand is included (Marcus 1989, 333). Muallem (2010, 120–137) presents maqām nahāvand within the nahāvand family, consisting of nahāvand, faraḥfazā, ꜥushshāq miṣrī, būsalīk, nahāvand muraṣṣaꜥ, and sulṭānī yakāh; all of these begin with a nahāvand species. With a variable (mutighayyir) $\hat{7}$ (Example 27), nahāvand is identical to the harmonic minor scale in ascending order and to the natural minor scale in descending order. Therefore, the primary ajnās (genera or species) of the scale are the disjunct tetrachords nahāvand (ṬBṬ; equivalent to the medieval navā) and ḥijāz (BWB; the tempered medieval ḥijāz) in ascent and the disjunct tetrachords nahāvand and kurd (BṬṬ; the medieval būsalīk) in descent. When a cadence from $\hat{8}$ to $\hat{4}$ is emphasized, an upper pentachord of navā-athar (ṬBWB) emerges, which may be considered a tempered medieval nayrīz (ṬJHB).⁽³⁶⁾ Marcus’s (1989, 215, 623) description of maqām nahāvand is similar to that of Muallem (2010). Both explain that there have been disputes among scholars not only on the basic form of maqām nahāvand, but also on how to interpret its variations (mostly on the upper tetrachord). It is clear that the basic ascending scale of nahāvand is similar to the tempered iṣfahān (Example 27). One difference is perhaps the main species in the basic forms of the two maqāms appears to be the lower tetrachord (navā) in nahāvand but the upper tetrachord (ḥijāz) in iṣfahān (specifically the darāmad). Muallem also demonstrates that the fourth reposition of the basic scale of nahāvand (with a major $\hat{7}$) forms the scale of ḥijāz-humāyūn. The modern Persian iṣfahān and humāyūn have a similar relationship.

[4.3] Signell (2008, 32–34) presents the Turkish makam puselik (also referred to as buselik) with a scale similar to those of the Persian iṣfahān and the Arabic nahāvand (Example 27). He considers puselik as one of the thirteen “basic scales” of the Turkish art music, made of a lower puselik pentachord (ṬBṬṬ; the medieval navā)⁽³⁷⁾ and an upper hicāz tetrachord (J₁HJ₁;⁽³⁸⁾ the modified medieval ḥijāz). No variable tone is marked by Signell. Although Signell does not explicitly identify a makam as iṣfahān, he mentions iṣfahān on a few occasions. On one occasion, he mentions iṣfahān as a “passing modulation” from hicaz-hümayun (81) but does not provide its modal scheme explicitly. Aydemir (2010, 84), on the other hand, presents both the Turkish makams buselik and nihavent (a variation of the word nahāvand) as well as isfahan. Aydemir presents makam buselik in two forms. The first form is made of a lower buselik pentachord (ṬBṬṬ) and an upper kurdī tetrachord (BṬṬ). The second form is very close to the scale presented by Signell (Example 27); the only difference is $\hat{6}$ (F) that is a comma higher in Aydemir’s scale (Fǂ), which is likely the correct notation based on the interval sizes presented even by Signell. Aydemir (87) explains that nihavent is basically a transposition of makam buselik (with the two forms) from A to G.

[4.4] The basic form of Turkish makam isfahan, according to Aydemir (2010, 149), comprises a lower uşşak tetrachord (J₂J₁Ṭ; the medieval nowrūz), and an upper buselik pentachord (ṬBṬṬ). He explains that the variations of scale degrees $\hat{2}$ and $\hat{3}$ (i.e., changing the lower tetrachord to rāst) is a characteristic of the Turkish makam isfahan. Based on this definition, the Turkish makam isfahan does not contain a tempered or untempered ḥijāz tetrachord. As shown in Example 27, the common species between the Turkish makams buselik/puselik (as well as the transposed form nihavent) and isfahan is the navā pentachord ṬBṬṬ (referred to as buselik in the contemporary Turkish music). This pentachord also appears to be the main species in the Arabic maqām nahāvand and the lower (but not the main) species of the Persian maqām iṣfahān. Although the navā tetrachord/pentachord was not the main species of the darāmad of iṣfahān, it assumed the nucleus of activity (including the rāst tetrachord/pentachord upon the third-tone variation) in many other gūshihs, such as bayāt-i rājiꜥ, sūz-u gudāz, owj/ꜥushshāq, ḥazīn, kirishmih, ruhāb, shāhkhatāyī, and ꜥirāq. The comparisons made in this preliminary evaluation indicate that, despite some differences, there are many connections among the three musical systems that merit further investigation.

5. Further Discussion

Medieval Iṣfahān and its Evolution

[5.1] As discussed in section 1, the most consistent form of the dawr iṣfahān among the Systematists was the cycle presented initially by Urmawi ([1235] 2001), and comprising a lower rāst tetrachord and an upper iṣfahān pentachord. Although Urmawi’s 84 listed adwār were established mathematically by permuting all combinations of an upper pentachord to a lower tetrachord, this does not necessarily mean that practitioners regarded the tone between the two species as prominent. It is likely that the dawr would simply represents the intervallic structure of the maqām. The failure to mark the prominent tones in the cycles is a shortcoming of Urmawi’s permutative theoretical approach that unfortunately was replicated by most Systematists. Due to this condition, two possibilities for the position of the prominent tone should be considered: the fourth degree (i.e., a cycle made of a rāst tetrachord and an iṣfahān pentachord) and the fifth degree (a cycle made of a rāst pentachord and an iṣfahān tetrachord).

[5.2] Shirazi (2008), in contrast, marks the prominent tones of the adwār, which makes his account more informative. For the dawr iṣfahān, he marks the tones at the two ends of the iṣfahān tetrachord (Example 28). However, his version of the dawr iṣfahān is slightly different from Urmawi’s. Shirazi’s cycle can be considered a dawr established on $\hat{2}$ of Urmawi’s dawr iṣfahān (Form 1 in Example 28: transposed). Rearranging the cycle so that a prominent tone occurs at the beginning of the scale (i.e., a scalar transposition or reposition) yields the second form in Example 28 with a lower iṣfahān tetrachord and an upper rāst pentachord. This form, identified as muḥayyir-i zīrkish by Shirazi (134), is consistent with the contemporary maqām humāyūn (also presented in Example 28) in terms of the intervallic structure and the prominent tones, with one slight modification, namely the omission of the third tone of the lower iṣfahān tetrachord (JJJB) that changes it to ḥijāz (JHB). This modification makes the octave species heptatonic, which has been the conventional scale form in Iran, as well as the rest of Western Asia. These accounts give evidence of the close relationship between the adwār humāyūn and iṣfahān. The two versions of the dawr iṣfahān, as also examined by Wright (1978, 76), may reflect a question among the Systematists on how to present the octave species of iṣfahān. As mentioned in Section 1, Jami (2000) presented both Urmawi’s and Shirazi’s cycles.

[5.3] The ambiguity in the order of the tetrachord and pentachord also appears in Hedayat’s (1938b) modal scheme of contemporary humāyūn, since it uses the intervallic structure JJṬ–JHBṬ (Example 28) and the ḥijāz species appears in the upper pentachord. His order of the two species is opposite of how the scale of humāyūn is typically shown (the row above Hedayat’s in Example 28). Hedayat did not clearly indicate the ending tone (a khātimih or a “maḥaṭṭ,” which he considered a criterion for establishing the dawr) for each “zamīnih” or scale he listed. For those he marked the concluding tone with an x, while discussing them in the text these were typically either $\hat{1}$ or $\hat{4}$ of the modal scheme (Hedayat 1938b, Part 3, 31). This means that the order of his listed species, perhaps in similar manner to the Systematist adwār, does not necessarily indicate whether $\hat{1}$ or $\hat{4}$ is the tonic (the typical concluding tone) in the modern concept of scale.

[5.4] A few additional adwār listed by Shirazi (2008) merit mention, as well. One is the dawr ḥijāz (Example 28) that, when rearranged to have one of the prominent tones as degree $\hat{1}$, becomes the contemporary humāyūn readily, without a need to omit any extra tone. The rearranged form becomes the cycle Shirazi (134), listed as nahuft-i ḥijāz. The other cycle relevant to our discussion is zangūlih, for which Shirazi explains that it is also called nahāvand by some. This cycle appears to be in between the contemporary Arabic nahāvand or Persian iṣfahān (Example 27) and the Systematist iṣfahān; it can be considered a cycle made of conjunct rāst and ḥijāz tetrachords, whereas the Systematist and the contemporary iṣfahān can be considered a cycle comprising disjunct rāst/navā (as variations) and ḥijāz (or the original iṣfahān) tetrachords. These observations attest to the relationships between the medieval adwār iṣfahān, humāyūn, ḥijāz, and nahāvand. Example 29 summarizes these relationships for iṣfahān, humāyūn, and ḥijāz and presents their possible evolution paths to the contemporary maqāms. They all appear to have roots in the peculiar, “singular” iṣfahān tetrachord with five tones and four intervals, from which either the iṣfahān and humāyūn pentachords can be established or the ḥijāz tetrachord (with the conventional three intervals and four tones) can be derived.

[5.5] To facilitate tracing the possible evolutionary steps of the dawr/maqām iṣfahān, Example 30 presents all the discussed octave species of iṣfahān in staff notation, along with the two suspected alterations or variations. The first form collectively comes from the Systematist accounts. The scale is basically Urmawi’s dawr iṣfahān—referred to as the authentic iṣfahān by Maraghi—with the prominent tones indicated by Shirazi (i.e., those enclosing the iṣfahān tetrachord). In the absence of any other or contradictory information, and as proposed by Wright (1978, 76), it is reasonable to assume that the same prominent tones would apply to Urmawi’s scale as well. These prominent tones are also consistent with those in the contemporary form of iṣfahān (specifically the darāmad), namely scale degrees $\hat{1}$ and $\hat{5}$ (shāhid and namāyān). The next two forms represent possible variations. There is some historical evidence for the substitution of the iṣfahān tetrachord with the ḥijāz tetrachord (i.e., the first variation in Example 30). In his Risālih dar Mūsīqī (Treatise on Music), the fifteenth-century scholar from the Timurid Herat (today’s Afghanistan), Banayi ([1484] 1989, 34), refers to the species of fifth with the intervallic structure JJJBṬ as humāyūn, with the provision that the last ṭanīnī is omitted; this becomes the iṣfahān tetrachord at a position a fourth above the original position of iṣfahān. On the other hand, a near contemporary in the Ottoman empire, Ladhiqi ([1485] 1939, 451), provides an example for humāyūn melody in his al-Risālah al-Fatḥīyyah (Book of Conquest) that demonstrates the JHB tetrachord as its core species.⁽³⁹⁾ Similar core species (JHB) is also assigned to humāyūn as well as nayrīz (a branch of iṣfahān) in the sixteenth-century treatise Taqsīm al-Naghamāt (Wright 2019, 72). An important point to reiterate here is that Urmawi did not recognize the interval H in constructing the tetrachord and pentachord species, nor did he recognize the ḥijāz tetrachord JHB. Therefore, every species that could contain the ḥijāz tetrachord (JHB) appeared either with the five-tone iṣfahān tetrachord or the ꜥirāq tetrachord (JṬJ).

[5.6] The evidence for Variation 2, which replaces the rāst tetrachord/pentachord with navā, can be found in an early post-Systematist treatise, Taqsīm al-Naghamāt (Distribution of Notes), written by an anonymous musician/scholar in the mid-sixteenth century Safavid Iran. Although the scholar does not present the complete scale of any maqām, he provides their melodic contours in short formulae on the instrument nay (reed flute), which makes his account outstanding compared to the other treatises from this period. For iṣfahān, he presents a series of notes (Wright 2019, 53, 362) that in Western notation on G would be: G, B♭, A, G, F♯, F, E, F, E. If the notes are placed in the ascending order, the following “scale” (conjunct species around G) will emerge: [D]–E^K,I–F–F♯–G^A–A–B♭–[c]. I have added the terminal notes D (dugāh in the treatise’s terminology) and c (yigāh/rāst), to cover two complete tetrachords; the two added notes appeared in the melodic formula of one of the shuꜥab (branches) of maqām iṣfahān, i.e., nayrīz, in Taqsīm al-Naghamāt (Wright 2019, 57, 375). In the above scalar form, I have also identified by superscripts the starting tone (āghāz) that was repeated (likely a sign of emphasis, i.e., possibly also the shāhid) and the ending tone (i.e., the īst or the khātimih). The repetition of the last two notes in the contour (F and E) may suggest a simple cadence formula. It is interesting to see that the īst/khātimih (sigāh in the treatise’s terminology) is a neutral third below the āghāz/shāhid (panjgāh), which is still practiced in the contemporary iṣfahān and was the main khātimih in the 19th-century taṣnīfs (Example 24). The octave scale form would eventually take shape as shown in Variation 2 in Example 30, with a lower navā pentachord (ṬBṬ) and an upper iṣfahān (JJJB) tetrachord.⁽⁴⁰⁾ As demonstrated in Section 3, the earlier status of scale degree $\hat{3}$ (a neutral 3rd) appears in some gūshihs of the dastgāh iṣfahān, and, as such, there is some justification for considering a mutighayyir on $\hat{3}$ in iṣfahān. This tone (becoming $\hat{6}$) is a distinctive mutighayyir in the dastgāh humāyūn.

[5.7] What is typically referred to as iṣfahān-i qadīm by the twentieth-century musicologists (Row 4 in Example 30) that exhibited an upper ꜥirāq tetrachord (JṬJ) instead of the ḥijāz tetrachord is likely a variation/ambiguity of the last interval size that apparently has a historical precedent (Example 2). The return and stabilization of a semitone as the last interval (Row 5 in Example 30) may have been promoted and supported by the spread of Western music (harmonic minor in Row 6) in Iran in the twentieth century. Even so, Westernization should not be considered the cause of the change, as the exact position of the “leading tone” appears to have been unclear even in the Systematist treatises, while including a semitone (baqīyyah) as the last interval appeared to be the most prevalent form.

Maqām Iṣfahān and its Repositions

[5.8] The analyses in this investigation have revealed that the contemporary scale of iṣfahān can be formulated as shown in Example 31 for the scalar yigāh (the base scale),⁽⁴¹⁾ with the main and characteristic degree functions (shāhid, khātimih, āghāz, mutighayyir, namāyān, and īst) as marked by the superscripts. In general, based on the concept of reposition or scalar transposition, any degree of a scale can take the role of the tonic/khātimih and/or the shāhid. However, the shāhid in dastgāh iṣfahān (i.e., among the gūshihs in the radīfs) is established on $\hat{1}$ (e.g. darāmad and sūz-u gudāz), on $\hat{2}$ (e.g. bayāt-i rājiꜥ and jāmihdarān), on $\hat{4}$ (e.g. ꜥirāq and ruhāb) or on $\hat{5}$ (ꜥushshāq/owj). The repositions on the other degrees, therefore, are basically theoretical; as such, no maqām or gūshih example is provided for them in Example 31. Readers may further note that the repositions beyond the scalar panjgāh in Example 31 essentially coincide with (an octave higher of) the scalar dugāh through the scalar chahārgāh of humāyūn (see Poorhaydari 2025). In establishing the scalar transpositions, a slight change in the status of $\hat{3}$ (mutighayyir), or sometimes $\hat{6}$ or $\hat{7}$, was made in order to either conform to the radīf traditions or to ensure that either a perfect fourth or a perfect fifth interval is achieved.

[5.9] Two noteworthy characteristics in the scale forms presented in Example 31, which are not emphasized adequately in the literature, are the mutighayyir on $\hat{3}$ and the shāhid on $\hat{4}$ (the scalar chahārgāh). A common interpretation is that a neutral $\hat{3}$ is associated with certain gūshihs that originate from other dastgāhs (as suggested by their titles, i.e. ꜥushshāq from shūr and ruhāb from afshārī) and facilitate modulation to the other dastgāhs. Once it is established that the earlier Systematist form of iṣfahān was established with a lower rāst tetrachord/pentachord (with a neutral $\hat{3}$), it becomes conceivable that these gūshihs are internal (rather than external) to the dastgāh iṣfahān and possibly originating from the medieval from. In addition, the idea that most gūshihs with a shāhid on $\hat{4}$ (and a neutral $\hat{3}$) originate from other dastgāhs may be why most literature does not recognize a shāhid on $\hat{4}$ in iṣfahān. Another reason could be that iṣfahān is typically interpreted with respect to humāyūn, thus a shāhid on $\hat{4}$ of iṣfahān would translate to a shāhid on $\hat{7}$ of humāyūn. Although a shāhid on the fourth degree of a modal system is common in the dastgāh tradition (e.g. abūꜥaṭāʾ in shūr or chakāvak and shūshtarī in humāyūn), a shāhid on $\hat{7}$ is not. In fact, the statistical analysis of shāhid in the dastgāh humāyūn (i.e., within the same five sources as examined in this study) revealed nearly no prominence on $\hat{6}$ or $\hat{7}$ of humāyūn (Poorhaydari 2025); the same was observed in Example 25 for iṣfahān. It may be said that a shāhid on $\hat{4}$ in iṣfahān gives this maqām/dastgāh an independent character, compared to humāyūn.

[5.10] The Systematists, for the most part, did not discuss the scalar transpositions of the famous cycles.⁽⁴²⁾ They generally adopted a purely mathematical approach, most likely not shared by practitioners, that listed the adwār based on combinations of the seven recognized tetrachords and the twelve or thirteen recognized pentachords. As a result, the scale notations started from the open string (naghmah alif). However, a search in the listed cycles finds the adwār presented in Example 32 for repositions of the Systematist iṣfahān. The second scale, zindihrūd, has the intervallic structure of Shirazi’s dawr iṣfahān (Example 28). The third scale, generally known as gavāsht, was also referred to as iṣfahānak. The title of the fourth scale, gardānīyā; or gardānīyih, was also used by Shirazi (2008, 128) to refer to the upper pentachord of the scale (JBṬJJ). As a dawr, gardānīyā had several forms. The title of the fifth scale (generally unnamed in the Systematist treatises) was suggested by Shirazi (135).⁽⁴³⁾ It is hard to imagine that such scalar transpositions were not of interest to the practitioners, even though very little information on their significance and application in the performance of iṣfahān in the past is available.

Conclusions

[6.1] The historical and theoretical examinations of maqām iṣfahān in this article lead to the following conclusions:

1. The relationship between Iṣfahān and humāyūn, which has changed in nature over centuries, can be traced in the Systematist treatises, with iṣfahān being the main species (tetrachord) and one of the “famous cycles.” The main species in both maqāms has been the peculiar iṣfahān tetrachord (JJJB) that appears to have been replaced by the ḥijāz tetrachord (JHB) upon the omission of the third tone (as J + J = H). This change would make the octave species heptatonic.

2. The melodic progression of the gūshihs in the dastgāh iṣfahān is based on the movement of the prominent tone, shāhid, from $\hat{1}$ (in darāmad) to $\hat{5}$ (in owj of humāyūn) and back to degree $\hat{1}$ of iṣfahān. The examination of the radīfs, as well as the literature on the radīfs, revealed the presence of some gūshihs with a shāhid on $\hat{4}$, although not explicitly mentioned or discussed in most literature.

3. The main variable tone, mutighayyir, is $\hat{3}$ of iṣfahān ($\hat{6}$ of humāyūn). A neutral 3rd, instead of a more common minor 3rd, is consistent with the “authentic” form of iṣfahān (iṣfahān-i ʾaṣl) according to the Systematists. This form is used mostly in the gūshihs of the radīfs with a shāhid on $\hat{4}$ or $\hat{5}$ of iṣfahān, facilitating modulations to the other dastgāhs (e.g. afshārī and shūr).

4. A conclusion (khātimih) on $\hat{6}$ of iṣfahān ($\hat{2}$ of humāyūn) can be considered an īst, usually to be followed by another piece in iṣfahān with a complete conclusion and resolution on the tonic/shāhid of iṣfahān. In practice, ending on $\hat{6}$ would also give iṣfahān a distinctive feature and a reminder of its relationship to humāyūn, as this tone is usually regarded as the shāhid of humāyūn’s darāmad.

5. The starting tone, āghāz, varied in the radīfs and taṣnīf collections, appearing mostly as the degrees $\hat{5}$ and $\hat{1}$, followed by $\hat{4}$.

6. The comparison between the (collectively determined) Systematist scale of iṣfahān and the contemporary form reveals that the two scales are not very different. The Systematist cycle can turn into the contemporary iṣfahān upon two slight changes or variations, namely a quartertone lower $\hat{3}$ and the omission of $\hat{7}$, for both of which there is some historical evidence.

7. Despite the common interpretation (or suspicion) that the twentieth-century iṣfahān with a semitonal last interval and typically referred to as iṣfahān jadīd results from Westernization, examination of the medieval octave species of iṣfahān showed that such last interval was part of the dawr iṣfahān based on its most common notation. It is suggested here that the nineteenth-century version, typically referred to as iṣfahān qadīm, was a minor variation that had some historical precedent.

8. A comparison between the nineteenth-century and twentieth-century taṣnīfs reveals an increase in the first-degree āghāz (at the expense of the fourth-degree āghāz), an increase in the first-degree khātimih (at the expense of the sixth-degree khātimih), and an increase in the third- and fifth-degree shāhid (at the expense of the first-degree shāhid) in the twentieth-century composed songs in iṣfahān. These changes might have been promoted by Westernization and the spread of harmonic minor scale in Iran.

9. A preliminary examination reveals that the counterparts of the contemporary maqām iṣfahān in the Arabic and Turkish musical systems are maqāms nahāvand and puselīk/buselīk, respectively.

[6.2] In conclusion, I hope that this investigation has shown that, upon careful analysis and comparison, connections can be made between the Systematist modal cycles and the contemporary dastgāhs/maqāms. With the two related articles published on iṣfahān and humāyūn (Poorhaydari 2025), this project is completed. The next step is an examination of the other Persian dastgāhs, perhaps with a similar methodology. There is significant amount of information in the Systematists treatises that can serve as clues on the roots and evolutionary stages of the current modal systems. The historical study can also help with determining relations among the three neighboring musical cultures, namely Persian, Arabic and Turkish.

Glossary of Terms

In this section, simple (or simplified) meanings are listed for Persian and Arabic musical terms used in this article as a reference for the readers not familiar with Persian Music. Note that some musicologists may consider somewhat different meanings for these terms and some of the terms have different meanings in different contexts.

āghāz: the starting tone

ajnās (sing. jins): genera or species

āvāz: a secondary/derivative grouping in radīf

baqīyyah: (approximately and typically) a semitone

darāmad: introductory piece in radīf

dastgāh: a modal system; a primary grouping in radīf

dawr (pl. adwār): cycle

gūshih: a piece in radīf; a modal sample

īst: the temporary stop or dwelling tone

jadīd: new

khātimih: the ending tone or conclusion

maqām: mode

mujannab: (approximately) a three-quarter tone

mulāyim: consonant

mutighayyir: the variable tone

namāyān: dominant

owj: climax

qadīm: old

radīf: ordered repertoire of Persian art music

shāhid: the prominent tone

shuꜥbah (pl. shuꜥab or shuꜥabāt): branch

tarkīb: combination

taṣnīf: composed song

ṭanīnī: a whole tone

Kioumars Poorhaydari
Department of Chemical & Materials Engineering
University of Alberta
116 St & 85 Ave
Edmonton, AB T6G 2R3
Canada
kioumars@ualberta.ca

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Footnotes

* I would like to express my gratitude to the reviewers for their valuable comments that helped improve the quality of this article.
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1. For more information on the radīf, its history and its main sources, see Tsuge 1974 (29), Nettl 1992 (4) and Khaleghi 1999 (Part 1, 114).
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2. The term iṣfahān refers to the ancient city Isfahan (also transliterated as Esfahan) in Central Iran.
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3. A statistical survey of modes (Poorhaydari 2025) in a large collection of contemporary Iranian songs (with 354 pieces) revealed that approximately 30% of the songs were in the mode of iṣfahān and 11% were in humāyūn. Interestingly, according to Ibn Sina (Farmer 1929, 203), iṣfahān was a popular mode in the eleventh century as well.
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4. The term Systematist was used by the European writers to refer to the scholars in the Muslim world from the thirteenth through the fifteenth century, who had significant contributions to the systematization of the musical intervals and cycles (Farmer 1929, 206; Farmer 1965, x; Wright 1978, 1; Shiloah 1995, 55).
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5. Each dawr (pl. adwār) was basically an octave species, made of two conjunct or disjunct tetrachords or a tetrachord and a pentachord.
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6. Humāyūn was identified as a tarkīb (combination) by the thirteenth-century scholar Quṭb al-Din Shirazi (2008, 149) and one of the 24 shuꜥabāt (branches) by the fifteenth-century scholar ʿAbd al-Qadir Maraghi ([1418] 1966, 64). It is not known when humāyūn became a main maqām or dastgāh. One piece of information comes from an anonymous and undated treatise, referred to as Bihjat al-Qulūb and believed by Khazrayi (2013, 157) to be written between the seventeenth and the nineteenth centuries (or more specifically the mid-eighteenth century according to Pourjavady 2019, 114), that consider humāyūn as one of the four main dastgāhs. In the mid-sixteenth century Iran (Wright 1978, 53, 61), iṣfahān was still one of the twelve “maqāms”, whereas humāyūn was one of the branches.
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7. It should be acknowledged that the characteristics of the contemporary iṣfahān were examined briefly and comparatively within four selected radīfs by As’adi (2008).
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8. Nettl 1972 is a good example of a study of the performance aspects of a dastgāh (i.e., chahārgāh), in terms of interpretative use of gūshihs (their orders and lengths), with a focus on darāmad, as well as the extension and the meaning of “improvisation,” in the performances of several musicians.
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9. Fakhreddini (2013, 99) wrote that the radīfs of the contemporary music of Iran has missing links to the old maqāmāt, which should be discovered and placed in their true positions in order to attain what we (Iranians) had in the past.
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10. See, for instance, Farhat 1990, 5; Mohammadi 2001, 52; Zonis 1965, 637; and Pourjavady 2001, 82.
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11. As examples of musical writings in this period, see Bihjat al-Rūḥ (Ibn Ṣafi al-Din 1967) and the two treatises, Risālah-yi Karāmiyyah and Risālah-yi Mūsīqī, examined by Fallahzadeh (2009). Upon examining the major treatises in the post-Systematist period, Pourjavady (2019, 108) also points out the absence of interval ratios and tetrachordal analysis of the modes in the sources from this period.
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12. Readers who wish to acquire more knowledge on the various aspects of the contemporary Persian art music can consult the short article by Zonis (1965) or, in more details, the books by Zonis (1973), Farhat (1990), During (2006), During, Mirabdolbaghi and Safvat (1991), and Nettl (1992).
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13. The interval H, referred to as ṭanīnī-yi mustazād (augmented tone) by Hedayat (1938a, 17) and bīsh-ṭanīnī by some current musicologists (Alizadeh et al. 1996, 21), appeared in many species recognized by Shirazi. The interval W (a whole tone plus an apotome), being close to the Western equal-temperament augmented tone (300 c), rarely appeared in his listed species (mainly in the māyih pentachord with the intervallic structure WJṬ), but it does appear in the contemporary Persian, Turkish and Arabic music.
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14. I have recently examined this issue of variability of intervals and fretting systems in Persian art music in detail elsewhere (Poorhaydari 2022 and 2023) and proposed two theoretical models for the fretting of the string instruments, one based on the modified Pythagorean intervals and the other on dieses or quartertones.
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15. As also recognized by Wright (1978, 49), the terms bilʾarbaꜥ or dhulʾarbaꜥ and bilkhams or dhulkhams used by the Systematists were meant to be species of fourth and fifth, respectively, regardless of the number of tones within the species. For simplicity, the terms tetrachords and pentachords are used in this article interchangeably with the species of fourth and fifth. Examining the (subjective) criteria for consonance and how Urmawi considers some of the listed pentachords conditionally (and not completely) consonant is beyond the scope of this article.
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16. The in the notations presented in this article refers to half flat. It should be noted that the exact interval from the referenced note (e.g. the interval between B and B is not necessarily a quartertone. Based on the fretting system advocated by Urmawi ([1267] 1938, 115; 2006, 131), this interval is theoretically a comma (ca. 23.5 c), but in practice it can be between a comma and a limma (ca. 90.2 c.). In Persian art music, the sizes of the neutral/median intervals have remained a subjective and contested matter (Poorhaydari 2022), and, in practice, they can vary according to the musician and the mode of the music (Talai 1993, 19). Additionally, I have used the symbol ǂ in this article to show half sharp in Persian music.
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17. The pentachord ṬJJṬ was referred to as panjgāhʾaṣl (authentic or principal fifth position), made of rāst (ṬJJ) and a ṭanīnī (Ṭ), by the Systematists (Ladhiqi [1485] 1939, 401). The term panjgāh zāyid refers to the same pentachord with a broken last ṭanīnī (ṬJJJB), as it would have a zāyid (extra) tone.
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18. Jurjani ([1375] 1938, 298), Maraghi ([1418] 1966, 36), Jami (2000, 190), Ladhiqi ([1485] 1939, 365), and Banayi ([1484] 1989, 31.
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19. The difference between the two and their relationship are discussed in Section 6.
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20. These musicologists include Mehdi Qoli Hedayat (1864–1955), Ali Naqi Vaziri (1886–1981), Rouhollah Khaleghi (1906–1965), Mehdi Brakeshli (1912–1988), Mohammad Taghi Massoudieh (1927–1999), Hormoz Farhat (1928–2021), Farhad Fakhreddini (b. 1938), Majid Kiani (b. 1941), Jean During (b. 1947), Hossein Alizadeh (b. 1951), Dariush Talai (b. 1953), and Nariman Hodjati. For the corresponding sources, see Hedayat 1938b, vol. 3, 22, 100; Vaziri 1934, Part 2, 158–164; Khaleghi 1982, Part 2, 161–166; Barkeshli 1976, 133–134; Massoudieh 1997, 76, 104–106; Farhat 1990, 76–80; Fakhreddini 2013, 303–322; Kiani 1992, 41; During 2006, 300; Alizadeh et al. 1996 1996, 70–72; Talai 2017, 17, 32; and Hodjati 1998, 77–78.
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21. There is also confusion between the two terms ꜥirāq and ḥijāz(ī) in the Systematist treatises. The tetrachord JṬJ was referred to as ḥijāzī by Maraghi ([1418] 1966, 68), Ladhiqi ([1485] 1939, 365), and Banayi ([1484] 1989, 31), but labeled as ꜥirāq in Urmawi’s al-Sharafīyyah (1938, 119; 2006, 135). Jurjani ([1375] 1938, 378) comments that the tetrachord JṬJ may be called ꜥirāq or, more frequently, ḥijāzī, depending on what species comes after that. Urmawi did not recognize the tetrachord JHB that was referred to as ḥijāz by Shirazi (2008, 235). Shirazi called the tetrachord JṬJ rū-yi ꜥirāq. I use the terms ꜥirāq for JṬJ and ḥijāz for JHB, which is consistent with the terminology used by Wright (1978, 50–51) and Rostami (Urmawi [1235] 2001, 21).
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22. In most radīfs, the term rāk (suspected to be a variation of the Indian term raga) refers to a number of gūshihs in the dastgāh māhūr (and repeated in the dastgāh rāst-panjgāh). Interestingly enough, the intervallic structure of these gūshihs in māhūr is based on the conjunct (or disjunct) tetrachords JHB and ṬBṬ with a shāhid on the tone between the two (Fakhreddini 2013, 157–159; Farhat 1990, 98), i.e., a modulation to (the “new”) iṣfahān.
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23. The traditional fretting of tār/sitār with third-tone intervals between F and G, i.e., with one fret between the theoretical Fǂ and F♯ (Farhat 1990, 17), may be related to the ambiguity of $\hat{7}$ in the scale of iṣfahān on G.
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24. Namāyān is the term Vaziri (1934) and Khaleghi (1982, vol. 1, 48) used for $\hat{5}$ instead of dominant.
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25. This interpretation is consistent with the notion of “suspended cadence” (āsmā karār) in Turkish art music (Aydemir 2010, 26), in which the piece ends on $\hat{2}$, $\hat{3}$, or $\hat{6}$ (depending on the makām), instead of $\hat{1}$ (tām karār or full cadence) or $\hat{5}$ (yārīm karār or half cadence).
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26. A popular and famous vocal gūshih in humāyūn is sūfīnāmih (Fakhreddini 2013, 291), which can also be performed at the end of the dastgāh iṣfahān as in Davami and Karimi’s radīfs, where it acts as a return to humāyūn (with a khātimih on $\hat{1}$ of humāyūn).
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27. A total tally resulting in one histogram or curve is suitable for simple and basic gūshihs and taṣnīfs, which represent one “maqām”. In such cases, a very clear peak appears on one of the tones, i.e. the shāhid. In musical pieces with significant melodic progression or comprising two “maqāms”, a clear prominent tone may or may not appear. In such cases, sometimes the determination of the shāhid(s) can be achieved by establishing separate curves for different sections. In some gūshihs with modulations, it is typically the shāhid of the initial section (or even the initial phrase) that represents the intended mode of the gūshih.
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28. For the iṣfahān gūshihs in the above-mentioned radīfs, see Massoudieh 2003, 107–123; Tahmasbi 1995, 239–260; Maꜥrufi 2011, 453–479; and Payvar 2011, 103–112.
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29. Davami’s collection represents the “classical taṣnīfs” (Caton 1983, 20–23) of Persian art music that were produced by such prominent composer-lyricists as Ali-Akbar Shayda (1843–1906) and ꜥAref Qazvini (1882–1934). The label “nineteenth century taṣnīfs” used in this article to refer to the Davami’s collection, which may include some early twentieth-century taṣnīfs, is mainly for convenience and distinction from the more recent taṣnīfs collected by Nasirifar.
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30. The term “tempered” here means lowering $\hat{6}$ a quartertone that results in a minor 6th (as in the harmonic minor scale) instead of a neutral 6th (that is a characteristic of the untempered iṣfahān). Tempering of Persian maqāms typically occurs when using Western musical instruments (such as a piano or a guitar).
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31. An arch-shaped progression is a generalized character of the gūshihs of a dastgāh in a radīf (Caton 2001, 2). Sometimes the arch is asymmetrically skewed so that the peak of the arch inclines toward the end (right side), as demonstrated by Zonis (1973, 45) using gūshih blocks.
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32. See, for instance, the analyses of ruhāb and shāh-khatāyī by Fakhreddini (2013, 313) that show some emphasis on $\hat{4}$ without an explicit determination of the shāhid. Similarly, see Farhat (1990, 79) on gūshih shāh-khatāyī. The only source I have encountered to point out $\hat{4}$ as a shāhid in some representative gūshihs (in some radīfs, not including Maꜥrufi’s) is the article by As’adi (2008, 51) on the modal variations in iṣfahān.
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33. A version of the taṣnīf sung by the vocal Maestro Mohammad-Reza Shajarian (1940–2020), along with the subsequent ring, can be accessed on YouTube (Persianmusictube 2012). I transcribed the pieces from the recording and simplified the taṣnīf for the analysis. The simplified notation is generally consistent with that of Payvar (2011, 172) based on Davami’s version. For brevity’s sake, the transcription of the ring is not presented here.
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34. The examined pieces were the melody lines of eleven vocalises (songs without words) in minor in the Royal Conservatory of Music (RCM) Resonance Series Levels 5 through 8 (2012). The examination revealed that the starting tone was $\hat{1}$ (45%), $\hat{3}$ (18%), or $\hat{5}$ (36%). The ending tone was $\hat{1}$ for all pieces. The overall prominent tone was either $\hat{1}$ (36%) or $\hat{5}$ (64%) based on duration and $\hat{1}$ (9%), $\hat{3}$ (27%), or $\hat{5}$ (64%) based on the frequency of appearance.
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35. Nahāvand is the name of an ancient city in western Iran. The Persian names of the modes that contain the letter v (e.g. navā and nahāvand) are replaced with the letter w in Arabic, since there is no v in the classic Arabic. Persian pronunciation is used in the transliteration of such words in this article.
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36. Two pentachords related to ḥijāz were nayrīzī or nayrīz (ṬJHB; Wright 1978, 60) and ꜥuzzāl (JHBṬ; Wright 1978, 56). In contemporary Arabic music (Marcus 1989, 521), the equivalent jins to nayrīzī is nakrīz or nawā athar.
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37. Marcus (1989, 294) also points out the relationship between the contemporary species nahāvand and “būsalīk” in Arabic music; the tetrachord ṬBṬ (Systematist navā) is “commonly called ‘nahawand’ when it occurs on C or F but is often called ‘busalik’ when it occurs on D or G.” This is just another example of variation of nomenclature in the contemporary Arabic, Turkish, and Persian musical systems (and non-conformance to the Systematist terminology), which becomes confusing in a historical examination of the maqāms. The Systematist būsalīk was BṬṬ.
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38. Signell (2008, 23) recognizes two sizes of mujannab in Turkish music: the small mujannab (which I show as J₁) of 5 commas or ca. 114 c and the large mujannab (J₂) of 8 commas or ca. 180 c. The “augmented second” (H) is 12 commas or ca. 270 c. Several accidentals determine the interval from the referenced tone in Turkish music (Signell 2008, 24; Aydemir 2010, 24). Among these are the Turkish symbols (lowering the pitch 4 commas or 1 limma; different from the Persian and Arabic ), (lowering 1 comma), ǂ (raising 1 comma; different from the Persian and Arabic ǂ) and ♯ (raising 4 commas).
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39. For more details on the analysis of Ladhiqi’s tarkīb humāyūn, see Poorhaydari 2025.
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40. This scale, which could be established by adding an upper iṣfahān pentachord to a lower navā tetrachord, was referred to as khazān (meaning autumn) in some of the medieval treatises (Jurjani [1375] 1938, 397; Banayi [1484] 1989, 49). Khazān was not among Urmawi’s twelve “famous cycles,” and its identification among the consonant cycles (adwār mulāyim) is credited to Ali Jurjani (Barkeshli 1976, 109).
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41. The terms yigāh, dugāh, sigāh, chahārgāh, panjgāh, shishgāh, haftgāh and hashtgāh (jawāb, i.e., response) refer to the repositions (or scalar transpositions) of a mode. The first five terms (i.e., for $\hat{1}$ through $\hat{5}$) have been used in Persian music for centuries (Shirazi 2008, 141; Wright 1978, 172), if not millennia, primarily for the basic maqām rāst (as yigāh) as well as the corresponding main frets (pardih) on a string instrument. The concept and the terms can be extended to any basic maqām, as theoretically considered by Shirazi (2008, 141; Wright 1978, 174) and as I have done for humāyūn (Poorhaydari 2025) and iṣfahān (here).
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42. An exception is the brief discussion by Shirazi (2008, 141) on the repositions of rāst.
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43. The sources for this list are: Urmawi (1235) 2001, 29–35; Jurjani (1375) 1938, 337–343; Ladhiqi (1485) 1939, 376–382; Jami 2000, 193–207; and Banayi (1484) 1989, 48–54. Note there are some variations in terminology and the intervallic structures among these sources.
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